Lin Zhang*, Anuradha M. Agarwal, Lionel C. Kimerling and ...

22
DOI 10.1515/nanoph-2013-0020 Nanophotonics 2014; 3(4-5): 247–268 © 2014 Science Wise Publishing & De Gruyter Review article Lin Zhang*, Anuradha M. Agarwal, Lionel C. Kimerling and Jurgen Michel Nonlinear Group IV photonics based on silicon and germanium: from near-infrared to mid-infrared Abstract: Group IV photonics hold great potential for nonlinear applications in the near- and mid-infrared (IR) wavelength ranges, exhibiting strong nonlinearities in bulk materials, high index contrast, CMOS compatibility, and cost-effectiveness. In this paper, we review our recent numerical work on various types of silicon and germa- nium waveguides for octave-spanning ultrafast nonlinear applications. We discuss the material properties of silicon, silicon nitride, silicon nano-crystals, silica, germanium, and chalcogenide glasses including arsenic sulfide and arsenic selenide to use them for waveguide core, cladding and slot layer. The waveguides are analyzed and improved for four spectrum ranges from visible, near-IR to mid-IR, with material dispersion given by Sellmeier equations and wavelength-dependent nonlinear Kerr index taken into account. Broadband dispersion engineering is empha- sized as a critical approach to achieving on-chip octave- spanning nonlinear functions. These include octave-wide supercontinuum generation, ultrashort pulse compres- sion to sub-cycle level, and mode-locked Kerr frequency comb generation based on few-cycle cavity solitons, which are potentially useful for next-generation optical communications, signal processing, imaging and sensing applications. Keywords: silicon photonics; Group IV photonics; nonlin- ear optics; dispersion; slot waveguide; micro-resonator; integrated optics; supercontinuum; pulse compression; frequency comb. *Corresponding author: Lin Zhang, Microphotonics Center and Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA, e-mail: [email protected] Anuradha M. Agarwal, Lionel C. Kimerling and Jurgen Michel: Microphotonics Center and Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA Edited by Chris Doerr 1 Introduction Nonlinear optics [1–3] was born immediately after the first laser was demonstrated, with many nonlinear effects reported in 1961 and 1962. Those include second-harmonic generation (SHG) [4, 5], third-harmonic generation (THG) [5], two-photon absorption (TPA) [6], stimulated Raman scattering (SRS) [7], and phase matching in parametric wave mixing [8, 9]. As an important branch of optics, nonlinear optics is at the heart of frequency conversion, amplification, soliton and pulse compression, super- continuum generation, and laser mode-locking and fre- quency comb generation, which have found a wide variety of applications in optical signal processing, communica- tions, sensing, imaging, and metrology. While nonlinear effects in atomic gases [10] have been extensively explored in research laboratories, other materials platforms based on nonlinear crystals [11] and optical fibers [12] have become more practical for real- world applications. Particularly, since the invention of photonic crystal fiber (PCF) [13], nonlinear fiber optics has experienced a revolutionary development [14, 15]. Super- continuum generation as an example is one of nonlinear applications enabled by PCFs [14]. Obtaining a wideband or even octave-spanning supercontinuum does not only require an in-depth understanding of nonlinear phenom- ena in optical fibers but also provides numerous commer- cial opportunities (see e.g., “http://www.leukos-systems. com/”). The success of PCFs in refreshing nonlinear fiber optics mainly relies on a great enhancement of nonlin- earity and flexible engineering of dispersion [15]. Both of these benefits are enabled by a large refractive index con- trast between glass and air. PCFs allow us to confine light much more tightly than standard fibers and enhance the contribution of waveguide dispersion that is highly tailor- able by designing fiber structures. The reasoning behind PCF’s success serves as one of motivations to explore new materials platforms with even higher index contrast for nonlinear optics. In this sense, silicon photonics that has an index contrast of 1.5~2 exhibits great potential to further enhance performance of nonlinear devices.

Transcript of Lin Zhang*, Anuradha M. Agarwal, Lionel C. Kimerling and ...

Page 1: Lin Zhang*, Anuradha M. Agarwal, Lionel C. Kimerling and ...

DOI 101515nanoph-2013-0020emspenspenspenspthinspemspNanophotonics 2014 3(4-5) 247ndash268

copy 2014 Science Wise Publishing amp De Gruyter

Review article

Lin Zhang Anuradha M Agarwal Lionel C Kimerling and Jurgen Michel

Nonlinear Group IV photonics based on silicon and germanium from near-infrared to mid-infrared

Abstract Group IV photonics hold great potential for nonlinear applications in the near- and mid-infrared (IR) wavelength ranges exhibiting strong nonlinearities in bulk materials high index contrast CMOS compatibility and cost-effectiveness In this paper we review our recent numerical work on various types of silicon and germa-nium waveguides for octave-spanning ultrafast nonlinear applications We discuss the material properties of silicon silicon nitride silicon nano-crystals silica germanium and chalcogenide glasses including arsenic sulfide and arsenic selenide to use them for waveguide core cladding and slot layer The waveguides are analyzed and improved for four spectrum ranges from visible near-IR to mid-IR with material dispersion given by Sellmeier equations and wavelength-dependent nonlinear Kerr index taken into account Broadband dispersion engineering is empha-sized as a critical approach to achieving on-chip octave-spanning nonlinear functions These include octave-wide supercontinuum generation ultrashort pulse compres-sion to sub-cycle level and mode-locked Kerr frequency comb generation based on few-cycle cavity solitons which are potentially useful for next-generation optical communications signal processing imaging and sensing applications

Keywords silicon photonics Group IV photonics nonlin-ear optics dispersion slot waveguide micro-resonator integrated optics supercontinuum pulse compression frequency comb

Corresponding author Lin Zhang Microphotonics Center and Department of Materials Science and Engineering Massachusetts Institute of Technology Cambridge MA 02139 USA e-mail linzhangmiteduAnuradha M Agarwal Lionel C Kimerling and Jurgen Michel Microphotonics Center and Department of Materials Science and Engineering Massachusetts Institute of Technology Cambridge MA 02139 USA

Edited by Chris Doerr

1 Introduction

Nonlinear optics [1ndash3] was born immediately after the first laser was demonstrated with many nonlinear effects reported in 1961 and 1962 Those include second-harmonic generation (SHG) [4 5] third-harmonic generation (THG) [5] two-photon absorption (TPA) [6] stimulated Raman scattering (SRS) [7] and phase matching in parametric wave mixing [8 9] As an important branch of optics nonlinear optics is at the heart of frequency conversion amplification soliton and pulse compression super-continuum generation and laser mode-locking and fre-quency comb generation which have found a wide variety of applications in optical signal processing communica-tions sensing imaging and metrology

While nonlinear effects in atomic gases [10] have been extensively explored in research laboratories other materials platforms based on nonlinear crystals [11] and optical fibers [12] have become more practical for real-world applications Particularly since the invention of photonic crystal fiber (PCF) [13] nonlinear fiber optics has experienced a revolutionary development [14 15] Super-continuum generation as an example is one of nonlinear applications enabled by PCFs [14] Obtaining a wideband or even octave-spanning supercontinuum does not only require an in-depth understanding of nonlinear phenom-ena in optical fibers but also provides numerous commer-cial opportunities (see eg ldquohttpwwwleukos-systemscomrdquo) The success of PCFs in refreshing nonlinear fiber optics mainly relies on a great enhancement of nonlin-earity and flexible engineering of dispersion [15] Both of these benefits are enabled by a large refractive index con-trast between glass and air PCFs allow us to confine light much more tightly than standard fibers and enhance the contribution of waveguide dispersion that is highly tailor-able by designing fiber structures The reasoning behind PCFrsquos success serves as one of motivations to explore new materials platforms with even higher index contrast for nonlinear optics In this sense silicon photonics that has an index contrast of 15~2 exhibits great potential to further enhance performance of nonlinear devices

248emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

In the past two decades silicon photonics [16ndash25] has become increasingly mature What silicon photonics can contribute to nonlinear optics is much more than a high index contrast Several fundamental advantages drive nonlinear silicon photonics [26ndash30]

First as bulk material crystalline silicon typically has stronger Kerr and Raman nonlinearities than silica by 2~3 orders of magnitude [26ndash30] depending on crystal orientation Materials engineering further enhanced the nonlinearity eg in amorphous silicon under certain deposition conditions [31ndash35] and in Si-rich silicon oxide (SRO) and nitride (SRN) based on the formation of silicon nano-crystals [36ndash41]

Second the high index contrast not only allows sub-wavelength light confinement [42] but also makes it possible to form novel waveguiding structures For example when a nano-scale low-index layer is sand-wiched between two high-index layers a slot waveguide can be formed [43ndash46] with a large fraction of modal power trapped in the thin layer Relative to many nonlin-ear materials such as SRO SRN chalcogenides and poly-mers silicon has a sufficiently large index to form a slot waveguide [47ndash51] Moreover adding a slot layer provides more design freedom to tailor chromatic dispersion as reported in standard slot waveguides [51ndash58] and stripslot hybrid waveguides [59ndash63] A high refractive index is also beneficial to build a slow light element with reduced group velocity of light which can effectively increase optical length for nonlinear interactions and reduce power requirement [64ndash66]

Third CMOS compatibility in silicon device process-ing and fabrication can be utilized for nonlinear silicon photonics Although optoelectronic integration of silicon devices has long been proposed [16] there have been few reports on the integration of nonlinear devices with elec-trical functionality As silicon photonics becomes more mature it is foreseeable that CMOS-compatible nonlinear silicon devices are seamlessly integrated with microelec-tronics on a single chip For example on-chip pumping using an integrated laser data encoding and modulation before nonlinear signal processing and on-chip signal detection and data analysis after nonlinear devices are all highly likely to be integrated together which is achievable by building nonlinear photonics on a silicon platform

Fourth cost-effectiveness and portability of devices enabled by silicon photonics can be directly transferred to the nonlinear optics branch Although probably not a key consideration in a very early stage of a research topic these factors will finally drive the technological develop-ment and determine how widely this technology will be used Nonlinear silicon photonic devices have unique

competence especially when a large amount of elements need to be incorporated in a (sub-) system

The above motivations led to considerable research efforts on nonlinear silicon photonics in recent years [26ndash30] Nonlinear effects such as SRS [67ndash83] self- and cross-phase modulation (SPM and XPM) [84ndash91] four-wave mixing (FWM) [92ndash102] and supercontinuum gen-eration [60 61 103ndash108] are actively investigated The main focus is on the near-IR wavelength range around the telecom window However TPA in silicon is a detri-mental effect in most cases [109 110] significantly limit-ing optical power that is actually available in nonlinear interactions TPA thus degrades nonlinear efficiency and bandwidth in the effects of interest such as wavelength conversion and supercontinuum generation and TPA-induced free carriers cause slow device responses [26] It is noted that both the desired nonlinear effect and TPA are accumulative over a certain distance so if one can engi-neer chromatic dispersion to make the desired nonlinear effect more efficient the negative influence of TPA can be mitigated [60 108] One can also use silicon nitride [111ndash115] to eliminate TPA or even three photon absorption (3PA) for a pumping wavelength in the near-IR because silicon nitride has a bandgap energy of ~53 eV [113]

It would be sometimes instructive to look at the trends in nonlinear optics based on non-integrated platforms in order to gain a vision on how nonlinear silicon photonics can evolve One of the recent trends in nonlinear optics is that a significantly larger portion of electromagnetic spectrum from X-ray to mid-IR and even THz is being exploited to acquire previously hardly accessible informa-tion [116ndash118] For nonlinear silicon photonics it is a natural step to extend to the mid-IR wavelength range [119ndash125] The definition of the term ldquomid-IRrdquo varies substantially in the literature according to different research communities and organizations Specific application scenarios correspond to different wavelength ranges These include but are not limited to (i) mid-IR spectroscopy and sensing from 25 to 15 μm [126] or from 25 to 25 μm according to infrared spectros-copy correlation table [127] ldquohttpenwikipediaorgwikiInfrared_spectroscopy_correlation_tablerdquo (ii) free space communications LADAR and remote sensing in atmos-phere transparent windows from 3 to 5 μm and from 8 to 12 μm [128 129] and (iii) astronomical instrumentation over a bandwidth from 5 to 20 μm [130]

These new opportunities in the mid-IR are open to silicon photonics from an application perspective while nonlinear silicon photonics also gains additional advan-tages in this wavelength range in terms of materials and devices First silicon has no TPA beyond 22 μm and nonlinear loss by 3PA is significantly less influential for

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp249

an optical intensity of below 5 GWcm2 [131 132] Second more Group IV elements eg germanium become trans-parent and can be used for nonlinear purposes In fact germanium exhibits higher refractive index and Kerr index n2 than silicon [133] Third at longer wavelengths device dimensions need to be scaled up according to wavelength and thus surface roughness induced in device fabrication causes relatively small scattering loss Fourth fabrication errors in device dimensions are a smaller fraction of target numbers which is beneficial to obtain a higher yield in device manufacture

However nonlinear photonics in the mid-IR also meet some challenges Although going beyond half-bandgap wavelengths one can remove TPA the nonlinear Kerr index n2 markedly decreases [134] With waveguide dimensions scaled up the effective mode area Aeff increases almost quadratically Therefore the nonlinear coefficient γ equal to 2πn2(λAeff) where λ is the wave-length in vacuum decreases quickly with wavelength This would require careful dispersion engineering for phase matching in nonlinear parametric processes in order to improve nonlinear efficiency [12]

Many nonlinear effects have been reported recently in silicon photonics touching the mid-IR wavelength range [60 61 106 108 114 115 135ndash145] It is noted that most of them address the short-wavelength end of the mid-IR from 2 to 25 μm which is mainly the short-wave IR [144] or transition from near-IR to mid-IR Little was reported in longer wavelength beyond 25 μm [136 138 142 145] In fact there are about two octaves of bandwidth in the mid-IR (eg from 25 to 10 μm) available much wider than that in the near-IR As an approach to creating new frequencies nonlinear optics is much more efficient than electro-optic modulation in terms of how far an optical spectrum can be extended We believe that the mid-IR would be an exciting arena for ultrafast octave-spanning nonlinear applications

In this paper we discuss the materials properties of the Group IV platform for nonlinear applications The waveguide-based devices are optimized for four different wavelength ranges from near-IR to mid-IR in terms of both nonlinearity and dispersion We show by simulation that our dispersion-engineering approach based on a stripslot hybrid structure is widely applicable and can drama-tically enhance nonlinear interaction efficiency and spec-trum broadening Supercontinuum and frequency comb generations are predicted to be octave-spanning accord-ing to our numerical simulations in which excellent spectral coherence of the generated wideband spectra is confirmed by the creation of ultrashort cycle-level optical pulses

Si

Si3N4

As2S3

As2Se3

1 2 3 4 5 6 7 8 9 10 11 12 13 14Wavelength (microm)

SiO2

Ge

Figure 1emspMaterials transparency windows (green bar) in near- and mid-infrared ranges Red bars indicate high-loss wavelength bands for each material and color transition from red to green is from bandgap wavelength to half-bandgap wavelength (blue lines)

2 MaterialsLoss nonlinearity and dispersion jointly determine the nonlinear performance of optical waveguides All the three are both material- and device-dependent In this section we survey the major material choices for nonlin-ear Group IV photonics in the near- and mid-IR

Figure 1 shows material transparency windows with an optical loss below 2 dBcm [122] for materials including silicon (Si ie crystalline silicon unless otherwise speci-fied) silicon nitride (Si3N4) silicon dioxide (SiO2) germa-nium (Ge) arsenic sulfide (As2S3) and arsenic selenide (As2Se3) Since TPA plays an important role in nonlinear applications [109 110] the color transition from red to green in Figure 1 is between the bandgap wavelength and the half-bandgap wavelength (two blue lines) where TPA decreases with wavelength For silicon almost two-octave bandwidth from 22 to 85 microm [146] is available for nonlin-ear applications without TPA covering a large fraction of mid-IR range It is important to note that amorphous silicon has a bandgap energy of 17 eV [32 33] and thus has TPA diminishing at a much shorter wavelength ( lt 155 μm) than crystalline silicon Both silicon nitride and silicon dioxide have large bandgap energies but silicon dioxide becomes highly lossy beyond 3 microm [119] Germanium has an indirect bandgap energy of 067 eV and is transparent until up to 14 microm [146] From Figure 1 one can see that germaniumrsquos green bar without TPA has no overlap with silicon dioxide

Chalcogenide glasses are actively investigated as photonic materials [147ndash149] and exhibit a wide trans-parency window in the near- and mid-IR For example As2S3 and As2Se3 have bandgap energies around 226 eV [150 151] and 177 eV [152] and they are transparent up to 12 and 15 microm [153] respectively Although in this paper

250emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

chalcogenide glasses are not considered a material for the core of a waveguide one may use them for waveguide cladding and slot layer [53 58]

Linear optical properties of the materials discussed here are collected in terms of refractive index and mate-rial dispersion as shown in Figure 2 The two ldquoXrdquo on the curves for silicon and germanium in Figure 2(A) indicate the half-bandgap wavelengths The refractive index is given by the Sellmeier equations for silicon [154] silicon nitride [155] silicon dioxide [156] SRO [51] germanium [157] arsenic sulfide [158] and arsenic selenide [159] as detailed in Appendix A For SRN there is no comprehen-sive measurement of material index found currently As shown in Figure 2(A) the materials under our considera-tion have strong index contrasts especially between ger-manium and chalcogenides in the mid-IR The refractive index decreases with wavelength and beyond the half-bandgap wavelength these materials have a relatively small index change One can properly choose materials for waveguide core and cladding and also a low-index slot layer based on the information given in Figure 2(A)

Overall dispersion in an integrated waveguide con-sists of material dispersion and waveguide dispersion that

40

35

30

25

Ref

ract

ive

inde

xD

ispe

rsio

n (p

snm

middotkm

)

20

200B

A

100

-100

-200

0

15

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Wavelength (microm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Wavelength (microm)

Si

Si

Si3N4

Si3N4

As2S3

As2S3

As2Se3

As2Se3

SiO2

SiO2

SRO

SRO

Ge

Ge

Figure 2emsp(A) Refractive indices and (B) material dispersion curves of the materials considered for nonlinear Group IV photonics in the near- and mid-IR wavelength ranges

is affected by index contrast and waveguide dimensions First material dispersion is shown in Figure 2(B) which is defined as D  =  -(cλ)middot(d2nmatdλ2 ) where nmat is material index and λ and c are wavelength and the speed of light in vacuum It is important to note that except for silicon dioxide all the other materials have a flat and low disper-sion within  plusmn 100 ps(nmmiddotkm) at the long-wavelength end of the bandwidth of interest This means that if wave-guides are not designed to tightly confine guided modes one can reduce the contribution of the waveguide disper-sion and have the overall dispersion close to the flat and low material dispersion However this will cause a large effective mode area and a small nonlinear coefficient

On the other hand we note from Figure 2(B) that at the short-wavelength end of the spectrum material dispersion changes quickly with wavelength for all the considered materials even if the material refractive index looks flat in Figure 2(A) beyond the half-bandgap wave-length This is because the dispersion is the 2nd-order derivative of the index with respect to wavelength To fully use the portion of the spectrum near the half-bandgap wavelength dispersion engineering by tailoring wave-guide dispersion is required

As a measure of nonlinear material property the non-linear index n2 is shown in Figure 3 for silicon silicon nitride SRO germanium and arsenic sulfide Looking at broadband nonlinear applications one needs to take the wavelength dependence of n2 into account Unfor-tunately there is often a lack of complete measurement data at a wavelength range of interest and also measure-ment results from different groups could vary widely For silicon data from several sources are available [160 161] A recently published review paper [133] shows a predic-tion of third-order nonlinear susceptibility χ(3)

1111 for silicon and germanium in the mid-IR range based on a two-band model which is used to fit wavelength-dependent

Non

linea

r in

dex

(m2 W

)

1E-16

1E-17

1E-18

1E-191 2 3 4 5 6 7 8 9 10 11 12 13 14

Wavelength (microm)

Si

Si3N4

SROGe

As2S3

Figure 3emspThe Kerr nonlinear index n2values of the considered mate-rials in near- and mid-IR ranges

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp251

measurements We obtain the Kerr nonlinear index n2 as a function of wavelength based on χ(3)

1111 using the results from [133] As shown in Figure 3 the n2 value peaks at 19 and 27 microm for silicon and germanium respectively and changes slightly from 33 to 48 microm beyond which both TPA and 3PA disappear The TPA coefficient βTPA vs wave-length is also extracted for silicon and germanium from [133] as detailed in Tables 1ndash4 in Appendix B

Hydrogenated amorphous silicon has been identi-fied as a potentially good nonlinear material not only because of large bandgap energy of 17 eV but also more importantly because of the large nonlinear index n2 and nonlinear figure of merit (FOM) n2βTPAλ [162] We did not include specific data in Figure 3 for amorphous silicon since different groups reported highly variable n2 and nonlinear FOM values in the near-IR [31ndash35] The n2 value could be one order of magnitude higher than that in silicon [33] while the nonlinear FOM can be as high as 5 [35] although these may not be obtained simultaneously [34] Moreover linear properties of amorphous silicon may also vary when fabrication conditions and its nonlin-ear characteristics change

Silicon nano-crystals in silicon dioxide and silicon nitride have also been investigated as a nonlinear material exhibiting higher nonlinear indices than crystalline silicon by an order of magnitude or more [36ndash41] The values of n2 βTPA and nonlinear FOM are also highly variable if silicon excess annealing temperature and wavelength change We include one data point (n2 = 48 times 10-17m2W) from [38] in Figure 3 Extremely high n2and FOM by 3~4 orders have been obtained experimentally [41] with large silicon excess (note that the FOM in [41] is defined as the reciprocal of ours here)

Both amorphous silicon and silicon nano-crystals exhibit great potential as a nonlinear material in the mid-IR which can be used to compensate for the reduc-tion of the nonlinear coefficient due to a large mode area at long wavelengths In particular with a small linear refractive index SRO is often chosen as a slot material to enhance nonlinearity in the near-IR [51 53 55 56 59] while SRN exhibits a great potential for nonlinear applica-tions beyond 3 microm Typically strong nonlinearity in bulk materials is associated with a high linear refractive index which is known as Miller rule However silicon nano-crys-tals exhibit unique properties to simultaneously possess strong nonlinearity and low linear index It is important to mention that the silicon nano-crystals (ie nano-clusters) could act as scattering centers of light causing an increased propagation loss in SRO slot waveguides Nevertheless relatively low propagation loss has been achieved which is 3~5 dBcm [163]

For silicon nitride one data point n2 = 24 times 10-19m2W from [111] is included in Figure 3 which was measured at 155 microm and is one-order lower than that in silicon Silicon dioxide has an n2 value around 26 times 10-20m2W in 155 microm as in single-mode optical fibers two orders lower than that in silicon A higher n2 value (115 times 10-19m2W) is estimated for 155 microm in high-index doped silica [164] Both values are not shown in Figure 3 Since both silicon nitride and silicon dioxide have large bandgap energies it is expected that their n2 values are almost constant over wavelength in the near- and mid-IR

Strong Kerr nonlinearities are obtained in chalcoge-nide glasses (arsenic sulfide and arsenic selenide) with negligible TPA from the near- to mid-IR as shown in Figure 1 We have found wavelength-dependent measure-ments of the nonlinear index n2 for arsenic sulfide from different data sources [150 165ndash174] As shown in Figure 3 although slightly scattered these n2 values in arsenic sulfide are as high as those in silicon and would not be strongly wavelength-dependent beyond 155 microm because it is longer than the half-bandgap wavelength Arsenic selenide has even higher n2 values than arsenic sulfide [173] and its n2 value is predicted as a function of wave-length in [175]

There has been little published on the wavelength dependence of the nonlinear Raman gain coefficient gR in literature for the materials that we consider here [133] Since SRS is not the major nonlinear effect that is used in this paper we will not discuss it in details here

Although the considered materials such as silicon germanium silicon nitride and silicon dioxide are cen-trosymmetric and show no second-order nonlinearity in bulk materials one can engineer them by applying strain [176ndash178] or forming interfaces between two centrosym-metric materials (eg between germanium and silicon [179] or between silicon nitride and silicon dioxide [180]) An alternative way is to integrate other materials with strong second-order susceptibility onto Group IV wave-guides (see eg [145]) For chalcogenide glasses different poling schemes are proposed to produce the second-order nonlinearity [181] The second-order susceptibility χ(2) induced to the Group IV platform can have a highly variable value depending on how the isotropy of materi-als is broken We believe that second-order nonlinearity is promising in nonlinear Group IV photonics but in this paper we will mainly focus on third-order nonlinearity

As described above the materials presented here have greatly different transparency windows and nonlin-ear coefficients It thus becomes critical to wisely choose a material combination for a specific application and doing this one may also need to pay special attention to material

252emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

compatibility in device fabrication On the other hand compared to the material choices device design (mainly on waveguide and resonator) can also produce widely var-iable dispersion and nonlinearity properties In the next section we will discuss enhanced waveguide properties using improved designs

3 DevicesOptical waveguides form the backbone of photonic devices Light propagation properties in a waveguide could be remarkably different from those in corresponding bulk materials especially when there is a high index con-trast between waveguide core and surrounding cladding Therefore understanding and optimizing the waveguide properties including loss dispersion and nonlinearity are essential in nonlinear photonics

Propagation loss in a waveguide includes material loss confinement loss scattering loss and nonlinear loss Working at a transparency window of a material especially beyond the half-bandgap wavelength one can primarily have low material and nonlinear loss caused by TPA Note that benefiting from the wide multi-octave bandwidth in the mid-IR one can even eliminate the impact of 3PA in silicon and germanium by pumping at  gt 33 microm and  gt 48 microm respectively Since the substrate index in a silicon wafer is higher than or equal to that in most of materials we consider for a waveguide core con-finement loss exists due to mode leakage to the silicon substrate This loss can be markedly reduced by increas-ing the spacing between waveguide core and the substrate or choosing low-index material between them In general scattering loss due to sidewall roughness of a waveguide is dominant in high-index-contrast silicon photonics which is mainly caused in device fabrication and can thus be reduced by improving the fabrication processes [182ndash184]

Compared to propagation loss chromatic disper-sion and nonlinearity in integrated waveguides are more de signable Since the dispersion is the second-order deriv-ative of the effective index with respect to wavelength it is particularly tailorable by changing waveguide shape and dimension Moreover dispersion has been recognized to be critical for broadband nonlinear effects [12 14 15 60 61 92ndash108 112ndash115 137ndash145] which is true especially for ultrafast octave-spanning applications [185] Spec-tral characteristics in a dispersion profile including the number and positions of zero-dispersion wavelengths (ZDWs) and dispersion slope greatly affect and often set the limit on the bandwidth of optical spectra the temporal

widths of pulses and conversion efficiency in nonlinear interactions [185] Generally speaking a flat dispersion profile (ie third- and higher-order dispersion terms are small) with low dispersion values is preferred

In conventional ultrafast nonlinear optics in a free-space setup many components were developed to control dispersion over a wide bandwidth [185 186] such as prisms gratings chirped mirrors and so on However in a waveguiding system eg in fiber-based ultrafast optics the dispersion-control toolkit is smaller and engineer-ing waveguide dispersion becomes critical In particular when waveguides are built on a silicon platform with a much higher index contrast than optical fibers dispersion in a highly nonlinear waveguide [187ndash190] often shows strong wavelength dependence which is not preferable for wideband nonlinear applications In [187 190] the ZDW in silicon rib and strip waveguides is mapped by scanning waveguide dimensions It is shown that tight confinement of a guided mode produces a ZDW in its dispersion profile around 12~14 μm close to the bandgap wavelength More-over even if the waveguide size is increased to move the ZDW to longer wavelength the dispersion slope near the ZDW is not small as shown in [187ndash189] causing a limited low-dispersion bandwidth

Recently a dispersion engineering technique for integrated high-index-contrast waveguides has been pro-posed in which an off-center nano-scale slot controls modal distribution at different wavelengths [59 60] The guided mode experiences a transition from strip-mode like to slot-mode like as wavelength increases This approach can produce a very flat dispersion profile over an ultra-wide bandwidth with dispersion flatness improved by 1ndash2 orders in terms of dispersion variation divided by low-dispersion bandwidth More importantly it is applicable to different material combinations and wavelength ranges [59ndash63]

Towards mid-IR applications different types of Group IV waveguides have been reported recently based on silicon-on-insulator (SOI) [191ndash193] silicon-on-sapphire [142 194 195] silicon-on-porous-silicon [192] silicon-on-nitride [196 197] suspended membrane silicon [198] silicon pedestal [199] and germanium-on-silicon [200] Most of the waveguides are not aimed specifically at non-linear applications and little attention has been paid to dispersion engineering [196]

In this section we survey different structures of Group IV waveguides for broadband nonlinear applica-tions from the near- to mid-IR There are three main goals in waveguide designs (i) we consider joint optimization on both dispersion and nonlinearity properties (ii) we tend to fully utilize the available bandwidth brought by

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp253

the materials in Figure 1 and (iii) we emphasize disper-sion engineering naturally as a result of aiming at octave-spanning broadband applications

Figure 4 shows a general illustration of various types of integrated waveguides for nonlinear Group IV photonics Looking at a specific wavelength range one can accord-ingly choose a materials combination for an appropriate index contrast and a desired level of nonlinearity Note that one may need low nonlinearity in some cases when high-power output is required Here we discuss waveguide design at four different wavelength ranges as follows

First we consider SOI waveguides for a wavelength range from the telecom window in the near-IR to the short-wave end in the mid-IR ie roughly from 14 to 25 microm This is the wavelength range that many of the current research efforts have been addressing [60 61 106 108 114 115 135 137 139ndash141 143 144] In this wavelength range a SOI strip waveguide as shown in Figure 4 can be used with air as an upper cladding (see eg [140]) One can change the width of the waveguide to tailor its disper-sion profile while the height of the waveguide is 220 nm set by SOI wafers From Figure 5(A) we note that a rela-tively small width W = 800 nm is corresponding to a dis-persion profile with two ZDWs at 1585 and 2345 microm and a peak value of anomalous dispersion 532 ps(nmmiddotkm) at 205 microm for the quasi-TE mode The anomalous disper-sion is typically useful for parametric amplification and oscillation soliton and soliton-based supercontinuum generation [12] With W  =  900 nm one can have a flatter dispersion profile but the anomalous band is smaller When W is increased to 1000 nm the dispersion is even flatter but no anomalous dispersion occurs Figure 5(A) shows a good example that tight mode confinement in a strip waveguide moves ZDW to short wavelengths and near ZDWs dispersion changes quickly with a large slope

Strip WG

Strip WG suspended

Air Air

Slot

Core

Upper cladding

Slab

Lower cladding

Si substrate

Slot WG suspended

Slot WG Rib WG

Figure 4emspDifferent types of Group IV waveguides (WGs) for disper-sion and nonlinearity engineering in the near- and mid-IR ranges

One can calculate the nonlinear coefficient γ as a function of wavelength with the nonlinear Kerr index n2 given in Tables 1ndash4 in Appendix B We show in Figure 5(B) that the nonlinear coefficient in the silicon strip wave-guide with W = 900 nm first increases to 187 (mmiddotW) with wavelength until 17 μm and then decreases to 56 (mmiddotW) at 25 μm This is caused by both the peaking of the silicon n2 value near 19 μm and the gradual increase of wave-length and mode area beyond that

A silicon stripslot hybrid waveguide exhibits very flat dispersion as presented in Figure 5(A) The SOI waveguide has crystalline silicon at the bottom a thin SRO slot and amorphous silicon at the top The upper cladding is silicon dioxide When setting the lower Si height to Hl = 430 nm slot height to Hs = 54 nm upper Si height to Hu = 160 nm and width to W = 660 nm we obtain an extremely flat disper-sion profile for the quasi-TM mode over a wide bandwidth between two ZDWs at 1545 and 2448 microm From 1605 to 238 microm the value of anomalous dispersion changes between 30 and 46 ps(nmmiddotkm) In this way one can have a flat and low anomalous dispersion between two far apart ZDWs The average dispersion value can be shifted by increasing Hu to move dispersion between normal and anomalous regimes Detailed explanation on how the flat-tened and saddle-shaped dispersion profile is produced is given in [59 60] Briefly the mode transition over wave-length for the quasi-TM mode is responsible for this behav-ior Due to the off-center slot the mode is mostly confined in the crystalline silicon at short wavelengths while the mode becomes more like a slot mode at long wavelengths As shown in Figure 5(C) we plot the mode power distribu-tions at wavelengths of 15 183 217 and 25 microm The mode transition adds negative dispersion in the middle of the low-dispersion bandwidth as explained in [60 201]

Having a slot one has an opportunity to fill the slot with highly nonlinear materials into it [49 51 53 55 56 58 59] which can overcome the decrease of the nonlinear coeffi-cient over wavelength In Figure 5(B) we show the γ value increasing to 306 (mmiddotW) with wavelength from 14 to 25 microm This is because the guided mode extends more to the highly nonlinear thin slot layer Note that the used n2 value in SRO [38] is currently the one measured at 155 microm so the n2 and γ thinspvalues may vary in the mid-IR but the trend is general

Next we explore the short-wavelength end of the near-IR spectrum Silicon-based devices become unus-able for nonlinear photonics as wavelength decreases to 11 microm and we thus look at silicon nitride for near-IR nonlinear applications extending to the visible light spec-trum Again a strip waveguide based on silicon nitride is examined first Figure 6(A) shows dispersion curves of the quasi-TE mode in two waveguides sized to be 1300 times 540

254emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

and 1400 times 800 nm2 The upper cladding is air and the lower cladding is silicon dioxide The anomalous disper-sion region in the dispersion curves shrinks when the waveguide is made smaller This is because of a relatively small index contrast between silicon nitride and silicon dioxide which makes the guided mode leak quickly to the substrate as wavelength increases For the strip waveguide with a cross-section of 1400 times 800 nm2 there are two ZDWs near 10 and 23 microm but one can see a strong dispersion of 250 ps(nmmiddotkm) between the two ZDWs in Figure 6(A) The nonlinear coefficient in the second silicon nitride wave-guide is shown in Figure 6(B) which is much smaller than that in silicon waveguides because of a one-order smaller n2 value and larger Aeff in the silicon nitride waveguide At 16 microm γ is about 123(mW)

One can also use a stripslot hybrid structure to tailor the dispersion profile in silicon nitride waveguides For example the slot and lower cladding are silicon dioxide and the upper cladding is air In Figure 6(A) we show the dispersion curves in two silicon nitride stripslot hybrid waveguides for comparison The waveguide 1 has Hl = 900 nm Hs = 124 nm Hu = 340 nm and W = 1000 nm and the waveguide 2 has Hl = 920 nm Hs = 154 nm Hu = 480 nm and W = 1300 nm These two waveguides produce increasingly flatter dispersion profiles as shown in Figure 6(A) The first waveguide has two ZDWs located at 106 and 22 microm with the peak dispersion of 67 ps(nmmiddotkm) The second waveguide has two ZDWs at 115 and 235 microm with the dispersion varying within 0~20 ps(nmmiddotkm) This octave-spanning dispersion flattening with different levels

1000A

B

C

500

-500

400

300

200

100

0

-100014 16

Strip WG W=800 nmStrip WG W=900 nm

Strip WG W=900 nm

Strip WG W=1000 nm

Slot WG Hu=160 nm

Slot WG Hu=160 nm

Slot WG Hu=163 nmSlot WG Hu=166 nm

18 20 22Wavelength (microm)

Dis

pers

ion

(ps

nmmiddotk

m)

Non

linea

r co

effic

ient

(m

middotW)

24 26

14 16 18 20 22

Wavelength (microm)

24 26

0

Figure 5emspIn a wavelength range from the telecom window in near-IR to the short-wave end in the mid-IR silicon strip and stripslot hybrid waveguides (WGs) are analyzed in terms of (A) dispersion and (B) nonlinearity (C) Mode power distributions at wavelengths of 15 183 217 and 25 microm in the stripslot hybrid waveguide

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp255

of dispersions can be used for multiple applications as detailed in the next section The nonlinear coefficients for the two waveguides are shown in Figure 6(B) We note that the stripslot hybrid waveguides have similar nonlinear coefficients as the strip waveguide which shows that the dispersion profile is much more tailorable by waveguide designs

Then we move to the mid-IR using silicon and silicon nitride for waveguiding A comparison of different types of silicon-on-nitride waveguides have been presented in [196] where rib waveguides were preferred due to the wideband low dispersion over an octave-spanning band-width from 24 to 66 microm for the quasi-TE mode This is a spectral range from siliconrsquos half-bandgap wavelength to the cut-off wavelength of silicon nitride In Figure 7(A) we plot the dispersion curve for a silicon-on-nitride rib waveguide with air as the upper cladding the rib width of 2000 nm the total height of 1200 nm and the slab height of 1000 nm which are the same parameters used in [196] It is shown that less confinement of optical modes reduces the contribution of waveguide dispersion and makes the overall dispersion profile closer to the material dispersion which is flat and low at long wavelengths as in Figure 2(B)

A

B

400

300

200

100

-100

8

6

4

2

0

0

Strip WG 1300times540 nm2

Strip WG 1400times800 nm2

Strip WG 1400times800 nm2

Slot WG 1Slot WG 2

Slot WG 1Slot WG 2

Dis

pers

ion

(ps

nmmiddotk

m)

Non

linea

r co

effic

ient

(m

middotW)

20 3010 15 2505Wavelength (microm)

2010 15 2505

Wavelength (microm)

Figure 6emspIn a wavelength range moved toward the short-wave-length end of near-IR spectrum silicon nitride strip and stripslot hybrid waveguides are designed in terms of (A) dispersion and (B) nonlinearity

Accordingly the nonlinear coefficient is small 285 (mmiddotW) at 3 microm as shown in Figure 7(B)

On the other hand if one needs a small Aeff to enhance nonlinearity additional dispersion tailoring (eg based on stripslot hybrid waveguides) would be beneficial Pursuing a higher nonlinear coefficient we use a 500-nm silicon nitride suspended membrane as illustrated in Figure 4 to support a silicon stripslot hybrid waveguide This helps confine light in the waveguide core Using W = 880 nm Hu = 550 nm Hs = 87 nm and Hl = 840 nm we obtain a saddle-shaped anomalous dispersion from 19 to 449 microm within 0~60 ps(nmmiddotkm) for the quasi-TM mode as shown in Figure 7(A) This structure produces much tighter mode confinement than the rib waveguide and exhibits a 3 times larger nonlinear coefficient in Figure 7(B) while having similar dispersion flatness

Finally we consider germanium-on-silicon wave-guides over a wavelength range from 33 to 85 microm between the half-bandgap wavelength of germanium and the cut-off wavelength of silicon This type of waveguide has been demonstrated with strain-free mono-crystal-line germanium [200] Here we assume that the germa-nium waveguide has a 10-nm silicon nitride layer on its

A

B

200

-200

60

40

20

0

100

-100

0

Rib WGSlot WG

Rib WGSlot WG

Dis

pers

ion

(ps

nmmiddotk

m)

Non

linea

r co

effic

ient

(m

middotW)

1 2 3 4 5 6 7Wavelength (microm)

1 2 3 4 5 6 7

Wavelength (microm)

Figure 7emspIn a wavelength range from the short-wave IR to mid-IR silicon rib waveguide on silicon nitride and stripslot hybrid waveguide on a suspended membrane are analyzed in terms of (A) dispersion and (B) nonlinearity

256emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

surface for passivation The upper cladding could be air or silicon which provides significantly different dispersion properties due to a varied index contrast For comparison only we also have silicon nitride as the upper cladding although silicon nitride becomes lossy for wavelengths longer than 67 microm Figure 8(A) shows the dispersion pro-files of four germanium-on-silicon strip waveguides with equal size 3000 times 1600 nm2 for the quasi-TE mode Air and silicon nitride as an upper cladding result in similar shape and bandwidth in the dispersion profiles Thus the air-cladded waveguide is chosen and discussed further The waveguide with silicon upper cladding has normal dispersion at all wavelengths since there is a relatively small index contrast between germanium and silicon and thus weak mode confinement A germanium strip wave-guide on a 600-nm-thick silicon suspended membrane is also considered to increase light confinement with an air upper cladding to maximize light confinement However as mentioned earlier strong confinement typically causes strong dispersion as shown in Figure 8(A) and therefore the germanium waveguide on a silicon membraneis not chosen for broadband nonlinear applications In contrast the germanium strip waveguide with air upper cladding exhibits a flat and low dispersion

The dimensions of the air-cladded germanium wave-guide are varied by simultaneously changing its height and width with a step of 200 nm for both polarization states It is interesting to see from Figure 8(B) and 8(C) that the dispersion peak value remains nearly unchanged for all the waveguide sizes although we have a widely tunable ZDW at long wavelengths For the quasi-TE mode the right ZDW moves from 605 microm to 841 microm while the left ZDW is always near 4 microm We can thus obtain an octave-spanning anomalous dispersion band with the peak value below 100 ps(nmmiddotkm) For the quasi-TM mode one can see similar dispersion properties but the anomalous disper-sion band is smaller Thus we choose the quasi-TE mode for further discussion in next section

The nonlinear coefficient in the germanium wave-guides for the quasi-TE mode is shown in Figure 8(D) which is about 10(mmiddotW) at 5 microm with a small variation for differ-ent waveguide sizes This is quite high considering that both wavelength and effective mode area become much larger over this wavelength range compared to the near-IR

From above we can see that the stripslot hybrid wave-guides enable unique controllability of dispersion and that this concept is applicable to different wavelength ranges However their performance may be sensitive to fabrication errors especially for inaccuracies in slot height Hs [59 60] A higher yield in device fabrication is expected using advanced fabrication technologies and facilities

A

C

D

B

400

300

200

100

-100

-200

0

Ge WG+air 3000times1600 nm2

Ge WG+air suspended 3000times1600 nm2

Ge WG+Si3N4 3000times1600 nm2

Ge WG+Si 3000times1600 nm2

Ge WG+air 2800times1400 nm2

Ge WG+air 3000times1600 nm2

Ge WG+air 3200times1800 nm2

Ge WG+air 3400times2000 nm2

Ge WG+air 2800times1400 nm2

Ge WG+air 3000times1600 nm2

Ge WG+air 3200times1800 nm2

Ge WG+air 3400times2000 nm2

Ge WG+air 2800times1400 nm2

Ge WG+air 3000times1600 nm2

Ge WG+air 3200times1800 nm2

Ge WG+air 3400times2000 nm2

Dis

pers

ion

(ps

nmmiddotk

m)

400

300

200

100

-100

-200

0

Dis

pers

ion

(ps

nmmiddotk

m)

400

300

200

100

-100

-200

50

40

30

20

10

0

0

Dis

pers

ion

(ps

nmmiddotk

m)

Non

linea

r co

effic

ient

(m

middotW)

3 4 5 6 7 8 9Wavelength (microm)

3 4 5 6 7 8 9Wavelength (microm)

3 4 5 6 7 8 9

Wavelength (microm)

3 4 5 6 7 8 9

Wavelength (microm)

Figure 8emspIn a wavelength range covering the main part of the mid-IR spectrum (A) on silicon substrate or on suspended silicon membrane are analyzed in terms of dispersion Germanium-on-silicon strip waveguides with an air upper cladding and different dimensions are characterized by (B) dispersion for the quasi-TE mode (C) dispersion for the quasi-TM mode and (D) nonlinearity for the quasi-TE mode

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp257

Besides photonic waveguides another important cat-egory of nonlinear devices is integrated resonators In the scope of this paper we consider relatively large resona-tors for frequency comb generation in which the bending radius of a ring resonator is varied from 50 microm to 100 microm depending on free spectral range (FSR) and the group index in the waveguide In these cases the waveguide-bending-induced dispersion is small and we would not discuss intra-cavity dispersion [202 203] in details here

4 ApplicationsBenefiting from the unique dispersion engineering over an octave-spanning bandwidth as described above one can develop ultra-wideband nonlinear applications that could hardly be attained in an integrated platform previously These include octave-spanning supercontinuum genera-tion pulse compression to a few-cycle or even sub-cycle level octave-spanning Kerr frequency comb generation and the associated mode-locked ultrashort pulse genera-tion using microresonators In this section we review our recent work on these topics

First we discuss the supercontinuum generation and pulse compression in a straight waveguide The nonlinear envelope equation used here to simulate supercontinuum generation is the following

βα infin

=

part part+ + = + part part sum

2

( - )( ) ( )

2

m mm

mm

ii A K A R A

z m t (1)

where

2

0 0

- -( ) 1- ( ) 2

n nn

nn

i i iK A A An t tγ δ δ

ω δ δ

infin

=

= sum

and

2shock_R( ) - 1- [ ( - ) | | ]δ

γ τδ minusinfin

= prime prime int

t

R RR A i i A h t t A dtt

We denote A  =  A(zt) as the complex amplitude of an optical pulse Note that its Fourier transform is

-

1( ) ( ) exp( - ) 2

A z A z t i t dtω ωπ

infin

infin

= int

In Eq (1) α is the total propagation loss and βm is the mth-order dispersion coefficient The frequency dependence of nonlinearity parameters including the nonlinear index n2 the TPA coefficient βTPA and the

effective mode area Aeff is included in the nth-order dis-persion coefficient γn of nonlinearity which is defined as γn = ω0middotpartn[γ(ω)ω]partωn where ω0 is the angular frequency of the carrier Therefore we can consider all-order linear dispersion terms and all-order dispersion of the nonlin-ear coefficient in Eq (1) Specifically in the simulations for a silicon and silicon nitride waveguides we have all-order linear dispersion and up to 6th-order and 2nd-order of the nonlinear coefficient dispersion included A detailed derivation of Eq (1) is given in [204] For the quasi-TM mode that experiences the engineered dispersion due to the mode transition SRS in silicon waveguides fabricated on the (001) surface can be ignored [27 96] For silicon nitride waveguide we include the SRS term in Eq (1) where γR = gRΓR(AeffΩR) and gR ΓR and ΩR represent the Raman gain coefficient the full width at half maximum of the gain spectrum and the Raman shift respectively The Raman shock time τshock_R is associated with γRrsquos fre-quency dependence which is 1ω0-[1Aeff(ω0)][dAeff(ω)dω] similarly as in [14] if we ignore frequency dependent gR ΓR and ΩR hR(t) is the Raman response function and it corresponds to the Raman gain spectrum

2

2 20 0

( ) -( - ) 2 ( - )

Ωω

Ω ω ω Γ ω ω=

+R

RR R

Hi

Note that the sign before the imaginary unit is differ-ent from that in [27] to be consistent with the expression of the Fourier transform that we used

We have considered supercontinuum generation in both silicon and silicon nitride waveguides with the slot-assisted dispersion tailoring Octave-spanning supercon-tinua in a silicon-based stripslot hybrid waveguide have been investigated in detail in [108] in which two-cycle optical pulses are obtained The main results in that work are shown in Figure 9 for comparison purposes

Here we mainly focus on the supercontinuum gen-erated in the silicon nitride stripslot hybrid waveguide (ie the slot WG 1 in Section III) whose dispersion and nonlinearity properties are shown in Figure 6 In the non-linear simulations we set the total propagation loss to be 1 dBcm The SRS parameters used here are the following [205] ΩR2π = 143 THz ΓR2π = 172 THz and gR = 1 times 10-12 mW τshock_R is calculated to be  = 156 fs

In our simulations we use a time step of 025 fs which is corresponding to a bandwidth of 4000 THz in the fre-quency domain For a femtosecond input pulse we set the time window length to 50 ps (ie frequency resolution Δf = 20 GHz)

We simulate the nonlinear propagation of a chirp-free hyperbolic secant pulse in the silicon nitride waveguide

258emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

The pulse center wavelength is at 1610 nm and its full width at half-maximum (FWHM) T0 is 120 fs Its peak power is 1200 W corresponding to pulse energy of 016 nJ

Figure 10(A) shows the supercontinua at different propagation distances At 48 mm the spectrum is greatly broadened at the -30 dB level covering a wavelength range from 0585 to 2833 microm which is more than two octaves The spectrum evolution in Figure 10(A) shows a similar spectrum shape as that in Figure 9(A) both featuring a ldquotriangularrdquo central spectrum bounded by two dispersive waves at the edges However it is important to note that the absence of TPA and 3PA in silicon nitride at the telecom window leads to a much more efficient spectrum broad-ening than that in silicon [108] The generated spectrum extends from the visible light to the mid-IR with excellent spectral coherence which is confirmed by the pulse wave-form shown in Figure 10(B) In the time domain the pulse is greatly compressed from 120 to 408 fs corresponding to 076 optical cycles at 161 microm wavelength

We examine the pulsewidth as a function of propa-gation distance Figure 11 shows that the pulse becomes increasingly narrower until the propagation distance reaches 47 mm For longer distances the pulsewidth

A

B

60 mm

48 mm

36 mm

24 mm

12 mm

Input

Spe

ctru

m (

10 d

Bd

iv)

Pow

er (

W)

12

246

24

18

12

6

0

248 250 252 254

14 16 18 20 22 24Wavelength (microm)

Time (ps)

Figure 9emsp(A) The supercontinuum generation in a silicon-based stripslot hybrid waveguide presented in [108] (B) The significant spectrum broadening at 425-mm distance is associated with a temporal compression of an input pulse (dash line) to the output waveform (solid line) with a FWHM of 12 fs

A

B

50 mm

48 mm

46 mm

44 mm

42 mm

Input

Spe

ctru

m (

10 d

Bd

iv)

Pow

er (

W)

8000

6000

4000

2000

0250249 251

06 09 12 15 18 21 24 27

Wavelength (microm)

Time (ps)

Figure 10emsp(A) Spectrum evolution of the pulse over propagation distance A supercontinuum of more than two octaves is achieved at 48 mm distance (B) Generated pulse waveform with a pulse width of 408 fs as short as 076 optical cycles Low pedestals are caused by dispersive waves generated at the two ends of the spectrum

remains almost constant However it is important to mention that after 48 mm the dispersive waves become increasingly stronger as shown in Figure 10(A) causing larger pedestals

Comparing the results in Figures 9 and 10 we note that the mid-IR wavelength range for silicon would be in analogy to the near-IR for silicon nitride in terms of non-linear optics operations Pumping at or beyond 33 microm one can use the waveguide designs shown in Figure 7 to produce very efficient nonlinear interactions without TPA and 3PA in silicon Ultrashort pulses in the mid-IR from parametric amplifiers [206 207] could be used to pump the Group IV waveguides

Another nonlinear application of the dispersion-engi-neered Group IV waveguides is micro-resonator-based Kerr frequency comb generation When such a waveguide is curved to form a microring resonator input CW light travels around the cavity and amplifies the noise in the source located at the frequencies with a high parametric gain As a result of modulation instability and cascaded FWM in the cavity a frequency comb can be generated [208ndash211] Mode-locked frequency combs have been reported pro-ducing low-noise pulse trains in time domain [212ndash214]

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp259

The formation of cavity solitons is identified as the main reason for the mode-locking in the Kerr frequency combs [215] This is instructive because one can thus predict the spectral bandwidth and temporal pulsewidth in the generated low-noise combs The 3-dB comb bandwidth is inversely proportional to the square root of the 2nd-order dispersion coefficient |β2| as given in [213 215] It is desira-ble that all comb lines that constitute the soliton spectrum experience the same |β2| In this sense the stripslot hybrid waveguides with flattened dispersion are preferably suit-able for supporting broadband Kerr comb generation and ultra-short cavity soliton generation

The Kerr frequency comb generation can be modeled using the generalized Lugiato-Lefever equation (LLE) [216ndash219]

20

2

( - )- - | |

2 2

m mm

R inmm

jkt j jl E kE j l E Et m

βαδ γ

τ

infin

=

part part+ + + = part part

sum (2)

where tR is the round-trip time E = E(tτ) and Ein are intra-cavity field and input field (pump power Pin  =  |Ein|2) t and τ are the slow and fast times δ0 is the cavity phase detuning defined as δ0  =  tRmiddot(ωn -ω0) where ω0 and ωn are the pumprsquos angular frequency and the nth angular reso-nance frequency that is pumped Other resonator param-eters include the power loss per round trip α the power coupling coefficient κ the nonlinear coefficient γ and the mth dispersion coefficient βm Since a flattened dispersion profile has a small β2 over a wide bandwidth it is impor-tant to take the influence of higher-order dispersion into account We include all-order dispersion terms in Eq (2) as we did in solving Eq (1)

To enhance the Kerr comb bandwidth in the near-IR we use the ultra-flattened dispersion profile in Figure 6(A) which is obtained in the slot WG 2 based on

Pul

se w

idth

(fs

)

14

12

10

8

6

4

242 44 46 48 50 52

Propagation distance (mm)

Figure 11emspPulse width first decreases with propagation distance and then remains stable After 48 mm dispersive waves get stronger causing more pedestals

Pow

er (

10 d

Bd

iv)

Pow

er (

W)

70A

B

60

50

40

30

20

10

-10

-20

600

400

200

0

80 120

0575 0600 0625 0650

160 200 240 280 320 360

0

Frequency (THz)

Time (ps)

Figure 12emsp(A) Frequency comb generation with a CW pump at 155 microm using a microring resonator based on a silicon stripslot hybrid waveguide Over an octave-spanning bandwidth from 135 to 270 THz the comb lines have a power drop of 20 dB (B) Generated pulse waveform with a pulse width of 82 fs as short as 16 optical cycles

silicon nitride The ring resonator has a bending radius of 104 microm corresponding to a FSR of 200 GHz Pumping near 155 microm with a pump power of 2 W the resonance peak is red-shifted and we need to red-shift the pump wavelength accordingly and tune it into the resonance from the short-wavelength side When the pump is step-by-step tuned by up to 63 resonance linewidths we obtain the comb spectrum and the mode-locked pulse waveform as shown in Figure 12 One can see that over an octave-spanning bandwidth from 133 to 268 THz the comb lines have a power drop by 20 dB from the center of the spectrum The spectral flatness of this comb is relatively good compared to the previously reported results [208ndash211] The comb bandwidth at -40 dB is as wide as two octaves There are two dispersive peaks in normal dispersion regions beyond the low-dispersion band Such a mode-locked broadband comb produces a train of sub-two-cycle optical pulses as shown in Figure 12(B) with one pulse per round trip The peak power of the pulse is up to 600 W Nonlinear conver-sion efficiency is estimated to be -267 dB

To generate frequency combs in the mid-IR the ger-manium-on-silicon strip waveguide is chosen We choose

260emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

a cross-section of 3200 times 1800 nm2 which has an octave-spanning low-dispersion band from 4 to 767 microm as shown in Figure 8(B) A germanium ring resonator is formed with a bending radius of 564 microm corresponding to a FSR of 200 GHz Pumping at 6 microm with a CW power of 14 W and detuning the pump wavelength by 10 resonance linewidth one can see that a mode-locked wideband mid-IR comb is generated from 358 to 644 THz (ie from 466 to 838 microm) at -40 dB level The FWHM of the produced pulses is 69 fs which corresponds to ~35 optical cycles The pulse peak power is 184 W and the nonlinear conversion efficiency is estimated to be -143 dB Since the pumping frequency is not at the center of the low-dispersion band we only see one peak in the comb spectrum caused by the dispersive wave in the normal dispersion region from Figure 13(A) There is another peak at higher frequencies beyond what is shown in the figure

As shown above broadband dispersion engineering is critical for octave-spanning nonlinear applications in both near- and mid-IR wavelength ranges which enables us to fully utilize the bandwidth allowed by the materials transparency windows Generally speaking the nonlinear applications mentioned here such as supercontinuum generation ultrafast pulse compression and frequency comb generation are often the intermediate steps towards higher-level system applications In the frequency domain a wide spectrum can serve as an electromagnetic carrier to acquire high-volume of information eg for sensing [220] and imaging [221] In the time domain an ultrashort pulse can be used as probe to sample ultrafast phenomena [222]

5 Summary and OutlookWe have presented a review of our recent work on nonlin-ear photonics based on silicon and germanium Various types of Group IV waveguides are analyzed and optimized for four different wavelength ranges from near- to mid-IR The recently proposed dispersion engineering technique based on stripslot hybrid waveguide structures is used for different material combinations and wavelength ranges Numerical simulations show that the dispersion-flattened Group IV waveguides are preferably suitable for octave-spanning nonlinear applications including on-chip supercontinuum generation ultrashort pulse compres-sion and mode-locked wideband frequency comb genera-tion based on micro-resonators

The presented approach to achieving octave-span-ning nonlinear applications on an integrated CMOS-compatible Group IV platform holds great potential for realizing chip-scale sensing imaging communications and signal processing system The ultrawide transparency windows in the mid-IR allowed by Group IV elements and compounds potentially together with other materi-als [223] provide an exciting arena for building powerful information acquisition and processing units enabled by nonlinear optics nano-photonics and ultrafast optics

Received June 14 2013 accepted October 29 2013 previously pub-lished online November 27 2013

Pow

er (

10 d

Bd

iv)

A

8030 40 50 60 70Frequency (THz)

Pow

er (

W)

B200

150

100

50

0

21 22 23 24 25Time (ps)

Figure 13emsp(A) Frequency comb generation with a CW pump at 6 microm using a microring resonator based on a germanium strip waveguide with air upper cladding (B) Generated pulse waveform with a pulse width of 69 fs as short as 35 optical cycles

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp261

Appendix

A Material index and dispersion

In this section we give the wavelength-dependent mate-rial index expressed as Sellmeier equations where wave-length λ is in μm

For silicon we use the following material index that is a fit curve from measurement results at room temperature (293 K) with 184 data points in total from 112 to 588 μm [154]

22 1 2 2

2 2 22

( )-

C Cn

λλ ε

λ λ λ= + +

where ε = 116858 C1 = 0939816 μm2 C2 = 000810461 and λ2 = 11071 μm

For silicon nitride the material index is affected by deposition conditions using plasma-enhanced chemical vapor deposition (PECVD) low-pressure chemical vapor deposition (LPCVD) and so on We use the following Sell-meier equation [155] which predicts the material index close to that in LPCVD silicon nitride films measured by a few groups [224]

22 1

2 21

( ) 1-

Cn

λλ

λ λ= +

where C1 = 28939 and λ1 = 013967 μmFor silicon dioxide we use the following Sellmeier

equation for fused silica [156]22 2

2 31 22 2 2 2 2 2

1 2 3

( ) 1- - -

CC Cn

λλ λλ

λ λ λ λ λ λ= + + +

where C1 = 06961663 C2 = 04079426 C3 = 08974794 λ1 = 00684043 μm λ2 = 01162414 μm and λ3 = 9896161 μm

For SRO the material index is affected by deposition conditions such as silicon excess annealing temperature and so on Here we choose the one with silicon excess of 8 and annealed at 1250oC [51]

22 22 31 2

2 2 2 2 2 21 2 3

( ) 1- - -

CC Cn

λλ λλ

λ λ λ λ λ λ= + + +

where C1 = 001 C2 = 196 C3 = 141 λ1 = 03 μm λ2 = 007071 μm and λ3 = 2775968 μm

For germanium the temperature-dependent mate-rial index was measured [157] Here we choose the one for room temperature (293 K)

2 22 1 2

2 2 2 21 2

( )- -

C Cn

λ λλ ε

λ λ λ λ= + +

where ε = 928156 C1 = 67288 C2 = 021307 λ1 = 0664116 μm and λ2 = 6221013 μm

For arsenic sulfide we use the material index pro-vided in [158]

2 2 22 22 3 4 51 2

2 2 2 2 2 2 2 2 2 21 2 3 4 5

( ) 1- - - - -

C C CC Cn

λ λ λλ λλ

λ λ λ λ λ λ λ λ λ λ= + + + + +

where C1 = 18983678 C2 = 19222979 C3 = 08765134 C4 = 01188704 C5 = 09569903 λ1 = 015 μm λ2 = 025 μm λ3 = 035 μm λ4 = 045 μm and λ5 = 27386128 μm

For arsenic selenide we fit ellipsometry measure-ments of our arsenic selenide thin films and the bulk material is provided by Prof Kathleen A Richardson group

22 22 31 2

2 2 2 2 2 21 2 3

( ) 1- - -

CC Cn

λλ λλ

λ λ λ λ λ λ= + + +

where C1 = 298463 C2 = 321011 C3 = 100182 λ1 = 044118 μm λ2 = 0000354953 μm and λ3 = 38413 μm

B Nonlinear Kerr index n2

The third-order nonlinear susceptibility χ(3)1111 for silicon and

germanium is predicted over the mid-IR range [133] based on a two-band model The effective nonlinear susceptibil-ity χ(3) is dependent on polarization and crystallographic orientation [225] For strong nonlinearity we consider a single-polarization incident light aligned to the crystal-lographic axis and we have χ(3) = χ(3)

1111 To investigate the octave-spanning nonlinear phenomena one need to take the wavelength-dependent nonlinear Kerr index n2 and TPA coefficient βTPA into account which are expressed as

( 3 )2 2

0

( 3 )2

0

3( ) ( )4 ( )

3( ) ( )( )

re

TPA im

ncn

cn

λ χ λε λ

πβ λ χ λ

λε λ

=

=

where ε0 and c are the vacuum permittivity and the speed of light in vacuum Using the material index given in Appendix A and χ(3) value from [133] we obtain the n2 and βTPA values tabulated as follows

262emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

Table 1enspNonlinear Kerr index n2 in silicon

λμm

  n2

10-18 m2W  λ

μm  n2

10-18 m2W  λ

μm  n2

10-18 m2W

130   234   310   389   490   312135   305   315   384   495   311140   378   320   379   500   310145   443   325   375   505   309150   501   330   371   510   307155   559   335   368   515   306160   618   340   365   520   304165   671   345   362   525   304170   710   350   360   530   303175   741   355   358   535   302180   766   360   355   540   302185   781   365   352   545   301190   783   370   350   550   300195   778   375   346   555   298200   762   380   343   560   297205   732   385   341   565   296210   699   390   338   570   296215   658   395   336   575   295220   612   400   334   580   295225   576   405   332   585   295230   547   410   331   590   294235   525   415   330   595   293240   508   420   329   600   292245   493   425   328   605   291250   479   430   327   610   290255   467   435   325   615   289260   456   440   324   620   288265   448   445   321   625   288270   440   450   319   630   288275   432   455   317   635   288280   424   460   315   640   288285   417   465   314   645   288290   410   470   313   650   288295   404   475   313   655   288300   398   480   312   660   288305   394   485   312    

Table 2enspTPA coefficient βTPA in silicon

λμm

  βTPA

10-12 mW  λ

μm  βTPA

10-12 mW  λ

μm  βTPA

10-12 mW

130   1334   165   812   200   180135   1284   170   713   205   115140   1222   175   613   210   064145   1154   180   522   215   024150   1079   185   424   220   0003155   995   190   333    160   905   195   254    

Table 3enspNonlinear Kerr index n2 in germanium

λμm

  n2

10-18 m2W  λ

μm  n2

10-18 m2W  λ

μm  n2

10-18 m2W

23  3932  63  1986  103  170524  4994  64  1972  104  169925  6007  65  1959  105  169426  6650  66  1946  106  169027  6772  67  1934  107  168728  6273  68  1923  108  168429  4897  69  1913  109  168230  4403  70  1904  110  168131  3970  71  1895  111  167932  3680  72  1886  112  167733  3470  73  1876  113  167534  3286  74  1868  114  167335  3128  75  1859  115  167036  2998  76  1850  116  166737  2895  77  1841  117  166338  2812  78  1833  118  165939  2737  79  1826  119  165640  2668  80  1819  120  165341  2605  81  1812  121  165142  2550  82  1807  122  164843  2498  83  1801  123  164644  2450  84  1797  124  164445  2406  85  1792  125  164346  2365  86  1787  126  164147  2328  87  1782  127  163948  2295  88  1777  128  163649  2266  89  1772  129  163450  2238  90  1767  130  163251  2212  91  1762  131  163052  2187  92  1758  132  162853  2164  93  1753  133  162654  2141  94  1749  134  162555  2121  95  1744  135  162356  2101  96  1740  136  162157  2083  97  1736  137  162058  2066  98  1731  138  161859  2049  99  1727  139  161760  2032  100  1722  140  161661  2016  101  1716   62  2001  102  1711   

Table 4enspTPA coefficient βTPA in germanium

λμm

  βTPA

10-8 mW  λμm

  βTPA

10-8 mW  λ

μm  βTPA

10-8 mW

23   130   25   088   27   03124   111   26   060   28   006

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp263

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[136] Raghunathan V Borlaug D Rice RR Jalali B Demonstration of a mid-infrared silicon Raman amplifier Opt Express 20071514355ndash62

[137] Chavez Boggio JM Windmiller JR Knutzen M Jiang R Bres C Alic N Stossel B Rottwitt K Radic S 730-nm optical parametric conversion from near- to short-wave infrared band Opt Express 2008165435ndash43

[138] Lin Q Johnson TJ Perahia R Michael CP Painter OJ A proposal for highly tunable optical parametric oscillation in silicon micro-resonators Opt Express 20081610596ndash610

[139] Turner-Foster AC Foster MA Salem R Gaeta AL Lipson M Frequency conversion over two-thirds of an octave in silicon nanowaveguides Opt Express 2010181904ndash8

[140] Liu X Osgood RM Vlasov YA Green WMJ Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides Nat Photonics 20104557ndash60

[141] Zlatanovic S Park JS Moro S Boggio JMC Divliansky IB Alic N Mookherjea S Radic S Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source Nat Photonics 20104561ndash4

[142] Tien EK Huang YW Gao S Song Q Qian F Kalyoncu SK Boyraz O Discrete parametric band conversion in silicon for mid-infrared applications Opt Exp 20101821981ndash9

[143] Lau RKW Meacutenard M Okawachi Y Foster MA A C Turner-Foster Salem R Lipson M Gaeta AL Continuous-wave mid-infrared frequency conversion in silicon nanowaveguides Opt Lett 2011361263ndash5

[144] Roelkens G Green WMJ Kuyken B Liu X Hattasan N Gassenq A Cerutti L Rodriguez JB Osgood RM Tournie E Baets R III-Vsilicon photonics for short-wave infrared spectroscopy IEEE J Quant Electron 201248292ndash8

[145] Alloatti L Korn D Weimann C Koos C Freude W Leuthold J Second-order nonlinear silicon-organic hybrid waveguides Opt Express 20122020506ndash15

[146] Harris DC Durable 3ndash5 μm transmitting infrared window materials Infrared Phys Technol 199839185ndash201

[147] Carlie N Musgraves JD Zdyrko B Luzinov I Hu J Singh V Agarwal A Kimerling LC Canciamilla A Morichetti F Melloni A Richardson K Integrated chalcogenide waveguide resonators for mid-IR sensing leveraging material properties to meet fabrication challenges Opt Express 20101826728ndash43

[148] Eggleton BJ B Luther-Davies Richardson K Chalcogenide photonics Nat Photonics 20115141ndash8

[149] Madden SJ Vu KT High-Performance Integrated Optics with Tellurite Glasses Status and Prospects Int J Appl Glass Sci 20123289ndash98

[150] Bindra KS Bookey HT Kar AK Wherrett BS Liu X Jha A Nonlinear optical properties of chalcogenide glasses observation of multiphoton absorption App Phys Lett 2001791939ndash41

[151] Zakery A Ruan Y ARode V Samoc M Luther-Davies B Low-loss waveguides in ultrafast laser-deposited As2S3 chalcogenide films J Opt Soc Am B 200391844ndash52

[152] Lenz G Zimmermann J Katsufuji T MLines E Hwang HY Spalter S Slusher RE Cheong SW Sanghera JS Aggarwal ID Large Kerr effect in bulk Se-based chalcogenide glasses Opt Lett 200025254ndash6

[153] Sanghera JS Shaw LB Aggarwal ID Application of chalcogenide glass optical fibers CR Chimie 20025873ndash83

[154] Palik ED Handbook of optical constants of solids San Diego CA Academic 1998

[155] Philipp HR Optical properties of silicon nitride J Electrochem Soc 1973120295ndash300

[156] Malitson IH Interspecimen comparison of the refractive index of fused silica J Opt Soc Am 1965551205ndash8

[157] Barnes NP Piltch MS Temperature-dependent Sellmeier coefficients and nonlinear optics average power limit for germanium J Opt Soc Am 197969178ndash80

[158] Rodney WS Malitson IH King TA Refractive index of arsenic trisulfide J Opt Soc Am 195848633ndash636

[159] Ellipsometry measurement on the thin film samples by our group[160] Bristow AD Rotenberg N van Driel HM Two-photon

absorption and Kerr coefficients of silicon for 850ndash2200 nm Appl Phys Lett 200790191104

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp267

[161] Lin Q Zhang J Piredda G Boyd RW Fauchet PM Agrawal GP Dispersion of silicon nonlinearities in the near infrared region Appl Phys Lett 200791021111

[162] Mizrahi V DeLong KW Stegeman GI Saifi MA Andrejco MJ Two-photon absorption as a limitation to all-optical switching Opt Lett 1989141140ndash2

[163] Guider R NDaldosso APitanti EJordana Fedeli J-M Pavesi L NanoSi low loss horizontal slot waveguides coupled to high Q ring resonators Opt Express 20091720762ndash70 and its erratum

[164] Ferrera M Razzari L Duchesne D Morandotti R Yang Z Liscidini M Sipe JE Chu S Little BE Moss DJ Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures Nat Photonics 20082 737ndash40

[165] Smektala F Quemard C Leneindre L Lucas J Barthelemy A De Angelis C Chalcogenide glasses with large non-linear refractive indices J Non-Crystalline Solids 1998239139ndash42

[166] Boudebs G Sanchez F Troles J Smektala F Nonlinear optical properties of chalcogenide glasses- comparison between Mach-Zehnder interferometry and Z-scan techniques Opt Comm 2001199425ndash33

[167] Asobe M Suzuki K Kanamori T Kubodera K Nonlinear refractive index measurement in chalcogenide-glass fibers by self-phase modulation APL 1992601153ndash4

[168] Asobe M Kanamori T Kubodera K Ultrafast all-optical switching using highly nonlinear chalcogenide glass fiber IEEE Photon Technol Lett 19924362ndash5

[169] Asobe M Kanamori T Kubodera K Applications of highly nonlinear chalcogenide glass fibers in ultrafast all-optical switches IEEE J Quant Electron 1993292325ndash33

[170] Ruan Y Luther-Davies B Li W Rode A Kolev V Madden S Large phase shifts in As2S3 waveguides for all-optical processing devices Opt Lett 2005302605ndash7

[171] Laniel JM Hocirc N Valleacutee R Villeneuve A Nonlinear-refractive-index measurement in As2S3 channel waveguides by asymmetric self-phase modulation J Opt Soc Am B 200522437ndash45

[172] Cerqua-Richardson KA McKinley JM Lawrence B Joshi S Villeneuve A Comparison of nonlinear optical properties of sulfide glasses in bulk and thin film form Opt Mater 199810155ndash9

[173] Harbold JM Ilday FOuml Wise FW Sanghera JS Nguyen VQ Shaw LB Aggarwal ID Highly nonlinear As-S-Se glasses for all-optical switching Opt Lett 200227119ndash121

[174] Ruan YL Li WT Jarvis R Madsen N Rode A Luther-Davies B Fabrication and characterization of low loss rib chalcogenide waveguides made by dry etching Opt Express 2004125140ndash5

[175] Slusher RE Lenz G Hodelin J Sanghera J Shaw LB Aggarwal ID Large Raman gain and nonlinear phase shifts in high-purity As2Se3 chalcogenide fibers J Opt Soc Am B 2004211146ndash55

[176] Jacobsen R Andersen K Borel P Fage-Pedersen J Frandsen L Hansen O Kristensen M Lavrinenko A Moulin G Ou H Peucheret C Zsigri B Bjarklev A Strained silicon as a new electro-optic material Nature 2006441199ndash202

[177] Cazzanelli M Bianco F Borga E Pucker G Ghulinyan M Degoli E Luppi E Veacuteniard V Ossicini S Modotto D Wabnitz S Pierobon R Pavesi L Second-harmonic generation in

silicon waveguides strained by silicon nitride Nat Mater 201111148ndash54

[178] Avrutsky I Soref R Phase-matched sum frequency generation in strained silicon waveguides using their second-order nonlinear optical susceptibility Opt Express 20111921707ndash16

[179] Ghahramani E Moss DJ Sipe JE Second-harmonic generation in odd-period strained (Si)n(Ge)nSi superlattices and at SiGe interfaces Phys Rev Lett 1990642815ndash8

[180] Levy JS Foster MA Gaeta AL Lipson M Harmonic generation in silicon nitride ring resonators Opt Express 20111911415

[181] Zakery A Elliott SR Optical nonlinearities in chalcogenide glasses and their applications Springer Series in Optical Sciences 2007135

[182] Lee KK Lim DR Kimerling LC Shin J Cerrina F Fabrication of ultralow-loss SiSiO2 waveguides by roughness reduction Opt Lett 2001261888ndash90

[183] Cardenas J Poitras CB Robinson JT Preston K Chen L Lipson M Low loss etchless silicon photonic waveguides Opt Express 2009174752ndash7

[184] Biberman A Shaw MJ Timurdogan E Wright JB Watts MR Ultralow-loss silicon ring resonators Opt Lett 2012374236ndash8

[185] Walmsley IA Waxer L Dorrer C The role of dispersion in ultrafast optics Rev Sci Instrum 2001721ndash29

[186] Torres JP MHendrych Valencia A Angular dispersion an enabling tool in nonlinear and quantum optics Adv Opt Photon 20102319ndash69

[187] Yin LH Lin Q Agrawal GP Dispersion tailoring and soliton propagation in silicon waveguides Opt Lett 2006311295ndash7

[188] Dulkeith E Xia FN Schares L Green WMJ Vlasov YA Group index and group velocity dispersion in silicon-on-insulator photonic wires Opt Express 2006143853ndash63

[189] Turner AC Manolatou C Schmidt BS Lipson M Tailored anomalous group-velocity dispersion in silicon channel waveguides Opt Express 2006144357ndash62

[190] Dadap JI Panoiu NC Chen X I-Hsieh W Liu X Chou C-Y Dulkeith E McNab SJ Xia F Green WMJ Sekaric L Vlasov YA Osgood RM Jr Nonlinear-optical phase modification in dispersion-engineered Si photonic wires Opt Express 2008161280ndash99

[191] Milosevic MM Matavulj PS Yang PY Bagolini A Mashanovich GZ Rib waveguides for mid-infrared silicon photonics J Opt Soc Am B 2009261760ndash6

[192] Mashanovich GZ Milošević MM Nedeljkovic M Owens N Xiong B Teo EJ Hu Y Low loss silicon waveguides for the mid-infrared Opt Express 2011197112ndash9

[193] Reimer C Nedeljkovic M Stothard DJM Esnault MOS Reardon C OrsquoFaolain L Dunn M Mashanovich GZ Krauss TF Mid-infrared photonic crystal waveguides in silicon Opt Express 20122029361ndash8

[194] Baehr-Jones T Spott A Ilic R Spott A Penkov B Asher W Hochberg M Silicon-on-sapphire integrated waveguides for the midinfrared Opt Express 20101812127ndash35

[195] Li F Jackson S Grillet C Magi E Hudson D Madden SJ Moghe Y OrsquoBrien C Read A Duvall SG Atanackovic P Eggleton BJ Moss D Low propagation loss silicon-on-sapphire waveguides for the midinfrared Opt Express 20111915212ndash20

268emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

[196] Yue Y Zhang L Huang H Beausoleil RG Willner AE Silicon-on-nitride waveguide with ultralow dispersion over an octave-spanning mid-infared wavelength range IEEE Photonics J 20124126ndash32

[197] Khan S Chiles J Ma J Fathpour S Silicon-on-nitride waveguides for mid-and near-infrared integrated photonics Appl Phys Lett 2013102121104

[198] Cheng Z Chen X Wong CY Xu K Tsang HK Mid-infrared suspended membrane waveguide and ring resonator on silicon-on-insulator IEEE Photonics J 201241510ndash9

[199] Lin P-T Singh V Cai Y Kimerling LC Agarwal A Air-clad silicon pedestal structures for broadband mid-infrared microphotonics Opt Lett 2013381031ndash3

[200] Chang YC Paeder V Hvozdara L Hartmann JM Herzig HP Low-loss germanium strip waveguides on silicon for the mid-infrared Opt Lett 2012372883ndash5

[201] Zhang L Yue Y Y Xiao-Li R G Beausoleil Willner AE Highly dispersive slot waveguides Opt Express 2009177095ndash101

[202] Zhang L Yue Y Beausoleil RG Willner AE Analysis and engineering of chromatic dispersion in silicon waveguide bends and ring resonators Opt Express 2011198102ndash7

[203] Zhang L Mu J Singh V Agarwal A Kimerling LC Michel J Intra-cavity dispersion of microresonators and its engineering for octave-spanning Kerr frequency comb generation to be published

[204] Lin Q Zhang L Generalized nonlinear envelope equation with high-order dispersion of nonlinearity to be published

[205] Wang Y Yue R Han H Liao X Raman study of structural order of a-SiNxH and its change upon thermal annealing J Non-Crystalline Solids 2001291107ndash12

[206] Brida D Marangoni M Manzoni C De Silvestri S Cerullo G Two-optical-cycle pulses in the mid-infrared from an optical parametric amplifier Opt Lett 2008332901ndash3

[207] Brida D Manzoni C Cirmi G Marangoni M Bonora S Villoresi P De Silvestri S Cerullo G Few-optical-cycle pulses tunable from the visible to the mid-infrared by optical parametric amplifiers J Opt 201012013001

[208] Kippenberg TJ Holzwarth R Diddams SA Microresonator-based optical frequency combs Science 2011332555ndash9

[209] Levy JS Gondarenko A Foster MA Turner-Foster AC Gaeta AL Lipson M CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects Nat Photonics 2009437ndash40

[210] DelrsquoHaye P Herr T Gavartin E Gorodetsky ML Holzwarth R Kippenberg TJ Octave spanningtunable frequency comb from a microresonator Phys Rev Lett 2011107063901

[211] Okawachi Y Saha K Levy JS Wen YH Lipson M Gaeta AL Octave-spanning frequency combgeneration in a silicon nitride chip Opt Lett 2011363398ndash400

[212] Matsko AB Savchenkov AA Liang W Ilchenko VS Seidel D Maleki L Mode-locked Kerr frequency combs Opt Lett 2011362845ndash7

[213] Herr T Brasch V Jost JD Wang CY Kondratiev NM Gorodetsky ML Kippenberg TJ Temporal solitons in optical microresonators httparxivorgabs12110733

[214] Saha K Okawachi Y Shim B Levy JS Salem R Johnson AR Foster MA Lamont MR Lipson M Gaeta AL Modelocking and femtosecond pulse generation in chip-based frequency combs Opt Express 2013211335ndash43

[215] Coen S Erkintalo M Universal scaling laws of Kerr frequency combs Opt Lett 2013381790ndash2

[216] Lugiato LA Lefever R Spatial dissipative structures in passive optical-systems Phys Rev Lett 1987582209ndash11

[217] Haelterman M Trillo S Wabnitz S Dissipative modulation instability in a nonlinear dispersive ring cavity Opt Commun 199291401ndash7

[218] Coen S Randle HG Sylvestre T Erkintalo M Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato-Lefever model Opt Lett 20133837ndash9

[219] Chembo YK Menyuk CR Spatiotemporal Lugiato-Lefever formalism for Kerr-comb generation in whispering-gallery-mode resonators Phys Rev A 201387053852

[220] Foltynowicz A Mas1owski P Ban T Adler F Cossel KC Briles TC Ye J Optical frequency comb spectroscopy Faraday Discussion 201115023ndash31

[221] Hartl I Li XD Chudoba C Ghanta RK Ko TH Fujimoto JG Ranka JK Windeler RS Ultrahigh-resolution optical coherence tomography using continuum generation in an air silica microstructure optical fiber Opt Lett 200126608ndash10

[222] Brabec T Krausz F Intense few-cycle laser fields Frontiers of nonlinear optics Rev Mod Phys 200072545ndash91

[223] Hu J Meyer J Richardson K Shah L Feature issue introduction mid-IR photonic materials Opt Mater Express 201331571ndash5

[224] Private communications with Dr Jacob Levy in Prof Lipsonrsquos group and Dr Johann Riemensberger in Prof Kippenbergrsquos group

[225] Zhang J Lin Q Piredda G Boyd RW Agrawal GP Fauchet PM Anisotropic nonlinear response of silicon in the near-infrared region Appl Phys Lett 200791071113

Page 2: Lin Zhang*, Anuradha M. Agarwal, Lionel C. Kimerling and ...

248emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

In the past two decades silicon photonics [16ndash25] has become increasingly mature What silicon photonics can contribute to nonlinear optics is much more than a high index contrast Several fundamental advantages drive nonlinear silicon photonics [26ndash30]

First as bulk material crystalline silicon typically has stronger Kerr and Raman nonlinearities than silica by 2~3 orders of magnitude [26ndash30] depending on crystal orientation Materials engineering further enhanced the nonlinearity eg in amorphous silicon under certain deposition conditions [31ndash35] and in Si-rich silicon oxide (SRO) and nitride (SRN) based on the formation of silicon nano-crystals [36ndash41]

Second the high index contrast not only allows sub-wavelength light confinement [42] but also makes it possible to form novel waveguiding structures For example when a nano-scale low-index layer is sand-wiched between two high-index layers a slot waveguide can be formed [43ndash46] with a large fraction of modal power trapped in the thin layer Relative to many nonlin-ear materials such as SRO SRN chalcogenides and poly-mers silicon has a sufficiently large index to form a slot waveguide [47ndash51] Moreover adding a slot layer provides more design freedom to tailor chromatic dispersion as reported in standard slot waveguides [51ndash58] and stripslot hybrid waveguides [59ndash63] A high refractive index is also beneficial to build a slow light element with reduced group velocity of light which can effectively increase optical length for nonlinear interactions and reduce power requirement [64ndash66]

Third CMOS compatibility in silicon device process-ing and fabrication can be utilized for nonlinear silicon photonics Although optoelectronic integration of silicon devices has long been proposed [16] there have been few reports on the integration of nonlinear devices with elec-trical functionality As silicon photonics becomes more mature it is foreseeable that CMOS-compatible nonlinear silicon devices are seamlessly integrated with microelec-tronics on a single chip For example on-chip pumping using an integrated laser data encoding and modulation before nonlinear signal processing and on-chip signal detection and data analysis after nonlinear devices are all highly likely to be integrated together which is achievable by building nonlinear photonics on a silicon platform

Fourth cost-effectiveness and portability of devices enabled by silicon photonics can be directly transferred to the nonlinear optics branch Although probably not a key consideration in a very early stage of a research topic these factors will finally drive the technological develop-ment and determine how widely this technology will be used Nonlinear silicon photonic devices have unique

competence especially when a large amount of elements need to be incorporated in a (sub-) system

The above motivations led to considerable research efforts on nonlinear silicon photonics in recent years [26ndash30] Nonlinear effects such as SRS [67ndash83] self- and cross-phase modulation (SPM and XPM) [84ndash91] four-wave mixing (FWM) [92ndash102] and supercontinuum gen-eration [60 61 103ndash108] are actively investigated The main focus is on the near-IR wavelength range around the telecom window However TPA in silicon is a detri-mental effect in most cases [109 110] significantly limit-ing optical power that is actually available in nonlinear interactions TPA thus degrades nonlinear efficiency and bandwidth in the effects of interest such as wavelength conversion and supercontinuum generation and TPA-induced free carriers cause slow device responses [26] It is noted that both the desired nonlinear effect and TPA are accumulative over a certain distance so if one can engi-neer chromatic dispersion to make the desired nonlinear effect more efficient the negative influence of TPA can be mitigated [60 108] One can also use silicon nitride [111ndash115] to eliminate TPA or even three photon absorption (3PA) for a pumping wavelength in the near-IR because silicon nitride has a bandgap energy of ~53 eV [113]

It would be sometimes instructive to look at the trends in nonlinear optics based on non-integrated platforms in order to gain a vision on how nonlinear silicon photonics can evolve One of the recent trends in nonlinear optics is that a significantly larger portion of electromagnetic spectrum from X-ray to mid-IR and even THz is being exploited to acquire previously hardly accessible informa-tion [116ndash118] For nonlinear silicon photonics it is a natural step to extend to the mid-IR wavelength range [119ndash125] The definition of the term ldquomid-IRrdquo varies substantially in the literature according to different research communities and organizations Specific application scenarios correspond to different wavelength ranges These include but are not limited to (i) mid-IR spectroscopy and sensing from 25 to 15 μm [126] or from 25 to 25 μm according to infrared spectros-copy correlation table [127] ldquohttpenwikipediaorgwikiInfrared_spectroscopy_correlation_tablerdquo (ii) free space communications LADAR and remote sensing in atmos-phere transparent windows from 3 to 5 μm and from 8 to 12 μm [128 129] and (iii) astronomical instrumentation over a bandwidth from 5 to 20 μm [130]

These new opportunities in the mid-IR are open to silicon photonics from an application perspective while nonlinear silicon photonics also gains additional advan-tages in this wavelength range in terms of materials and devices First silicon has no TPA beyond 22 μm and nonlinear loss by 3PA is significantly less influential for

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp249

an optical intensity of below 5 GWcm2 [131 132] Second more Group IV elements eg germanium become trans-parent and can be used for nonlinear purposes In fact germanium exhibits higher refractive index and Kerr index n2 than silicon [133] Third at longer wavelengths device dimensions need to be scaled up according to wavelength and thus surface roughness induced in device fabrication causes relatively small scattering loss Fourth fabrication errors in device dimensions are a smaller fraction of target numbers which is beneficial to obtain a higher yield in device manufacture

However nonlinear photonics in the mid-IR also meet some challenges Although going beyond half-bandgap wavelengths one can remove TPA the nonlinear Kerr index n2 markedly decreases [134] With waveguide dimensions scaled up the effective mode area Aeff increases almost quadratically Therefore the nonlinear coefficient γ equal to 2πn2(λAeff) where λ is the wave-length in vacuum decreases quickly with wavelength This would require careful dispersion engineering for phase matching in nonlinear parametric processes in order to improve nonlinear efficiency [12]

Many nonlinear effects have been reported recently in silicon photonics touching the mid-IR wavelength range [60 61 106 108 114 115 135ndash145] It is noted that most of them address the short-wavelength end of the mid-IR from 2 to 25 μm which is mainly the short-wave IR [144] or transition from near-IR to mid-IR Little was reported in longer wavelength beyond 25 μm [136 138 142 145] In fact there are about two octaves of bandwidth in the mid-IR (eg from 25 to 10 μm) available much wider than that in the near-IR As an approach to creating new frequencies nonlinear optics is much more efficient than electro-optic modulation in terms of how far an optical spectrum can be extended We believe that the mid-IR would be an exciting arena for ultrafast octave-spanning nonlinear applications

In this paper we discuss the materials properties of the Group IV platform for nonlinear applications The waveguide-based devices are optimized for four different wavelength ranges from near-IR to mid-IR in terms of both nonlinearity and dispersion We show by simulation that our dispersion-engineering approach based on a stripslot hybrid structure is widely applicable and can drama-tically enhance nonlinear interaction efficiency and spec-trum broadening Supercontinuum and frequency comb generations are predicted to be octave-spanning accord-ing to our numerical simulations in which excellent spectral coherence of the generated wideband spectra is confirmed by the creation of ultrashort cycle-level optical pulses

Si

Si3N4

As2S3

As2Se3

1 2 3 4 5 6 7 8 9 10 11 12 13 14Wavelength (microm)

SiO2

Ge

Figure 1emspMaterials transparency windows (green bar) in near- and mid-infrared ranges Red bars indicate high-loss wavelength bands for each material and color transition from red to green is from bandgap wavelength to half-bandgap wavelength (blue lines)

2 MaterialsLoss nonlinearity and dispersion jointly determine the nonlinear performance of optical waveguides All the three are both material- and device-dependent In this section we survey the major material choices for nonlin-ear Group IV photonics in the near- and mid-IR

Figure 1 shows material transparency windows with an optical loss below 2 dBcm [122] for materials including silicon (Si ie crystalline silicon unless otherwise speci-fied) silicon nitride (Si3N4) silicon dioxide (SiO2) germa-nium (Ge) arsenic sulfide (As2S3) and arsenic selenide (As2Se3) Since TPA plays an important role in nonlinear applications [109 110] the color transition from red to green in Figure 1 is between the bandgap wavelength and the half-bandgap wavelength (two blue lines) where TPA decreases with wavelength For silicon almost two-octave bandwidth from 22 to 85 microm [146] is available for nonlin-ear applications without TPA covering a large fraction of mid-IR range It is important to note that amorphous silicon has a bandgap energy of 17 eV [32 33] and thus has TPA diminishing at a much shorter wavelength ( lt 155 μm) than crystalline silicon Both silicon nitride and silicon dioxide have large bandgap energies but silicon dioxide becomes highly lossy beyond 3 microm [119] Germanium has an indirect bandgap energy of 067 eV and is transparent until up to 14 microm [146] From Figure 1 one can see that germaniumrsquos green bar without TPA has no overlap with silicon dioxide

Chalcogenide glasses are actively investigated as photonic materials [147ndash149] and exhibit a wide trans-parency window in the near- and mid-IR For example As2S3 and As2Se3 have bandgap energies around 226 eV [150 151] and 177 eV [152] and they are transparent up to 12 and 15 microm [153] respectively Although in this paper

250emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

chalcogenide glasses are not considered a material for the core of a waveguide one may use them for waveguide cladding and slot layer [53 58]

Linear optical properties of the materials discussed here are collected in terms of refractive index and mate-rial dispersion as shown in Figure 2 The two ldquoXrdquo on the curves for silicon and germanium in Figure 2(A) indicate the half-bandgap wavelengths The refractive index is given by the Sellmeier equations for silicon [154] silicon nitride [155] silicon dioxide [156] SRO [51] germanium [157] arsenic sulfide [158] and arsenic selenide [159] as detailed in Appendix A For SRN there is no comprehen-sive measurement of material index found currently As shown in Figure 2(A) the materials under our considera-tion have strong index contrasts especially between ger-manium and chalcogenides in the mid-IR The refractive index decreases with wavelength and beyond the half-bandgap wavelength these materials have a relatively small index change One can properly choose materials for waveguide core and cladding and also a low-index slot layer based on the information given in Figure 2(A)

Overall dispersion in an integrated waveguide con-sists of material dispersion and waveguide dispersion that

40

35

30

25

Ref

ract

ive

inde

xD

ispe

rsio

n (p

snm

middotkm

)

20

200B

A

100

-100

-200

0

15

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Wavelength (microm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Wavelength (microm)

Si

Si

Si3N4

Si3N4

As2S3

As2S3

As2Se3

As2Se3

SiO2

SiO2

SRO

SRO

Ge

Ge

Figure 2emsp(A) Refractive indices and (B) material dispersion curves of the materials considered for nonlinear Group IV photonics in the near- and mid-IR wavelength ranges

is affected by index contrast and waveguide dimensions First material dispersion is shown in Figure 2(B) which is defined as D  =  -(cλ)middot(d2nmatdλ2 ) where nmat is material index and λ and c are wavelength and the speed of light in vacuum It is important to note that except for silicon dioxide all the other materials have a flat and low disper-sion within  plusmn 100 ps(nmmiddotkm) at the long-wavelength end of the bandwidth of interest This means that if wave-guides are not designed to tightly confine guided modes one can reduce the contribution of the waveguide disper-sion and have the overall dispersion close to the flat and low material dispersion However this will cause a large effective mode area and a small nonlinear coefficient

On the other hand we note from Figure 2(B) that at the short-wavelength end of the spectrum material dispersion changes quickly with wavelength for all the considered materials even if the material refractive index looks flat in Figure 2(A) beyond the half-bandgap wave-length This is because the dispersion is the 2nd-order derivative of the index with respect to wavelength To fully use the portion of the spectrum near the half-bandgap wavelength dispersion engineering by tailoring wave-guide dispersion is required

As a measure of nonlinear material property the non-linear index n2 is shown in Figure 3 for silicon silicon nitride SRO germanium and arsenic sulfide Looking at broadband nonlinear applications one needs to take the wavelength dependence of n2 into account Unfor-tunately there is often a lack of complete measurement data at a wavelength range of interest and also measure-ment results from different groups could vary widely For silicon data from several sources are available [160 161] A recently published review paper [133] shows a predic-tion of third-order nonlinear susceptibility χ(3)

1111 for silicon and germanium in the mid-IR range based on a two-band model which is used to fit wavelength-dependent

Non

linea

r in

dex

(m2 W

)

1E-16

1E-17

1E-18

1E-191 2 3 4 5 6 7 8 9 10 11 12 13 14

Wavelength (microm)

Si

Si3N4

SROGe

As2S3

Figure 3emspThe Kerr nonlinear index n2values of the considered mate-rials in near- and mid-IR ranges

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp251

measurements We obtain the Kerr nonlinear index n2 as a function of wavelength based on χ(3)

1111 using the results from [133] As shown in Figure 3 the n2 value peaks at 19 and 27 microm for silicon and germanium respectively and changes slightly from 33 to 48 microm beyond which both TPA and 3PA disappear The TPA coefficient βTPA vs wave-length is also extracted for silicon and germanium from [133] as detailed in Tables 1ndash4 in Appendix B

Hydrogenated amorphous silicon has been identi-fied as a potentially good nonlinear material not only because of large bandgap energy of 17 eV but also more importantly because of the large nonlinear index n2 and nonlinear figure of merit (FOM) n2βTPAλ [162] We did not include specific data in Figure 3 for amorphous silicon since different groups reported highly variable n2 and nonlinear FOM values in the near-IR [31ndash35] The n2 value could be one order of magnitude higher than that in silicon [33] while the nonlinear FOM can be as high as 5 [35] although these may not be obtained simultaneously [34] Moreover linear properties of amorphous silicon may also vary when fabrication conditions and its nonlin-ear characteristics change

Silicon nano-crystals in silicon dioxide and silicon nitride have also been investigated as a nonlinear material exhibiting higher nonlinear indices than crystalline silicon by an order of magnitude or more [36ndash41] The values of n2 βTPA and nonlinear FOM are also highly variable if silicon excess annealing temperature and wavelength change We include one data point (n2 = 48 times 10-17m2W) from [38] in Figure 3 Extremely high n2and FOM by 3~4 orders have been obtained experimentally [41] with large silicon excess (note that the FOM in [41] is defined as the reciprocal of ours here)

Both amorphous silicon and silicon nano-crystals exhibit great potential as a nonlinear material in the mid-IR which can be used to compensate for the reduc-tion of the nonlinear coefficient due to a large mode area at long wavelengths In particular with a small linear refractive index SRO is often chosen as a slot material to enhance nonlinearity in the near-IR [51 53 55 56 59] while SRN exhibits a great potential for nonlinear applica-tions beyond 3 microm Typically strong nonlinearity in bulk materials is associated with a high linear refractive index which is known as Miller rule However silicon nano-crys-tals exhibit unique properties to simultaneously possess strong nonlinearity and low linear index It is important to mention that the silicon nano-crystals (ie nano-clusters) could act as scattering centers of light causing an increased propagation loss in SRO slot waveguides Nevertheless relatively low propagation loss has been achieved which is 3~5 dBcm [163]

For silicon nitride one data point n2 = 24 times 10-19m2W from [111] is included in Figure 3 which was measured at 155 microm and is one-order lower than that in silicon Silicon dioxide has an n2 value around 26 times 10-20m2W in 155 microm as in single-mode optical fibers two orders lower than that in silicon A higher n2 value (115 times 10-19m2W) is estimated for 155 microm in high-index doped silica [164] Both values are not shown in Figure 3 Since both silicon nitride and silicon dioxide have large bandgap energies it is expected that their n2 values are almost constant over wavelength in the near- and mid-IR

Strong Kerr nonlinearities are obtained in chalcoge-nide glasses (arsenic sulfide and arsenic selenide) with negligible TPA from the near- to mid-IR as shown in Figure 1 We have found wavelength-dependent measure-ments of the nonlinear index n2 for arsenic sulfide from different data sources [150 165ndash174] As shown in Figure 3 although slightly scattered these n2 values in arsenic sulfide are as high as those in silicon and would not be strongly wavelength-dependent beyond 155 microm because it is longer than the half-bandgap wavelength Arsenic selenide has even higher n2 values than arsenic sulfide [173] and its n2 value is predicted as a function of wave-length in [175]

There has been little published on the wavelength dependence of the nonlinear Raman gain coefficient gR in literature for the materials that we consider here [133] Since SRS is not the major nonlinear effect that is used in this paper we will not discuss it in details here

Although the considered materials such as silicon germanium silicon nitride and silicon dioxide are cen-trosymmetric and show no second-order nonlinearity in bulk materials one can engineer them by applying strain [176ndash178] or forming interfaces between two centrosym-metric materials (eg between germanium and silicon [179] or between silicon nitride and silicon dioxide [180]) An alternative way is to integrate other materials with strong second-order susceptibility onto Group IV wave-guides (see eg [145]) For chalcogenide glasses different poling schemes are proposed to produce the second-order nonlinearity [181] The second-order susceptibility χ(2) induced to the Group IV platform can have a highly variable value depending on how the isotropy of materi-als is broken We believe that second-order nonlinearity is promising in nonlinear Group IV photonics but in this paper we will mainly focus on third-order nonlinearity

As described above the materials presented here have greatly different transparency windows and nonlin-ear coefficients It thus becomes critical to wisely choose a material combination for a specific application and doing this one may also need to pay special attention to material

252emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

compatibility in device fabrication On the other hand compared to the material choices device design (mainly on waveguide and resonator) can also produce widely var-iable dispersion and nonlinearity properties In the next section we will discuss enhanced waveguide properties using improved designs

3 DevicesOptical waveguides form the backbone of photonic devices Light propagation properties in a waveguide could be remarkably different from those in corresponding bulk materials especially when there is a high index con-trast between waveguide core and surrounding cladding Therefore understanding and optimizing the waveguide properties including loss dispersion and nonlinearity are essential in nonlinear photonics

Propagation loss in a waveguide includes material loss confinement loss scattering loss and nonlinear loss Working at a transparency window of a material especially beyond the half-bandgap wavelength one can primarily have low material and nonlinear loss caused by TPA Note that benefiting from the wide multi-octave bandwidth in the mid-IR one can even eliminate the impact of 3PA in silicon and germanium by pumping at  gt 33 microm and  gt 48 microm respectively Since the substrate index in a silicon wafer is higher than or equal to that in most of materials we consider for a waveguide core con-finement loss exists due to mode leakage to the silicon substrate This loss can be markedly reduced by increas-ing the spacing between waveguide core and the substrate or choosing low-index material between them In general scattering loss due to sidewall roughness of a waveguide is dominant in high-index-contrast silicon photonics which is mainly caused in device fabrication and can thus be reduced by improving the fabrication processes [182ndash184]

Compared to propagation loss chromatic disper-sion and nonlinearity in integrated waveguides are more de signable Since the dispersion is the second-order deriv-ative of the effective index with respect to wavelength it is particularly tailorable by changing waveguide shape and dimension Moreover dispersion has been recognized to be critical for broadband nonlinear effects [12 14 15 60 61 92ndash108 112ndash115 137ndash145] which is true especially for ultrafast octave-spanning applications [185] Spec-tral characteristics in a dispersion profile including the number and positions of zero-dispersion wavelengths (ZDWs) and dispersion slope greatly affect and often set the limit on the bandwidth of optical spectra the temporal

widths of pulses and conversion efficiency in nonlinear interactions [185] Generally speaking a flat dispersion profile (ie third- and higher-order dispersion terms are small) with low dispersion values is preferred

In conventional ultrafast nonlinear optics in a free-space setup many components were developed to control dispersion over a wide bandwidth [185 186] such as prisms gratings chirped mirrors and so on However in a waveguiding system eg in fiber-based ultrafast optics the dispersion-control toolkit is smaller and engineer-ing waveguide dispersion becomes critical In particular when waveguides are built on a silicon platform with a much higher index contrast than optical fibers dispersion in a highly nonlinear waveguide [187ndash190] often shows strong wavelength dependence which is not preferable for wideband nonlinear applications In [187 190] the ZDW in silicon rib and strip waveguides is mapped by scanning waveguide dimensions It is shown that tight confinement of a guided mode produces a ZDW in its dispersion profile around 12~14 μm close to the bandgap wavelength More-over even if the waveguide size is increased to move the ZDW to longer wavelength the dispersion slope near the ZDW is not small as shown in [187ndash189] causing a limited low-dispersion bandwidth

Recently a dispersion engineering technique for integrated high-index-contrast waveguides has been pro-posed in which an off-center nano-scale slot controls modal distribution at different wavelengths [59 60] The guided mode experiences a transition from strip-mode like to slot-mode like as wavelength increases This approach can produce a very flat dispersion profile over an ultra-wide bandwidth with dispersion flatness improved by 1ndash2 orders in terms of dispersion variation divided by low-dispersion bandwidth More importantly it is applicable to different material combinations and wavelength ranges [59ndash63]

Towards mid-IR applications different types of Group IV waveguides have been reported recently based on silicon-on-insulator (SOI) [191ndash193] silicon-on-sapphire [142 194 195] silicon-on-porous-silicon [192] silicon-on-nitride [196 197] suspended membrane silicon [198] silicon pedestal [199] and germanium-on-silicon [200] Most of the waveguides are not aimed specifically at non-linear applications and little attention has been paid to dispersion engineering [196]

In this section we survey different structures of Group IV waveguides for broadband nonlinear applica-tions from the near- to mid-IR There are three main goals in waveguide designs (i) we consider joint optimization on both dispersion and nonlinearity properties (ii) we tend to fully utilize the available bandwidth brought by

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp253

the materials in Figure 1 and (iii) we emphasize disper-sion engineering naturally as a result of aiming at octave-spanning broadband applications

Figure 4 shows a general illustration of various types of integrated waveguides for nonlinear Group IV photonics Looking at a specific wavelength range one can accord-ingly choose a materials combination for an appropriate index contrast and a desired level of nonlinearity Note that one may need low nonlinearity in some cases when high-power output is required Here we discuss waveguide design at four different wavelength ranges as follows

First we consider SOI waveguides for a wavelength range from the telecom window in the near-IR to the short-wave end in the mid-IR ie roughly from 14 to 25 microm This is the wavelength range that many of the current research efforts have been addressing [60 61 106 108 114 115 135 137 139ndash141 143 144] In this wavelength range a SOI strip waveguide as shown in Figure 4 can be used with air as an upper cladding (see eg [140]) One can change the width of the waveguide to tailor its disper-sion profile while the height of the waveguide is 220 nm set by SOI wafers From Figure 5(A) we note that a rela-tively small width W = 800 nm is corresponding to a dis-persion profile with two ZDWs at 1585 and 2345 microm and a peak value of anomalous dispersion 532 ps(nmmiddotkm) at 205 microm for the quasi-TE mode The anomalous disper-sion is typically useful for parametric amplification and oscillation soliton and soliton-based supercontinuum generation [12] With W  =  900 nm one can have a flatter dispersion profile but the anomalous band is smaller When W is increased to 1000 nm the dispersion is even flatter but no anomalous dispersion occurs Figure 5(A) shows a good example that tight mode confinement in a strip waveguide moves ZDW to short wavelengths and near ZDWs dispersion changes quickly with a large slope

Strip WG

Strip WG suspended

Air Air

Slot

Core

Upper cladding

Slab

Lower cladding

Si substrate

Slot WG suspended

Slot WG Rib WG

Figure 4emspDifferent types of Group IV waveguides (WGs) for disper-sion and nonlinearity engineering in the near- and mid-IR ranges

One can calculate the nonlinear coefficient γ as a function of wavelength with the nonlinear Kerr index n2 given in Tables 1ndash4 in Appendix B We show in Figure 5(B) that the nonlinear coefficient in the silicon strip wave-guide with W = 900 nm first increases to 187 (mmiddotW) with wavelength until 17 μm and then decreases to 56 (mmiddotW) at 25 μm This is caused by both the peaking of the silicon n2 value near 19 μm and the gradual increase of wave-length and mode area beyond that

A silicon stripslot hybrid waveguide exhibits very flat dispersion as presented in Figure 5(A) The SOI waveguide has crystalline silicon at the bottom a thin SRO slot and amorphous silicon at the top The upper cladding is silicon dioxide When setting the lower Si height to Hl = 430 nm slot height to Hs = 54 nm upper Si height to Hu = 160 nm and width to W = 660 nm we obtain an extremely flat disper-sion profile for the quasi-TM mode over a wide bandwidth between two ZDWs at 1545 and 2448 microm From 1605 to 238 microm the value of anomalous dispersion changes between 30 and 46 ps(nmmiddotkm) In this way one can have a flat and low anomalous dispersion between two far apart ZDWs The average dispersion value can be shifted by increasing Hu to move dispersion between normal and anomalous regimes Detailed explanation on how the flat-tened and saddle-shaped dispersion profile is produced is given in [59 60] Briefly the mode transition over wave-length for the quasi-TM mode is responsible for this behav-ior Due to the off-center slot the mode is mostly confined in the crystalline silicon at short wavelengths while the mode becomes more like a slot mode at long wavelengths As shown in Figure 5(C) we plot the mode power distribu-tions at wavelengths of 15 183 217 and 25 microm The mode transition adds negative dispersion in the middle of the low-dispersion bandwidth as explained in [60 201]

Having a slot one has an opportunity to fill the slot with highly nonlinear materials into it [49 51 53 55 56 58 59] which can overcome the decrease of the nonlinear coeffi-cient over wavelength In Figure 5(B) we show the γ value increasing to 306 (mmiddotW) with wavelength from 14 to 25 microm This is because the guided mode extends more to the highly nonlinear thin slot layer Note that the used n2 value in SRO [38] is currently the one measured at 155 microm so the n2 and γ thinspvalues may vary in the mid-IR but the trend is general

Next we explore the short-wavelength end of the near-IR spectrum Silicon-based devices become unus-able for nonlinear photonics as wavelength decreases to 11 microm and we thus look at silicon nitride for near-IR nonlinear applications extending to the visible light spec-trum Again a strip waveguide based on silicon nitride is examined first Figure 6(A) shows dispersion curves of the quasi-TE mode in two waveguides sized to be 1300 times 540

254emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

and 1400 times 800 nm2 The upper cladding is air and the lower cladding is silicon dioxide The anomalous disper-sion region in the dispersion curves shrinks when the waveguide is made smaller This is because of a relatively small index contrast between silicon nitride and silicon dioxide which makes the guided mode leak quickly to the substrate as wavelength increases For the strip waveguide with a cross-section of 1400 times 800 nm2 there are two ZDWs near 10 and 23 microm but one can see a strong dispersion of 250 ps(nmmiddotkm) between the two ZDWs in Figure 6(A) The nonlinear coefficient in the second silicon nitride wave-guide is shown in Figure 6(B) which is much smaller than that in silicon waveguides because of a one-order smaller n2 value and larger Aeff in the silicon nitride waveguide At 16 microm γ is about 123(mW)

One can also use a stripslot hybrid structure to tailor the dispersion profile in silicon nitride waveguides For example the slot and lower cladding are silicon dioxide and the upper cladding is air In Figure 6(A) we show the dispersion curves in two silicon nitride stripslot hybrid waveguides for comparison The waveguide 1 has Hl = 900 nm Hs = 124 nm Hu = 340 nm and W = 1000 nm and the waveguide 2 has Hl = 920 nm Hs = 154 nm Hu = 480 nm and W = 1300 nm These two waveguides produce increasingly flatter dispersion profiles as shown in Figure 6(A) The first waveguide has two ZDWs located at 106 and 22 microm with the peak dispersion of 67 ps(nmmiddotkm) The second waveguide has two ZDWs at 115 and 235 microm with the dispersion varying within 0~20 ps(nmmiddotkm) This octave-spanning dispersion flattening with different levels

1000A

B

C

500

-500

400

300

200

100

0

-100014 16

Strip WG W=800 nmStrip WG W=900 nm

Strip WG W=900 nm

Strip WG W=1000 nm

Slot WG Hu=160 nm

Slot WG Hu=160 nm

Slot WG Hu=163 nmSlot WG Hu=166 nm

18 20 22Wavelength (microm)

Dis

pers

ion

(ps

nmmiddotk

m)

Non

linea

r co

effic

ient

(m

middotW)

24 26

14 16 18 20 22

Wavelength (microm)

24 26

0

Figure 5emspIn a wavelength range from the telecom window in near-IR to the short-wave end in the mid-IR silicon strip and stripslot hybrid waveguides (WGs) are analyzed in terms of (A) dispersion and (B) nonlinearity (C) Mode power distributions at wavelengths of 15 183 217 and 25 microm in the stripslot hybrid waveguide

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp255

of dispersions can be used for multiple applications as detailed in the next section The nonlinear coefficients for the two waveguides are shown in Figure 6(B) We note that the stripslot hybrid waveguides have similar nonlinear coefficients as the strip waveguide which shows that the dispersion profile is much more tailorable by waveguide designs

Then we move to the mid-IR using silicon and silicon nitride for waveguiding A comparison of different types of silicon-on-nitride waveguides have been presented in [196] where rib waveguides were preferred due to the wideband low dispersion over an octave-spanning band-width from 24 to 66 microm for the quasi-TE mode This is a spectral range from siliconrsquos half-bandgap wavelength to the cut-off wavelength of silicon nitride In Figure 7(A) we plot the dispersion curve for a silicon-on-nitride rib waveguide with air as the upper cladding the rib width of 2000 nm the total height of 1200 nm and the slab height of 1000 nm which are the same parameters used in [196] It is shown that less confinement of optical modes reduces the contribution of waveguide dispersion and makes the overall dispersion profile closer to the material dispersion which is flat and low at long wavelengths as in Figure 2(B)

A

B

400

300

200

100

-100

8

6

4

2

0

0

Strip WG 1300times540 nm2

Strip WG 1400times800 nm2

Strip WG 1400times800 nm2

Slot WG 1Slot WG 2

Slot WG 1Slot WG 2

Dis

pers

ion

(ps

nmmiddotk

m)

Non

linea

r co

effic

ient

(m

middotW)

20 3010 15 2505Wavelength (microm)

2010 15 2505

Wavelength (microm)

Figure 6emspIn a wavelength range moved toward the short-wave-length end of near-IR spectrum silicon nitride strip and stripslot hybrid waveguides are designed in terms of (A) dispersion and (B) nonlinearity

Accordingly the nonlinear coefficient is small 285 (mmiddotW) at 3 microm as shown in Figure 7(B)

On the other hand if one needs a small Aeff to enhance nonlinearity additional dispersion tailoring (eg based on stripslot hybrid waveguides) would be beneficial Pursuing a higher nonlinear coefficient we use a 500-nm silicon nitride suspended membrane as illustrated in Figure 4 to support a silicon stripslot hybrid waveguide This helps confine light in the waveguide core Using W = 880 nm Hu = 550 nm Hs = 87 nm and Hl = 840 nm we obtain a saddle-shaped anomalous dispersion from 19 to 449 microm within 0~60 ps(nmmiddotkm) for the quasi-TM mode as shown in Figure 7(A) This structure produces much tighter mode confinement than the rib waveguide and exhibits a 3 times larger nonlinear coefficient in Figure 7(B) while having similar dispersion flatness

Finally we consider germanium-on-silicon wave-guides over a wavelength range from 33 to 85 microm between the half-bandgap wavelength of germanium and the cut-off wavelength of silicon This type of waveguide has been demonstrated with strain-free mono-crystal-line germanium [200] Here we assume that the germa-nium waveguide has a 10-nm silicon nitride layer on its

A

B

200

-200

60

40

20

0

100

-100

0

Rib WGSlot WG

Rib WGSlot WG

Dis

pers

ion

(ps

nmmiddotk

m)

Non

linea

r co

effic

ient

(m

middotW)

1 2 3 4 5 6 7Wavelength (microm)

1 2 3 4 5 6 7

Wavelength (microm)

Figure 7emspIn a wavelength range from the short-wave IR to mid-IR silicon rib waveguide on silicon nitride and stripslot hybrid waveguide on a suspended membrane are analyzed in terms of (A) dispersion and (B) nonlinearity

256emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

surface for passivation The upper cladding could be air or silicon which provides significantly different dispersion properties due to a varied index contrast For comparison only we also have silicon nitride as the upper cladding although silicon nitride becomes lossy for wavelengths longer than 67 microm Figure 8(A) shows the dispersion pro-files of four germanium-on-silicon strip waveguides with equal size 3000 times 1600 nm2 for the quasi-TE mode Air and silicon nitride as an upper cladding result in similar shape and bandwidth in the dispersion profiles Thus the air-cladded waveguide is chosen and discussed further The waveguide with silicon upper cladding has normal dispersion at all wavelengths since there is a relatively small index contrast between germanium and silicon and thus weak mode confinement A germanium strip wave-guide on a 600-nm-thick silicon suspended membrane is also considered to increase light confinement with an air upper cladding to maximize light confinement However as mentioned earlier strong confinement typically causes strong dispersion as shown in Figure 8(A) and therefore the germanium waveguide on a silicon membraneis not chosen for broadband nonlinear applications In contrast the germanium strip waveguide with air upper cladding exhibits a flat and low dispersion

The dimensions of the air-cladded germanium wave-guide are varied by simultaneously changing its height and width with a step of 200 nm for both polarization states It is interesting to see from Figure 8(B) and 8(C) that the dispersion peak value remains nearly unchanged for all the waveguide sizes although we have a widely tunable ZDW at long wavelengths For the quasi-TE mode the right ZDW moves from 605 microm to 841 microm while the left ZDW is always near 4 microm We can thus obtain an octave-spanning anomalous dispersion band with the peak value below 100 ps(nmmiddotkm) For the quasi-TM mode one can see similar dispersion properties but the anomalous disper-sion band is smaller Thus we choose the quasi-TE mode for further discussion in next section

The nonlinear coefficient in the germanium wave-guides for the quasi-TE mode is shown in Figure 8(D) which is about 10(mmiddotW) at 5 microm with a small variation for differ-ent waveguide sizes This is quite high considering that both wavelength and effective mode area become much larger over this wavelength range compared to the near-IR

From above we can see that the stripslot hybrid wave-guides enable unique controllability of dispersion and that this concept is applicable to different wavelength ranges However their performance may be sensitive to fabrication errors especially for inaccuracies in slot height Hs [59 60] A higher yield in device fabrication is expected using advanced fabrication technologies and facilities

A

C

D

B

400

300

200

100

-100

-200

0

Ge WG+air 3000times1600 nm2

Ge WG+air suspended 3000times1600 nm2

Ge WG+Si3N4 3000times1600 nm2

Ge WG+Si 3000times1600 nm2

Ge WG+air 2800times1400 nm2

Ge WG+air 3000times1600 nm2

Ge WG+air 3200times1800 nm2

Ge WG+air 3400times2000 nm2

Ge WG+air 2800times1400 nm2

Ge WG+air 3000times1600 nm2

Ge WG+air 3200times1800 nm2

Ge WG+air 3400times2000 nm2

Ge WG+air 2800times1400 nm2

Ge WG+air 3000times1600 nm2

Ge WG+air 3200times1800 nm2

Ge WG+air 3400times2000 nm2

Dis

pers

ion

(ps

nmmiddotk

m)

400

300

200

100

-100

-200

0

Dis

pers

ion

(ps

nmmiddotk

m)

400

300

200

100

-100

-200

50

40

30

20

10

0

0

Dis

pers

ion

(ps

nmmiddotk

m)

Non

linea

r co

effic

ient

(m

middotW)

3 4 5 6 7 8 9Wavelength (microm)

3 4 5 6 7 8 9Wavelength (microm)

3 4 5 6 7 8 9

Wavelength (microm)

3 4 5 6 7 8 9

Wavelength (microm)

Figure 8emspIn a wavelength range covering the main part of the mid-IR spectrum (A) on silicon substrate or on suspended silicon membrane are analyzed in terms of dispersion Germanium-on-silicon strip waveguides with an air upper cladding and different dimensions are characterized by (B) dispersion for the quasi-TE mode (C) dispersion for the quasi-TM mode and (D) nonlinearity for the quasi-TE mode

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp257

Besides photonic waveguides another important cat-egory of nonlinear devices is integrated resonators In the scope of this paper we consider relatively large resona-tors for frequency comb generation in which the bending radius of a ring resonator is varied from 50 microm to 100 microm depending on free spectral range (FSR) and the group index in the waveguide In these cases the waveguide-bending-induced dispersion is small and we would not discuss intra-cavity dispersion [202 203] in details here

4 ApplicationsBenefiting from the unique dispersion engineering over an octave-spanning bandwidth as described above one can develop ultra-wideband nonlinear applications that could hardly be attained in an integrated platform previously These include octave-spanning supercontinuum genera-tion pulse compression to a few-cycle or even sub-cycle level octave-spanning Kerr frequency comb generation and the associated mode-locked ultrashort pulse genera-tion using microresonators In this section we review our recent work on these topics

First we discuss the supercontinuum generation and pulse compression in a straight waveguide The nonlinear envelope equation used here to simulate supercontinuum generation is the following

βα infin

=

part part+ + = + part part sum

2

( - )( ) ( )

2

m mm

mm

ii A K A R A

z m t (1)

where

2

0 0

- -( ) 1- ( ) 2

n nn

nn

i i iK A A An t tγ δ δ

ω δ δ

infin

=

= sum

and

2shock_R( ) - 1- [ ( - ) | | ]δ

γ τδ minusinfin

= prime prime int

t

R RR A i i A h t t A dtt

We denote A  =  A(zt) as the complex amplitude of an optical pulse Note that its Fourier transform is

-

1( ) ( ) exp( - ) 2

A z A z t i t dtω ωπ

infin

infin

= int

In Eq (1) α is the total propagation loss and βm is the mth-order dispersion coefficient The frequency dependence of nonlinearity parameters including the nonlinear index n2 the TPA coefficient βTPA and the

effective mode area Aeff is included in the nth-order dis-persion coefficient γn of nonlinearity which is defined as γn = ω0middotpartn[γ(ω)ω]partωn where ω0 is the angular frequency of the carrier Therefore we can consider all-order linear dispersion terms and all-order dispersion of the nonlin-ear coefficient in Eq (1) Specifically in the simulations for a silicon and silicon nitride waveguides we have all-order linear dispersion and up to 6th-order and 2nd-order of the nonlinear coefficient dispersion included A detailed derivation of Eq (1) is given in [204] For the quasi-TM mode that experiences the engineered dispersion due to the mode transition SRS in silicon waveguides fabricated on the (001) surface can be ignored [27 96] For silicon nitride waveguide we include the SRS term in Eq (1) where γR = gRΓR(AeffΩR) and gR ΓR and ΩR represent the Raman gain coefficient the full width at half maximum of the gain spectrum and the Raman shift respectively The Raman shock time τshock_R is associated with γRrsquos fre-quency dependence which is 1ω0-[1Aeff(ω0)][dAeff(ω)dω] similarly as in [14] if we ignore frequency dependent gR ΓR and ΩR hR(t) is the Raman response function and it corresponds to the Raman gain spectrum

2

2 20 0

( ) -( - ) 2 ( - )

Ωω

Ω ω ω Γ ω ω=

+R

RR R

Hi

Note that the sign before the imaginary unit is differ-ent from that in [27] to be consistent with the expression of the Fourier transform that we used

We have considered supercontinuum generation in both silicon and silicon nitride waveguides with the slot-assisted dispersion tailoring Octave-spanning supercon-tinua in a silicon-based stripslot hybrid waveguide have been investigated in detail in [108] in which two-cycle optical pulses are obtained The main results in that work are shown in Figure 9 for comparison purposes

Here we mainly focus on the supercontinuum gen-erated in the silicon nitride stripslot hybrid waveguide (ie the slot WG 1 in Section III) whose dispersion and nonlinearity properties are shown in Figure 6 In the non-linear simulations we set the total propagation loss to be 1 dBcm The SRS parameters used here are the following [205] ΩR2π = 143 THz ΓR2π = 172 THz and gR = 1 times 10-12 mW τshock_R is calculated to be  = 156 fs

In our simulations we use a time step of 025 fs which is corresponding to a bandwidth of 4000 THz in the fre-quency domain For a femtosecond input pulse we set the time window length to 50 ps (ie frequency resolution Δf = 20 GHz)

We simulate the nonlinear propagation of a chirp-free hyperbolic secant pulse in the silicon nitride waveguide

258emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

The pulse center wavelength is at 1610 nm and its full width at half-maximum (FWHM) T0 is 120 fs Its peak power is 1200 W corresponding to pulse energy of 016 nJ

Figure 10(A) shows the supercontinua at different propagation distances At 48 mm the spectrum is greatly broadened at the -30 dB level covering a wavelength range from 0585 to 2833 microm which is more than two octaves The spectrum evolution in Figure 10(A) shows a similar spectrum shape as that in Figure 9(A) both featuring a ldquotriangularrdquo central spectrum bounded by two dispersive waves at the edges However it is important to note that the absence of TPA and 3PA in silicon nitride at the telecom window leads to a much more efficient spectrum broad-ening than that in silicon [108] The generated spectrum extends from the visible light to the mid-IR with excellent spectral coherence which is confirmed by the pulse wave-form shown in Figure 10(B) In the time domain the pulse is greatly compressed from 120 to 408 fs corresponding to 076 optical cycles at 161 microm wavelength

We examine the pulsewidth as a function of propa-gation distance Figure 11 shows that the pulse becomes increasingly narrower until the propagation distance reaches 47 mm For longer distances the pulsewidth

A

B

60 mm

48 mm

36 mm

24 mm

12 mm

Input

Spe

ctru

m (

10 d

Bd

iv)

Pow

er (

W)

12

246

24

18

12

6

0

248 250 252 254

14 16 18 20 22 24Wavelength (microm)

Time (ps)

Figure 9emsp(A) The supercontinuum generation in a silicon-based stripslot hybrid waveguide presented in [108] (B) The significant spectrum broadening at 425-mm distance is associated with a temporal compression of an input pulse (dash line) to the output waveform (solid line) with a FWHM of 12 fs

A

B

50 mm

48 mm

46 mm

44 mm

42 mm

Input

Spe

ctru

m (

10 d

Bd

iv)

Pow

er (

W)

8000

6000

4000

2000

0250249 251

06 09 12 15 18 21 24 27

Wavelength (microm)

Time (ps)

Figure 10emsp(A) Spectrum evolution of the pulse over propagation distance A supercontinuum of more than two octaves is achieved at 48 mm distance (B) Generated pulse waveform with a pulse width of 408 fs as short as 076 optical cycles Low pedestals are caused by dispersive waves generated at the two ends of the spectrum

remains almost constant However it is important to mention that after 48 mm the dispersive waves become increasingly stronger as shown in Figure 10(A) causing larger pedestals

Comparing the results in Figures 9 and 10 we note that the mid-IR wavelength range for silicon would be in analogy to the near-IR for silicon nitride in terms of non-linear optics operations Pumping at or beyond 33 microm one can use the waveguide designs shown in Figure 7 to produce very efficient nonlinear interactions without TPA and 3PA in silicon Ultrashort pulses in the mid-IR from parametric amplifiers [206 207] could be used to pump the Group IV waveguides

Another nonlinear application of the dispersion-engi-neered Group IV waveguides is micro-resonator-based Kerr frequency comb generation When such a waveguide is curved to form a microring resonator input CW light travels around the cavity and amplifies the noise in the source located at the frequencies with a high parametric gain As a result of modulation instability and cascaded FWM in the cavity a frequency comb can be generated [208ndash211] Mode-locked frequency combs have been reported pro-ducing low-noise pulse trains in time domain [212ndash214]

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp259

The formation of cavity solitons is identified as the main reason for the mode-locking in the Kerr frequency combs [215] This is instructive because one can thus predict the spectral bandwidth and temporal pulsewidth in the generated low-noise combs The 3-dB comb bandwidth is inversely proportional to the square root of the 2nd-order dispersion coefficient |β2| as given in [213 215] It is desira-ble that all comb lines that constitute the soliton spectrum experience the same |β2| In this sense the stripslot hybrid waveguides with flattened dispersion are preferably suit-able for supporting broadband Kerr comb generation and ultra-short cavity soliton generation

The Kerr frequency comb generation can be modeled using the generalized Lugiato-Lefever equation (LLE) [216ndash219]

20

2

( - )- - | |

2 2

m mm

R inmm

jkt j jl E kE j l E Et m

βαδ γ

τ

infin

=

part part+ + + = part part

sum (2)

where tR is the round-trip time E = E(tτ) and Ein are intra-cavity field and input field (pump power Pin  =  |Ein|2) t and τ are the slow and fast times δ0 is the cavity phase detuning defined as δ0  =  tRmiddot(ωn -ω0) where ω0 and ωn are the pumprsquos angular frequency and the nth angular reso-nance frequency that is pumped Other resonator param-eters include the power loss per round trip α the power coupling coefficient κ the nonlinear coefficient γ and the mth dispersion coefficient βm Since a flattened dispersion profile has a small β2 over a wide bandwidth it is impor-tant to take the influence of higher-order dispersion into account We include all-order dispersion terms in Eq (2) as we did in solving Eq (1)

To enhance the Kerr comb bandwidth in the near-IR we use the ultra-flattened dispersion profile in Figure 6(A) which is obtained in the slot WG 2 based on

Pul

se w

idth

(fs

)

14

12

10

8

6

4

242 44 46 48 50 52

Propagation distance (mm)

Figure 11emspPulse width first decreases with propagation distance and then remains stable After 48 mm dispersive waves get stronger causing more pedestals

Pow

er (

10 d

Bd

iv)

Pow

er (

W)

70A

B

60

50

40

30

20

10

-10

-20

600

400

200

0

80 120

0575 0600 0625 0650

160 200 240 280 320 360

0

Frequency (THz)

Time (ps)

Figure 12emsp(A) Frequency comb generation with a CW pump at 155 microm using a microring resonator based on a silicon stripslot hybrid waveguide Over an octave-spanning bandwidth from 135 to 270 THz the comb lines have a power drop of 20 dB (B) Generated pulse waveform with a pulse width of 82 fs as short as 16 optical cycles

silicon nitride The ring resonator has a bending radius of 104 microm corresponding to a FSR of 200 GHz Pumping near 155 microm with a pump power of 2 W the resonance peak is red-shifted and we need to red-shift the pump wavelength accordingly and tune it into the resonance from the short-wavelength side When the pump is step-by-step tuned by up to 63 resonance linewidths we obtain the comb spectrum and the mode-locked pulse waveform as shown in Figure 12 One can see that over an octave-spanning bandwidth from 133 to 268 THz the comb lines have a power drop by 20 dB from the center of the spectrum The spectral flatness of this comb is relatively good compared to the previously reported results [208ndash211] The comb bandwidth at -40 dB is as wide as two octaves There are two dispersive peaks in normal dispersion regions beyond the low-dispersion band Such a mode-locked broadband comb produces a train of sub-two-cycle optical pulses as shown in Figure 12(B) with one pulse per round trip The peak power of the pulse is up to 600 W Nonlinear conver-sion efficiency is estimated to be -267 dB

To generate frequency combs in the mid-IR the ger-manium-on-silicon strip waveguide is chosen We choose

260emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

a cross-section of 3200 times 1800 nm2 which has an octave-spanning low-dispersion band from 4 to 767 microm as shown in Figure 8(B) A germanium ring resonator is formed with a bending radius of 564 microm corresponding to a FSR of 200 GHz Pumping at 6 microm with a CW power of 14 W and detuning the pump wavelength by 10 resonance linewidth one can see that a mode-locked wideband mid-IR comb is generated from 358 to 644 THz (ie from 466 to 838 microm) at -40 dB level The FWHM of the produced pulses is 69 fs which corresponds to ~35 optical cycles The pulse peak power is 184 W and the nonlinear conversion efficiency is estimated to be -143 dB Since the pumping frequency is not at the center of the low-dispersion band we only see one peak in the comb spectrum caused by the dispersive wave in the normal dispersion region from Figure 13(A) There is another peak at higher frequencies beyond what is shown in the figure

As shown above broadband dispersion engineering is critical for octave-spanning nonlinear applications in both near- and mid-IR wavelength ranges which enables us to fully utilize the bandwidth allowed by the materials transparency windows Generally speaking the nonlinear applications mentioned here such as supercontinuum generation ultrafast pulse compression and frequency comb generation are often the intermediate steps towards higher-level system applications In the frequency domain a wide spectrum can serve as an electromagnetic carrier to acquire high-volume of information eg for sensing [220] and imaging [221] In the time domain an ultrashort pulse can be used as probe to sample ultrafast phenomena [222]

5 Summary and OutlookWe have presented a review of our recent work on nonlin-ear photonics based on silicon and germanium Various types of Group IV waveguides are analyzed and optimized for four different wavelength ranges from near- to mid-IR The recently proposed dispersion engineering technique based on stripslot hybrid waveguide structures is used for different material combinations and wavelength ranges Numerical simulations show that the dispersion-flattened Group IV waveguides are preferably suitable for octave-spanning nonlinear applications including on-chip supercontinuum generation ultrashort pulse compres-sion and mode-locked wideband frequency comb genera-tion based on micro-resonators

The presented approach to achieving octave-span-ning nonlinear applications on an integrated CMOS-compatible Group IV platform holds great potential for realizing chip-scale sensing imaging communications and signal processing system The ultrawide transparency windows in the mid-IR allowed by Group IV elements and compounds potentially together with other materi-als [223] provide an exciting arena for building powerful information acquisition and processing units enabled by nonlinear optics nano-photonics and ultrafast optics

Received June 14 2013 accepted October 29 2013 previously pub-lished online November 27 2013

Pow

er (

10 d

Bd

iv)

A

8030 40 50 60 70Frequency (THz)

Pow

er (

W)

B200

150

100

50

0

21 22 23 24 25Time (ps)

Figure 13emsp(A) Frequency comb generation with a CW pump at 6 microm using a microring resonator based on a germanium strip waveguide with air upper cladding (B) Generated pulse waveform with a pulse width of 69 fs as short as 35 optical cycles

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp261

Appendix

A Material index and dispersion

In this section we give the wavelength-dependent mate-rial index expressed as Sellmeier equations where wave-length λ is in μm

For silicon we use the following material index that is a fit curve from measurement results at room temperature (293 K) with 184 data points in total from 112 to 588 μm [154]

22 1 2 2

2 2 22

( )-

C Cn

λλ ε

λ λ λ= + +

where ε = 116858 C1 = 0939816 μm2 C2 = 000810461 and λ2 = 11071 μm

For silicon nitride the material index is affected by deposition conditions using plasma-enhanced chemical vapor deposition (PECVD) low-pressure chemical vapor deposition (LPCVD) and so on We use the following Sell-meier equation [155] which predicts the material index close to that in LPCVD silicon nitride films measured by a few groups [224]

22 1

2 21

( ) 1-

Cn

λλ

λ λ= +

where C1 = 28939 and λ1 = 013967 μmFor silicon dioxide we use the following Sellmeier

equation for fused silica [156]22 2

2 31 22 2 2 2 2 2

1 2 3

( ) 1- - -

CC Cn

λλ λλ

λ λ λ λ λ λ= + + +

where C1 = 06961663 C2 = 04079426 C3 = 08974794 λ1 = 00684043 μm λ2 = 01162414 μm and λ3 = 9896161 μm

For SRO the material index is affected by deposition conditions such as silicon excess annealing temperature and so on Here we choose the one with silicon excess of 8 and annealed at 1250oC [51]

22 22 31 2

2 2 2 2 2 21 2 3

( ) 1- - -

CC Cn

λλ λλ

λ λ λ λ λ λ= + + +

where C1 = 001 C2 = 196 C3 = 141 λ1 = 03 μm λ2 = 007071 μm and λ3 = 2775968 μm

For germanium the temperature-dependent mate-rial index was measured [157] Here we choose the one for room temperature (293 K)

2 22 1 2

2 2 2 21 2

( )- -

C Cn

λ λλ ε

λ λ λ λ= + +

where ε = 928156 C1 = 67288 C2 = 021307 λ1 = 0664116 μm and λ2 = 6221013 μm

For arsenic sulfide we use the material index pro-vided in [158]

2 2 22 22 3 4 51 2

2 2 2 2 2 2 2 2 2 21 2 3 4 5

( ) 1- - - - -

C C CC Cn

λ λ λλ λλ

λ λ λ λ λ λ λ λ λ λ= + + + + +

where C1 = 18983678 C2 = 19222979 C3 = 08765134 C4 = 01188704 C5 = 09569903 λ1 = 015 μm λ2 = 025 μm λ3 = 035 μm λ4 = 045 μm and λ5 = 27386128 μm

For arsenic selenide we fit ellipsometry measure-ments of our arsenic selenide thin films and the bulk material is provided by Prof Kathleen A Richardson group

22 22 31 2

2 2 2 2 2 21 2 3

( ) 1- - -

CC Cn

λλ λλ

λ λ λ λ λ λ= + + +

where C1 = 298463 C2 = 321011 C3 = 100182 λ1 = 044118 μm λ2 = 0000354953 μm and λ3 = 38413 μm

B Nonlinear Kerr index n2

The third-order nonlinear susceptibility χ(3)1111 for silicon and

germanium is predicted over the mid-IR range [133] based on a two-band model The effective nonlinear susceptibil-ity χ(3) is dependent on polarization and crystallographic orientation [225] For strong nonlinearity we consider a single-polarization incident light aligned to the crystal-lographic axis and we have χ(3) = χ(3)

1111 To investigate the octave-spanning nonlinear phenomena one need to take the wavelength-dependent nonlinear Kerr index n2 and TPA coefficient βTPA into account which are expressed as

( 3 )2 2

0

( 3 )2

0

3( ) ( )4 ( )

3( ) ( )( )

re

TPA im

ncn

cn

λ χ λε λ

πβ λ χ λ

λε λ

=

=

where ε0 and c are the vacuum permittivity and the speed of light in vacuum Using the material index given in Appendix A and χ(3) value from [133] we obtain the n2 and βTPA values tabulated as follows

262emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

Table 1enspNonlinear Kerr index n2 in silicon

λμm

  n2

10-18 m2W  λ

μm  n2

10-18 m2W  λ

μm  n2

10-18 m2W

130   234   310   389   490   312135   305   315   384   495   311140   378   320   379   500   310145   443   325   375   505   309150   501   330   371   510   307155   559   335   368   515   306160   618   340   365   520   304165   671   345   362   525   304170   710   350   360   530   303175   741   355   358   535   302180   766   360   355   540   302185   781   365   352   545   301190   783   370   350   550   300195   778   375   346   555   298200   762   380   343   560   297205   732   385   341   565   296210   699   390   338   570   296215   658   395   336   575   295220   612   400   334   580   295225   576   405   332   585   295230   547   410   331   590   294235   525   415   330   595   293240   508   420   329   600   292245   493   425   328   605   291250   479   430   327   610   290255   467   435   325   615   289260   456   440   324   620   288265   448   445   321   625   288270   440   450   319   630   288275   432   455   317   635   288280   424   460   315   640   288285   417   465   314   645   288290   410   470   313   650   288295   404   475   313   655   288300   398   480   312   660   288305   394   485   312    

Table 2enspTPA coefficient βTPA in silicon

λμm

  βTPA

10-12 mW  λ

μm  βTPA

10-12 mW  λ

μm  βTPA

10-12 mW

130   1334   165   812   200   180135   1284   170   713   205   115140   1222   175   613   210   064145   1154   180   522   215   024150   1079   185   424   220   0003155   995   190   333    160   905   195   254    

Table 3enspNonlinear Kerr index n2 in germanium

λμm

  n2

10-18 m2W  λ

μm  n2

10-18 m2W  λ

μm  n2

10-18 m2W

23  3932  63  1986  103  170524  4994  64  1972  104  169925  6007  65  1959  105  169426  6650  66  1946  106  169027  6772  67  1934  107  168728  6273  68  1923  108  168429  4897  69  1913  109  168230  4403  70  1904  110  168131  3970  71  1895  111  167932  3680  72  1886  112  167733  3470  73  1876  113  167534  3286  74  1868  114  167335  3128  75  1859  115  167036  2998  76  1850  116  166737  2895  77  1841  117  166338  2812  78  1833  118  165939  2737  79  1826  119  165640  2668  80  1819  120  165341  2605  81  1812  121  165142  2550  82  1807  122  164843  2498  83  1801  123  164644  2450  84  1797  124  164445  2406  85  1792  125  164346  2365  86  1787  126  164147  2328  87  1782  127  163948  2295  88  1777  128  163649  2266  89  1772  129  163450  2238  90  1767  130  163251  2212  91  1762  131  163052  2187  92  1758  132  162853  2164  93  1753  133  162654  2141  94  1749  134  162555  2121  95  1744  135  162356  2101  96  1740  136  162157  2083  97  1736  137  162058  2066  98  1731  138  161859  2049  99  1727  139  161760  2032  100  1722  140  161661  2016  101  1716   62  2001  102  1711   

Table 4enspTPA coefficient βTPA in germanium

λμm

  βTPA

10-8 mW  λμm

  βTPA

10-8 mW  λ

μm  βTPA

10-8 mW

23   130   25   088   27   03124   111   26   060   28   006

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp263

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[15] Dudley JM Taylor JR Ten years of nonlinear optics in photonic crystal fibre Nature Photonics 2009385ndash90

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[25] Kirchain R Kimerling L A roadmap for nanophotonics Nature Photonics 20071303ndash5

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[30] Leuthold J Koos C Freude W Nonlinear silicon photonics Nature Photonics 20104535ndash44

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[78] Chen X Panoiu NC Osgood RM Jr Theory of Raman-mediated pulsed amplification in silicon-wire waveguides IEEE J Quantum Electron 200642160ndash70

[79] Rong H Kuo Y-H Xu S Cohen O Raday O Paniccia M Recent development on silicon-based Raman lasers and amplifiers Proc SPIE 6389 638904-1-9 2006

[80] Okawachi Y Foster MA Sharping JE Gaeta AL Xu Q Lipson M All-optical slow-light on a photonic chip Opt Express 2006142317ndash22

[81] Jalali B Raghunathan V Dimitropoulos D Boyraz O Raman-based silicon photonics IEEE J Sel Top Quantum Electron 200612412ndash21

[82] Rong H Xu S Kuo Y Sih V Cohen O Raday O Paniccia M Low-threshold continuous-wave Raman silicon laser Nature Photon 20071232ndash7

[83] De Leonardis F Passaro VMN Ultrafast Raman pulses in SOI waveguides for nonlinear signal processing IEEE J Sel Top Quant 200814739ndash51

[84] Tsang HK Wong CS Liang TK Day IE Roberts SW Harpin A Drake J Asghari M Optical dispersion two-photon absorption and self-phase modulation in silicon waveguides at 15 μm wavelength Appl Phys Lett 200280416ndash8

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp265

[85] Boyraz O Indukuri T Jalali B Self-phase-modulation induced spectral broadening in silicon waveguides Opt Express 200412829ndash34

[86] Rieger GW Virk KS Yong JF Nonlinear propagation of ultrafast 15 μm pulses in high-index-contrast silicon-on-insulator waveguides Appl Phys Lett 200484900ndash2

[87] Dulkeith E Vlasov YA Chen X Panoiu NC Osgood RM Jr Self-phase-modulation in submicron silicon-on-insulator photonic wires Opt Express 2006145524ndash34

[88] Hsieh I-W Chen X Dadap JI Panoiu NC Osgood RM Jr McNab SJ Vlasov YA Ultrafast-pulse self-phase modulation and third-order dispersion in Si photonic wire-waveguides Opt Express 20061412380ndash7

[89] Hsieh I-W Chen X Dadap JI Panoiu NC Osgood RM Jr McNab SJ Vlasov YA Cross phase modulation-induced spectral and temporal effects on co-propagating femtosecond pulses in silicon photonic wires Opt Express 2007151135ndash46

[90] Zhang J Lin Q Piredda G Boyd RW Agrawal GP Fauchet PM Optical solitons in a silicon waveguide Opt Express 2007157682ndash8

[91] Salem R Foster MA Turner AC Geraghty DF Lipson M Gaeta AL All-optical regeneration on a silicon chip Opt Express 2007157802ndash9

[92] Claps R Raghunathan V Dimitropoulos D Jalali B Anti-Sotkes Raman conversion in silicon waveguides Opt Express 2003112862ndash72

[93] Espinola RL Dadap JI Osgood RM Jr McNab SJ Vlasov YA C-band wavelength conversion in silicon photonic wire waveguides Opt Express 2005134341ndash9

[94] Fukuda H Yamada K Shoji T Takahashi M Tsuchizawa T Watanabe T Takahashi J Itabashi S Four-wave mixing in silicon wire waveguides Opt Express 2005134629ndash37

[95] Rong H Kuo Y Liu A Paniccia M Cohen O High efficiency wavelength conversion of 10 Gbs data in silicon waveguides Opt Express 2006141182ndash8

[96] Lin Q Zhang J Fauchet PM Agrawal GP Ultrabroadband parametric generation and wavelength conversion in silicon waveguides Opt Express 2006144786ndash99

[97] Foster MA Turner AC Sharping JE Schmidt BS Lipson M Gaeta AL Broad-band optical parametric gain on a silicon photonic chip Nature 2006441960ndash3

[98] Yamada K Fukuda H Tsuchizawa T Watanabe T Shoji T Itabashi S All-optical efficient wavelength conversion using silicon photonic wire waveguide IEEE Photon Technol Lett 2006181046ndash8

[99] Kuo Y Rong H Sih V Xu S Paniccia M Cohen O Demonstration of wavelength conversion at 40 Gbs data rate in silicon waveguides Opt Express 20061411721ndash6

[100] Foster MA Turner AC Salem R Lipson M Gaeta AL Broad-band continuous-wave parametric wavelength conversion in silicon nanowaveguides Opt Express 20071512949ndash58

[101] Dai Y Chen X Okawachi Y Turner-Foster AC Foster MA Lipson M Gaeta AL Xu C 1 μs tunable delay using parametric mixing and optical phase conjugation in Si waveguides Opt Express 2009177004ndash10

[102] De Leonardis F Passaro VMN Efficient wavelength conversion in optimized SOI waveguides via pulsed four wave mixing IEEE J Lightwave Technol 2011293523ndash35

[103] Yin L Lin Q Agrawal GP Soliton fission and supercontinuum generation in silicon waveguides Opt Lett 200732391ndash3

[104] Koonath P Solli DR Jalali B Continuum generation and carving on a silicon chip Appl Phys Lett 200791061111

[105] Hsieh I-W Chen X Liu X Dadap JI Panoiu NC C-Chou Y Xia F Green WM Vlasov YA Osgood RM Jr Supercontinuum generation in silicon photonic wires Opt Express 20071515242ndash8

[106] Kuyken B Liu X Osgood RM Jr Baets R Roelkens G Green WMJ Mid-infrared to telecom-band supercontinuum generation in highly nonlinear silicon-on-insulator wire waveguides Opt Express 20111920172ndash81

[107] DeVore PTS Solli DR Ropers C Koonath P Jalali B Stimulated supercontinuum generation extends broadening limits in silicon Appl Phys Lett 2012100101111

[108] Zhang L Lin Q Yue Y Yan Y Beausoleil RG Agarwal A Kimerling LC Michel J Wilner AE On-chip octave-spanning supercontinuum in nanostructured silicon waveguides using ultralow pulse energy IEEE J Sel Top Quant 2012181799ndash806

[109] Claps R Raghunathan V Dimitropoulos D Jalali B Influence of nonlinear absorption on Raman amplification in silicon waveguides Opt Express 2004122774ndash80

[110] Yin L Agrawal GP Impact of two-photon absorption on self-phase modulation in silicon waveguides Opt Lett 2007322031ndash3

[111] Ikeda K Saperstein RE Alic N Fainman Y Thermal and Kerr nonlinear properties of plasma-deposited silicon nitridesilicon dioxide waveguides Opt Express 20081612987ndash94

[112] Levy JS Gondarenko A Foster MA Turner-Foster AC Gaeta AL Lipson M CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects Nat Photonics 2010437ndash40

[113] Tan DTH Ikeda K Sun PC Fainman Y Group velocity dispersion and self phase modulation in silicon nitride waveguides Appl Phys Lett 201096061101

[114] Zhang L Yan Y Yue Y Lin Q Painter O Beausoleil RG Willner AE On-chip two-octave supercontinuum generation by enhancing self-steepening of optical pulses Opt Exp 20111911584ndash90

[115] Halir R Okawachi Y Levy JS Foster MA Lipson M Gaeta AL Ultrabroadband supercontinuum generation in a CMOS-compatible platform Opt Lett 2012371685

[116] Ye J Frequency comb spectroscopy from mid-infrared to extreme ultraviolet Conference on Lasers and Electro-Optics (CLEO) 2012 Tutorial CW1J4

[117] Popmintchev T Chen M-C Popmintchev D Arpin P Brown S Alisauskas S Andriukaitis G Balciunas T Mucke OD Pugzlys A Baltuska A Shim B Schrauth SE Gaeta A Hernandez-Garcia C Plaja L Becker A Jaron-Becker A Murnane MM Kapteyn HC Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers Science 20123361287ndash91

[118] Qin GS Yan X Kito C Liao M Chaudhari C Suzuki T Ohishi Y Ultrabroadband supercontinuum generation from ultraviolet to 628 microm in a fluoride fiber Appl Phys Lett 200995 161103ndash1ndash161103-3

[119] Soref RA Emelett SJ Buchwald WR Silicon waveguided components for the long-wave infrared region J Opt A 20068840ndash8

266emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

[120] Soref R Towards Silicon-based Longwave Integrated Optoelectronics (LIO) SPIE Proceedings 6898 (2008) paper 6898-5 SPIE Photonics West Silicon Photonics III Conference San Jose CA (21 Jan 2008)

[121] Mashanovich GZ Milosevic M Matavulj P Timotijevic B Stankovic S Yang PY Teo EJ Breese MBH Bettiol AA Reed GT Silicon photonic waveguides for different wavelength regions Semiconductor Sci Technol 200823064002

[122] Soref R Mid-infrared photonics in silicon and germanium Nat Photonics 20104495ndash7

[123] Green WMJ Liu X Osgood RM Vlasov YA Mid-infrared nonlinear optics in silicon photonic wire waveguides Photonics Society Summer Topical Meeting Series 201062ndash63

[124] Milosevic MM Nedeljkovic M Masaud T-B Jaberansary E Chong HMH Emerson NG Reed GT Mashanovich GZ Silicon waveguides and devices for the mid-infrared Appl Phys Lett 2012101121105

[125] Soref R Group IV photonics for the mid infrared SPIE Photonics West 2013 Proc of SPIE 20138629paper 862902

[126] Crowder JG Smith SD Vass A Keddie J Infrared methods for gas detection in Mid-Infrared Semiconductor Optoelec-tronics New York Springer-Verlag 2006

[127] George Socrates Infrared and Raman Characteristic Group Frequencies Tables and Charts 3rd Ed Chichester John Wiley amp Sons 2001

[128] Longshore R Raimondi P Lumpkin M Selection of detector peak wavelength for optimum infrared system performance Infrared Phys 197616639ndash47

[129] Findlay GA Cutten DR Comparison of performance of 3ndash5-and 8ndash12-microm infrared systems Appl Opt 1989285029ndash37

[130] Labadie L Wallner O Mid-infrared guided optics a perspective for astronomical instruments Opt Express 2009171947ndash62

[131] Pearl S Rotenberg N van Driel HM Three photon absorption in silicon for 2300ndash3300 nm Appl Phys Lett 200893131102

[132] Wang Z Liu H Huang N Sun Q Wen J Li X Influence of three-photon absorption on Mid-infrared cross-phase modulation in silicon-on-sapphire waveguides Opt Express 2013211840ndash8

[133] Hon NK Soref RA Jalali B The third-order nonlinear optical coefficients of Si Ge and Si1-xGex in the midwave and longwave infrared J Appl Phys 2011110011301

[134] Sheik-Bahae M Hutchings DC Hagan DJ Stryland EWV Dispersion of bound electric nonlinear refraction in solids IEEE J Quant Electron 1991271296ndash1309

[135] Jalali B Raghunathan V Shori R Fathpour S Prospects for silicon mid-IR Raman lasers IEEE J Sel Top Quantum Electron 2006121618ndash27

[136] Raghunathan V Borlaug D Rice RR Jalali B Demonstration of a mid-infrared silicon Raman amplifier Opt Express 20071514355ndash62

[137] Chavez Boggio JM Windmiller JR Knutzen M Jiang R Bres C Alic N Stossel B Rottwitt K Radic S 730-nm optical parametric conversion from near- to short-wave infrared band Opt Express 2008165435ndash43

[138] Lin Q Johnson TJ Perahia R Michael CP Painter OJ A proposal for highly tunable optical parametric oscillation in silicon micro-resonators Opt Express 20081610596ndash610

[139] Turner-Foster AC Foster MA Salem R Gaeta AL Lipson M Frequency conversion over two-thirds of an octave in silicon nanowaveguides Opt Express 2010181904ndash8

[140] Liu X Osgood RM Vlasov YA Green WMJ Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides Nat Photonics 20104557ndash60

[141] Zlatanovic S Park JS Moro S Boggio JMC Divliansky IB Alic N Mookherjea S Radic S Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source Nat Photonics 20104561ndash4

[142] Tien EK Huang YW Gao S Song Q Qian F Kalyoncu SK Boyraz O Discrete parametric band conversion in silicon for mid-infrared applications Opt Exp 20101821981ndash9

[143] Lau RKW Meacutenard M Okawachi Y Foster MA A C Turner-Foster Salem R Lipson M Gaeta AL Continuous-wave mid-infrared frequency conversion in silicon nanowaveguides Opt Lett 2011361263ndash5

[144] Roelkens G Green WMJ Kuyken B Liu X Hattasan N Gassenq A Cerutti L Rodriguez JB Osgood RM Tournie E Baets R III-Vsilicon photonics for short-wave infrared spectroscopy IEEE J Quant Electron 201248292ndash8

[145] Alloatti L Korn D Weimann C Koos C Freude W Leuthold J Second-order nonlinear silicon-organic hybrid waveguides Opt Express 20122020506ndash15

[146] Harris DC Durable 3ndash5 μm transmitting infrared window materials Infrared Phys Technol 199839185ndash201

[147] Carlie N Musgraves JD Zdyrko B Luzinov I Hu J Singh V Agarwal A Kimerling LC Canciamilla A Morichetti F Melloni A Richardson K Integrated chalcogenide waveguide resonators for mid-IR sensing leveraging material properties to meet fabrication challenges Opt Express 20101826728ndash43

[148] Eggleton BJ B Luther-Davies Richardson K Chalcogenide photonics Nat Photonics 20115141ndash8

[149] Madden SJ Vu KT High-Performance Integrated Optics with Tellurite Glasses Status and Prospects Int J Appl Glass Sci 20123289ndash98

[150] Bindra KS Bookey HT Kar AK Wherrett BS Liu X Jha A Nonlinear optical properties of chalcogenide glasses observation of multiphoton absorption App Phys Lett 2001791939ndash41

[151] Zakery A Ruan Y ARode V Samoc M Luther-Davies B Low-loss waveguides in ultrafast laser-deposited As2S3 chalcogenide films J Opt Soc Am B 200391844ndash52

[152] Lenz G Zimmermann J Katsufuji T MLines E Hwang HY Spalter S Slusher RE Cheong SW Sanghera JS Aggarwal ID Large Kerr effect in bulk Se-based chalcogenide glasses Opt Lett 200025254ndash6

[153] Sanghera JS Shaw LB Aggarwal ID Application of chalcogenide glass optical fibers CR Chimie 20025873ndash83

[154] Palik ED Handbook of optical constants of solids San Diego CA Academic 1998

[155] Philipp HR Optical properties of silicon nitride J Electrochem Soc 1973120295ndash300

[156] Malitson IH Interspecimen comparison of the refractive index of fused silica J Opt Soc Am 1965551205ndash8

[157] Barnes NP Piltch MS Temperature-dependent Sellmeier coefficients and nonlinear optics average power limit for germanium J Opt Soc Am 197969178ndash80

[158] Rodney WS Malitson IH King TA Refractive index of arsenic trisulfide J Opt Soc Am 195848633ndash636

[159] Ellipsometry measurement on the thin film samples by our group[160] Bristow AD Rotenberg N van Driel HM Two-photon

absorption and Kerr coefficients of silicon for 850ndash2200 nm Appl Phys Lett 200790191104

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp267

[161] Lin Q Zhang J Piredda G Boyd RW Fauchet PM Agrawal GP Dispersion of silicon nonlinearities in the near infrared region Appl Phys Lett 200791021111

[162] Mizrahi V DeLong KW Stegeman GI Saifi MA Andrejco MJ Two-photon absorption as a limitation to all-optical switching Opt Lett 1989141140ndash2

[163] Guider R NDaldosso APitanti EJordana Fedeli J-M Pavesi L NanoSi low loss horizontal slot waveguides coupled to high Q ring resonators Opt Express 20091720762ndash70 and its erratum

[164] Ferrera M Razzari L Duchesne D Morandotti R Yang Z Liscidini M Sipe JE Chu S Little BE Moss DJ Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures Nat Photonics 20082 737ndash40

[165] Smektala F Quemard C Leneindre L Lucas J Barthelemy A De Angelis C Chalcogenide glasses with large non-linear refractive indices J Non-Crystalline Solids 1998239139ndash42

[166] Boudebs G Sanchez F Troles J Smektala F Nonlinear optical properties of chalcogenide glasses- comparison between Mach-Zehnder interferometry and Z-scan techniques Opt Comm 2001199425ndash33

[167] Asobe M Suzuki K Kanamori T Kubodera K Nonlinear refractive index measurement in chalcogenide-glass fibers by self-phase modulation APL 1992601153ndash4

[168] Asobe M Kanamori T Kubodera K Ultrafast all-optical switching using highly nonlinear chalcogenide glass fiber IEEE Photon Technol Lett 19924362ndash5

[169] Asobe M Kanamori T Kubodera K Applications of highly nonlinear chalcogenide glass fibers in ultrafast all-optical switches IEEE J Quant Electron 1993292325ndash33

[170] Ruan Y Luther-Davies B Li W Rode A Kolev V Madden S Large phase shifts in As2S3 waveguides for all-optical processing devices Opt Lett 2005302605ndash7

[171] Laniel JM Hocirc N Valleacutee R Villeneuve A Nonlinear-refractive-index measurement in As2S3 channel waveguides by asymmetric self-phase modulation J Opt Soc Am B 200522437ndash45

[172] Cerqua-Richardson KA McKinley JM Lawrence B Joshi S Villeneuve A Comparison of nonlinear optical properties of sulfide glasses in bulk and thin film form Opt Mater 199810155ndash9

[173] Harbold JM Ilday FOuml Wise FW Sanghera JS Nguyen VQ Shaw LB Aggarwal ID Highly nonlinear As-S-Se glasses for all-optical switching Opt Lett 200227119ndash121

[174] Ruan YL Li WT Jarvis R Madsen N Rode A Luther-Davies B Fabrication and characterization of low loss rib chalcogenide waveguides made by dry etching Opt Express 2004125140ndash5

[175] Slusher RE Lenz G Hodelin J Sanghera J Shaw LB Aggarwal ID Large Raman gain and nonlinear phase shifts in high-purity As2Se3 chalcogenide fibers J Opt Soc Am B 2004211146ndash55

[176] Jacobsen R Andersen K Borel P Fage-Pedersen J Frandsen L Hansen O Kristensen M Lavrinenko A Moulin G Ou H Peucheret C Zsigri B Bjarklev A Strained silicon as a new electro-optic material Nature 2006441199ndash202

[177] Cazzanelli M Bianco F Borga E Pucker G Ghulinyan M Degoli E Luppi E Veacuteniard V Ossicini S Modotto D Wabnitz S Pierobon R Pavesi L Second-harmonic generation in

silicon waveguides strained by silicon nitride Nat Mater 201111148ndash54

[178] Avrutsky I Soref R Phase-matched sum frequency generation in strained silicon waveguides using their second-order nonlinear optical susceptibility Opt Express 20111921707ndash16

[179] Ghahramani E Moss DJ Sipe JE Second-harmonic generation in odd-period strained (Si)n(Ge)nSi superlattices and at SiGe interfaces Phys Rev Lett 1990642815ndash8

[180] Levy JS Foster MA Gaeta AL Lipson M Harmonic generation in silicon nitride ring resonators Opt Express 20111911415

[181] Zakery A Elliott SR Optical nonlinearities in chalcogenide glasses and their applications Springer Series in Optical Sciences 2007135

[182] Lee KK Lim DR Kimerling LC Shin J Cerrina F Fabrication of ultralow-loss SiSiO2 waveguides by roughness reduction Opt Lett 2001261888ndash90

[183] Cardenas J Poitras CB Robinson JT Preston K Chen L Lipson M Low loss etchless silicon photonic waveguides Opt Express 2009174752ndash7

[184] Biberman A Shaw MJ Timurdogan E Wright JB Watts MR Ultralow-loss silicon ring resonators Opt Lett 2012374236ndash8

[185] Walmsley IA Waxer L Dorrer C The role of dispersion in ultrafast optics Rev Sci Instrum 2001721ndash29

[186] Torres JP MHendrych Valencia A Angular dispersion an enabling tool in nonlinear and quantum optics Adv Opt Photon 20102319ndash69

[187] Yin LH Lin Q Agrawal GP Dispersion tailoring and soliton propagation in silicon waveguides Opt Lett 2006311295ndash7

[188] Dulkeith E Xia FN Schares L Green WMJ Vlasov YA Group index and group velocity dispersion in silicon-on-insulator photonic wires Opt Express 2006143853ndash63

[189] Turner AC Manolatou C Schmidt BS Lipson M Tailored anomalous group-velocity dispersion in silicon channel waveguides Opt Express 2006144357ndash62

[190] Dadap JI Panoiu NC Chen X I-Hsieh W Liu X Chou C-Y Dulkeith E McNab SJ Xia F Green WMJ Sekaric L Vlasov YA Osgood RM Jr Nonlinear-optical phase modification in dispersion-engineered Si photonic wires Opt Express 2008161280ndash99

[191] Milosevic MM Matavulj PS Yang PY Bagolini A Mashanovich GZ Rib waveguides for mid-infrared silicon photonics J Opt Soc Am B 2009261760ndash6

[192] Mashanovich GZ Milošević MM Nedeljkovic M Owens N Xiong B Teo EJ Hu Y Low loss silicon waveguides for the mid-infrared Opt Express 2011197112ndash9

[193] Reimer C Nedeljkovic M Stothard DJM Esnault MOS Reardon C OrsquoFaolain L Dunn M Mashanovich GZ Krauss TF Mid-infrared photonic crystal waveguides in silicon Opt Express 20122029361ndash8

[194] Baehr-Jones T Spott A Ilic R Spott A Penkov B Asher W Hochberg M Silicon-on-sapphire integrated waveguides for the midinfrared Opt Express 20101812127ndash35

[195] Li F Jackson S Grillet C Magi E Hudson D Madden SJ Moghe Y OrsquoBrien C Read A Duvall SG Atanackovic P Eggleton BJ Moss D Low propagation loss silicon-on-sapphire waveguides for the midinfrared Opt Express 20111915212ndash20

268emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

[196] Yue Y Zhang L Huang H Beausoleil RG Willner AE Silicon-on-nitride waveguide with ultralow dispersion over an octave-spanning mid-infared wavelength range IEEE Photonics J 20124126ndash32

[197] Khan S Chiles J Ma J Fathpour S Silicon-on-nitride waveguides for mid-and near-infrared integrated photonics Appl Phys Lett 2013102121104

[198] Cheng Z Chen X Wong CY Xu K Tsang HK Mid-infrared suspended membrane waveguide and ring resonator on silicon-on-insulator IEEE Photonics J 201241510ndash9

[199] Lin P-T Singh V Cai Y Kimerling LC Agarwal A Air-clad silicon pedestal structures for broadband mid-infrared microphotonics Opt Lett 2013381031ndash3

[200] Chang YC Paeder V Hvozdara L Hartmann JM Herzig HP Low-loss germanium strip waveguides on silicon for the mid-infrared Opt Lett 2012372883ndash5

[201] Zhang L Yue Y Y Xiao-Li R G Beausoleil Willner AE Highly dispersive slot waveguides Opt Express 2009177095ndash101

[202] Zhang L Yue Y Beausoleil RG Willner AE Analysis and engineering of chromatic dispersion in silicon waveguide bends and ring resonators Opt Express 2011198102ndash7

[203] Zhang L Mu J Singh V Agarwal A Kimerling LC Michel J Intra-cavity dispersion of microresonators and its engineering for octave-spanning Kerr frequency comb generation to be published

[204] Lin Q Zhang L Generalized nonlinear envelope equation with high-order dispersion of nonlinearity to be published

[205] Wang Y Yue R Han H Liao X Raman study of structural order of a-SiNxH and its change upon thermal annealing J Non-Crystalline Solids 2001291107ndash12

[206] Brida D Marangoni M Manzoni C De Silvestri S Cerullo G Two-optical-cycle pulses in the mid-infrared from an optical parametric amplifier Opt Lett 2008332901ndash3

[207] Brida D Manzoni C Cirmi G Marangoni M Bonora S Villoresi P De Silvestri S Cerullo G Few-optical-cycle pulses tunable from the visible to the mid-infrared by optical parametric amplifiers J Opt 201012013001

[208] Kippenberg TJ Holzwarth R Diddams SA Microresonator-based optical frequency combs Science 2011332555ndash9

[209] Levy JS Gondarenko A Foster MA Turner-Foster AC Gaeta AL Lipson M CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects Nat Photonics 2009437ndash40

[210] DelrsquoHaye P Herr T Gavartin E Gorodetsky ML Holzwarth R Kippenberg TJ Octave spanningtunable frequency comb from a microresonator Phys Rev Lett 2011107063901

[211] Okawachi Y Saha K Levy JS Wen YH Lipson M Gaeta AL Octave-spanning frequency combgeneration in a silicon nitride chip Opt Lett 2011363398ndash400

[212] Matsko AB Savchenkov AA Liang W Ilchenko VS Seidel D Maleki L Mode-locked Kerr frequency combs Opt Lett 2011362845ndash7

[213] Herr T Brasch V Jost JD Wang CY Kondratiev NM Gorodetsky ML Kippenberg TJ Temporal solitons in optical microresonators httparxivorgabs12110733

[214] Saha K Okawachi Y Shim B Levy JS Salem R Johnson AR Foster MA Lamont MR Lipson M Gaeta AL Modelocking and femtosecond pulse generation in chip-based frequency combs Opt Express 2013211335ndash43

[215] Coen S Erkintalo M Universal scaling laws of Kerr frequency combs Opt Lett 2013381790ndash2

[216] Lugiato LA Lefever R Spatial dissipative structures in passive optical-systems Phys Rev Lett 1987582209ndash11

[217] Haelterman M Trillo S Wabnitz S Dissipative modulation instability in a nonlinear dispersive ring cavity Opt Commun 199291401ndash7

[218] Coen S Randle HG Sylvestre T Erkintalo M Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato-Lefever model Opt Lett 20133837ndash9

[219] Chembo YK Menyuk CR Spatiotemporal Lugiato-Lefever formalism for Kerr-comb generation in whispering-gallery-mode resonators Phys Rev A 201387053852

[220] Foltynowicz A Mas1owski P Ban T Adler F Cossel KC Briles TC Ye J Optical frequency comb spectroscopy Faraday Discussion 201115023ndash31

[221] Hartl I Li XD Chudoba C Ghanta RK Ko TH Fujimoto JG Ranka JK Windeler RS Ultrahigh-resolution optical coherence tomography using continuum generation in an air silica microstructure optical fiber Opt Lett 200126608ndash10

[222] Brabec T Krausz F Intense few-cycle laser fields Frontiers of nonlinear optics Rev Mod Phys 200072545ndash91

[223] Hu J Meyer J Richardson K Shah L Feature issue introduction mid-IR photonic materials Opt Mater Express 201331571ndash5

[224] Private communications with Dr Jacob Levy in Prof Lipsonrsquos group and Dr Johann Riemensberger in Prof Kippenbergrsquos group

[225] Zhang J Lin Q Piredda G Boyd RW Agrawal GP Fauchet PM Anisotropic nonlinear response of silicon in the near-infrared region Appl Phys Lett 200791071113

Page 3: Lin Zhang*, Anuradha M. Agarwal, Lionel C. Kimerling and ...

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp249

an optical intensity of below 5 GWcm2 [131 132] Second more Group IV elements eg germanium become trans-parent and can be used for nonlinear purposes In fact germanium exhibits higher refractive index and Kerr index n2 than silicon [133] Third at longer wavelengths device dimensions need to be scaled up according to wavelength and thus surface roughness induced in device fabrication causes relatively small scattering loss Fourth fabrication errors in device dimensions are a smaller fraction of target numbers which is beneficial to obtain a higher yield in device manufacture

However nonlinear photonics in the mid-IR also meet some challenges Although going beyond half-bandgap wavelengths one can remove TPA the nonlinear Kerr index n2 markedly decreases [134] With waveguide dimensions scaled up the effective mode area Aeff increases almost quadratically Therefore the nonlinear coefficient γ equal to 2πn2(λAeff) where λ is the wave-length in vacuum decreases quickly with wavelength This would require careful dispersion engineering for phase matching in nonlinear parametric processes in order to improve nonlinear efficiency [12]

Many nonlinear effects have been reported recently in silicon photonics touching the mid-IR wavelength range [60 61 106 108 114 115 135ndash145] It is noted that most of them address the short-wavelength end of the mid-IR from 2 to 25 μm which is mainly the short-wave IR [144] or transition from near-IR to mid-IR Little was reported in longer wavelength beyond 25 μm [136 138 142 145] In fact there are about two octaves of bandwidth in the mid-IR (eg from 25 to 10 μm) available much wider than that in the near-IR As an approach to creating new frequencies nonlinear optics is much more efficient than electro-optic modulation in terms of how far an optical spectrum can be extended We believe that the mid-IR would be an exciting arena for ultrafast octave-spanning nonlinear applications

In this paper we discuss the materials properties of the Group IV platform for nonlinear applications The waveguide-based devices are optimized for four different wavelength ranges from near-IR to mid-IR in terms of both nonlinearity and dispersion We show by simulation that our dispersion-engineering approach based on a stripslot hybrid structure is widely applicable and can drama-tically enhance nonlinear interaction efficiency and spec-trum broadening Supercontinuum and frequency comb generations are predicted to be octave-spanning accord-ing to our numerical simulations in which excellent spectral coherence of the generated wideband spectra is confirmed by the creation of ultrashort cycle-level optical pulses

Si

Si3N4

As2S3

As2Se3

1 2 3 4 5 6 7 8 9 10 11 12 13 14Wavelength (microm)

SiO2

Ge

Figure 1emspMaterials transparency windows (green bar) in near- and mid-infrared ranges Red bars indicate high-loss wavelength bands for each material and color transition from red to green is from bandgap wavelength to half-bandgap wavelength (blue lines)

2 MaterialsLoss nonlinearity and dispersion jointly determine the nonlinear performance of optical waveguides All the three are both material- and device-dependent In this section we survey the major material choices for nonlin-ear Group IV photonics in the near- and mid-IR

Figure 1 shows material transparency windows with an optical loss below 2 dBcm [122] for materials including silicon (Si ie crystalline silicon unless otherwise speci-fied) silicon nitride (Si3N4) silicon dioxide (SiO2) germa-nium (Ge) arsenic sulfide (As2S3) and arsenic selenide (As2Se3) Since TPA plays an important role in nonlinear applications [109 110] the color transition from red to green in Figure 1 is between the bandgap wavelength and the half-bandgap wavelength (two blue lines) where TPA decreases with wavelength For silicon almost two-octave bandwidth from 22 to 85 microm [146] is available for nonlin-ear applications without TPA covering a large fraction of mid-IR range It is important to note that amorphous silicon has a bandgap energy of 17 eV [32 33] and thus has TPA diminishing at a much shorter wavelength ( lt 155 μm) than crystalline silicon Both silicon nitride and silicon dioxide have large bandgap energies but silicon dioxide becomes highly lossy beyond 3 microm [119] Germanium has an indirect bandgap energy of 067 eV and is transparent until up to 14 microm [146] From Figure 1 one can see that germaniumrsquos green bar without TPA has no overlap with silicon dioxide

Chalcogenide glasses are actively investigated as photonic materials [147ndash149] and exhibit a wide trans-parency window in the near- and mid-IR For example As2S3 and As2Se3 have bandgap energies around 226 eV [150 151] and 177 eV [152] and they are transparent up to 12 and 15 microm [153] respectively Although in this paper

250emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

chalcogenide glasses are not considered a material for the core of a waveguide one may use them for waveguide cladding and slot layer [53 58]

Linear optical properties of the materials discussed here are collected in terms of refractive index and mate-rial dispersion as shown in Figure 2 The two ldquoXrdquo on the curves for silicon and germanium in Figure 2(A) indicate the half-bandgap wavelengths The refractive index is given by the Sellmeier equations for silicon [154] silicon nitride [155] silicon dioxide [156] SRO [51] germanium [157] arsenic sulfide [158] and arsenic selenide [159] as detailed in Appendix A For SRN there is no comprehen-sive measurement of material index found currently As shown in Figure 2(A) the materials under our considera-tion have strong index contrasts especially between ger-manium and chalcogenides in the mid-IR The refractive index decreases with wavelength and beyond the half-bandgap wavelength these materials have a relatively small index change One can properly choose materials for waveguide core and cladding and also a low-index slot layer based on the information given in Figure 2(A)

Overall dispersion in an integrated waveguide con-sists of material dispersion and waveguide dispersion that

40

35

30

25

Ref

ract

ive

inde

xD

ispe

rsio

n (p

snm

middotkm

)

20

200B

A

100

-100

-200

0

15

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Wavelength (microm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Wavelength (microm)

Si

Si

Si3N4

Si3N4

As2S3

As2S3

As2Se3

As2Se3

SiO2

SiO2

SRO

SRO

Ge

Ge

Figure 2emsp(A) Refractive indices and (B) material dispersion curves of the materials considered for nonlinear Group IV photonics in the near- and mid-IR wavelength ranges

is affected by index contrast and waveguide dimensions First material dispersion is shown in Figure 2(B) which is defined as D  =  -(cλ)middot(d2nmatdλ2 ) where nmat is material index and λ and c are wavelength and the speed of light in vacuum It is important to note that except for silicon dioxide all the other materials have a flat and low disper-sion within  plusmn 100 ps(nmmiddotkm) at the long-wavelength end of the bandwidth of interest This means that if wave-guides are not designed to tightly confine guided modes one can reduce the contribution of the waveguide disper-sion and have the overall dispersion close to the flat and low material dispersion However this will cause a large effective mode area and a small nonlinear coefficient

On the other hand we note from Figure 2(B) that at the short-wavelength end of the spectrum material dispersion changes quickly with wavelength for all the considered materials even if the material refractive index looks flat in Figure 2(A) beyond the half-bandgap wave-length This is because the dispersion is the 2nd-order derivative of the index with respect to wavelength To fully use the portion of the spectrum near the half-bandgap wavelength dispersion engineering by tailoring wave-guide dispersion is required

As a measure of nonlinear material property the non-linear index n2 is shown in Figure 3 for silicon silicon nitride SRO germanium and arsenic sulfide Looking at broadband nonlinear applications one needs to take the wavelength dependence of n2 into account Unfor-tunately there is often a lack of complete measurement data at a wavelength range of interest and also measure-ment results from different groups could vary widely For silicon data from several sources are available [160 161] A recently published review paper [133] shows a predic-tion of third-order nonlinear susceptibility χ(3)

1111 for silicon and germanium in the mid-IR range based on a two-band model which is used to fit wavelength-dependent

Non

linea

r in

dex

(m2 W

)

1E-16

1E-17

1E-18

1E-191 2 3 4 5 6 7 8 9 10 11 12 13 14

Wavelength (microm)

Si

Si3N4

SROGe

As2S3

Figure 3emspThe Kerr nonlinear index n2values of the considered mate-rials in near- and mid-IR ranges

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp251

measurements We obtain the Kerr nonlinear index n2 as a function of wavelength based on χ(3)

1111 using the results from [133] As shown in Figure 3 the n2 value peaks at 19 and 27 microm for silicon and germanium respectively and changes slightly from 33 to 48 microm beyond which both TPA and 3PA disappear The TPA coefficient βTPA vs wave-length is also extracted for silicon and germanium from [133] as detailed in Tables 1ndash4 in Appendix B

Hydrogenated amorphous silicon has been identi-fied as a potentially good nonlinear material not only because of large bandgap energy of 17 eV but also more importantly because of the large nonlinear index n2 and nonlinear figure of merit (FOM) n2βTPAλ [162] We did not include specific data in Figure 3 for amorphous silicon since different groups reported highly variable n2 and nonlinear FOM values in the near-IR [31ndash35] The n2 value could be one order of magnitude higher than that in silicon [33] while the nonlinear FOM can be as high as 5 [35] although these may not be obtained simultaneously [34] Moreover linear properties of amorphous silicon may also vary when fabrication conditions and its nonlin-ear characteristics change

Silicon nano-crystals in silicon dioxide and silicon nitride have also been investigated as a nonlinear material exhibiting higher nonlinear indices than crystalline silicon by an order of magnitude or more [36ndash41] The values of n2 βTPA and nonlinear FOM are also highly variable if silicon excess annealing temperature and wavelength change We include one data point (n2 = 48 times 10-17m2W) from [38] in Figure 3 Extremely high n2and FOM by 3~4 orders have been obtained experimentally [41] with large silicon excess (note that the FOM in [41] is defined as the reciprocal of ours here)

Both amorphous silicon and silicon nano-crystals exhibit great potential as a nonlinear material in the mid-IR which can be used to compensate for the reduc-tion of the nonlinear coefficient due to a large mode area at long wavelengths In particular with a small linear refractive index SRO is often chosen as a slot material to enhance nonlinearity in the near-IR [51 53 55 56 59] while SRN exhibits a great potential for nonlinear applica-tions beyond 3 microm Typically strong nonlinearity in bulk materials is associated with a high linear refractive index which is known as Miller rule However silicon nano-crys-tals exhibit unique properties to simultaneously possess strong nonlinearity and low linear index It is important to mention that the silicon nano-crystals (ie nano-clusters) could act as scattering centers of light causing an increased propagation loss in SRO slot waveguides Nevertheless relatively low propagation loss has been achieved which is 3~5 dBcm [163]

For silicon nitride one data point n2 = 24 times 10-19m2W from [111] is included in Figure 3 which was measured at 155 microm and is one-order lower than that in silicon Silicon dioxide has an n2 value around 26 times 10-20m2W in 155 microm as in single-mode optical fibers two orders lower than that in silicon A higher n2 value (115 times 10-19m2W) is estimated for 155 microm in high-index doped silica [164] Both values are not shown in Figure 3 Since both silicon nitride and silicon dioxide have large bandgap energies it is expected that their n2 values are almost constant over wavelength in the near- and mid-IR

Strong Kerr nonlinearities are obtained in chalcoge-nide glasses (arsenic sulfide and arsenic selenide) with negligible TPA from the near- to mid-IR as shown in Figure 1 We have found wavelength-dependent measure-ments of the nonlinear index n2 for arsenic sulfide from different data sources [150 165ndash174] As shown in Figure 3 although slightly scattered these n2 values in arsenic sulfide are as high as those in silicon and would not be strongly wavelength-dependent beyond 155 microm because it is longer than the half-bandgap wavelength Arsenic selenide has even higher n2 values than arsenic sulfide [173] and its n2 value is predicted as a function of wave-length in [175]

There has been little published on the wavelength dependence of the nonlinear Raman gain coefficient gR in literature for the materials that we consider here [133] Since SRS is not the major nonlinear effect that is used in this paper we will not discuss it in details here

Although the considered materials such as silicon germanium silicon nitride and silicon dioxide are cen-trosymmetric and show no second-order nonlinearity in bulk materials one can engineer them by applying strain [176ndash178] or forming interfaces between two centrosym-metric materials (eg between germanium and silicon [179] or between silicon nitride and silicon dioxide [180]) An alternative way is to integrate other materials with strong second-order susceptibility onto Group IV wave-guides (see eg [145]) For chalcogenide glasses different poling schemes are proposed to produce the second-order nonlinearity [181] The second-order susceptibility χ(2) induced to the Group IV platform can have a highly variable value depending on how the isotropy of materi-als is broken We believe that second-order nonlinearity is promising in nonlinear Group IV photonics but in this paper we will mainly focus on third-order nonlinearity

As described above the materials presented here have greatly different transparency windows and nonlin-ear coefficients It thus becomes critical to wisely choose a material combination for a specific application and doing this one may also need to pay special attention to material

252emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

compatibility in device fabrication On the other hand compared to the material choices device design (mainly on waveguide and resonator) can also produce widely var-iable dispersion and nonlinearity properties In the next section we will discuss enhanced waveguide properties using improved designs

3 DevicesOptical waveguides form the backbone of photonic devices Light propagation properties in a waveguide could be remarkably different from those in corresponding bulk materials especially when there is a high index con-trast between waveguide core and surrounding cladding Therefore understanding and optimizing the waveguide properties including loss dispersion and nonlinearity are essential in nonlinear photonics

Propagation loss in a waveguide includes material loss confinement loss scattering loss and nonlinear loss Working at a transparency window of a material especially beyond the half-bandgap wavelength one can primarily have low material and nonlinear loss caused by TPA Note that benefiting from the wide multi-octave bandwidth in the mid-IR one can even eliminate the impact of 3PA in silicon and germanium by pumping at  gt 33 microm and  gt 48 microm respectively Since the substrate index in a silicon wafer is higher than or equal to that in most of materials we consider for a waveguide core con-finement loss exists due to mode leakage to the silicon substrate This loss can be markedly reduced by increas-ing the spacing between waveguide core and the substrate or choosing low-index material between them In general scattering loss due to sidewall roughness of a waveguide is dominant in high-index-contrast silicon photonics which is mainly caused in device fabrication and can thus be reduced by improving the fabrication processes [182ndash184]

Compared to propagation loss chromatic disper-sion and nonlinearity in integrated waveguides are more de signable Since the dispersion is the second-order deriv-ative of the effective index with respect to wavelength it is particularly tailorable by changing waveguide shape and dimension Moreover dispersion has been recognized to be critical for broadband nonlinear effects [12 14 15 60 61 92ndash108 112ndash115 137ndash145] which is true especially for ultrafast octave-spanning applications [185] Spec-tral characteristics in a dispersion profile including the number and positions of zero-dispersion wavelengths (ZDWs) and dispersion slope greatly affect and often set the limit on the bandwidth of optical spectra the temporal

widths of pulses and conversion efficiency in nonlinear interactions [185] Generally speaking a flat dispersion profile (ie third- and higher-order dispersion terms are small) with low dispersion values is preferred

In conventional ultrafast nonlinear optics in a free-space setup many components were developed to control dispersion over a wide bandwidth [185 186] such as prisms gratings chirped mirrors and so on However in a waveguiding system eg in fiber-based ultrafast optics the dispersion-control toolkit is smaller and engineer-ing waveguide dispersion becomes critical In particular when waveguides are built on a silicon platform with a much higher index contrast than optical fibers dispersion in a highly nonlinear waveguide [187ndash190] often shows strong wavelength dependence which is not preferable for wideband nonlinear applications In [187 190] the ZDW in silicon rib and strip waveguides is mapped by scanning waveguide dimensions It is shown that tight confinement of a guided mode produces a ZDW in its dispersion profile around 12~14 μm close to the bandgap wavelength More-over even if the waveguide size is increased to move the ZDW to longer wavelength the dispersion slope near the ZDW is not small as shown in [187ndash189] causing a limited low-dispersion bandwidth

Recently a dispersion engineering technique for integrated high-index-contrast waveguides has been pro-posed in which an off-center nano-scale slot controls modal distribution at different wavelengths [59 60] The guided mode experiences a transition from strip-mode like to slot-mode like as wavelength increases This approach can produce a very flat dispersion profile over an ultra-wide bandwidth with dispersion flatness improved by 1ndash2 orders in terms of dispersion variation divided by low-dispersion bandwidth More importantly it is applicable to different material combinations and wavelength ranges [59ndash63]

Towards mid-IR applications different types of Group IV waveguides have been reported recently based on silicon-on-insulator (SOI) [191ndash193] silicon-on-sapphire [142 194 195] silicon-on-porous-silicon [192] silicon-on-nitride [196 197] suspended membrane silicon [198] silicon pedestal [199] and germanium-on-silicon [200] Most of the waveguides are not aimed specifically at non-linear applications and little attention has been paid to dispersion engineering [196]

In this section we survey different structures of Group IV waveguides for broadband nonlinear applica-tions from the near- to mid-IR There are three main goals in waveguide designs (i) we consider joint optimization on both dispersion and nonlinearity properties (ii) we tend to fully utilize the available bandwidth brought by

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp253

the materials in Figure 1 and (iii) we emphasize disper-sion engineering naturally as a result of aiming at octave-spanning broadband applications

Figure 4 shows a general illustration of various types of integrated waveguides for nonlinear Group IV photonics Looking at a specific wavelength range one can accord-ingly choose a materials combination for an appropriate index contrast and a desired level of nonlinearity Note that one may need low nonlinearity in some cases when high-power output is required Here we discuss waveguide design at four different wavelength ranges as follows

First we consider SOI waveguides for a wavelength range from the telecom window in the near-IR to the short-wave end in the mid-IR ie roughly from 14 to 25 microm This is the wavelength range that many of the current research efforts have been addressing [60 61 106 108 114 115 135 137 139ndash141 143 144] In this wavelength range a SOI strip waveguide as shown in Figure 4 can be used with air as an upper cladding (see eg [140]) One can change the width of the waveguide to tailor its disper-sion profile while the height of the waveguide is 220 nm set by SOI wafers From Figure 5(A) we note that a rela-tively small width W = 800 nm is corresponding to a dis-persion profile with two ZDWs at 1585 and 2345 microm and a peak value of anomalous dispersion 532 ps(nmmiddotkm) at 205 microm for the quasi-TE mode The anomalous disper-sion is typically useful for parametric amplification and oscillation soliton and soliton-based supercontinuum generation [12] With W  =  900 nm one can have a flatter dispersion profile but the anomalous band is smaller When W is increased to 1000 nm the dispersion is even flatter but no anomalous dispersion occurs Figure 5(A) shows a good example that tight mode confinement in a strip waveguide moves ZDW to short wavelengths and near ZDWs dispersion changes quickly with a large slope

Strip WG

Strip WG suspended

Air Air

Slot

Core

Upper cladding

Slab

Lower cladding

Si substrate

Slot WG suspended

Slot WG Rib WG

Figure 4emspDifferent types of Group IV waveguides (WGs) for disper-sion and nonlinearity engineering in the near- and mid-IR ranges

One can calculate the nonlinear coefficient γ as a function of wavelength with the nonlinear Kerr index n2 given in Tables 1ndash4 in Appendix B We show in Figure 5(B) that the nonlinear coefficient in the silicon strip wave-guide with W = 900 nm first increases to 187 (mmiddotW) with wavelength until 17 μm and then decreases to 56 (mmiddotW) at 25 μm This is caused by both the peaking of the silicon n2 value near 19 μm and the gradual increase of wave-length and mode area beyond that

A silicon stripslot hybrid waveguide exhibits very flat dispersion as presented in Figure 5(A) The SOI waveguide has crystalline silicon at the bottom a thin SRO slot and amorphous silicon at the top The upper cladding is silicon dioxide When setting the lower Si height to Hl = 430 nm slot height to Hs = 54 nm upper Si height to Hu = 160 nm and width to W = 660 nm we obtain an extremely flat disper-sion profile for the quasi-TM mode over a wide bandwidth between two ZDWs at 1545 and 2448 microm From 1605 to 238 microm the value of anomalous dispersion changes between 30 and 46 ps(nmmiddotkm) In this way one can have a flat and low anomalous dispersion between two far apart ZDWs The average dispersion value can be shifted by increasing Hu to move dispersion between normal and anomalous regimes Detailed explanation on how the flat-tened and saddle-shaped dispersion profile is produced is given in [59 60] Briefly the mode transition over wave-length for the quasi-TM mode is responsible for this behav-ior Due to the off-center slot the mode is mostly confined in the crystalline silicon at short wavelengths while the mode becomes more like a slot mode at long wavelengths As shown in Figure 5(C) we plot the mode power distribu-tions at wavelengths of 15 183 217 and 25 microm The mode transition adds negative dispersion in the middle of the low-dispersion bandwidth as explained in [60 201]

Having a slot one has an opportunity to fill the slot with highly nonlinear materials into it [49 51 53 55 56 58 59] which can overcome the decrease of the nonlinear coeffi-cient over wavelength In Figure 5(B) we show the γ value increasing to 306 (mmiddotW) with wavelength from 14 to 25 microm This is because the guided mode extends more to the highly nonlinear thin slot layer Note that the used n2 value in SRO [38] is currently the one measured at 155 microm so the n2 and γ thinspvalues may vary in the mid-IR but the trend is general

Next we explore the short-wavelength end of the near-IR spectrum Silicon-based devices become unus-able for nonlinear photonics as wavelength decreases to 11 microm and we thus look at silicon nitride for near-IR nonlinear applications extending to the visible light spec-trum Again a strip waveguide based on silicon nitride is examined first Figure 6(A) shows dispersion curves of the quasi-TE mode in two waveguides sized to be 1300 times 540

254emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

and 1400 times 800 nm2 The upper cladding is air and the lower cladding is silicon dioxide The anomalous disper-sion region in the dispersion curves shrinks when the waveguide is made smaller This is because of a relatively small index contrast between silicon nitride and silicon dioxide which makes the guided mode leak quickly to the substrate as wavelength increases For the strip waveguide with a cross-section of 1400 times 800 nm2 there are two ZDWs near 10 and 23 microm but one can see a strong dispersion of 250 ps(nmmiddotkm) between the two ZDWs in Figure 6(A) The nonlinear coefficient in the second silicon nitride wave-guide is shown in Figure 6(B) which is much smaller than that in silicon waveguides because of a one-order smaller n2 value and larger Aeff in the silicon nitride waveguide At 16 microm γ is about 123(mW)

One can also use a stripslot hybrid structure to tailor the dispersion profile in silicon nitride waveguides For example the slot and lower cladding are silicon dioxide and the upper cladding is air In Figure 6(A) we show the dispersion curves in two silicon nitride stripslot hybrid waveguides for comparison The waveguide 1 has Hl = 900 nm Hs = 124 nm Hu = 340 nm and W = 1000 nm and the waveguide 2 has Hl = 920 nm Hs = 154 nm Hu = 480 nm and W = 1300 nm These two waveguides produce increasingly flatter dispersion profiles as shown in Figure 6(A) The first waveguide has two ZDWs located at 106 and 22 microm with the peak dispersion of 67 ps(nmmiddotkm) The second waveguide has two ZDWs at 115 and 235 microm with the dispersion varying within 0~20 ps(nmmiddotkm) This octave-spanning dispersion flattening with different levels

1000A

B

C

500

-500

400

300

200

100

0

-100014 16

Strip WG W=800 nmStrip WG W=900 nm

Strip WG W=900 nm

Strip WG W=1000 nm

Slot WG Hu=160 nm

Slot WG Hu=160 nm

Slot WG Hu=163 nmSlot WG Hu=166 nm

18 20 22Wavelength (microm)

Dis

pers

ion

(ps

nmmiddotk

m)

Non

linea

r co

effic

ient

(m

middotW)

24 26

14 16 18 20 22

Wavelength (microm)

24 26

0

Figure 5emspIn a wavelength range from the telecom window in near-IR to the short-wave end in the mid-IR silicon strip and stripslot hybrid waveguides (WGs) are analyzed in terms of (A) dispersion and (B) nonlinearity (C) Mode power distributions at wavelengths of 15 183 217 and 25 microm in the stripslot hybrid waveguide

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp255

of dispersions can be used for multiple applications as detailed in the next section The nonlinear coefficients for the two waveguides are shown in Figure 6(B) We note that the stripslot hybrid waveguides have similar nonlinear coefficients as the strip waveguide which shows that the dispersion profile is much more tailorable by waveguide designs

Then we move to the mid-IR using silicon and silicon nitride for waveguiding A comparison of different types of silicon-on-nitride waveguides have been presented in [196] where rib waveguides were preferred due to the wideband low dispersion over an octave-spanning band-width from 24 to 66 microm for the quasi-TE mode This is a spectral range from siliconrsquos half-bandgap wavelength to the cut-off wavelength of silicon nitride In Figure 7(A) we plot the dispersion curve for a silicon-on-nitride rib waveguide with air as the upper cladding the rib width of 2000 nm the total height of 1200 nm and the slab height of 1000 nm which are the same parameters used in [196] It is shown that less confinement of optical modes reduces the contribution of waveguide dispersion and makes the overall dispersion profile closer to the material dispersion which is flat and low at long wavelengths as in Figure 2(B)

A

B

400

300

200

100

-100

8

6

4

2

0

0

Strip WG 1300times540 nm2

Strip WG 1400times800 nm2

Strip WG 1400times800 nm2

Slot WG 1Slot WG 2

Slot WG 1Slot WG 2

Dis

pers

ion

(ps

nmmiddotk

m)

Non

linea

r co

effic

ient

(m

middotW)

20 3010 15 2505Wavelength (microm)

2010 15 2505

Wavelength (microm)

Figure 6emspIn a wavelength range moved toward the short-wave-length end of near-IR spectrum silicon nitride strip and stripslot hybrid waveguides are designed in terms of (A) dispersion and (B) nonlinearity

Accordingly the nonlinear coefficient is small 285 (mmiddotW) at 3 microm as shown in Figure 7(B)

On the other hand if one needs a small Aeff to enhance nonlinearity additional dispersion tailoring (eg based on stripslot hybrid waveguides) would be beneficial Pursuing a higher nonlinear coefficient we use a 500-nm silicon nitride suspended membrane as illustrated in Figure 4 to support a silicon stripslot hybrid waveguide This helps confine light in the waveguide core Using W = 880 nm Hu = 550 nm Hs = 87 nm and Hl = 840 nm we obtain a saddle-shaped anomalous dispersion from 19 to 449 microm within 0~60 ps(nmmiddotkm) for the quasi-TM mode as shown in Figure 7(A) This structure produces much tighter mode confinement than the rib waveguide and exhibits a 3 times larger nonlinear coefficient in Figure 7(B) while having similar dispersion flatness

Finally we consider germanium-on-silicon wave-guides over a wavelength range from 33 to 85 microm between the half-bandgap wavelength of germanium and the cut-off wavelength of silicon This type of waveguide has been demonstrated with strain-free mono-crystal-line germanium [200] Here we assume that the germa-nium waveguide has a 10-nm silicon nitride layer on its

A

B

200

-200

60

40

20

0

100

-100

0

Rib WGSlot WG

Rib WGSlot WG

Dis

pers

ion

(ps

nmmiddotk

m)

Non

linea

r co

effic

ient

(m

middotW)

1 2 3 4 5 6 7Wavelength (microm)

1 2 3 4 5 6 7

Wavelength (microm)

Figure 7emspIn a wavelength range from the short-wave IR to mid-IR silicon rib waveguide on silicon nitride and stripslot hybrid waveguide on a suspended membrane are analyzed in terms of (A) dispersion and (B) nonlinearity

256emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

surface for passivation The upper cladding could be air or silicon which provides significantly different dispersion properties due to a varied index contrast For comparison only we also have silicon nitride as the upper cladding although silicon nitride becomes lossy for wavelengths longer than 67 microm Figure 8(A) shows the dispersion pro-files of four germanium-on-silicon strip waveguides with equal size 3000 times 1600 nm2 for the quasi-TE mode Air and silicon nitride as an upper cladding result in similar shape and bandwidth in the dispersion profiles Thus the air-cladded waveguide is chosen and discussed further The waveguide with silicon upper cladding has normal dispersion at all wavelengths since there is a relatively small index contrast between germanium and silicon and thus weak mode confinement A germanium strip wave-guide on a 600-nm-thick silicon suspended membrane is also considered to increase light confinement with an air upper cladding to maximize light confinement However as mentioned earlier strong confinement typically causes strong dispersion as shown in Figure 8(A) and therefore the germanium waveguide on a silicon membraneis not chosen for broadband nonlinear applications In contrast the germanium strip waveguide with air upper cladding exhibits a flat and low dispersion

The dimensions of the air-cladded germanium wave-guide are varied by simultaneously changing its height and width with a step of 200 nm for both polarization states It is interesting to see from Figure 8(B) and 8(C) that the dispersion peak value remains nearly unchanged for all the waveguide sizes although we have a widely tunable ZDW at long wavelengths For the quasi-TE mode the right ZDW moves from 605 microm to 841 microm while the left ZDW is always near 4 microm We can thus obtain an octave-spanning anomalous dispersion band with the peak value below 100 ps(nmmiddotkm) For the quasi-TM mode one can see similar dispersion properties but the anomalous disper-sion band is smaller Thus we choose the quasi-TE mode for further discussion in next section

The nonlinear coefficient in the germanium wave-guides for the quasi-TE mode is shown in Figure 8(D) which is about 10(mmiddotW) at 5 microm with a small variation for differ-ent waveguide sizes This is quite high considering that both wavelength and effective mode area become much larger over this wavelength range compared to the near-IR

From above we can see that the stripslot hybrid wave-guides enable unique controllability of dispersion and that this concept is applicable to different wavelength ranges However their performance may be sensitive to fabrication errors especially for inaccuracies in slot height Hs [59 60] A higher yield in device fabrication is expected using advanced fabrication technologies and facilities

A

C

D

B

400

300

200

100

-100

-200

0

Ge WG+air 3000times1600 nm2

Ge WG+air suspended 3000times1600 nm2

Ge WG+Si3N4 3000times1600 nm2

Ge WG+Si 3000times1600 nm2

Ge WG+air 2800times1400 nm2

Ge WG+air 3000times1600 nm2

Ge WG+air 3200times1800 nm2

Ge WG+air 3400times2000 nm2

Ge WG+air 2800times1400 nm2

Ge WG+air 3000times1600 nm2

Ge WG+air 3200times1800 nm2

Ge WG+air 3400times2000 nm2

Ge WG+air 2800times1400 nm2

Ge WG+air 3000times1600 nm2

Ge WG+air 3200times1800 nm2

Ge WG+air 3400times2000 nm2

Dis

pers

ion

(ps

nmmiddotk

m)

400

300

200

100

-100

-200

0

Dis

pers

ion

(ps

nmmiddotk

m)

400

300

200

100

-100

-200

50

40

30

20

10

0

0

Dis

pers

ion

(ps

nmmiddotk

m)

Non

linea

r co

effic

ient

(m

middotW)

3 4 5 6 7 8 9Wavelength (microm)

3 4 5 6 7 8 9Wavelength (microm)

3 4 5 6 7 8 9

Wavelength (microm)

3 4 5 6 7 8 9

Wavelength (microm)

Figure 8emspIn a wavelength range covering the main part of the mid-IR spectrum (A) on silicon substrate or on suspended silicon membrane are analyzed in terms of dispersion Germanium-on-silicon strip waveguides with an air upper cladding and different dimensions are characterized by (B) dispersion for the quasi-TE mode (C) dispersion for the quasi-TM mode and (D) nonlinearity for the quasi-TE mode

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp257

Besides photonic waveguides another important cat-egory of nonlinear devices is integrated resonators In the scope of this paper we consider relatively large resona-tors for frequency comb generation in which the bending radius of a ring resonator is varied from 50 microm to 100 microm depending on free spectral range (FSR) and the group index in the waveguide In these cases the waveguide-bending-induced dispersion is small and we would not discuss intra-cavity dispersion [202 203] in details here

4 ApplicationsBenefiting from the unique dispersion engineering over an octave-spanning bandwidth as described above one can develop ultra-wideband nonlinear applications that could hardly be attained in an integrated platform previously These include octave-spanning supercontinuum genera-tion pulse compression to a few-cycle or even sub-cycle level octave-spanning Kerr frequency comb generation and the associated mode-locked ultrashort pulse genera-tion using microresonators In this section we review our recent work on these topics

First we discuss the supercontinuum generation and pulse compression in a straight waveguide The nonlinear envelope equation used here to simulate supercontinuum generation is the following

βα infin

=

part part+ + = + part part sum

2

( - )( ) ( )

2

m mm

mm

ii A K A R A

z m t (1)

where

2

0 0

- -( ) 1- ( ) 2

n nn

nn

i i iK A A An t tγ δ δ

ω δ δ

infin

=

= sum

and

2shock_R( ) - 1- [ ( - ) | | ]δ

γ τδ minusinfin

= prime prime int

t

R RR A i i A h t t A dtt

We denote A  =  A(zt) as the complex amplitude of an optical pulse Note that its Fourier transform is

-

1( ) ( ) exp( - ) 2

A z A z t i t dtω ωπ

infin

infin

= int

In Eq (1) α is the total propagation loss and βm is the mth-order dispersion coefficient The frequency dependence of nonlinearity parameters including the nonlinear index n2 the TPA coefficient βTPA and the

effective mode area Aeff is included in the nth-order dis-persion coefficient γn of nonlinearity which is defined as γn = ω0middotpartn[γ(ω)ω]partωn where ω0 is the angular frequency of the carrier Therefore we can consider all-order linear dispersion terms and all-order dispersion of the nonlin-ear coefficient in Eq (1) Specifically in the simulations for a silicon and silicon nitride waveguides we have all-order linear dispersion and up to 6th-order and 2nd-order of the nonlinear coefficient dispersion included A detailed derivation of Eq (1) is given in [204] For the quasi-TM mode that experiences the engineered dispersion due to the mode transition SRS in silicon waveguides fabricated on the (001) surface can be ignored [27 96] For silicon nitride waveguide we include the SRS term in Eq (1) where γR = gRΓR(AeffΩR) and gR ΓR and ΩR represent the Raman gain coefficient the full width at half maximum of the gain spectrum and the Raman shift respectively The Raman shock time τshock_R is associated with γRrsquos fre-quency dependence which is 1ω0-[1Aeff(ω0)][dAeff(ω)dω] similarly as in [14] if we ignore frequency dependent gR ΓR and ΩR hR(t) is the Raman response function and it corresponds to the Raman gain spectrum

2

2 20 0

( ) -( - ) 2 ( - )

Ωω

Ω ω ω Γ ω ω=

+R

RR R

Hi

Note that the sign before the imaginary unit is differ-ent from that in [27] to be consistent with the expression of the Fourier transform that we used

We have considered supercontinuum generation in both silicon and silicon nitride waveguides with the slot-assisted dispersion tailoring Octave-spanning supercon-tinua in a silicon-based stripslot hybrid waveguide have been investigated in detail in [108] in which two-cycle optical pulses are obtained The main results in that work are shown in Figure 9 for comparison purposes

Here we mainly focus on the supercontinuum gen-erated in the silicon nitride stripslot hybrid waveguide (ie the slot WG 1 in Section III) whose dispersion and nonlinearity properties are shown in Figure 6 In the non-linear simulations we set the total propagation loss to be 1 dBcm The SRS parameters used here are the following [205] ΩR2π = 143 THz ΓR2π = 172 THz and gR = 1 times 10-12 mW τshock_R is calculated to be  = 156 fs

In our simulations we use a time step of 025 fs which is corresponding to a bandwidth of 4000 THz in the fre-quency domain For a femtosecond input pulse we set the time window length to 50 ps (ie frequency resolution Δf = 20 GHz)

We simulate the nonlinear propagation of a chirp-free hyperbolic secant pulse in the silicon nitride waveguide

258emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

The pulse center wavelength is at 1610 nm and its full width at half-maximum (FWHM) T0 is 120 fs Its peak power is 1200 W corresponding to pulse energy of 016 nJ

Figure 10(A) shows the supercontinua at different propagation distances At 48 mm the spectrum is greatly broadened at the -30 dB level covering a wavelength range from 0585 to 2833 microm which is more than two octaves The spectrum evolution in Figure 10(A) shows a similar spectrum shape as that in Figure 9(A) both featuring a ldquotriangularrdquo central spectrum bounded by two dispersive waves at the edges However it is important to note that the absence of TPA and 3PA in silicon nitride at the telecom window leads to a much more efficient spectrum broad-ening than that in silicon [108] The generated spectrum extends from the visible light to the mid-IR with excellent spectral coherence which is confirmed by the pulse wave-form shown in Figure 10(B) In the time domain the pulse is greatly compressed from 120 to 408 fs corresponding to 076 optical cycles at 161 microm wavelength

We examine the pulsewidth as a function of propa-gation distance Figure 11 shows that the pulse becomes increasingly narrower until the propagation distance reaches 47 mm For longer distances the pulsewidth

A

B

60 mm

48 mm

36 mm

24 mm

12 mm

Input

Spe

ctru

m (

10 d

Bd

iv)

Pow

er (

W)

12

246

24

18

12

6

0

248 250 252 254

14 16 18 20 22 24Wavelength (microm)

Time (ps)

Figure 9emsp(A) The supercontinuum generation in a silicon-based stripslot hybrid waveguide presented in [108] (B) The significant spectrum broadening at 425-mm distance is associated with a temporal compression of an input pulse (dash line) to the output waveform (solid line) with a FWHM of 12 fs

A

B

50 mm

48 mm

46 mm

44 mm

42 mm

Input

Spe

ctru

m (

10 d

Bd

iv)

Pow

er (

W)

8000

6000

4000

2000

0250249 251

06 09 12 15 18 21 24 27

Wavelength (microm)

Time (ps)

Figure 10emsp(A) Spectrum evolution of the pulse over propagation distance A supercontinuum of more than two octaves is achieved at 48 mm distance (B) Generated pulse waveform with a pulse width of 408 fs as short as 076 optical cycles Low pedestals are caused by dispersive waves generated at the two ends of the spectrum

remains almost constant However it is important to mention that after 48 mm the dispersive waves become increasingly stronger as shown in Figure 10(A) causing larger pedestals

Comparing the results in Figures 9 and 10 we note that the mid-IR wavelength range for silicon would be in analogy to the near-IR for silicon nitride in terms of non-linear optics operations Pumping at or beyond 33 microm one can use the waveguide designs shown in Figure 7 to produce very efficient nonlinear interactions without TPA and 3PA in silicon Ultrashort pulses in the mid-IR from parametric amplifiers [206 207] could be used to pump the Group IV waveguides

Another nonlinear application of the dispersion-engi-neered Group IV waveguides is micro-resonator-based Kerr frequency comb generation When such a waveguide is curved to form a microring resonator input CW light travels around the cavity and amplifies the noise in the source located at the frequencies with a high parametric gain As a result of modulation instability and cascaded FWM in the cavity a frequency comb can be generated [208ndash211] Mode-locked frequency combs have been reported pro-ducing low-noise pulse trains in time domain [212ndash214]

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp259

The formation of cavity solitons is identified as the main reason for the mode-locking in the Kerr frequency combs [215] This is instructive because one can thus predict the spectral bandwidth and temporal pulsewidth in the generated low-noise combs The 3-dB comb bandwidth is inversely proportional to the square root of the 2nd-order dispersion coefficient |β2| as given in [213 215] It is desira-ble that all comb lines that constitute the soliton spectrum experience the same |β2| In this sense the stripslot hybrid waveguides with flattened dispersion are preferably suit-able for supporting broadband Kerr comb generation and ultra-short cavity soliton generation

The Kerr frequency comb generation can be modeled using the generalized Lugiato-Lefever equation (LLE) [216ndash219]

20

2

( - )- - | |

2 2

m mm

R inmm

jkt j jl E kE j l E Et m

βαδ γ

τ

infin

=

part part+ + + = part part

sum (2)

where tR is the round-trip time E = E(tτ) and Ein are intra-cavity field and input field (pump power Pin  =  |Ein|2) t and τ are the slow and fast times δ0 is the cavity phase detuning defined as δ0  =  tRmiddot(ωn -ω0) where ω0 and ωn are the pumprsquos angular frequency and the nth angular reso-nance frequency that is pumped Other resonator param-eters include the power loss per round trip α the power coupling coefficient κ the nonlinear coefficient γ and the mth dispersion coefficient βm Since a flattened dispersion profile has a small β2 over a wide bandwidth it is impor-tant to take the influence of higher-order dispersion into account We include all-order dispersion terms in Eq (2) as we did in solving Eq (1)

To enhance the Kerr comb bandwidth in the near-IR we use the ultra-flattened dispersion profile in Figure 6(A) which is obtained in the slot WG 2 based on

Pul

se w

idth

(fs

)

14

12

10

8

6

4

242 44 46 48 50 52

Propagation distance (mm)

Figure 11emspPulse width first decreases with propagation distance and then remains stable After 48 mm dispersive waves get stronger causing more pedestals

Pow

er (

10 d

Bd

iv)

Pow

er (

W)

70A

B

60

50

40

30

20

10

-10

-20

600

400

200

0

80 120

0575 0600 0625 0650

160 200 240 280 320 360

0

Frequency (THz)

Time (ps)

Figure 12emsp(A) Frequency comb generation with a CW pump at 155 microm using a microring resonator based on a silicon stripslot hybrid waveguide Over an octave-spanning bandwidth from 135 to 270 THz the comb lines have a power drop of 20 dB (B) Generated pulse waveform with a pulse width of 82 fs as short as 16 optical cycles

silicon nitride The ring resonator has a bending radius of 104 microm corresponding to a FSR of 200 GHz Pumping near 155 microm with a pump power of 2 W the resonance peak is red-shifted and we need to red-shift the pump wavelength accordingly and tune it into the resonance from the short-wavelength side When the pump is step-by-step tuned by up to 63 resonance linewidths we obtain the comb spectrum and the mode-locked pulse waveform as shown in Figure 12 One can see that over an octave-spanning bandwidth from 133 to 268 THz the comb lines have a power drop by 20 dB from the center of the spectrum The spectral flatness of this comb is relatively good compared to the previously reported results [208ndash211] The comb bandwidth at -40 dB is as wide as two octaves There are two dispersive peaks in normal dispersion regions beyond the low-dispersion band Such a mode-locked broadband comb produces a train of sub-two-cycle optical pulses as shown in Figure 12(B) with one pulse per round trip The peak power of the pulse is up to 600 W Nonlinear conver-sion efficiency is estimated to be -267 dB

To generate frequency combs in the mid-IR the ger-manium-on-silicon strip waveguide is chosen We choose

260emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

a cross-section of 3200 times 1800 nm2 which has an octave-spanning low-dispersion band from 4 to 767 microm as shown in Figure 8(B) A germanium ring resonator is formed with a bending radius of 564 microm corresponding to a FSR of 200 GHz Pumping at 6 microm with a CW power of 14 W and detuning the pump wavelength by 10 resonance linewidth one can see that a mode-locked wideband mid-IR comb is generated from 358 to 644 THz (ie from 466 to 838 microm) at -40 dB level The FWHM of the produced pulses is 69 fs which corresponds to ~35 optical cycles The pulse peak power is 184 W and the nonlinear conversion efficiency is estimated to be -143 dB Since the pumping frequency is not at the center of the low-dispersion band we only see one peak in the comb spectrum caused by the dispersive wave in the normal dispersion region from Figure 13(A) There is another peak at higher frequencies beyond what is shown in the figure

As shown above broadband dispersion engineering is critical for octave-spanning nonlinear applications in both near- and mid-IR wavelength ranges which enables us to fully utilize the bandwidth allowed by the materials transparency windows Generally speaking the nonlinear applications mentioned here such as supercontinuum generation ultrafast pulse compression and frequency comb generation are often the intermediate steps towards higher-level system applications In the frequency domain a wide spectrum can serve as an electromagnetic carrier to acquire high-volume of information eg for sensing [220] and imaging [221] In the time domain an ultrashort pulse can be used as probe to sample ultrafast phenomena [222]

5 Summary and OutlookWe have presented a review of our recent work on nonlin-ear photonics based on silicon and germanium Various types of Group IV waveguides are analyzed and optimized for four different wavelength ranges from near- to mid-IR The recently proposed dispersion engineering technique based on stripslot hybrid waveguide structures is used for different material combinations and wavelength ranges Numerical simulations show that the dispersion-flattened Group IV waveguides are preferably suitable for octave-spanning nonlinear applications including on-chip supercontinuum generation ultrashort pulse compres-sion and mode-locked wideband frequency comb genera-tion based on micro-resonators

The presented approach to achieving octave-span-ning nonlinear applications on an integrated CMOS-compatible Group IV platform holds great potential for realizing chip-scale sensing imaging communications and signal processing system The ultrawide transparency windows in the mid-IR allowed by Group IV elements and compounds potentially together with other materi-als [223] provide an exciting arena for building powerful information acquisition and processing units enabled by nonlinear optics nano-photonics and ultrafast optics

Received June 14 2013 accepted October 29 2013 previously pub-lished online November 27 2013

Pow

er (

10 d

Bd

iv)

A

8030 40 50 60 70Frequency (THz)

Pow

er (

W)

B200

150

100

50

0

21 22 23 24 25Time (ps)

Figure 13emsp(A) Frequency comb generation with a CW pump at 6 microm using a microring resonator based on a germanium strip waveguide with air upper cladding (B) Generated pulse waveform with a pulse width of 69 fs as short as 35 optical cycles

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp261

Appendix

A Material index and dispersion

In this section we give the wavelength-dependent mate-rial index expressed as Sellmeier equations where wave-length λ is in μm

For silicon we use the following material index that is a fit curve from measurement results at room temperature (293 K) with 184 data points in total from 112 to 588 μm [154]

22 1 2 2

2 2 22

( )-

C Cn

λλ ε

λ λ λ= + +

where ε = 116858 C1 = 0939816 μm2 C2 = 000810461 and λ2 = 11071 μm

For silicon nitride the material index is affected by deposition conditions using plasma-enhanced chemical vapor deposition (PECVD) low-pressure chemical vapor deposition (LPCVD) and so on We use the following Sell-meier equation [155] which predicts the material index close to that in LPCVD silicon nitride films measured by a few groups [224]

22 1

2 21

( ) 1-

Cn

λλ

λ λ= +

where C1 = 28939 and λ1 = 013967 μmFor silicon dioxide we use the following Sellmeier

equation for fused silica [156]22 2

2 31 22 2 2 2 2 2

1 2 3

( ) 1- - -

CC Cn

λλ λλ

λ λ λ λ λ λ= + + +

where C1 = 06961663 C2 = 04079426 C3 = 08974794 λ1 = 00684043 μm λ2 = 01162414 μm and λ3 = 9896161 μm

For SRO the material index is affected by deposition conditions such as silicon excess annealing temperature and so on Here we choose the one with silicon excess of 8 and annealed at 1250oC [51]

22 22 31 2

2 2 2 2 2 21 2 3

( ) 1- - -

CC Cn

λλ λλ

λ λ λ λ λ λ= + + +

where C1 = 001 C2 = 196 C3 = 141 λ1 = 03 μm λ2 = 007071 μm and λ3 = 2775968 μm

For germanium the temperature-dependent mate-rial index was measured [157] Here we choose the one for room temperature (293 K)

2 22 1 2

2 2 2 21 2

( )- -

C Cn

λ λλ ε

λ λ λ λ= + +

where ε = 928156 C1 = 67288 C2 = 021307 λ1 = 0664116 μm and λ2 = 6221013 μm

For arsenic sulfide we use the material index pro-vided in [158]

2 2 22 22 3 4 51 2

2 2 2 2 2 2 2 2 2 21 2 3 4 5

( ) 1- - - - -

C C CC Cn

λ λ λλ λλ

λ λ λ λ λ λ λ λ λ λ= + + + + +

where C1 = 18983678 C2 = 19222979 C3 = 08765134 C4 = 01188704 C5 = 09569903 λ1 = 015 μm λ2 = 025 μm λ3 = 035 μm λ4 = 045 μm and λ5 = 27386128 μm

For arsenic selenide we fit ellipsometry measure-ments of our arsenic selenide thin films and the bulk material is provided by Prof Kathleen A Richardson group

22 22 31 2

2 2 2 2 2 21 2 3

( ) 1- - -

CC Cn

λλ λλ

λ λ λ λ λ λ= + + +

where C1 = 298463 C2 = 321011 C3 = 100182 λ1 = 044118 μm λ2 = 0000354953 μm and λ3 = 38413 μm

B Nonlinear Kerr index n2

The third-order nonlinear susceptibility χ(3)1111 for silicon and

germanium is predicted over the mid-IR range [133] based on a two-band model The effective nonlinear susceptibil-ity χ(3) is dependent on polarization and crystallographic orientation [225] For strong nonlinearity we consider a single-polarization incident light aligned to the crystal-lographic axis and we have χ(3) = χ(3)

1111 To investigate the octave-spanning nonlinear phenomena one need to take the wavelength-dependent nonlinear Kerr index n2 and TPA coefficient βTPA into account which are expressed as

( 3 )2 2

0

( 3 )2

0

3( ) ( )4 ( )

3( ) ( )( )

re

TPA im

ncn

cn

λ χ λε λ

πβ λ χ λ

λε λ

=

=

where ε0 and c are the vacuum permittivity and the speed of light in vacuum Using the material index given in Appendix A and χ(3) value from [133] we obtain the n2 and βTPA values tabulated as follows

262emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

Table 1enspNonlinear Kerr index n2 in silicon

λμm

  n2

10-18 m2W  λ

μm  n2

10-18 m2W  λ

μm  n2

10-18 m2W

130   234   310   389   490   312135   305   315   384   495   311140   378   320   379   500   310145   443   325   375   505   309150   501   330   371   510   307155   559   335   368   515   306160   618   340   365   520   304165   671   345   362   525   304170   710   350   360   530   303175   741   355   358   535   302180   766   360   355   540   302185   781   365   352   545   301190   783   370   350   550   300195   778   375   346   555   298200   762   380   343   560   297205   732   385   341   565   296210   699   390   338   570   296215   658   395   336   575   295220   612   400   334   580   295225   576   405   332   585   295230   547   410   331   590   294235   525   415   330   595   293240   508   420   329   600   292245   493   425   328   605   291250   479   430   327   610   290255   467   435   325   615   289260   456   440   324   620   288265   448   445   321   625   288270   440   450   319   630   288275   432   455   317   635   288280   424   460   315   640   288285   417   465   314   645   288290   410   470   313   650   288295   404   475   313   655   288300   398   480   312   660   288305   394   485   312    

Table 2enspTPA coefficient βTPA in silicon

λμm

  βTPA

10-12 mW  λ

μm  βTPA

10-12 mW  λ

μm  βTPA

10-12 mW

130   1334   165   812   200   180135   1284   170   713   205   115140   1222   175   613   210   064145   1154   180   522   215   024150   1079   185   424   220   0003155   995   190   333    160   905   195   254    

Table 3enspNonlinear Kerr index n2 in germanium

λμm

  n2

10-18 m2W  λ

μm  n2

10-18 m2W  λ

μm  n2

10-18 m2W

23  3932  63  1986  103  170524  4994  64  1972  104  169925  6007  65  1959  105  169426  6650  66  1946  106  169027  6772  67  1934  107  168728  6273  68  1923  108  168429  4897  69  1913  109  168230  4403  70  1904  110  168131  3970  71  1895  111  167932  3680  72  1886  112  167733  3470  73  1876  113  167534  3286  74  1868  114  167335  3128  75  1859  115  167036  2998  76  1850  116  166737  2895  77  1841  117  166338  2812  78  1833  118  165939  2737  79  1826  119  165640  2668  80  1819  120  165341  2605  81  1812  121  165142  2550  82  1807  122  164843  2498  83  1801  123  164644  2450  84  1797  124  164445  2406  85  1792  125  164346  2365  86  1787  126  164147  2328  87  1782  127  163948  2295  88  1777  128  163649  2266  89  1772  129  163450  2238  90  1767  130  163251  2212  91  1762  131  163052  2187  92  1758  132  162853  2164  93  1753  133  162654  2141  94  1749  134  162555  2121  95  1744  135  162356  2101  96  1740  136  162157  2083  97  1736  137  162058  2066  98  1731  138  161859  2049  99  1727  139  161760  2032  100  1722  140  161661  2016  101  1716   62  2001  102  1711   

Table 4enspTPA coefficient βTPA in germanium

λμm

  βTPA

10-8 mW  λμm

  βTPA

10-8 mW  λ

μm  βTPA

10-8 mW

23   130   25   088   27   03124   111   26   060   28   006

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp263

References[1] Bloembergen N Nonlinear Optics London World Scientific 1996[2] Yuen-Ron S The Principles of Nonlinear Optics Hoboken New

Jersey Wiley-Interscience 2002[3] Robert B Nonlinear Optics (3rd ed) Amsterdam Boston

Academic Press 2008[4] Franken P Hill A Peters C Weinreich G Generation of optical

harmonics Phys Rev Lett 19617118ndash9[5] Terhune RW Maker PD Savage CM Optical harmonic

generation in calcite Phys Rev Lett 19628404ndash6[6] Kaiser W Garrett CGB Two-photon excitation in CaF2Eu2+

Phys Rev Lett 19617229ndash32[7] Eckhardt G Hellwarth RW McClung FJ Schwarz SE Weiner D

Woodbury EJ Stimulated raman scattering from organic liquids Phys Rev Lett 19629455ndash7

[8] Giordmaine JA Mixing of light beams in crystals Phys Rev Lett 1962819ndash20

[9] Maker PD Terhune RW Nisenoff M Savage CM Effects of dispersion and focusing on the production of optical harmonics Phys Rev Lett 1962821ndash22

[10] Delone NB Kraĭnov VP Fundamentals of nonlinear optics of atomic gases New York Wiley 1987

[11] Nikogosyan DN Nonlinear optical crystals a complete survey Springer Berlin 2005

[12] Govind A Nonlinear fiber optics (4th ed) San Diego California Academic Press 2007

[13] Russell PSTJ Birks TA Lloyd-Lucas FD Photonic Bloch waves and photonic band gaps In lsquoConfined electrons and photons New physics and applicationsrsquo New York Plenum Press 1995

[14] Dudley JM Genty G Coen S Supercontinuum generation in photonic crystal fiber Rev Mod Phys 2006781135ndash1184

[15] Dudley JM Taylor JR Ten years of nonlinear optics in photonic crystal fibre Nature Photonics 2009385ndash90

[16] Soref RA Silicon-based optoelectronics Proceedings of the IEEE 1993811687ndash1706

[17] Kimerling LC Silicon for photonics Proc SPIE 3002 1997192[18] Kimerling LC Silicon materials engineering for the next

millennium Sol St Phen 199970131ndash142[19] Pavesi L Lockwood DJ editors Silicon Photonics New York

Springer 2004[20] Reed GT Knights AP Silicon photonics an introduction Wiley

Hoboken NJ 2004[21] Lipson M Guiding modulating and emitting light on silicon -

challenges and opportunities IEEE J Lightwave Technol 2005 234222

[22] Soref RA The past present and future of silicon photonics IEEE J Sel Top Quantum Electron 2006121678ndash87

[23] Jalali B Paniccia M Reed G Silicon photonics IEEE Microwave Magazine 2006758ndash68

[24] Jalali B Fathpour S Silicon photonics J Lightwave Technol 2006 244600ndash15

[25] Kirchain R Kimerling L A roadmap for nanophotonics Nature Photonics 20071303ndash5

[26] Dekker R Usechak N Foumlrst M Driessen A Ultrafast nonlinear all-optical processes in silicon-on-insulator waveguides J Phys D Appl Phys 200740R249ndash71

[27] Lin Q Painter OJ Agrawal GP Nonlinear optical phenomena in silicon waveguides Modeling and applications Opt Express 20071516604ndash44

[28] Tsang HK Liu Y Nonlinear optical properties of silicon waveguides Semicond Sci Technol 2008 23064007

[29] Osgood RM Jr Panoiu NC Dadap JI Liu X Chen X Hsieh I-W Dulkeith E Green WM Vlasov YA Engineering nonlinearities in nanoscalse optical systems Physics and applications in dispersion-engineered silicon nonaphotonics wires Adv Opt Photon 20091162ndash235

[30] Leuthold J Koos C Freude W Nonlinear silicon photonics Nature Photonics 20104535ndash44

[31] Ikeda K Shen Y Fainman Y Enhanced optical nonlinearity in amorphous silicon and its application to waveguide devices Opt Express 20071517761ndash71

[32] Shoji Y Ogasawara T Kamei T Sakakibara Y Suda S Kintaka K Kawashima H Okano M Hasama T Ishikawa H Mori M Ultrafast nonlinear effects in hydrogenated amorphous silicon wire waveguide Opt Express 2010185668ndash73

[33] Narayanan K Preble SF Optical nonlinearities in hydrogenated-amorphous silicon waveguides Opt Express 2010188998ndash9005

[34] Grillet C Carletti L Monat C Grosse P Ben Bakir B Menezo S Fedeli JM Moss DJ Amorphous silicon nanowires combining high nonlinearity FOM and optical stability Opt Express 20122022609ndash15

[35] Matres J Ballesteros GC Gautier P Feacutedeacuteli J-M Martiacute J Oton CJ High nonlinear figure-of-merit amorphous silicon waveguides Opt Express 2013213932ndash40

[36] Hernaacutendez S Pellegrino P Martiacutenez A Lebour Y Garrido B Spano R Cazzanelli M Daldosso N Pavesi L Jordana E Fedeli JM Linear and nonlinear optical properties of Si nanocrystals in SiO2 deposited by plasma-enhanced chemical-vapor deposition J Appl Phys 2008103 064309

[37] Yuan Z Anopchenko A Daldosso N Guider R Navarro-Urrios D Pitanti A Spano R Pavesi L Silicon Nanocrystals as an Enabling Material for Silicon Photonics Proc IEEE 2009971250ndash68

[38] Spano R Daldosso N Cazzanelli M Ferraioli L Tartara L Yu J Degiorgio V Giordana E Fedeli JM Pavesi L Bound electronic and free carrier nonlinearities in Silicon nanocrystals at 1550 nm Opt Express 2009173941ndash50

[39] Rukhlenko ID Zhu W Premaratne M Agrawal GP Effective third-order susceptibility of silicon-nanocrystal-doped silica Opt Express 20122026275ndash84

[40] Loacutepez-Suaacuterez A Torres-Torres C Rangel-Rojo R Reyes-Esqueda JA Santana G Alonso JC Ortiz A Oliver A Modification of the nonlinear optical absorption and optical Kerr response exhibited by nc-Si embedded in a silicon-nitride film Opt Express 20091710056ndash68

[41] Minissale S Yerci S Dal Negro L Nonlinear optical properties of low temperature annealed silicon-rich oxide and silicon-rich nitride materials for silicon photonics Appl Phys Lett 2012100021109

[42] Yamada H Shirane M Chu T Yokoyama H Ishida S Arakawa Y Nonlinear-optic silicon-nanowire waveguides Japanese J Appl Phys 2005446541ndash5

[43] Almeida VR Xu QF Barrios CA Lipson M Guiding and confining light in void nanostructure Opt Lett 2004291209ndash11

264emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

[44] Xu Q Almeida VR Panepucci RR Lipson M Experimental demonstration of guiding and confining light in nanometer-size low-refractive-index material Opt Lett 2004291626ndash8

[45] Baehr-Jones T Hochberg M Walker C Scherer A High-Q optical resonators in silicon-on-insulator based slot waveguides Appl Phys Lett 200586081101

[46] Sun R Dong P Feng N-N Hong C-Y Michel J Lipson M Kimerling L Horizontal single and multiple slot waveguides optical transmission at λ = 1550 nm Opt Express 20071517967ndash72

[47] Fujisawa T Koshiba M Guided modes of nonlinear slot waveguides IEEE Photon Technol Lett 2006181530ndash32

[48] Sanchis P Blasco J Martiacutenez A Martiacute J Design of silicon-based slot waveguide configurations for optimum nonlinear performance J Lightwave Technol 2007251298ndash1305

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[141] Zlatanovic S Park JS Moro S Boggio JMC Divliansky IB Alic N Mookherjea S Radic S Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source Nat Photonics 20104561ndash4

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[188] Dulkeith E Xia FN Schares L Green WMJ Vlasov YA Group index and group velocity dispersion in silicon-on-insulator photonic wires Opt Express 2006143853ndash63

[189] Turner AC Manolatou C Schmidt BS Lipson M Tailored anomalous group-velocity dispersion in silicon channel waveguides Opt Express 2006144357ndash62

[190] Dadap JI Panoiu NC Chen X I-Hsieh W Liu X Chou C-Y Dulkeith E McNab SJ Xia F Green WMJ Sekaric L Vlasov YA Osgood RM Jr Nonlinear-optical phase modification in dispersion-engineered Si photonic wires Opt Express 2008161280ndash99

[191] Milosevic MM Matavulj PS Yang PY Bagolini A Mashanovich GZ Rib waveguides for mid-infrared silicon photonics J Opt Soc Am B 2009261760ndash6

[192] Mashanovich GZ Milošević MM Nedeljkovic M Owens N Xiong B Teo EJ Hu Y Low loss silicon waveguides for the mid-infrared Opt Express 2011197112ndash9

[193] Reimer C Nedeljkovic M Stothard DJM Esnault MOS Reardon C OrsquoFaolain L Dunn M Mashanovich GZ Krauss TF Mid-infrared photonic crystal waveguides in silicon Opt Express 20122029361ndash8

[194] Baehr-Jones T Spott A Ilic R Spott A Penkov B Asher W Hochberg M Silicon-on-sapphire integrated waveguides for the midinfrared Opt Express 20101812127ndash35

[195] Li F Jackson S Grillet C Magi E Hudson D Madden SJ Moghe Y OrsquoBrien C Read A Duvall SG Atanackovic P Eggleton BJ Moss D Low propagation loss silicon-on-sapphire waveguides for the midinfrared Opt Express 20111915212ndash20

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[196] Yue Y Zhang L Huang H Beausoleil RG Willner AE Silicon-on-nitride waveguide with ultralow dispersion over an octave-spanning mid-infared wavelength range IEEE Photonics J 20124126ndash32

[197] Khan S Chiles J Ma J Fathpour S Silicon-on-nitride waveguides for mid-and near-infrared integrated photonics Appl Phys Lett 2013102121104

[198] Cheng Z Chen X Wong CY Xu K Tsang HK Mid-infrared suspended membrane waveguide and ring resonator on silicon-on-insulator IEEE Photonics J 201241510ndash9

[199] Lin P-T Singh V Cai Y Kimerling LC Agarwal A Air-clad silicon pedestal structures for broadband mid-infrared microphotonics Opt Lett 2013381031ndash3

[200] Chang YC Paeder V Hvozdara L Hartmann JM Herzig HP Low-loss germanium strip waveguides on silicon for the mid-infrared Opt Lett 2012372883ndash5

[201] Zhang L Yue Y Y Xiao-Li R G Beausoleil Willner AE Highly dispersive slot waveguides Opt Express 2009177095ndash101

[202] Zhang L Yue Y Beausoleil RG Willner AE Analysis and engineering of chromatic dispersion in silicon waveguide bends and ring resonators Opt Express 2011198102ndash7

[203] Zhang L Mu J Singh V Agarwal A Kimerling LC Michel J Intra-cavity dispersion of microresonators and its engineering for octave-spanning Kerr frequency comb generation to be published

[204] Lin Q Zhang L Generalized nonlinear envelope equation with high-order dispersion of nonlinearity to be published

[205] Wang Y Yue R Han H Liao X Raman study of structural order of a-SiNxH and its change upon thermal annealing J Non-Crystalline Solids 2001291107ndash12

[206] Brida D Marangoni M Manzoni C De Silvestri S Cerullo G Two-optical-cycle pulses in the mid-infrared from an optical parametric amplifier Opt Lett 2008332901ndash3

[207] Brida D Manzoni C Cirmi G Marangoni M Bonora S Villoresi P De Silvestri S Cerullo G Few-optical-cycle pulses tunable from the visible to the mid-infrared by optical parametric amplifiers J Opt 201012013001

[208] Kippenberg TJ Holzwarth R Diddams SA Microresonator-based optical frequency combs Science 2011332555ndash9

[209] Levy JS Gondarenko A Foster MA Turner-Foster AC Gaeta AL Lipson M CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects Nat Photonics 2009437ndash40

[210] DelrsquoHaye P Herr T Gavartin E Gorodetsky ML Holzwarth R Kippenberg TJ Octave spanningtunable frequency comb from a microresonator Phys Rev Lett 2011107063901

[211] Okawachi Y Saha K Levy JS Wen YH Lipson M Gaeta AL Octave-spanning frequency combgeneration in a silicon nitride chip Opt Lett 2011363398ndash400

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[213] Herr T Brasch V Jost JD Wang CY Kondratiev NM Gorodetsky ML Kippenberg TJ Temporal solitons in optical microresonators httparxivorgabs12110733

[214] Saha K Okawachi Y Shim B Levy JS Salem R Johnson AR Foster MA Lamont MR Lipson M Gaeta AL Modelocking and femtosecond pulse generation in chip-based frequency combs Opt Express 2013211335ndash43

[215] Coen S Erkintalo M Universal scaling laws of Kerr frequency combs Opt Lett 2013381790ndash2

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[218] Coen S Randle HG Sylvestre T Erkintalo M Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato-Lefever model Opt Lett 20133837ndash9

[219] Chembo YK Menyuk CR Spatiotemporal Lugiato-Lefever formalism for Kerr-comb generation in whispering-gallery-mode resonators Phys Rev A 201387053852

[220] Foltynowicz A Mas1owski P Ban T Adler F Cossel KC Briles TC Ye J Optical frequency comb spectroscopy Faraday Discussion 201115023ndash31

[221] Hartl I Li XD Chudoba C Ghanta RK Ko TH Fujimoto JG Ranka JK Windeler RS Ultrahigh-resolution optical coherence tomography using continuum generation in an air silica microstructure optical fiber Opt Lett 200126608ndash10

[222] Brabec T Krausz F Intense few-cycle laser fields Frontiers of nonlinear optics Rev Mod Phys 200072545ndash91

[223] Hu J Meyer J Richardson K Shah L Feature issue introduction mid-IR photonic materials Opt Mater Express 201331571ndash5

[224] Private communications with Dr Jacob Levy in Prof Lipsonrsquos group and Dr Johann Riemensberger in Prof Kippenbergrsquos group

[225] Zhang J Lin Q Piredda G Boyd RW Agrawal GP Fauchet PM Anisotropic nonlinear response of silicon in the near-infrared region Appl Phys Lett 200791071113

Page 4: Lin Zhang*, Anuradha M. Agarwal, Lionel C. Kimerling and ...

250emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

chalcogenide glasses are not considered a material for the core of a waveguide one may use them for waveguide cladding and slot layer [53 58]

Linear optical properties of the materials discussed here are collected in terms of refractive index and mate-rial dispersion as shown in Figure 2 The two ldquoXrdquo on the curves for silicon and germanium in Figure 2(A) indicate the half-bandgap wavelengths The refractive index is given by the Sellmeier equations for silicon [154] silicon nitride [155] silicon dioxide [156] SRO [51] germanium [157] arsenic sulfide [158] and arsenic selenide [159] as detailed in Appendix A For SRN there is no comprehen-sive measurement of material index found currently As shown in Figure 2(A) the materials under our considera-tion have strong index contrasts especially between ger-manium and chalcogenides in the mid-IR The refractive index decreases with wavelength and beyond the half-bandgap wavelength these materials have a relatively small index change One can properly choose materials for waveguide core and cladding and also a low-index slot layer based on the information given in Figure 2(A)

Overall dispersion in an integrated waveguide con-sists of material dispersion and waveguide dispersion that

40

35

30

25

Ref

ract

ive

inde

xD

ispe

rsio

n (p

snm

middotkm

)

20

200B

A

100

-100

-200

0

15

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Wavelength (microm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Wavelength (microm)

Si

Si

Si3N4

Si3N4

As2S3

As2S3

As2Se3

As2Se3

SiO2

SiO2

SRO

SRO

Ge

Ge

Figure 2emsp(A) Refractive indices and (B) material dispersion curves of the materials considered for nonlinear Group IV photonics in the near- and mid-IR wavelength ranges

is affected by index contrast and waveguide dimensions First material dispersion is shown in Figure 2(B) which is defined as D  =  -(cλ)middot(d2nmatdλ2 ) where nmat is material index and λ and c are wavelength and the speed of light in vacuum It is important to note that except for silicon dioxide all the other materials have a flat and low disper-sion within  plusmn 100 ps(nmmiddotkm) at the long-wavelength end of the bandwidth of interest This means that if wave-guides are not designed to tightly confine guided modes one can reduce the contribution of the waveguide disper-sion and have the overall dispersion close to the flat and low material dispersion However this will cause a large effective mode area and a small nonlinear coefficient

On the other hand we note from Figure 2(B) that at the short-wavelength end of the spectrum material dispersion changes quickly with wavelength for all the considered materials even if the material refractive index looks flat in Figure 2(A) beyond the half-bandgap wave-length This is because the dispersion is the 2nd-order derivative of the index with respect to wavelength To fully use the portion of the spectrum near the half-bandgap wavelength dispersion engineering by tailoring wave-guide dispersion is required

As a measure of nonlinear material property the non-linear index n2 is shown in Figure 3 for silicon silicon nitride SRO germanium and arsenic sulfide Looking at broadband nonlinear applications one needs to take the wavelength dependence of n2 into account Unfor-tunately there is often a lack of complete measurement data at a wavelength range of interest and also measure-ment results from different groups could vary widely For silicon data from several sources are available [160 161] A recently published review paper [133] shows a predic-tion of third-order nonlinear susceptibility χ(3)

1111 for silicon and germanium in the mid-IR range based on a two-band model which is used to fit wavelength-dependent

Non

linea

r in

dex

(m2 W

)

1E-16

1E-17

1E-18

1E-191 2 3 4 5 6 7 8 9 10 11 12 13 14

Wavelength (microm)

Si

Si3N4

SROGe

As2S3

Figure 3emspThe Kerr nonlinear index n2values of the considered mate-rials in near- and mid-IR ranges

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp251

measurements We obtain the Kerr nonlinear index n2 as a function of wavelength based on χ(3)

1111 using the results from [133] As shown in Figure 3 the n2 value peaks at 19 and 27 microm for silicon and germanium respectively and changes slightly from 33 to 48 microm beyond which both TPA and 3PA disappear The TPA coefficient βTPA vs wave-length is also extracted for silicon and germanium from [133] as detailed in Tables 1ndash4 in Appendix B

Hydrogenated amorphous silicon has been identi-fied as a potentially good nonlinear material not only because of large bandgap energy of 17 eV but also more importantly because of the large nonlinear index n2 and nonlinear figure of merit (FOM) n2βTPAλ [162] We did not include specific data in Figure 3 for amorphous silicon since different groups reported highly variable n2 and nonlinear FOM values in the near-IR [31ndash35] The n2 value could be one order of magnitude higher than that in silicon [33] while the nonlinear FOM can be as high as 5 [35] although these may not be obtained simultaneously [34] Moreover linear properties of amorphous silicon may also vary when fabrication conditions and its nonlin-ear characteristics change

Silicon nano-crystals in silicon dioxide and silicon nitride have also been investigated as a nonlinear material exhibiting higher nonlinear indices than crystalline silicon by an order of magnitude or more [36ndash41] The values of n2 βTPA and nonlinear FOM are also highly variable if silicon excess annealing temperature and wavelength change We include one data point (n2 = 48 times 10-17m2W) from [38] in Figure 3 Extremely high n2and FOM by 3~4 orders have been obtained experimentally [41] with large silicon excess (note that the FOM in [41] is defined as the reciprocal of ours here)

Both amorphous silicon and silicon nano-crystals exhibit great potential as a nonlinear material in the mid-IR which can be used to compensate for the reduc-tion of the nonlinear coefficient due to a large mode area at long wavelengths In particular with a small linear refractive index SRO is often chosen as a slot material to enhance nonlinearity in the near-IR [51 53 55 56 59] while SRN exhibits a great potential for nonlinear applica-tions beyond 3 microm Typically strong nonlinearity in bulk materials is associated with a high linear refractive index which is known as Miller rule However silicon nano-crys-tals exhibit unique properties to simultaneously possess strong nonlinearity and low linear index It is important to mention that the silicon nano-crystals (ie nano-clusters) could act as scattering centers of light causing an increased propagation loss in SRO slot waveguides Nevertheless relatively low propagation loss has been achieved which is 3~5 dBcm [163]

For silicon nitride one data point n2 = 24 times 10-19m2W from [111] is included in Figure 3 which was measured at 155 microm and is one-order lower than that in silicon Silicon dioxide has an n2 value around 26 times 10-20m2W in 155 microm as in single-mode optical fibers two orders lower than that in silicon A higher n2 value (115 times 10-19m2W) is estimated for 155 microm in high-index doped silica [164] Both values are not shown in Figure 3 Since both silicon nitride and silicon dioxide have large bandgap energies it is expected that their n2 values are almost constant over wavelength in the near- and mid-IR

Strong Kerr nonlinearities are obtained in chalcoge-nide glasses (arsenic sulfide and arsenic selenide) with negligible TPA from the near- to mid-IR as shown in Figure 1 We have found wavelength-dependent measure-ments of the nonlinear index n2 for arsenic sulfide from different data sources [150 165ndash174] As shown in Figure 3 although slightly scattered these n2 values in arsenic sulfide are as high as those in silicon and would not be strongly wavelength-dependent beyond 155 microm because it is longer than the half-bandgap wavelength Arsenic selenide has even higher n2 values than arsenic sulfide [173] and its n2 value is predicted as a function of wave-length in [175]

There has been little published on the wavelength dependence of the nonlinear Raman gain coefficient gR in literature for the materials that we consider here [133] Since SRS is not the major nonlinear effect that is used in this paper we will not discuss it in details here

Although the considered materials such as silicon germanium silicon nitride and silicon dioxide are cen-trosymmetric and show no second-order nonlinearity in bulk materials one can engineer them by applying strain [176ndash178] or forming interfaces between two centrosym-metric materials (eg between germanium and silicon [179] or between silicon nitride and silicon dioxide [180]) An alternative way is to integrate other materials with strong second-order susceptibility onto Group IV wave-guides (see eg [145]) For chalcogenide glasses different poling schemes are proposed to produce the second-order nonlinearity [181] The second-order susceptibility χ(2) induced to the Group IV platform can have a highly variable value depending on how the isotropy of materi-als is broken We believe that second-order nonlinearity is promising in nonlinear Group IV photonics but in this paper we will mainly focus on third-order nonlinearity

As described above the materials presented here have greatly different transparency windows and nonlin-ear coefficients It thus becomes critical to wisely choose a material combination for a specific application and doing this one may also need to pay special attention to material

252emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

compatibility in device fabrication On the other hand compared to the material choices device design (mainly on waveguide and resonator) can also produce widely var-iable dispersion and nonlinearity properties In the next section we will discuss enhanced waveguide properties using improved designs

3 DevicesOptical waveguides form the backbone of photonic devices Light propagation properties in a waveguide could be remarkably different from those in corresponding bulk materials especially when there is a high index con-trast between waveguide core and surrounding cladding Therefore understanding and optimizing the waveguide properties including loss dispersion and nonlinearity are essential in nonlinear photonics

Propagation loss in a waveguide includes material loss confinement loss scattering loss and nonlinear loss Working at a transparency window of a material especially beyond the half-bandgap wavelength one can primarily have low material and nonlinear loss caused by TPA Note that benefiting from the wide multi-octave bandwidth in the mid-IR one can even eliminate the impact of 3PA in silicon and germanium by pumping at  gt 33 microm and  gt 48 microm respectively Since the substrate index in a silicon wafer is higher than or equal to that in most of materials we consider for a waveguide core con-finement loss exists due to mode leakage to the silicon substrate This loss can be markedly reduced by increas-ing the spacing between waveguide core and the substrate or choosing low-index material between them In general scattering loss due to sidewall roughness of a waveguide is dominant in high-index-contrast silicon photonics which is mainly caused in device fabrication and can thus be reduced by improving the fabrication processes [182ndash184]

Compared to propagation loss chromatic disper-sion and nonlinearity in integrated waveguides are more de signable Since the dispersion is the second-order deriv-ative of the effective index with respect to wavelength it is particularly tailorable by changing waveguide shape and dimension Moreover dispersion has been recognized to be critical for broadband nonlinear effects [12 14 15 60 61 92ndash108 112ndash115 137ndash145] which is true especially for ultrafast octave-spanning applications [185] Spec-tral characteristics in a dispersion profile including the number and positions of zero-dispersion wavelengths (ZDWs) and dispersion slope greatly affect and often set the limit on the bandwidth of optical spectra the temporal

widths of pulses and conversion efficiency in nonlinear interactions [185] Generally speaking a flat dispersion profile (ie third- and higher-order dispersion terms are small) with low dispersion values is preferred

In conventional ultrafast nonlinear optics in a free-space setup many components were developed to control dispersion over a wide bandwidth [185 186] such as prisms gratings chirped mirrors and so on However in a waveguiding system eg in fiber-based ultrafast optics the dispersion-control toolkit is smaller and engineer-ing waveguide dispersion becomes critical In particular when waveguides are built on a silicon platform with a much higher index contrast than optical fibers dispersion in a highly nonlinear waveguide [187ndash190] often shows strong wavelength dependence which is not preferable for wideband nonlinear applications In [187 190] the ZDW in silicon rib and strip waveguides is mapped by scanning waveguide dimensions It is shown that tight confinement of a guided mode produces a ZDW in its dispersion profile around 12~14 μm close to the bandgap wavelength More-over even if the waveguide size is increased to move the ZDW to longer wavelength the dispersion slope near the ZDW is not small as shown in [187ndash189] causing a limited low-dispersion bandwidth

Recently a dispersion engineering technique for integrated high-index-contrast waveguides has been pro-posed in which an off-center nano-scale slot controls modal distribution at different wavelengths [59 60] The guided mode experiences a transition from strip-mode like to slot-mode like as wavelength increases This approach can produce a very flat dispersion profile over an ultra-wide bandwidth with dispersion flatness improved by 1ndash2 orders in terms of dispersion variation divided by low-dispersion bandwidth More importantly it is applicable to different material combinations and wavelength ranges [59ndash63]

Towards mid-IR applications different types of Group IV waveguides have been reported recently based on silicon-on-insulator (SOI) [191ndash193] silicon-on-sapphire [142 194 195] silicon-on-porous-silicon [192] silicon-on-nitride [196 197] suspended membrane silicon [198] silicon pedestal [199] and germanium-on-silicon [200] Most of the waveguides are not aimed specifically at non-linear applications and little attention has been paid to dispersion engineering [196]

In this section we survey different structures of Group IV waveguides for broadband nonlinear applica-tions from the near- to mid-IR There are three main goals in waveguide designs (i) we consider joint optimization on both dispersion and nonlinearity properties (ii) we tend to fully utilize the available bandwidth brought by

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp253

the materials in Figure 1 and (iii) we emphasize disper-sion engineering naturally as a result of aiming at octave-spanning broadband applications

Figure 4 shows a general illustration of various types of integrated waveguides for nonlinear Group IV photonics Looking at a specific wavelength range one can accord-ingly choose a materials combination for an appropriate index contrast and a desired level of nonlinearity Note that one may need low nonlinearity in some cases when high-power output is required Here we discuss waveguide design at four different wavelength ranges as follows

First we consider SOI waveguides for a wavelength range from the telecom window in the near-IR to the short-wave end in the mid-IR ie roughly from 14 to 25 microm This is the wavelength range that many of the current research efforts have been addressing [60 61 106 108 114 115 135 137 139ndash141 143 144] In this wavelength range a SOI strip waveguide as shown in Figure 4 can be used with air as an upper cladding (see eg [140]) One can change the width of the waveguide to tailor its disper-sion profile while the height of the waveguide is 220 nm set by SOI wafers From Figure 5(A) we note that a rela-tively small width W = 800 nm is corresponding to a dis-persion profile with two ZDWs at 1585 and 2345 microm and a peak value of anomalous dispersion 532 ps(nmmiddotkm) at 205 microm for the quasi-TE mode The anomalous disper-sion is typically useful for parametric amplification and oscillation soliton and soliton-based supercontinuum generation [12] With W  =  900 nm one can have a flatter dispersion profile but the anomalous band is smaller When W is increased to 1000 nm the dispersion is even flatter but no anomalous dispersion occurs Figure 5(A) shows a good example that tight mode confinement in a strip waveguide moves ZDW to short wavelengths and near ZDWs dispersion changes quickly with a large slope

Strip WG

Strip WG suspended

Air Air

Slot

Core

Upper cladding

Slab

Lower cladding

Si substrate

Slot WG suspended

Slot WG Rib WG

Figure 4emspDifferent types of Group IV waveguides (WGs) for disper-sion and nonlinearity engineering in the near- and mid-IR ranges

One can calculate the nonlinear coefficient γ as a function of wavelength with the nonlinear Kerr index n2 given in Tables 1ndash4 in Appendix B We show in Figure 5(B) that the nonlinear coefficient in the silicon strip wave-guide with W = 900 nm first increases to 187 (mmiddotW) with wavelength until 17 μm and then decreases to 56 (mmiddotW) at 25 μm This is caused by both the peaking of the silicon n2 value near 19 μm and the gradual increase of wave-length and mode area beyond that

A silicon stripslot hybrid waveguide exhibits very flat dispersion as presented in Figure 5(A) The SOI waveguide has crystalline silicon at the bottom a thin SRO slot and amorphous silicon at the top The upper cladding is silicon dioxide When setting the lower Si height to Hl = 430 nm slot height to Hs = 54 nm upper Si height to Hu = 160 nm and width to W = 660 nm we obtain an extremely flat disper-sion profile for the quasi-TM mode over a wide bandwidth between two ZDWs at 1545 and 2448 microm From 1605 to 238 microm the value of anomalous dispersion changes between 30 and 46 ps(nmmiddotkm) In this way one can have a flat and low anomalous dispersion between two far apart ZDWs The average dispersion value can be shifted by increasing Hu to move dispersion between normal and anomalous regimes Detailed explanation on how the flat-tened and saddle-shaped dispersion profile is produced is given in [59 60] Briefly the mode transition over wave-length for the quasi-TM mode is responsible for this behav-ior Due to the off-center slot the mode is mostly confined in the crystalline silicon at short wavelengths while the mode becomes more like a slot mode at long wavelengths As shown in Figure 5(C) we plot the mode power distribu-tions at wavelengths of 15 183 217 and 25 microm The mode transition adds negative dispersion in the middle of the low-dispersion bandwidth as explained in [60 201]

Having a slot one has an opportunity to fill the slot with highly nonlinear materials into it [49 51 53 55 56 58 59] which can overcome the decrease of the nonlinear coeffi-cient over wavelength In Figure 5(B) we show the γ value increasing to 306 (mmiddotW) with wavelength from 14 to 25 microm This is because the guided mode extends more to the highly nonlinear thin slot layer Note that the used n2 value in SRO [38] is currently the one measured at 155 microm so the n2 and γ thinspvalues may vary in the mid-IR but the trend is general

Next we explore the short-wavelength end of the near-IR spectrum Silicon-based devices become unus-able for nonlinear photonics as wavelength decreases to 11 microm and we thus look at silicon nitride for near-IR nonlinear applications extending to the visible light spec-trum Again a strip waveguide based on silicon nitride is examined first Figure 6(A) shows dispersion curves of the quasi-TE mode in two waveguides sized to be 1300 times 540

254emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

and 1400 times 800 nm2 The upper cladding is air and the lower cladding is silicon dioxide The anomalous disper-sion region in the dispersion curves shrinks when the waveguide is made smaller This is because of a relatively small index contrast between silicon nitride and silicon dioxide which makes the guided mode leak quickly to the substrate as wavelength increases For the strip waveguide with a cross-section of 1400 times 800 nm2 there are two ZDWs near 10 and 23 microm but one can see a strong dispersion of 250 ps(nmmiddotkm) between the two ZDWs in Figure 6(A) The nonlinear coefficient in the second silicon nitride wave-guide is shown in Figure 6(B) which is much smaller than that in silicon waveguides because of a one-order smaller n2 value and larger Aeff in the silicon nitride waveguide At 16 microm γ is about 123(mW)

One can also use a stripslot hybrid structure to tailor the dispersion profile in silicon nitride waveguides For example the slot and lower cladding are silicon dioxide and the upper cladding is air In Figure 6(A) we show the dispersion curves in two silicon nitride stripslot hybrid waveguides for comparison The waveguide 1 has Hl = 900 nm Hs = 124 nm Hu = 340 nm and W = 1000 nm and the waveguide 2 has Hl = 920 nm Hs = 154 nm Hu = 480 nm and W = 1300 nm These two waveguides produce increasingly flatter dispersion profiles as shown in Figure 6(A) The first waveguide has two ZDWs located at 106 and 22 microm with the peak dispersion of 67 ps(nmmiddotkm) The second waveguide has two ZDWs at 115 and 235 microm with the dispersion varying within 0~20 ps(nmmiddotkm) This octave-spanning dispersion flattening with different levels

1000A

B

C

500

-500

400

300

200

100

0

-100014 16

Strip WG W=800 nmStrip WG W=900 nm

Strip WG W=900 nm

Strip WG W=1000 nm

Slot WG Hu=160 nm

Slot WG Hu=160 nm

Slot WG Hu=163 nmSlot WG Hu=166 nm

18 20 22Wavelength (microm)

Dis

pers

ion

(ps

nmmiddotk

m)

Non

linea

r co

effic

ient

(m

middotW)

24 26

14 16 18 20 22

Wavelength (microm)

24 26

0

Figure 5emspIn a wavelength range from the telecom window in near-IR to the short-wave end in the mid-IR silicon strip and stripslot hybrid waveguides (WGs) are analyzed in terms of (A) dispersion and (B) nonlinearity (C) Mode power distributions at wavelengths of 15 183 217 and 25 microm in the stripslot hybrid waveguide

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp255

of dispersions can be used for multiple applications as detailed in the next section The nonlinear coefficients for the two waveguides are shown in Figure 6(B) We note that the stripslot hybrid waveguides have similar nonlinear coefficients as the strip waveguide which shows that the dispersion profile is much more tailorable by waveguide designs

Then we move to the mid-IR using silicon and silicon nitride for waveguiding A comparison of different types of silicon-on-nitride waveguides have been presented in [196] where rib waveguides were preferred due to the wideband low dispersion over an octave-spanning band-width from 24 to 66 microm for the quasi-TE mode This is a spectral range from siliconrsquos half-bandgap wavelength to the cut-off wavelength of silicon nitride In Figure 7(A) we plot the dispersion curve for a silicon-on-nitride rib waveguide with air as the upper cladding the rib width of 2000 nm the total height of 1200 nm and the slab height of 1000 nm which are the same parameters used in [196] It is shown that less confinement of optical modes reduces the contribution of waveguide dispersion and makes the overall dispersion profile closer to the material dispersion which is flat and low at long wavelengths as in Figure 2(B)

A

B

400

300

200

100

-100

8

6

4

2

0

0

Strip WG 1300times540 nm2

Strip WG 1400times800 nm2

Strip WG 1400times800 nm2

Slot WG 1Slot WG 2

Slot WG 1Slot WG 2

Dis

pers

ion

(ps

nmmiddotk

m)

Non

linea

r co

effic

ient

(m

middotW)

20 3010 15 2505Wavelength (microm)

2010 15 2505

Wavelength (microm)

Figure 6emspIn a wavelength range moved toward the short-wave-length end of near-IR spectrum silicon nitride strip and stripslot hybrid waveguides are designed in terms of (A) dispersion and (B) nonlinearity

Accordingly the nonlinear coefficient is small 285 (mmiddotW) at 3 microm as shown in Figure 7(B)

On the other hand if one needs a small Aeff to enhance nonlinearity additional dispersion tailoring (eg based on stripslot hybrid waveguides) would be beneficial Pursuing a higher nonlinear coefficient we use a 500-nm silicon nitride suspended membrane as illustrated in Figure 4 to support a silicon stripslot hybrid waveguide This helps confine light in the waveguide core Using W = 880 nm Hu = 550 nm Hs = 87 nm and Hl = 840 nm we obtain a saddle-shaped anomalous dispersion from 19 to 449 microm within 0~60 ps(nmmiddotkm) for the quasi-TM mode as shown in Figure 7(A) This structure produces much tighter mode confinement than the rib waveguide and exhibits a 3 times larger nonlinear coefficient in Figure 7(B) while having similar dispersion flatness

Finally we consider germanium-on-silicon wave-guides over a wavelength range from 33 to 85 microm between the half-bandgap wavelength of germanium and the cut-off wavelength of silicon This type of waveguide has been demonstrated with strain-free mono-crystal-line germanium [200] Here we assume that the germa-nium waveguide has a 10-nm silicon nitride layer on its

A

B

200

-200

60

40

20

0

100

-100

0

Rib WGSlot WG

Rib WGSlot WG

Dis

pers

ion

(ps

nmmiddotk

m)

Non

linea

r co

effic

ient

(m

middotW)

1 2 3 4 5 6 7Wavelength (microm)

1 2 3 4 5 6 7

Wavelength (microm)

Figure 7emspIn a wavelength range from the short-wave IR to mid-IR silicon rib waveguide on silicon nitride and stripslot hybrid waveguide on a suspended membrane are analyzed in terms of (A) dispersion and (B) nonlinearity

256emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

surface for passivation The upper cladding could be air or silicon which provides significantly different dispersion properties due to a varied index contrast For comparison only we also have silicon nitride as the upper cladding although silicon nitride becomes lossy for wavelengths longer than 67 microm Figure 8(A) shows the dispersion pro-files of four germanium-on-silicon strip waveguides with equal size 3000 times 1600 nm2 for the quasi-TE mode Air and silicon nitride as an upper cladding result in similar shape and bandwidth in the dispersion profiles Thus the air-cladded waveguide is chosen and discussed further The waveguide with silicon upper cladding has normal dispersion at all wavelengths since there is a relatively small index contrast between germanium and silicon and thus weak mode confinement A germanium strip wave-guide on a 600-nm-thick silicon suspended membrane is also considered to increase light confinement with an air upper cladding to maximize light confinement However as mentioned earlier strong confinement typically causes strong dispersion as shown in Figure 8(A) and therefore the germanium waveguide on a silicon membraneis not chosen for broadband nonlinear applications In contrast the germanium strip waveguide with air upper cladding exhibits a flat and low dispersion

The dimensions of the air-cladded germanium wave-guide are varied by simultaneously changing its height and width with a step of 200 nm for both polarization states It is interesting to see from Figure 8(B) and 8(C) that the dispersion peak value remains nearly unchanged for all the waveguide sizes although we have a widely tunable ZDW at long wavelengths For the quasi-TE mode the right ZDW moves from 605 microm to 841 microm while the left ZDW is always near 4 microm We can thus obtain an octave-spanning anomalous dispersion band with the peak value below 100 ps(nmmiddotkm) For the quasi-TM mode one can see similar dispersion properties but the anomalous disper-sion band is smaller Thus we choose the quasi-TE mode for further discussion in next section

The nonlinear coefficient in the germanium wave-guides for the quasi-TE mode is shown in Figure 8(D) which is about 10(mmiddotW) at 5 microm with a small variation for differ-ent waveguide sizes This is quite high considering that both wavelength and effective mode area become much larger over this wavelength range compared to the near-IR

From above we can see that the stripslot hybrid wave-guides enable unique controllability of dispersion and that this concept is applicable to different wavelength ranges However their performance may be sensitive to fabrication errors especially for inaccuracies in slot height Hs [59 60] A higher yield in device fabrication is expected using advanced fabrication technologies and facilities

A

C

D

B

400

300

200

100

-100

-200

0

Ge WG+air 3000times1600 nm2

Ge WG+air suspended 3000times1600 nm2

Ge WG+Si3N4 3000times1600 nm2

Ge WG+Si 3000times1600 nm2

Ge WG+air 2800times1400 nm2

Ge WG+air 3000times1600 nm2

Ge WG+air 3200times1800 nm2

Ge WG+air 3400times2000 nm2

Ge WG+air 2800times1400 nm2

Ge WG+air 3000times1600 nm2

Ge WG+air 3200times1800 nm2

Ge WG+air 3400times2000 nm2

Ge WG+air 2800times1400 nm2

Ge WG+air 3000times1600 nm2

Ge WG+air 3200times1800 nm2

Ge WG+air 3400times2000 nm2

Dis

pers

ion

(ps

nmmiddotk

m)

400

300

200

100

-100

-200

0

Dis

pers

ion

(ps

nmmiddotk

m)

400

300

200

100

-100

-200

50

40

30

20

10

0

0

Dis

pers

ion

(ps

nmmiddotk

m)

Non

linea

r co

effic

ient

(m

middotW)

3 4 5 6 7 8 9Wavelength (microm)

3 4 5 6 7 8 9Wavelength (microm)

3 4 5 6 7 8 9

Wavelength (microm)

3 4 5 6 7 8 9

Wavelength (microm)

Figure 8emspIn a wavelength range covering the main part of the mid-IR spectrum (A) on silicon substrate or on suspended silicon membrane are analyzed in terms of dispersion Germanium-on-silicon strip waveguides with an air upper cladding and different dimensions are characterized by (B) dispersion for the quasi-TE mode (C) dispersion for the quasi-TM mode and (D) nonlinearity for the quasi-TE mode

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp257

Besides photonic waveguides another important cat-egory of nonlinear devices is integrated resonators In the scope of this paper we consider relatively large resona-tors for frequency comb generation in which the bending radius of a ring resonator is varied from 50 microm to 100 microm depending on free spectral range (FSR) and the group index in the waveguide In these cases the waveguide-bending-induced dispersion is small and we would not discuss intra-cavity dispersion [202 203] in details here

4 ApplicationsBenefiting from the unique dispersion engineering over an octave-spanning bandwidth as described above one can develop ultra-wideband nonlinear applications that could hardly be attained in an integrated platform previously These include octave-spanning supercontinuum genera-tion pulse compression to a few-cycle or even sub-cycle level octave-spanning Kerr frequency comb generation and the associated mode-locked ultrashort pulse genera-tion using microresonators In this section we review our recent work on these topics

First we discuss the supercontinuum generation and pulse compression in a straight waveguide The nonlinear envelope equation used here to simulate supercontinuum generation is the following

βα infin

=

part part+ + = + part part sum

2

( - )( ) ( )

2

m mm

mm

ii A K A R A

z m t (1)

where

2

0 0

- -( ) 1- ( ) 2

n nn

nn

i i iK A A An t tγ δ δ

ω δ δ

infin

=

= sum

and

2shock_R( ) - 1- [ ( - ) | | ]δ

γ τδ minusinfin

= prime prime int

t

R RR A i i A h t t A dtt

We denote A  =  A(zt) as the complex amplitude of an optical pulse Note that its Fourier transform is

-

1( ) ( ) exp( - ) 2

A z A z t i t dtω ωπ

infin

infin

= int

In Eq (1) α is the total propagation loss and βm is the mth-order dispersion coefficient The frequency dependence of nonlinearity parameters including the nonlinear index n2 the TPA coefficient βTPA and the

effective mode area Aeff is included in the nth-order dis-persion coefficient γn of nonlinearity which is defined as γn = ω0middotpartn[γ(ω)ω]partωn where ω0 is the angular frequency of the carrier Therefore we can consider all-order linear dispersion terms and all-order dispersion of the nonlin-ear coefficient in Eq (1) Specifically in the simulations for a silicon and silicon nitride waveguides we have all-order linear dispersion and up to 6th-order and 2nd-order of the nonlinear coefficient dispersion included A detailed derivation of Eq (1) is given in [204] For the quasi-TM mode that experiences the engineered dispersion due to the mode transition SRS in silicon waveguides fabricated on the (001) surface can be ignored [27 96] For silicon nitride waveguide we include the SRS term in Eq (1) where γR = gRΓR(AeffΩR) and gR ΓR and ΩR represent the Raman gain coefficient the full width at half maximum of the gain spectrum and the Raman shift respectively The Raman shock time τshock_R is associated with γRrsquos fre-quency dependence which is 1ω0-[1Aeff(ω0)][dAeff(ω)dω] similarly as in [14] if we ignore frequency dependent gR ΓR and ΩR hR(t) is the Raman response function and it corresponds to the Raman gain spectrum

2

2 20 0

( ) -( - ) 2 ( - )

Ωω

Ω ω ω Γ ω ω=

+R

RR R

Hi

Note that the sign before the imaginary unit is differ-ent from that in [27] to be consistent with the expression of the Fourier transform that we used

We have considered supercontinuum generation in both silicon and silicon nitride waveguides with the slot-assisted dispersion tailoring Octave-spanning supercon-tinua in a silicon-based stripslot hybrid waveguide have been investigated in detail in [108] in which two-cycle optical pulses are obtained The main results in that work are shown in Figure 9 for comparison purposes

Here we mainly focus on the supercontinuum gen-erated in the silicon nitride stripslot hybrid waveguide (ie the slot WG 1 in Section III) whose dispersion and nonlinearity properties are shown in Figure 6 In the non-linear simulations we set the total propagation loss to be 1 dBcm The SRS parameters used here are the following [205] ΩR2π = 143 THz ΓR2π = 172 THz and gR = 1 times 10-12 mW τshock_R is calculated to be  = 156 fs

In our simulations we use a time step of 025 fs which is corresponding to a bandwidth of 4000 THz in the fre-quency domain For a femtosecond input pulse we set the time window length to 50 ps (ie frequency resolution Δf = 20 GHz)

We simulate the nonlinear propagation of a chirp-free hyperbolic secant pulse in the silicon nitride waveguide

258emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

The pulse center wavelength is at 1610 nm and its full width at half-maximum (FWHM) T0 is 120 fs Its peak power is 1200 W corresponding to pulse energy of 016 nJ

Figure 10(A) shows the supercontinua at different propagation distances At 48 mm the spectrum is greatly broadened at the -30 dB level covering a wavelength range from 0585 to 2833 microm which is more than two octaves The spectrum evolution in Figure 10(A) shows a similar spectrum shape as that in Figure 9(A) both featuring a ldquotriangularrdquo central spectrum bounded by two dispersive waves at the edges However it is important to note that the absence of TPA and 3PA in silicon nitride at the telecom window leads to a much more efficient spectrum broad-ening than that in silicon [108] The generated spectrum extends from the visible light to the mid-IR with excellent spectral coherence which is confirmed by the pulse wave-form shown in Figure 10(B) In the time domain the pulse is greatly compressed from 120 to 408 fs corresponding to 076 optical cycles at 161 microm wavelength

We examine the pulsewidth as a function of propa-gation distance Figure 11 shows that the pulse becomes increasingly narrower until the propagation distance reaches 47 mm For longer distances the pulsewidth

A

B

60 mm

48 mm

36 mm

24 mm

12 mm

Input

Spe

ctru

m (

10 d

Bd

iv)

Pow

er (

W)

12

246

24

18

12

6

0

248 250 252 254

14 16 18 20 22 24Wavelength (microm)

Time (ps)

Figure 9emsp(A) The supercontinuum generation in a silicon-based stripslot hybrid waveguide presented in [108] (B) The significant spectrum broadening at 425-mm distance is associated with a temporal compression of an input pulse (dash line) to the output waveform (solid line) with a FWHM of 12 fs

A

B

50 mm

48 mm

46 mm

44 mm

42 mm

Input

Spe

ctru

m (

10 d

Bd

iv)

Pow

er (

W)

8000

6000

4000

2000

0250249 251

06 09 12 15 18 21 24 27

Wavelength (microm)

Time (ps)

Figure 10emsp(A) Spectrum evolution of the pulse over propagation distance A supercontinuum of more than two octaves is achieved at 48 mm distance (B) Generated pulse waveform with a pulse width of 408 fs as short as 076 optical cycles Low pedestals are caused by dispersive waves generated at the two ends of the spectrum

remains almost constant However it is important to mention that after 48 mm the dispersive waves become increasingly stronger as shown in Figure 10(A) causing larger pedestals

Comparing the results in Figures 9 and 10 we note that the mid-IR wavelength range for silicon would be in analogy to the near-IR for silicon nitride in terms of non-linear optics operations Pumping at or beyond 33 microm one can use the waveguide designs shown in Figure 7 to produce very efficient nonlinear interactions without TPA and 3PA in silicon Ultrashort pulses in the mid-IR from parametric amplifiers [206 207] could be used to pump the Group IV waveguides

Another nonlinear application of the dispersion-engi-neered Group IV waveguides is micro-resonator-based Kerr frequency comb generation When such a waveguide is curved to form a microring resonator input CW light travels around the cavity and amplifies the noise in the source located at the frequencies with a high parametric gain As a result of modulation instability and cascaded FWM in the cavity a frequency comb can be generated [208ndash211] Mode-locked frequency combs have been reported pro-ducing low-noise pulse trains in time domain [212ndash214]

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp259

The formation of cavity solitons is identified as the main reason for the mode-locking in the Kerr frequency combs [215] This is instructive because one can thus predict the spectral bandwidth and temporal pulsewidth in the generated low-noise combs The 3-dB comb bandwidth is inversely proportional to the square root of the 2nd-order dispersion coefficient |β2| as given in [213 215] It is desira-ble that all comb lines that constitute the soliton spectrum experience the same |β2| In this sense the stripslot hybrid waveguides with flattened dispersion are preferably suit-able for supporting broadband Kerr comb generation and ultra-short cavity soliton generation

The Kerr frequency comb generation can be modeled using the generalized Lugiato-Lefever equation (LLE) [216ndash219]

20

2

( - )- - | |

2 2

m mm

R inmm

jkt j jl E kE j l E Et m

βαδ γ

τ

infin

=

part part+ + + = part part

sum (2)

where tR is the round-trip time E = E(tτ) and Ein are intra-cavity field and input field (pump power Pin  =  |Ein|2) t and τ are the slow and fast times δ0 is the cavity phase detuning defined as δ0  =  tRmiddot(ωn -ω0) where ω0 and ωn are the pumprsquos angular frequency and the nth angular reso-nance frequency that is pumped Other resonator param-eters include the power loss per round trip α the power coupling coefficient κ the nonlinear coefficient γ and the mth dispersion coefficient βm Since a flattened dispersion profile has a small β2 over a wide bandwidth it is impor-tant to take the influence of higher-order dispersion into account We include all-order dispersion terms in Eq (2) as we did in solving Eq (1)

To enhance the Kerr comb bandwidth in the near-IR we use the ultra-flattened dispersion profile in Figure 6(A) which is obtained in the slot WG 2 based on

Pul

se w

idth

(fs

)

14

12

10

8

6

4

242 44 46 48 50 52

Propagation distance (mm)

Figure 11emspPulse width first decreases with propagation distance and then remains stable After 48 mm dispersive waves get stronger causing more pedestals

Pow

er (

10 d

Bd

iv)

Pow

er (

W)

70A

B

60

50

40

30

20

10

-10

-20

600

400

200

0

80 120

0575 0600 0625 0650

160 200 240 280 320 360

0

Frequency (THz)

Time (ps)

Figure 12emsp(A) Frequency comb generation with a CW pump at 155 microm using a microring resonator based on a silicon stripslot hybrid waveguide Over an octave-spanning bandwidth from 135 to 270 THz the comb lines have a power drop of 20 dB (B) Generated pulse waveform with a pulse width of 82 fs as short as 16 optical cycles

silicon nitride The ring resonator has a bending radius of 104 microm corresponding to a FSR of 200 GHz Pumping near 155 microm with a pump power of 2 W the resonance peak is red-shifted and we need to red-shift the pump wavelength accordingly and tune it into the resonance from the short-wavelength side When the pump is step-by-step tuned by up to 63 resonance linewidths we obtain the comb spectrum and the mode-locked pulse waveform as shown in Figure 12 One can see that over an octave-spanning bandwidth from 133 to 268 THz the comb lines have a power drop by 20 dB from the center of the spectrum The spectral flatness of this comb is relatively good compared to the previously reported results [208ndash211] The comb bandwidth at -40 dB is as wide as two octaves There are two dispersive peaks in normal dispersion regions beyond the low-dispersion band Such a mode-locked broadband comb produces a train of sub-two-cycle optical pulses as shown in Figure 12(B) with one pulse per round trip The peak power of the pulse is up to 600 W Nonlinear conver-sion efficiency is estimated to be -267 dB

To generate frequency combs in the mid-IR the ger-manium-on-silicon strip waveguide is chosen We choose

260emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

a cross-section of 3200 times 1800 nm2 which has an octave-spanning low-dispersion band from 4 to 767 microm as shown in Figure 8(B) A germanium ring resonator is formed with a bending radius of 564 microm corresponding to a FSR of 200 GHz Pumping at 6 microm with a CW power of 14 W and detuning the pump wavelength by 10 resonance linewidth one can see that a mode-locked wideband mid-IR comb is generated from 358 to 644 THz (ie from 466 to 838 microm) at -40 dB level The FWHM of the produced pulses is 69 fs which corresponds to ~35 optical cycles The pulse peak power is 184 W and the nonlinear conversion efficiency is estimated to be -143 dB Since the pumping frequency is not at the center of the low-dispersion band we only see one peak in the comb spectrum caused by the dispersive wave in the normal dispersion region from Figure 13(A) There is another peak at higher frequencies beyond what is shown in the figure

As shown above broadband dispersion engineering is critical for octave-spanning nonlinear applications in both near- and mid-IR wavelength ranges which enables us to fully utilize the bandwidth allowed by the materials transparency windows Generally speaking the nonlinear applications mentioned here such as supercontinuum generation ultrafast pulse compression and frequency comb generation are often the intermediate steps towards higher-level system applications In the frequency domain a wide spectrum can serve as an electromagnetic carrier to acquire high-volume of information eg for sensing [220] and imaging [221] In the time domain an ultrashort pulse can be used as probe to sample ultrafast phenomena [222]

5 Summary and OutlookWe have presented a review of our recent work on nonlin-ear photonics based on silicon and germanium Various types of Group IV waveguides are analyzed and optimized for four different wavelength ranges from near- to mid-IR The recently proposed dispersion engineering technique based on stripslot hybrid waveguide structures is used for different material combinations and wavelength ranges Numerical simulations show that the dispersion-flattened Group IV waveguides are preferably suitable for octave-spanning nonlinear applications including on-chip supercontinuum generation ultrashort pulse compres-sion and mode-locked wideband frequency comb genera-tion based on micro-resonators

The presented approach to achieving octave-span-ning nonlinear applications on an integrated CMOS-compatible Group IV platform holds great potential for realizing chip-scale sensing imaging communications and signal processing system The ultrawide transparency windows in the mid-IR allowed by Group IV elements and compounds potentially together with other materi-als [223] provide an exciting arena for building powerful information acquisition and processing units enabled by nonlinear optics nano-photonics and ultrafast optics

Received June 14 2013 accepted October 29 2013 previously pub-lished online November 27 2013

Pow

er (

10 d

Bd

iv)

A

8030 40 50 60 70Frequency (THz)

Pow

er (

W)

B200

150

100

50

0

21 22 23 24 25Time (ps)

Figure 13emsp(A) Frequency comb generation with a CW pump at 6 microm using a microring resonator based on a germanium strip waveguide with air upper cladding (B) Generated pulse waveform with a pulse width of 69 fs as short as 35 optical cycles

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp261

Appendix

A Material index and dispersion

In this section we give the wavelength-dependent mate-rial index expressed as Sellmeier equations where wave-length λ is in μm

For silicon we use the following material index that is a fit curve from measurement results at room temperature (293 K) with 184 data points in total from 112 to 588 μm [154]

22 1 2 2

2 2 22

( )-

C Cn

λλ ε

λ λ λ= + +

where ε = 116858 C1 = 0939816 μm2 C2 = 000810461 and λ2 = 11071 μm

For silicon nitride the material index is affected by deposition conditions using plasma-enhanced chemical vapor deposition (PECVD) low-pressure chemical vapor deposition (LPCVD) and so on We use the following Sell-meier equation [155] which predicts the material index close to that in LPCVD silicon nitride films measured by a few groups [224]

22 1

2 21

( ) 1-

Cn

λλ

λ λ= +

where C1 = 28939 and λ1 = 013967 μmFor silicon dioxide we use the following Sellmeier

equation for fused silica [156]22 2

2 31 22 2 2 2 2 2

1 2 3

( ) 1- - -

CC Cn

λλ λλ

λ λ λ λ λ λ= + + +

where C1 = 06961663 C2 = 04079426 C3 = 08974794 λ1 = 00684043 μm λ2 = 01162414 μm and λ3 = 9896161 μm

For SRO the material index is affected by deposition conditions such as silicon excess annealing temperature and so on Here we choose the one with silicon excess of 8 and annealed at 1250oC [51]

22 22 31 2

2 2 2 2 2 21 2 3

( ) 1- - -

CC Cn

λλ λλ

λ λ λ λ λ λ= + + +

where C1 = 001 C2 = 196 C3 = 141 λ1 = 03 μm λ2 = 007071 μm and λ3 = 2775968 μm

For germanium the temperature-dependent mate-rial index was measured [157] Here we choose the one for room temperature (293 K)

2 22 1 2

2 2 2 21 2

( )- -

C Cn

λ λλ ε

λ λ λ λ= + +

where ε = 928156 C1 = 67288 C2 = 021307 λ1 = 0664116 μm and λ2 = 6221013 μm

For arsenic sulfide we use the material index pro-vided in [158]

2 2 22 22 3 4 51 2

2 2 2 2 2 2 2 2 2 21 2 3 4 5

( ) 1- - - - -

C C CC Cn

λ λ λλ λλ

λ λ λ λ λ λ λ λ λ λ= + + + + +

where C1 = 18983678 C2 = 19222979 C3 = 08765134 C4 = 01188704 C5 = 09569903 λ1 = 015 μm λ2 = 025 μm λ3 = 035 μm λ4 = 045 μm and λ5 = 27386128 μm

For arsenic selenide we fit ellipsometry measure-ments of our arsenic selenide thin films and the bulk material is provided by Prof Kathleen A Richardson group

22 22 31 2

2 2 2 2 2 21 2 3

( ) 1- - -

CC Cn

λλ λλ

λ λ λ λ λ λ= + + +

where C1 = 298463 C2 = 321011 C3 = 100182 λ1 = 044118 μm λ2 = 0000354953 μm and λ3 = 38413 μm

B Nonlinear Kerr index n2

The third-order nonlinear susceptibility χ(3)1111 for silicon and

germanium is predicted over the mid-IR range [133] based on a two-band model The effective nonlinear susceptibil-ity χ(3) is dependent on polarization and crystallographic orientation [225] For strong nonlinearity we consider a single-polarization incident light aligned to the crystal-lographic axis and we have χ(3) = χ(3)

1111 To investigate the octave-spanning nonlinear phenomena one need to take the wavelength-dependent nonlinear Kerr index n2 and TPA coefficient βTPA into account which are expressed as

( 3 )2 2

0

( 3 )2

0

3( ) ( )4 ( )

3( ) ( )( )

re

TPA im

ncn

cn

λ χ λε λ

πβ λ χ λ

λε λ

=

=

where ε0 and c are the vacuum permittivity and the speed of light in vacuum Using the material index given in Appendix A and χ(3) value from [133] we obtain the n2 and βTPA values tabulated as follows

262emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

Table 1enspNonlinear Kerr index n2 in silicon

λμm

  n2

10-18 m2W  λ

μm  n2

10-18 m2W  λ

μm  n2

10-18 m2W

130   234   310   389   490   312135   305   315   384   495   311140   378   320   379   500   310145   443   325   375   505   309150   501   330   371   510   307155   559   335   368   515   306160   618   340   365   520   304165   671   345   362   525   304170   710   350   360   530   303175   741   355   358   535   302180   766   360   355   540   302185   781   365   352   545   301190   783   370   350   550   300195   778   375   346   555   298200   762   380   343   560   297205   732   385   341   565   296210   699   390   338   570   296215   658   395   336   575   295220   612   400   334   580   295225   576   405   332   585   295230   547   410   331   590   294235   525   415   330   595   293240   508   420   329   600   292245   493   425   328   605   291250   479   430   327   610   290255   467   435   325   615   289260   456   440   324   620   288265   448   445   321   625   288270   440   450   319   630   288275   432   455   317   635   288280   424   460   315   640   288285   417   465   314   645   288290   410   470   313   650   288295   404   475   313   655   288300   398   480   312   660   288305   394   485   312    

Table 2enspTPA coefficient βTPA in silicon

λμm

  βTPA

10-12 mW  λ

μm  βTPA

10-12 mW  λ

μm  βTPA

10-12 mW

130   1334   165   812   200   180135   1284   170   713   205   115140   1222   175   613   210   064145   1154   180   522   215   024150   1079   185   424   220   0003155   995   190   333    160   905   195   254    

Table 3enspNonlinear Kerr index n2 in germanium

λμm

  n2

10-18 m2W  λ

μm  n2

10-18 m2W  λ

μm  n2

10-18 m2W

23  3932  63  1986  103  170524  4994  64  1972  104  169925  6007  65  1959  105  169426  6650  66  1946  106  169027  6772  67  1934  107  168728  6273  68  1923  108  168429  4897  69  1913  109  168230  4403  70  1904  110  168131  3970  71  1895  111  167932  3680  72  1886  112  167733  3470  73  1876  113  167534  3286  74  1868  114  167335  3128  75  1859  115  167036  2998  76  1850  116  166737  2895  77  1841  117  166338  2812  78  1833  118  165939  2737  79  1826  119  165640  2668  80  1819  120  165341  2605  81  1812  121  165142  2550  82  1807  122  164843  2498  83  1801  123  164644  2450  84  1797  124  164445  2406  85  1792  125  164346  2365  86  1787  126  164147  2328  87  1782  127  163948  2295  88  1777  128  163649  2266  89  1772  129  163450  2238  90  1767  130  163251  2212  91  1762  131  163052  2187  92  1758  132  162853  2164  93  1753  133  162654  2141  94  1749  134  162555  2121  95  1744  135  162356  2101  96  1740  136  162157  2083  97  1736  137  162058  2066  98  1731  138  161859  2049  99  1727  139  161760  2032  100  1722  140  161661  2016  101  1716   62  2001  102  1711   

Table 4enspTPA coefficient βTPA in germanium

λμm

  βTPA

10-8 mW  λμm

  βTPA

10-8 mW  λ

μm  βTPA

10-8 mW

23   130   25   088   27   03124   111   26   060   28   006

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp263

References[1] Bloembergen N Nonlinear Optics London World Scientific 1996[2] Yuen-Ron S The Principles of Nonlinear Optics Hoboken New

Jersey Wiley-Interscience 2002[3] Robert B Nonlinear Optics (3rd ed) Amsterdam Boston

Academic Press 2008[4] Franken P Hill A Peters C Weinreich G Generation of optical

harmonics Phys Rev Lett 19617118ndash9[5] Terhune RW Maker PD Savage CM Optical harmonic

generation in calcite Phys Rev Lett 19628404ndash6[6] Kaiser W Garrett CGB Two-photon excitation in CaF2Eu2+

Phys Rev Lett 19617229ndash32[7] Eckhardt G Hellwarth RW McClung FJ Schwarz SE Weiner D

Woodbury EJ Stimulated raman scattering from organic liquids Phys Rev Lett 19629455ndash7

[8] Giordmaine JA Mixing of light beams in crystals Phys Rev Lett 1962819ndash20

[9] Maker PD Terhune RW Nisenoff M Savage CM Effects of dispersion and focusing on the production of optical harmonics Phys Rev Lett 1962821ndash22

[10] Delone NB Kraĭnov VP Fundamentals of nonlinear optics of atomic gases New York Wiley 1987

[11] Nikogosyan DN Nonlinear optical crystals a complete survey Springer Berlin 2005

[12] Govind A Nonlinear fiber optics (4th ed) San Diego California Academic Press 2007

[13] Russell PSTJ Birks TA Lloyd-Lucas FD Photonic Bloch waves and photonic band gaps In lsquoConfined electrons and photons New physics and applicationsrsquo New York Plenum Press 1995

[14] Dudley JM Genty G Coen S Supercontinuum generation in photonic crystal fiber Rev Mod Phys 2006781135ndash1184

[15] Dudley JM Taylor JR Ten years of nonlinear optics in photonic crystal fibre Nature Photonics 2009385ndash90

[16] Soref RA Silicon-based optoelectronics Proceedings of the IEEE 1993811687ndash1706

[17] Kimerling LC Silicon for photonics Proc SPIE 3002 1997192[18] Kimerling LC Silicon materials engineering for the next

millennium Sol St Phen 199970131ndash142[19] Pavesi L Lockwood DJ editors Silicon Photonics New York

Springer 2004[20] Reed GT Knights AP Silicon photonics an introduction Wiley

Hoboken NJ 2004[21] Lipson M Guiding modulating and emitting light on silicon -

challenges and opportunities IEEE J Lightwave Technol 2005 234222

[22] Soref RA The past present and future of silicon photonics IEEE J Sel Top Quantum Electron 2006121678ndash87

[23] Jalali B Paniccia M Reed G Silicon photonics IEEE Microwave Magazine 2006758ndash68

[24] Jalali B Fathpour S Silicon photonics J Lightwave Technol 2006 244600ndash15

[25] Kirchain R Kimerling L A roadmap for nanophotonics Nature Photonics 20071303ndash5

[26] Dekker R Usechak N Foumlrst M Driessen A Ultrafast nonlinear all-optical processes in silicon-on-insulator waveguides J Phys D Appl Phys 200740R249ndash71

[27] Lin Q Painter OJ Agrawal GP Nonlinear optical phenomena in silicon waveguides Modeling and applications Opt Express 20071516604ndash44

[28] Tsang HK Liu Y Nonlinear optical properties of silicon waveguides Semicond Sci Technol 2008 23064007

[29] Osgood RM Jr Panoiu NC Dadap JI Liu X Chen X Hsieh I-W Dulkeith E Green WM Vlasov YA Engineering nonlinearities in nanoscalse optical systems Physics and applications in dispersion-engineered silicon nonaphotonics wires Adv Opt Photon 20091162ndash235

[30] Leuthold J Koos C Freude W Nonlinear silicon photonics Nature Photonics 20104535ndash44

[31] Ikeda K Shen Y Fainman Y Enhanced optical nonlinearity in amorphous silicon and its application to waveguide devices Opt Express 20071517761ndash71

[32] Shoji Y Ogasawara T Kamei T Sakakibara Y Suda S Kintaka K Kawashima H Okano M Hasama T Ishikawa H Mori M Ultrafast nonlinear effects in hydrogenated amorphous silicon wire waveguide Opt Express 2010185668ndash73

[33] Narayanan K Preble SF Optical nonlinearities in hydrogenated-amorphous silicon waveguides Opt Express 2010188998ndash9005

[34] Grillet C Carletti L Monat C Grosse P Ben Bakir B Menezo S Fedeli JM Moss DJ Amorphous silicon nanowires combining high nonlinearity FOM and optical stability Opt Express 20122022609ndash15

[35] Matres J Ballesteros GC Gautier P Feacutedeacuteli J-M Martiacute J Oton CJ High nonlinear figure-of-merit amorphous silicon waveguides Opt Express 2013213932ndash40

[36] Hernaacutendez S Pellegrino P Martiacutenez A Lebour Y Garrido B Spano R Cazzanelli M Daldosso N Pavesi L Jordana E Fedeli JM Linear and nonlinear optical properties of Si nanocrystals in SiO2 deposited by plasma-enhanced chemical-vapor deposition J Appl Phys 2008103 064309

[37] Yuan Z Anopchenko A Daldosso N Guider R Navarro-Urrios D Pitanti A Spano R Pavesi L Silicon Nanocrystals as an Enabling Material for Silicon Photonics Proc IEEE 2009971250ndash68

[38] Spano R Daldosso N Cazzanelli M Ferraioli L Tartara L Yu J Degiorgio V Giordana E Fedeli JM Pavesi L Bound electronic and free carrier nonlinearities in Silicon nanocrystals at 1550 nm Opt Express 2009173941ndash50

[39] Rukhlenko ID Zhu W Premaratne M Agrawal GP Effective third-order susceptibility of silicon-nanocrystal-doped silica Opt Express 20122026275ndash84

[40] Loacutepez-Suaacuterez A Torres-Torres C Rangel-Rojo R Reyes-Esqueda JA Santana G Alonso JC Ortiz A Oliver A Modification of the nonlinear optical absorption and optical Kerr response exhibited by nc-Si embedded in a silicon-nitride film Opt Express 20091710056ndash68

[41] Minissale S Yerci S Dal Negro L Nonlinear optical properties of low temperature annealed silicon-rich oxide and silicon-rich nitride materials for silicon photonics Appl Phys Lett 2012100021109

[42] Yamada H Shirane M Chu T Yokoyama H Ishida S Arakawa Y Nonlinear-optic silicon-nanowire waveguides Japanese J Appl Phys 2005446541ndash5

[43] Almeida VR Xu QF Barrios CA Lipson M Guiding and confining light in void nanostructure Opt Lett 2004291209ndash11

264emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

[44] Xu Q Almeida VR Panepucci RR Lipson M Experimental demonstration of guiding and confining light in nanometer-size low-refractive-index material Opt Lett 2004291626ndash8

[45] Baehr-Jones T Hochberg M Walker C Scherer A High-Q optical resonators in silicon-on-insulator based slot waveguides Appl Phys Lett 200586081101

[46] Sun R Dong P Feng N-N Hong C-Y Michel J Lipson M Kimerling L Horizontal single and multiple slot waveguides optical transmission at λ = 1550 nm Opt Express 20071517967ndash72

[47] Fujisawa T Koshiba M Guided modes of nonlinear slot waveguides IEEE Photon Technol Lett 2006181530ndash32

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[141] Zlatanovic S Park JS Moro S Boggio JMC Divliansky IB Alic N Mookherjea S Radic S Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source Nat Photonics 20104561ndash4

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[188] Dulkeith E Xia FN Schares L Green WMJ Vlasov YA Group index and group velocity dispersion in silicon-on-insulator photonic wires Opt Express 2006143853ndash63

[189] Turner AC Manolatou C Schmidt BS Lipson M Tailored anomalous group-velocity dispersion in silicon channel waveguides Opt Express 2006144357ndash62

[190] Dadap JI Panoiu NC Chen X I-Hsieh W Liu X Chou C-Y Dulkeith E McNab SJ Xia F Green WMJ Sekaric L Vlasov YA Osgood RM Jr Nonlinear-optical phase modification in dispersion-engineered Si photonic wires Opt Express 2008161280ndash99

[191] Milosevic MM Matavulj PS Yang PY Bagolini A Mashanovich GZ Rib waveguides for mid-infrared silicon photonics J Opt Soc Am B 2009261760ndash6

[192] Mashanovich GZ Milošević MM Nedeljkovic M Owens N Xiong B Teo EJ Hu Y Low loss silicon waveguides for the mid-infrared Opt Express 2011197112ndash9

[193] Reimer C Nedeljkovic M Stothard DJM Esnault MOS Reardon C OrsquoFaolain L Dunn M Mashanovich GZ Krauss TF Mid-infrared photonic crystal waveguides in silicon Opt Express 20122029361ndash8

[194] Baehr-Jones T Spott A Ilic R Spott A Penkov B Asher W Hochberg M Silicon-on-sapphire integrated waveguides for the midinfrared Opt Express 20101812127ndash35

[195] Li F Jackson S Grillet C Magi E Hudson D Madden SJ Moghe Y OrsquoBrien C Read A Duvall SG Atanackovic P Eggleton BJ Moss D Low propagation loss silicon-on-sapphire waveguides for the midinfrared Opt Express 20111915212ndash20

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[196] Yue Y Zhang L Huang H Beausoleil RG Willner AE Silicon-on-nitride waveguide with ultralow dispersion over an octave-spanning mid-infared wavelength range IEEE Photonics J 20124126ndash32

[197] Khan S Chiles J Ma J Fathpour S Silicon-on-nitride waveguides for mid-and near-infrared integrated photonics Appl Phys Lett 2013102121104

[198] Cheng Z Chen X Wong CY Xu K Tsang HK Mid-infrared suspended membrane waveguide and ring resonator on silicon-on-insulator IEEE Photonics J 201241510ndash9

[199] Lin P-T Singh V Cai Y Kimerling LC Agarwal A Air-clad silicon pedestal structures for broadband mid-infrared microphotonics Opt Lett 2013381031ndash3

[200] Chang YC Paeder V Hvozdara L Hartmann JM Herzig HP Low-loss germanium strip waveguides on silicon for the mid-infrared Opt Lett 2012372883ndash5

[201] Zhang L Yue Y Y Xiao-Li R G Beausoleil Willner AE Highly dispersive slot waveguides Opt Express 2009177095ndash101

[202] Zhang L Yue Y Beausoleil RG Willner AE Analysis and engineering of chromatic dispersion in silicon waveguide bends and ring resonators Opt Express 2011198102ndash7

[203] Zhang L Mu J Singh V Agarwal A Kimerling LC Michel J Intra-cavity dispersion of microresonators and its engineering for octave-spanning Kerr frequency comb generation to be published

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[205] Wang Y Yue R Han H Liao X Raman study of structural order of a-SiNxH and its change upon thermal annealing J Non-Crystalline Solids 2001291107ndash12

[206] Brida D Marangoni M Manzoni C De Silvestri S Cerullo G Two-optical-cycle pulses in the mid-infrared from an optical parametric amplifier Opt Lett 2008332901ndash3

[207] Brida D Manzoni C Cirmi G Marangoni M Bonora S Villoresi P De Silvestri S Cerullo G Few-optical-cycle pulses tunable from the visible to the mid-infrared by optical parametric amplifiers J Opt 201012013001

[208] Kippenberg TJ Holzwarth R Diddams SA Microresonator-based optical frequency combs Science 2011332555ndash9

[209] Levy JS Gondarenko A Foster MA Turner-Foster AC Gaeta AL Lipson M CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects Nat Photonics 2009437ndash40

[210] DelrsquoHaye P Herr T Gavartin E Gorodetsky ML Holzwarth R Kippenberg TJ Octave spanningtunable frequency comb from a microresonator Phys Rev Lett 2011107063901

[211] Okawachi Y Saha K Levy JS Wen YH Lipson M Gaeta AL Octave-spanning frequency combgeneration in a silicon nitride chip Opt Lett 2011363398ndash400

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[213] Herr T Brasch V Jost JD Wang CY Kondratiev NM Gorodetsky ML Kippenberg TJ Temporal solitons in optical microresonators httparxivorgabs12110733

[214] Saha K Okawachi Y Shim B Levy JS Salem R Johnson AR Foster MA Lamont MR Lipson M Gaeta AL Modelocking and femtosecond pulse generation in chip-based frequency combs Opt Express 2013211335ndash43

[215] Coen S Erkintalo M Universal scaling laws of Kerr frequency combs Opt Lett 2013381790ndash2

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[218] Coen S Randle HG Sylvestre T Erkintalo M Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato-Lefever model Opt Lett 20133837ndash9

[219] Chembo YK Menyuk CR Spatiotemporal Lugiato-Lefever formalism for Kerr-comb generation in whispering-gallery-mode resonators Phys Rev A 201387053852

[220] Foltynowicz A Mas1owski P Ban T Adler F Cossel KC Briles TC Ye J Optical frequency comb spectroscopy Faraday Discussion 201115023ndash31

[221] Hartl I Li XD Chudoba C Ghanta RK Ko TH Fujimoto JG Ranka JK Windeler RS Ultrahigh-resolution optical coherence tomography using continuum generation in an air silica microstructure optical fiber Opt Lett 200126608ndash10

[222] Brabec T Krausz F Intense few-cycle laser fields Frontiers of nonlinear optics Rev Mod Phys 200072545ndash91

[223] Hu J Meyer J Richardson K Shah L Feature issue introduction mid-IR photonic materials Opt Mater Express 201331571ndash5

[224] Private communications with Dr Jacob Levy in Prof Lipsonrsquos group and Dr Johann Riemensberger in Prof Kippenbergrsquos group

[225] Zhang J Lin Q Piredda G Boyd RW Agrawal GP Fauchet PM Anisotropic nonlinear response of silicon in the near-infrared region Appl Phys Lett 200791071113

Page 5: Lin Zhang*, Anuradha M. Agarwal, Lionel C. Kimerling and ...

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp251

measurements We obtain the Kerr nonlinear index n2 as a function of wavelength based on χ(3)

1111 using the results from [133] As shown in Figure 3 the n2 value peaks at 19 and 27 microm for silicon and germanium respectively and changes slightly from 33 to 48 microm beyond which both TPA and 3PA disappear The TPA coefficient βTPA vs wave-length is also extracted for silicon and germanium from [133] as detailed in Tables 1ndash4 in Appendix B

Hydrogenated amorphous silicon has been identi-fied as a potentially good nonlinear material not only because of large bandgap energy of 17 eV but also more importantly because of the large nonlinear index n2 and nonlinear figure of merit (FOM) n2βTPAλ [162] We did not include specific data in Figure 3 for amorphous silicon since different groups reported highly variable n2 and nonlinear FOM values in the near-IR [31ndash35] The n2 value could be one order of magnitude higher than that in silicon [33] while the nonlinear FOM can be as high as 5 [35] although these may not be obtained simultaneously [34] Moreover linear properties of amorphous silicon may also vary when fabrication conditions and its nonlin-ear characteristics change

Silicon nano-crystals in silicon dioxide and silicon nitride have also been investigated as a nonlinear material exhibiting higher nonlinear indices than crystalline silicon by an order of magnitude or more [36ndash41] The values of n2 βTPA and nonlinear FOM are also highly variable if silicon excess annealing temperature and wavelength change We include one data point (n2 = 48 times 10-17m2W) from [38] in Figure 3 Extremely high n2and FOM by 3~4 orders have been obtained experimentally [41] with large silicon excess (note that the FOM in [41] is defined as the reciprocal of ours here)

Both amorphous silicon and silicon nano-crystals exhibit great potential as a nonlinear material in the mid-IR which can be used to compensate for the reduc-tion of the nonlinear coefficient due to a large mode area at long wavelengths In particular with a small linear refractive index SRO is often chosen as a slot material to enhance nonlinearity in the near-IR [51 53 55 56 59] while SRN exhibits a great potential for nonlinear applica-tions beyond 3 microm Typically strong nonlinearity in bulk materials is associated with a high linear refractive index which is known as Miller rule However silicon nano-crys-tals exhibit unique properties to simultaneously possess strong nonlinearity and low linear index It is important to mention that the silicon nano-crystals (ie nano-clusters) could act as scattering centers of light causing an increased propagation loss in SRO slot waveguides Nevertheless relatively low propagation loss has been achieved which is 3~5 dBcm [163]

For silicon nitride one data point n2 = 24 times 10-19m2W from [111] is included in Figure 3 which was measured at 155 microm and is one-order lower than that in silicon Silicon dioxide has an n2 value around 26 times 10-20m2W in 155 microm as in single-mode optical fibers two orders lower than that in silicon A higher n2 value (115 times 10-19m2W) is estimated for 155 microm in high-index doped silica [164] Both values are not shown in Figure 3 Since both silicon nitride and silicon dioxide have large bandgap energies it is expected that their n2 values are almost constant over wavelength in the near- and mid-IR

Strong Kerr nonlinearities are obtained in chalcoge-nide glasses (arsenic sulfide and arsenic selenide) with negligible TPA from the near- to mid-IR as shown in Figure 1 We have found wavelength-dependent measure-ments of the nonlinear index n2 for arsenic sulfide from different data sources [150 165ndash174] As shown in Figure 3 although slightly scattered these n2 values in arsenic sulfide are as high as those in silicon and would not be strongly wavelength-dependent beyond 155 microm because it is longer than the half-bandgap wavelength Arsenic selenide has even higher n2 values than arsenic sulfide [173] and its n2 value is predicted as a function of wave-length in [175]

There has been little published on the wavelength dependence of the nonlinear Raman gain coefficient gR in literature for the materials that we consider here [133] Since SRS is not the major nonlinear effect that is used in this paper we will not discuss it in details here

Although the considered materials such as silicon germanium silicon nitride and silicon dioxide are cen-trosymmetric and show no second-order nonlinearity in bulk materials one can engineer them by applying strain [176ndash178] or forming interfaces between two centrosym-metric materials (eg between germanium and silicon [179] or between silicon nitride and silicon dioxide [180]) An alternative way is to integrate other materials with strong second-order susceptibility onto Group IV wave-guides (see eg [145]) For chalcogenide glasses different poling schemes are proposed to produce the second-order nonlinearity [181] The second-order susceptibility χ(2) induced to the Group IV platform can have a highly variable value depending on how the isotropy of materi-als is broken We believe that second-order nonlinearity is promising in nonlinear Group IV photonics but in this paper we will mainly focus on third-order nonlinearity

As described above the materials presented here have greatly different transparency windows and nonlin-ear coefficients It thus becomes critical to wisely choose a material combination for a specific application and doing this one may also need to pay special attention to material

252emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

compatibility in device fabrication On the other hand compared to the material choices device design (mainly on waveguide and resonator) can also produce widely var-iable dispersion and nonlinearity properties In the next section we will discuss enhanced waveguide properties using improved designs

3 DevicesOptical waveguides form the backbone of photonic devices Light propagation properties in a waveguide could be remarkably different from those in corresponding bulk materials especially when there is a high index con-trast between waveguide core and surrounding cladding Therefore understanding and optimizing the waveguide properties including loss dispersion and nonlinearity are essential in nonlinear photonics

Propagation loss in a waveguide includes material loss confinement loss scattering loss and nonlinear loss Working at a transparency window of a material especially beyond the half-bandgap wavelength one can primarily have low material and nonlinear loss caused by TPA Note that benefiting from the wide multi-octave bandwidth in the mid-IR one can even eliminate the impact of 3PA in silicon and germanium by pumping at  gt 33 microm and  gt 48 microm respectively Since the substrate index in a silicon wafer is higher than or equal to that in most of materials we consider for a waveguide core con-finement loss exists due to mode leakage to the silicon substrate This loss can be markedly reduced by increas-ing the spacing between waveguide core and the substrate or choosing low-index material between them In general scattering loss due to sidewall roughness of a waveguide is dominant in high-index-contrast silicon photonics which is mainly caused in device fabrication and can thus be reduced by improving the fabrication processes [182ndash184]

Compared to propagation loss chromatic disper-sion and nonlinearity in integrated waveguides are more de signable Since the dispersion is the second-order deriv-ative of the effective index with respect to wavelength it is particularly tailorable by changing waveguide shape and dimension Moreover dispersion has been recognized to be critical for broadband nonlinear effects [12 14 15 60 61 92ndash108 112ndash115 137ndash145] which is true especially for ultrafast octave-spanning applications [185] Spec-tral characteristics in a dispersion profile including the number and positions of zero-dispersion wavelengths (ZDWs) and dispersion slope greatly affect and often set the limit on the bandwidth of optical spectra the temporal

widths of pulses and conversion efficiency in nonlinear interactions [185] Generally speaking a flat dispersion profile (ie third- and higher-order dispersion terms are small) with low dispersion values is preferred

In conventional ultrafast nonlinear optics in a free-space setup many components were developed to control dispersion over a wide bandwidth [185 186] such as prisms gratings chirped mirrors and so on However in a waveguiding system eg in fiber-based ultrafast optics the dispersion-control toolkit is smaller and engineer-ing waveguide dispersion becomes critical In particular when waveguides are built on a silicon platform with a much higher index contrast than optical fibers dispersion in a highly nonlinear waveguide [187ndash190] often shows strong wavelength dependence which is not preferable for wideband nonlinear applications In [187 190] the ZDW in silicon rib and strip waveguides is mapped by scanning waveguide dimensions It is shown that tight confinement of a guided mode produces a ZDW in its dispersion profile around 12~14 μm close to the bandgap wavelength More-over even if the waveguide size is increased to move the ZDW to longer wavelength the dispersion slope near the ZDW is not small as shown in [187ndash189] causing a limited low-dispersion bandwidth

Recently a dispersion engineering technique for integrated high-index-contrast waveguides has been pro-posed in which an off-center nano-scale slot controls modal distribution at different wavelengths [59 60] The guided mode experiences a transition from strip-mode like to slot-mode like as wavelength increases This approach can produce a very flat dispersion profile over an ultra-wide bandwidth with dispersion flatness improved by 1ndash2 orders in terms of dispersion variation divided by low-dispersion bandwidth More importantly it is applicable to different material combinations and wavelength ranges [59ndash63]

Towards mid-IR applications different types of Group IV waveguides have been reported recently based on silicon-on-insulator (SOI) [191ndash193] silicon-on-sapphire [142 194 195] silicon-on-porous-silicon [192] silicon-on-nitride [196 197] suspended membrane silicon [198] silicon pedestal [199] and germanium-on-silicon [200] Most of the waveguides are not aimed specifically at non-linear applications and little attention has been paid to dispersion engineering [196]

In this section we survey different structures of Group IV waveguides for broadband nonlinear applica-tions from the near- to mid-IR There are three main goals in waveguide designs (i) we consider joint optimization on both dispersion and nonlinearity properties (ii) we tend to fully utilize the available bandwidth brought by

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp253

the materials in Figure 1 and (iii) we emphasize disper-sion engineering naturally as a result of aiming at octave-spanning broadband applications

Figure 4 shows a general illustration of various types of integrated waveguides for nonlinear Group IV photonics Looking at a specific wavelength range one can accord-ingly choose a materials combination for an appropriate index contrast and a desired level of nonlinearity Note that one may need low nonlinearity in some cases when high-power output is required Here we discuss waveguide design at four different wavelength ranges as follows

First we consider SOI waveguides for a wavelength range from the telecom window in the near-IR to the short-wave end in the mid-IR ie roughly from 14 to 25 microm This is the wavelength range that many of the current research efforts have been addressing [60 61 106 108 114 115 135 137 139ndash141 143 144] In this wavelength range a SOI strip waveguide as shown in Figure 4 can be used with air as an upper cladding (see eg [140]) One can change the width of the waveguide to tailor its disper-sion profile while the height of the waveguide is 220 nm set by SOI wafers From Figure 5(A) we note that a rela-tively small width W = 800 nm is corresponding to a dis-persion profile with two ZDWs at 1585 and 2345 microm and a peak value of anomalous dispersion 532 ps(nmmiddotkm) at 205 microm for the quasi-TE mode The anomalous disper-sion is typically useful for parametric amplification and oscillation soliton and soliton-based supercontinuum generation [12] With W  =  900 nm one can have a flatter dispersion profile but the anomalous band is smaller When W is increased to 1000 nm the dispersion is even flatter but no anomalous dispersion occurs Figure 5(A) shows a good example that tight mode confinement in a strip waveguide moves ZDW to short wavelengths and near ZDWs dispersion changes quickly with a large slope

Strip WG

Strip WG suspended

Air Air

Slot

Core

Upper cladding

Slab

Lower cladding

Si substrate

Slot WG suspended

Slot WG Rib WG

Figure 4emspDifferent types of Group IV waveguides (WGs) for disper-sion and nonlinearity engineering in the near- and mid-IR ranges

One can calculate the nonlinear coefficient γ as a function of wavelength with the nonlinear Kerr index n2 given in Tables 1ndash4 in Appendix B We show in Figure 5(B) that the nonlinear coefficient in the silicon strip wave-guide with W = 900 nm first increases to 187 (mmiddotW) with wavelength until 17 μm and then decreases to 56 (mmiddotW) at 25 μm This is caused by both the peaking of the silicon n2 value near 19 μm and the gradual increase of wave-length and mode area beyond that

A silicon stripslot hybrid waveguide exhibits very flat dispersion as presented in Figure 5(A) The SOI waveguide has crystalline silicon at the bottom a thin SRO slot and amorphous silicon at the top The upper cladding is silicon dioxide When setting the lower Si height to Hl = 430 nm slot height to Hs = 54 nm upper Si height to Hu = 160 nm and width to W = 660 nm we obtain an extremely flat disper-sion profile for the quasi-TM mode over a wide bandwidth between two ZDWs at 1545 and 2448 microm From 1605 to 238 microm the value of anomalous dispersion changes between 30 and 46 ps(nmmiddotkm) In this way one can have a flat and low anomalous dispersion between two far apart ZDWs The average dispersion value can be shifted by increasing Hu to move dispersion between normal and anomalous regimes Detailed explanation on how the flat-tened and saddle-shaped dispersion profile is produced is given in [59 60] Briefly the mode transition over wave-length for the quasi-TM mode is responsible for this behav-ior Due to the off-center slot the mode is mostly confined in the crystalline silicon at short wavelengths while the mode becomes more like a slot mode at long wavelengths As shown in Figure 5(C) we plot the mode power distribu-tions at wavelengths of 15 183 217 and 25 microm The mode transition adds negative dispersion in the middle of the low-dispersion bandwidth as explained in [60 201]

Having a slot one has an opportunity to fill the slot with highly nonlinear materials into it [49 51 53 55 56 58 59] which can overcome the decrease of the nonlinear coeffi-cient over wavelength In Figure 5(B) we show the γ value increasing to 306 (mmiddotW) with wavelength from 14 to 25 microm This is because the guided mode extends more to the highly nonlinear thin slot layer Note that the used n2 value in SRO [38] is currently the one measured at 155 microm so the n2 and γ thinspvalues may vary in the mid-IR but the trend is general

Next we explore the short-wavelength end of the near-IR spectrum Silicon-based devices become unus-able for nonlinear photonics as wavelength decreases to 11 microm and we thus look at silicon nitride for near-IR nonlinear applications extending to the visible light spec-trum Again a strip waveguide based on silicon nitride is examined first Figure 6(A) shows dispersion curves of the quasi-TE mode in two waveguides sized to be 1300 times 540

254emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

and 1400 times 800 nm2 The upper cladding is air and the lower cladding is silicon dioxide The anomalous disper-sion region in the dispersion curves shrinks when the waveguide is made smaller This is because of a relatively small index contrast between silicon nitride and silicon dioxide which makes the guided mode leak quickly to the substrate as wavelength increases For the strip waveguide with a cross-section of 1400 times 800 nm2 there are two ZDWs near 10 and 23 microm but one can see a strong dispersion of 250 ps(nmmiddotkm) between the two ZDWs in Figure 6(A) The nonlinear coefficient in the second silicon nitride wave-guide is shown in Figure 6(B) which is much smaller than that in silicon waveguides because of a one-order smaller n2 value and larger Aeff in the silicon nitride waveguide At 16 microm γ is about 123(mW)

One can also use a stripslot hybrid structure to tailor the dispersion profile in silicon nitride waveguides For example the slot and lower cladding are silicon dioxide and the upper cladding is air In Figure 6(A) we show the dispersion curves in two silicon nitride stripslot hybrid waveguides for comparison The waveguide 1 has Hl = 900 nm Hs = 124 nm Hu = 340 nm and W = 1000 nm and the waveguide 2 has Hl = 920 nm Hs = 154 nm Hu = 480 nm and W = 1300 nm These two waveguides produce increasingly flatter dispersion profiles as shown in Figure 6(A) The first waveguide has two ZDWs located at 106 and 22 microm with the peak dispersion of 67 ps(nmmiddotkm) The second waveguide has two ZDWs at 115 and 235 microm with the dispersion varying within 0~20 ps(nmmiddotkm) This octave-spanning dispersion flattening with different levels

1000A

B

C

500

-500

400

300

200

100

0

-100014 16

Strip WG W=800 nmStrip WG W=900 nm

Strip WG W=900 nm

Strip WG W=1000 nm

Slot WG Hu=160 nm

Slot WG Hu=160 nm

Slot WG Hu=163 nmSlot WG Hu=166 nm

18 20 22Wavelength (microm)

Dis

pers

ion

(ps

nmmiddotk

m)

Non

linea

r co

effic

ient

(m

middotW)

24 26

14 16 18 20 22

Wavelength (microm)

24 26

0

Figure 5emspIn a wavelength range from the telecom window in near-IR to the short-wave end in the mid-IR silicon strip and stripslot hybrid waveguides (WGs) are analyzed in terms of (A) dispersion and (B) nonlinearity (C) Mode power distributions at wavelengths of 15 183 217 and 25 microm in the stripslot hybrid waveguide

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp255

of dispersions can be used for multiple applications as detailed in the next section The nonlinear coefficients for the two waveguides are shown in Figure 6(B) We note that the stripslot hybrid waveguides have similar nonlinear coefficients as the strip waveguide which shows that the dispersion profile is much more tailorable by waveguide designs

Then we move to the mid-IR using silicon and silicon nitride for waveguiding A comparison of different types of silicon-on-nitride waveguides have been presented in [196] where rib waveguides were preferred due to the wideband low dispersion over an octave-spanning band-width from 24 to 66 microm for the quasi-TE mode This is a spectral range from siliconrsquos half-bandgap wavelength to the cut-off wavelength of silicon nitride In Figure 7(A) we plot the dispersion curve for a silicon-on-nitride rib waveguide with air as the upper cladding the rib width of 2000 nm the total height of 1200 nm and the slab height of 1000 nm which are the same parameters used in [196] It is shown that less confinement of optical modes reduces the contribution of waveguide dispersion and makes the overall dispersion profile closer to the material dispersion which is flat and low at long wavelengths as in Figure 2(B)

A

B

400

300

200

100

-100

8

6

4

2

0

0

Strip WG 1300times540 nm2

Strip WG 1400times800 nm2

Strip WG 1400times800 nm2

Slot WG 1Slot WG 2

Slot WG 1Slot WG 2

Dis

pers

ion

(ps

nmmiddotk

m)

Non

linea

r co

effic

ient

(m

middotW)

20 3010 15 2505Wavelength (microm)

2010 15 2505

Wavelength (microm)

Figure 6emspIn a wavelength range moved toward the short-wave-length end of near-IR spectrum silicon nitride strip and stripslot hybrid waveguides are designed in terms of (A) dispersion and (B) nonlinearity

Accordingly the nonlinear coefficient is small 285 (mmiddotW) at 3 microm as shown in Figure 7(B)

On the other hand if one needs a small Aeff to enhance nonlinearity additional dispersion tailoring (eg based on stripslot hybrid waveguides) would be beneficial Pursuing a higher nonlinear coefficient we use a 500-nm silicon nitride suspended membrane as illustrated in Figure 4 to support a silicon stripslot hybrid waveguide This helps confine light in the waveguide core Using W = 880 nm Hu = 550 nm Hs = 87 nm and Hl = 840 nm we obtain a saddle-shaped anomalous dispersion from 19 to 449 microm within 0~60 ps(nmmiddotkm) for the quasi-TM mode as shown in Figure 7(A) This structure produces much tighter mode confinement than the rib waveguide and exhibits a 3 times larger nonlinear coefficient in Figure 7(B) while having similar dispersion flatness

Finally we consider germanium-on-silicon wave-guides over a wavelength range from 33 to 85 microm between the half-bandgap wavelength of germanium and the cut-off wavelength of silicon This type of waveguide has been demonstrated with strain-free mono-crystal-line germanium [200] Here we assume that the germa-nium waveguide has a 10-nm silicon nitride layer on its

A

B

200

-200

60

40

20

0

100

-100

0

Rib WGSlot WG

Rib WGSlot WG

Dis

pers

ion

(ps

nmmiddotk

m)

Non

linea

r co

effic

ient

(m

middotW)

1 2 3 4 5 6 7Wavelength (microm)

1 2 3 4 5 6 7

Wavelength (microm)

Figure 7emspIn a wavelength range from the short-wave IR to mid-IR silicon rib waveguide on silicon nitride and stripslot hybrid waveguide on a suspended membrane are analyzed in terms of (A) dispersion and (B) nonlinearity

256emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

surface for passivation The upper cladding could be air or silicon which provides significantly different dispersion properties due to a varied index contrast For comparison only we also have silicon nitride as the upper cladding although silicon nitride becomes lossy for wavelengths longer than 67 microm Figure 8(A) shows the dispersion pro-files of four germanium-on-silicon strip waveguides with equal size 3000 times 1600 nm2 for the quasi-TE mode Air and silicon nitride as an upper cladding result in similar shape and bandwidth in the dispersion profiles Thus the air-cladded waveguide is chosen and discussed further The waveguide with silicon upper cladding has normal dispersion at all wavelengths since there is a relatively small index contrast between germanium and silicon and thus weak mode confinement A germanium strip wave-guide on a 600-nm-thick silicon suspended membrane is also considered to increase light confinement with an air upper cladding to maximize light confinement However as mentioned earlier strong confinement typically causes strong dispersion as shown in Figure 8(A) and therefore the germanium waveguide on a silicon membraneis not chosen for broadband nonlinear applications In contrast the germanium strip waveguide with air upper cladding exhibits a flat and low dispersion

The dimensions of the air-cladded germanium wave-guide are varied by simultaneously changing its height and width with a step of 200 nm for both polarization states It is interesting to see from Figure 8(B) and 8(C) that the dispersion peak value remains nearly unchanged for all the waveguide sizes although we have a widely tunable ZDW at long wavelengths For the quasi-TE mode the right ZDW moves from 605 microm to 841 microm while the left ZDW is always near 4 microm We can thus obtain an octave-spanning anomalous dispersion band with the peak value below 100 ps(nmmiddotkm) For the quasi-TM mode one can see similar dispersion properties but the anomalous disper-sion band is smaller Thus we choose the quasi-TE mode for further discussion in next section

The nonlinear coefficient in the germanium wave-guides for the quasi-TE mode is shown in Figure 8(D) which is about 10(mmiddotW) at 5 microm with a small variation for differ-ent waveguide sizes This is quite high considering that both wavelength and effective mode area become much larger over this wavelength range compared to the near-IR

From above we can see that the stripslot hybrid wave-guides enable unique controllability of dispersion and that this concept is applicable to different wavelength ranges However their performance may be sensitive to fabrication errors especially for inaccuracies in slot height Hs [59 60] A higher yield in device fabrication is expected using advanced fabrication technologies and facilities

A

C

D

B

400

300

200

100

-100

-200

0

Ge WG+air 3000times1600 nm2

Ge WG+air suspended 3000times1600 nm2

Ge WG+Si3N4 3000times1600 nm2

Ge WG+Si 3000times1600 nm2

Ge WG+air 2800times1400 nm2

Ge WG+air 3000times1600 nm2

Ge WG+air 3200times1800 nm2

Ge WG+air 3400times2000 nm2

Ge WG+air 2800times1400 nm2

Ge WG+air 3000times1600 nm2

Ge WG+air 3200times1800 nm2

Ge WG+air 3400times2000 nm2

Ge WG+air 2800times1400 nm2

Ge WG+air 3000times1600 nm2

Ge WG+air 3200times1800 nm2

Ge WG+air 3400times2000 nm2

Dis

pers

ion

(ps

nmmiddotk

m)

400

300

200

100

-100

-200

0

Dis

pers

ion

(ps

nmmiddotk

m)

400

300

200

100

-100

-200

50

40

30

20

10

0

0

Dis

pers

ion

(ps

nmmiddotk

m)

Non

linea

r co

effic

ient

(m

middotW)

3 4 5 6 7 8 9Wavelength (microm)

3 4 5 6 7 8 9Wavelength (microm)

3 4 5 6 7 8 9

Wavelength (microm)

3 4 5 6 7 8 9

Wavelength (microm)

Figure 8emspIn a wavelength range covering the main part of the mid-IR spectrum (A) on silicon substrate or on suspended silicon membrane are analyzed in terms of dispersion Germanium-on-silicon strip waveguides with an air upper cladding and different dimensions are characterized by (B) dispersion for the quasi-TE mode (C) dispersion for the quasi-TM mode and (D) nonlinearity for the quasi-TE mode

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp257

Besides photonic waveguides another important cat-egory of nonlinear devices is integrated resonators In the scope of this paper we consider relatively large resona-tors for frequency comb generation in which the bending radius of a ring resonator is varied from 50 microm to 100 microm depending on free spectral range (FSR) and the group index in the waveguide In these cases the waveguide-bending-induced dispersion is small and we would not discuss intra-cavity dispersion [202 203] in details here

4 ApplicationsBenefiting from the unique dispersion engineering over an octave-spanning bandwidth as described above one can develop ultra-wideband nonlinear applications that could hardly be attained in an integrated platform previously These include octave-spanning supercontinuum genera-tion pulse compression to a few-cycle or even sub-cycle level octave-spanning Kerr frequency comb generation and the associated mode-locked ultrashort pulse genera-tion using microresonators In this section we review our recent work on these topics

First we discuss the supercontinuum generation and pulse compression in a straight waveguide The nonlinear envelope equation used here to simulate supercontinuum generation is the following

βα infin

=

part part+ + = + part part sum

2

( - )( ) ( )

2

m mm

mm

ii A K A R A

z m t (1)

where

2

0 0

- -( ) 1- ( ) 2

n nn

nn

i i iK A A An t tγ δ δ

ω δ δ

infin

=

= sum

and

2shock_R( ) - 1- [ ( - ) | | ]δ

γ τδ minusinfin

= prime prime int

t

R RR A i i A h t t A dtt

We denote A  =  A(zt) as the complex amplitude of an optical pulse Note that its Fourier transform is

-

1( ) ( ) exp( - ) 2

A z A z t i t dtω ωπ

infin

infin

= int

In Eq (1) α is the total propagation loss and βm is the mth-order dispersion coefficient The frequency dependence of nonlinearity parameters including the nonlinear index n2 the TPA coefficient βTPA and the

effective mode area Aeff is included in the nth-order dis-persion coefficient γn of nonlinearity which is defined as γn = ω0middotpartn[γ(ω)ω]partωn where ω0 is the angular frequency of the carrier Therefore we can consider all-order linear dispersion terms and all-order dispersion of the nonlin-ear coefficient in Eq (1) Specifically in the simulations for a silicon and silicon nitride waveguides we have all-order linear dispersion and up to 6th-order and 2nd-order of the nonlinear coefficient dispersion included A detailed derivation of Eq (1) is given in [204] For the quasi-TM mode that experiences the engineered dispersion due to the mode transition SRS in silicon waveguides fabricated on the (001) surface can be ignored [27 96] For silicon nitride waveguide we include the SRS term in Eq (1) where γR = gRΓR(AeffΩR) and gR ΓR and ΩR represent the Raman gain coefficient the full width at half maximum of the gain spectrum and the Raman shift respectively The Raman shock time τshock_R is associated with γRrsquos fre-quency dependence which is 1ω0-[1Aeff(ω0)][dAeff(ω)dω] similarly as in [14] if we ignore frequency dependent gR ΓR and ΩR hR(t) is the Raman response function and it corresponds to the Raman gain spectrum

2

2 20 0

( ) -( - ) 2 ( - )

Ωω

Ω ω ω Γ ω ω=

+R

RR R

Hi

Note that the sign before the imaginary unit is differ-ent from that in [27] to be consistent with the expression of the Fourier transform that we used

We have considered supercontinuum generation in both silicon and silicon nitride waveguides with the slot-assisted dispersion tailoring Octave-spanning supercon-tinua in a silicon-based stripslot hybrid waveguide have been investigated in detail in [108] in which two-cycle optical pulses are obtained The main results in that work are shown in Figure 9 for comparison purposes

Here we mainly focus on the supercontinuum gen-erated in the silicon nitride stripslot hybrid waveguide (ie the slot WG 1 in Section III) whose dispersion and nonlinearity properties are shown in Figure 6 In the non-linear simulations we set the total propagation loss to be 1 dBcm The SRS parameters used here are the following [205] ΩR2π = 143 THz ΓR2π = 172 THz and gR = 1 times 10-12 mW τshock_R is calculated to be  = 156 fs

In our simulations we use a time step of 025 fs which is corresponding to a bandwidth of 4000 THz in the fre-quency domain For a femtosecond input pulse we set the time window length to 50 ps (ie frequency resolution Δf = 20 GHz)

We simulate the nonlinear propagation of a chirp-free hyperbolic secant pulse in the silicon nitride waveguide

258emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

The pulse center wavelength is at 1610 nm and its full width at half-maximum (FWHM) T0 is 120 fs Its peak power is 1200 W corresponding to pulse energy of 016 nJ

Figure 10(A) shows the supercontinua at different propagation distances At 48 mm the spectrum is greatly broadened at the -30 dB level covering a wavelength range from 0585 to 2833 microm which is more than two octaves The spectrum evolution in Figure 10(A) shows a similar spectrum shape as that in Figure 9(A) both featuring a ldquotriangularrdquo central spectrum bounded by two dispersive waves at the edges However it is important to note that the absence of TPA and 3PA in silicon nitride at the telecom window leads to a much more efficient spectrum broad-ening than that in silicon [108] The generated spectrum extends from the visible light to the mid-IR with excellent spectral coherence which is confirmed by the pulse wave-form shown in Figure 10(B) In the time domain the pulse is greatly compressed from 120 to 408 fs corresponding to 076 optical cycles at 161 microm wavelength

We examine the pulsewidth as a function of propa-gation distance Figure 11 shows that the pulse becomes increasingly narrower until the propagation distance reaches 47 mm For longer distances the pulsewidth

A

B

60 mm

48 mm

36 mm

24 mm

12 mm

Input

Spe

ctru

m (

10 d

Bd

iv)

Pow

er (

W)

12

246

24

18

12

6

0

248 250 252 254

14 16 18 20 22 24Wavelength (microm)

Time (ps)

Figure 9emsp(A) The supercontinuum generation in a silicon-based stripslot hybrid waveguide presented in [108] (B) The significant spectrum broadening at 425-mm distance is associated with a temporal compression of an input pulse (dash line) to the output waveform (solid line) with a FWHM of 12 fs

A

B

50 mm

48 mm

46 mm

44 mm

42 mm

Input

Spe

ctru

m (

10 d

Bd

iv)

Pow

er (

W)

8000

6000

4000

2000

0250249 251

06 09 12 15 18 21 24 27

Wavelength (microm)

Time (ps)

Figure 10emsp(A) Spectrum evolution of the pulse over propagation distance A supercontinuum of more than two octaves is achieved at 48 mm distance (B) Generated pulse waveform with a pulse width of 408 fs as short as 076 optical cycles Low pedestals are caused by dispersive waves generated at the two ends of the spectrum

remains almost constant However it is important to mention that after 48 mm the dispersive waves become increasingly stronger as shown in Figure 10(A) causing larger pedestals

Comparing the results in Figures 9 and 10 we note that the mid-IR wavelength range for silicon would be in analogy to the near-IR for silicon nitride in terms of non-linear optics operations Pumping at or beyond 33 microm one can use the waveguide designs shown in Figure 7 to produce very efficient nonlinear interactions without TPA and 3PA in silicon Ultrashort pulses in the mid-IR from parametric amplifiers [206 207] could be used to pump the Group IV waveguides

Another nonlinear application of the dispersion-engi-neered Group IV waveguides is micro-resonator-based Kerr frequency comb generation When such a waveguide is curved to form a microring resonator input CW light travels around the cavity and amplifies the noise in the source located at the frequencies with a high parametric gain As a result of modulation instability and cascaded FWM in the cavity a frequency comb can be generated [208ndash211] Mode-locked frequency combs have been reported pro-ducing low-noise pulse trains in time domain [212ndash214]

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp259

The formation of cavity solitons is identified as the main reason for the mode-locking in the Kerr frequency combs [215] This is instructive because one can thus predict the spectral bandwidth and temporal pulsewidth in the generated low-noise combs The 3-dB comb bandwidth is inversely proportional to the square root of the 2nd-order dispersion coefficient |β2| as given in [213 215] It is desira-ble that all comb lines that constitute the soliton spectrum experience the same |β2| In this sense the stripslot hybrid waveguides with flattened dispersion are preferably suit-able for supporting broadband Kerr comb generation and ultra-short cavity soliton generation

The Kerr frequency comb generation can be modeled using the generalized Lugiato-Lefever equation (LLE) [216ndash219]

20

2

( - )- - | |

2 2

m mm

R inmm

jkt j jl E kE j l E Et m

βαδ γ

τ

infin

=

part part+ + + = part part

sum (2)

where tR is the round-trip time E = E(tτ) and Ein are intra-cavity field and input field (pump power Pin  =  |Ein|2) t and τ are the slow and fast times δ0 is the cavity phase detuning defined as δ0  =  tRmiddot(ωn -ω0) where ω0 and ωn are the pumprsquos angular frequency and the nth angular reso-nance frequency that is pumped Other resonator param-eters include the power loss per round trip α the power coupling coefficient κ the nonlinear coefficient γ and the mth dispersion coefficient βm Since a flattened dispersion profile has a small β2 over a wide bandwidth it is impor-tant to take the influence of higher-order dispersion into account We include all-order dispersion terms in Eq (2) as we did in solving Eq (1)

To enhance the Kerr comb bandwidth in the near-IR we use the ultra-flattened dispersion profile in Figure 6(A) which is obtained in the slot WG 2 based on

Pul

se w

idth

(fs

)

14

12

10

8

6

4

242 44 46 48 50 52

Propagation distance (mm)

Figure 11emspPulse width first decreases with propagation distance and then remains stable After 48 mm dispersive waves get stronger causing more pedestals

Pow

er (

10 d

Bd

iv)

Pow

er (

W)

70A

B

60

50

40

30

20

10

-10

-20

600

400

200

0

80 120

0575 0600 0625 0650

160 200 240 280 320 360

0

Frequency (THz)

Time (ps)

Figure 12emsp(A) Frequency comb generation with a CW pump at 155 microm using a microring resonator based on a silicon stripslot hybrid waveguide Over an octave-spanning bandwidth from 135 to 270 THz the comb lines have a power drop of 20 dB (B) Generated pulse waveform with a pulse width of 82 fs as short as 16 optical cycles

silicon nitride The ring resonator has a bending radius of 104 microm corresponding to a FSR of 200 GHz Pumping near 155 microm with a pump power of 2 W the resonance peak is red-shifted and we need to red-shift the pump wavelength accordingly and tune it into the resonance from the short-wavelength side When the pump is step-by-step tuned by up to 63 resonance linewidths we obtain the comb spectrum and the mode-locked pulse waveform as shown in Figure 12 One can see that over an octave-spanning bandwidth from 133 to 268 THz the comb lines have a power drop by 20 dB from the center of the spectrum The spectral flatness of this comb is relatively good compared to the previously reported results [208ndash211] The comb bandwidth at -40 dB is as wide as two octaves There are two dispersive peaks in normal dispersion regions beyond the low-dispersion band Such a mode-locked broadband comb produces a train of sub-two-cycle optical pulses as shown in Figure 12(B) with one pulse per round trip The peak power of the pulse is up to 600 W Nonlinear conver-sion efficiency is estimated to be -267 dB

To generate frequency combs in the mid-IR the ger-manium-on-silicon strip waveguide is chosen We choose

260emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

a cross-section of 3200 times 1800 nm2 which has an octave-spanning low-dispersion band from 4 to 767 microm as shown in Figure 8(B) A germanium ring resonator is formed with a bending radius of 564 microm corresponding to a FSR of 200 GHz Pumping at 6 microm with a CW power of 14 W and detuning the pump wavelength by 10 resonance linewidth one can see that a mode-locked wideband mid-IR comb is generated from 358 to 644 THz (ie from 466 to 838 microm) at -40 dB level The FWHM of the produced pulses is 69 fs which corresponds to ~35 optical cycles The pulse peak power is 184 W and the nonlinear conversion efficiency is estimated to be -143 dB Since the pumping frequency is not at the center of the low-dispersion band we only see one peak in the comb spectrum caused by the dispersive wave in the normal dispersion region from Figure 13(A) There is another peak at higher frequencies beyond what is shown in the figure

As shown above broadband dispersion engineering is critical for octave-spanning nonlinear applications in both near- and mid-IR wavelength ranges which enables us to fully utilize the bandwidth allowed by the materials transparency windows Generally speaking the nonlinear applications mentioned here such as supercontinuum generation ultrafast pulse compression and frequency comb generation are often the intermediate steps towards higher-level system applications In the frequency domain a wide spectrum can serve as an electromagnetic carrier to acquire high-volume of information eg for sensing [220] and imaging [221] In the time domain an ultrashort pulse can be used as probe to sample ultrafast phenomena [222]

5 Summary and OutlookWe have presented a review of our recent work on nonlin-ear photonics based on silicon and germanium Various types of Group IV waveguides are analyzed and optimized for four different wavelength ranges from near- to mid-IR The recently proposed dispersion engineering technique based on stripslot hybrid waveguide structures is used for different material combinations and wavelength ranges Numerical simulations show that the dispersion-flattened Group IV waveguides are preferably suitable for octave-spanning nonlinear applications including on-chip supercontinuum generation ultrashort pulse compres-sion and mode-locked wideband frequency comb genera-tion based on micro-resonators

The presented approach to achieving octave-span-ning nonlinear applications on an integrated CMOS-compatible Group IV platform holds great potential for realizing chip-scale sensing imaging communications and signal processing system The ultrawide transparency windows in the mid-IR allowed by Group IV elements and compounds potentially together with other materi-als [223] provide an exciting arena for building powerful information acquisition and processing units enabled by nonlinear optics nano-photonics and ultrafast optics

Received June 14 2013 accepted October 29 2013 previously pub-lished online November 27 2013

Pow

er (

10 d

Bd

iv)

A

8030 40 50 60 70Frequency (THz)

Pow

er (

W)

B200

150

100

50

0

21 22 23 24 25Time (ps)

Figure 13emsp(A) Frequency comb generation with a CW pump at 6 microm using a microring resonator based on a germanium strip waveguide with air upper cladding (B) Generated pulse waveform with a pulse width of 69 fs as short as 35 optical cycles

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp261

Appendix

A Material index and dispersion

In this section we give the wavelength-dependent mate-rial index expressed as Sellmeier equations where wave-length λ is in μm

For silicon we use the following material index that is a fit curve from measurement results at room temperature (293 K) with 184 data points in total from 112 to 588 μm [154]

22 1 2 2

2 2 22

( )-

C Cn

λλ ε

λ λ λ= + +

where ε = 116858 C1 = 0939816 μm2 C2 = 000810461 and λ2 = 11071 μm

For silicon nitride the material index is affected by deposition conditions using plasma-enhanced chemical vapor deposition (PECVD) low-pressure chemical vapor deposition (LPCVD) and so on We use the following Sell-meier equation [155] which predicts the material index close to that in LPCVD silicon nitride films measured by a few groups [224]

22 1

2 21

( ) 1-

Cn

λλ

λ λ= +

where C1 = 28939 and λ1 = 013967 μmFor silicon dioxide we use the following Sellmeier

equation for fused silica [156]22 2

2 31 22 2 2 2 2 2

1 2 3

( ) 1- - -

CC Cn

λλ λλ

λ λ λ λ λ λ= + + +

where C1 = 06961663 C2 = 04079426 C3 = 08974794 λ1 = 00684043 μm λ2 = 01162414 μm and λ3 = 9896161 μm

For SRO the material index is affected by deposition conditions such as silicon excess annealing temperature and so on Here we choose the one with silicon excess of 8 and annealed at 1250oC [51]

22 22 31 2

2 2 2 2 2 21 2 3

( ) 1- - -

CC Cn

λλ λλ

λ λ λ λ λ λ= + + +

where C1 = 001 C2 = 196 C3 = 141 λ1 = 03 μm λ2 = 007071 μm and λ3 = 2775968 μm

For germanium the temperature-dependent mate-rial index was measured [157] Here we choose the one for room temperature (293 K)

2 22 1 2

2 2 2 21 2

( )- -

C Cn

λ λλ ε

λ λ λ λ= + +

where ε = 928156 C1 = 67288 C2 = 021307 λ1 = 0664116 μm and λ2 = 6221013 μm

For arsenic sulfide we use the material index pro-vided in [158]

2 2 22 22 3 4 51 2

2 2 2 2 2 2 2 2 2 21 2 3 4 5

( ) 1- - - - -

C C CC Cn

λ λ λλ λλ

λ λ λ λ λ λ λ λ λ λ= + + + + +

where C1 = 18983678 C2 = 19222979 C3 = 08765134 C4 = 01188704 C5 = 09569903 λ1 = 015 μm λ2 = 025 μm λ3 = 035 μm λ4 = 045 μm and λ5 = 27386128 μm

For arsenic selenide we fit ellipsometry measure-ments of our arsenic selenide thin films and the bulk material is provided by Prof Kathleen A Richardson group

22 22 31 2

2 2 2 2 2 21 2 3

( ) 1- - -

CC Cn

λλ λλ

λ λ λ λ λ λ= + + +

where C1 = 298463 C2 = 321011 C3 = 100182 λ1 = 044118 μm λ2 = 0000354953 μm and λ3 = 38413 μm

B Nonlinear Kerr index n2

The third-order nonlinear susceptibility χ(3)1111 for silicon and

germanium is predicted over the mid-IR range [133] based on a two-band model The effective nonlinear susceptibil-ity χ(3) is dependent on polarization and crystallographic orientation [225] For strong nonlinearity we consider a single-polarization incident light aligned to the crystal-lographic axis and we have χ(3) = χ(3)

1111 To investigate the octave-spanning nonlinear phenomena one need to take the wavelength-dependent nonlinear Kerr index n2 and TPA coefficient βTPA into account which are expressed as

( 3 )2 2

0

( 3 )2

0

3( ) ( )4 ( )

3( ) ( )( )

re

TPA im

ncn

cn

λ χ λε λ

πβ λ χ λ

λε λ

=

=

where ε0 and c are the vacuum permittivity and the speed of light in vacuum Using the material index given in Appendix A and χ(3) value from [133] we obtain the n2 and βTPA values tabulated as follows

262emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

Table 1enspNonlinear Kerr index n2 in silicon

λμm

  n2

10-18 m2W  λ

μm  n2

10-18 m2W  λ

μm  n2

10-18 m2W

130   234   310   389   490   312135   305   315   384   495   311140   378   320   379   500   310145   443   325   375   505   309150   501   330   371   510   307155   559   335   368   515   306160   618   340   365   520   304165   671   345   362   525   304170   710   350   360   530   303175   741   355   358   535   302180   766   360   355   540   302185   781   365   352   545   301190   783   370   350   550   300195   778   375   346   555   298200   762   380   343   560   297205   732   385   341   565   296210   699   390   338   570   296215   658   395   336   575   295220   612   400   334   580   295225   576   405   332   585   295230   547   410   331   590   294235   525   415   330   595   293240   508   420   329   600   292245   493   425   328   605   291250   479   430   327   610   290255   467   435   325   615   289260   456   440   324   620   288265   448   445   321   625   288270   440   450   319   630   288275   432   455   317   635   288280   424   460   315   640   288285   417   465   314   645   288290   410   470   313   650   288295   404   475   313   655   288300   398   480   312   660   288305   394   485   312    

Table 2enspTPA coefficient βTPA in silicon

λμm

  βTPA

10-12 mW  λ

μm  βTPA

10-12 mW  λ

μm  βTPA

10-12 mW

130   1334   165   812   200   180135   1284   170   713   205   115140   1222   175   613   210   064145   1154   180   522   215   024150   1079   185   424   220   0003155   995   190   333    160   905   195   254    

Table 3enspNonlinear Kerr index n2 in germanium

λμm

  n2

10-18 m2W  λ

μm  n2

10-18 m2W  λ

μm  n2

10-18 m2W

23  3932  63  1986  103  170524  4994  64  1972  104  169925  6007  65  1959  105  169426  6650  66  1946  106  169027  6772  67  1934  107  168728  6273  68  1923  108  168429  4897  69  1913  109  168230  4403  70  1904  110  168131  3970  71  1895  111  167932  3680  72  1886  112  167733  3470  73  1876  113  167534  3286  74  1868  114  167335  3128  75  1859  115  167036  2998  76  1850  116  166737  2895  77  1841  117  166338  2812  78  1833  118  165939  2737  79  1826  119  165640  2668  80  1819  120  165341  2605  81  1812  121  165142  2550  82  1807  122  164843  2498  83  1801  123  164644  2450  84  1797  124  164445  2406  85  1792  125  164346  2365  86  1787  126  164147  2328  87  1782  127  163948  2295  88  1777  128  163649  2266  89  1772  129  163450  2238  90  1767  130  163251  2212  91  1762  131  163052  2187  92  1758  132  162853  2164  93  1753  133  162654  2141  94  1749  134  162555  2121  95  1744  135  162356  2101  96  1740  136  162157  2083  97  1736  137  162058  2066  98  1731  138  161859  2049  99  1727  139  161760  2032  100  1722  140  161661  2016  101  1716   62  2001  102  1711   

Table 4enspTPA coefficient βTPA in germanium

λμm

  βTPA

10-8 mW  λμm

  βTPA

10-8 mW  λ

μm  βTPA

10-8 mW

23   130   25   088   27   03124   111   26   060   28   006

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp263

References[1] Bloembergen N Nonlinear Optics London World Scientific 1996[2] Yuen-Ron S The Principles of Nonlinear Optics Hoboken New

Jersey Wiley-Interscience 2002[3] Robert B Nonlinear Optics (3rd ed) Amsterdam Boston

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Woodbury EJ Stimulated raman scattering from organic liquids Phys Rev Lett 19629455ndash7

[8] Giordmaine JA Mixing of light beams in crystals Phys Rev Lett 1962819ndash20

[9] Maker PD Terhune RW Nisenoff M Savage CM Effects of dispersion and focusing on the production of optical harmonics Phys Rev Lett 1962821ndash22

[10] Delone NB Kraĭnov VP Fundamentals of nonlinear optics of atomic gases New York Wiley 1987

[11] Nikogosyan DN Nonlinear optical crystals a complete survey Springer Berlin 2005

[12] Govind A Nonlinear fiber optics (4th ed) San Diego California Academic Press 2007

[13] Russell PSTJ Birks TA Lloyd-Lucas FD Photonic Bloch waves and photonic band gaps In lsquoConfined electrons and photons New physics and applicationsrsquo New York Plenum Press 1995

[14] Dudley JM Genty G Coen S Supercontinuum generation in photonic crystal fiber Rev Mod Phys 2006781135ndash1184

[15] Dudley JM Taylor JR Ten years of nonlinear optics in photonic crystal fibre Nature Photonics 2009385ndash90

[16] Soref RA Silicon-based optoelectronics Proceedings of the IEEE 1993811687ndash1706

[17] Kimerling LC Silicon for photonics Proc SPIE 3002 1997192[18] Kimerling LC Silicon materials engineering for the next

millennium Sol St Phen 199970131ndash142[19] Pavesi L Lockwood DJ editors Silicon Photonics New York

Springer 2004[20] Reed GT Knights AP Silicon photonics an introduction Wiley

Hoboken NJ 2004[21] Lipson M Guiding modulating and emitting light on silicon -

challenges and opportunities IEEE J Lightwave Technol 2005 234222

[22] Soref RA The past present and future of silicon photonics IEEE J Sel Top Quantum Electron 2006121678ndash87

[23] Jalali B Paniccia M Reed G Silicon photonics IEEE Microwave Magazine 2006758ndash68

[24] Jalali B Fathpour S Silicon photonics J Lightwave Technol 2006 244600ndash15

[25] Kirchain R Kimerling L A roadmap for nanophotonics Nature Photonics 20071303ndash5

[26] Dekker R Usechak N Foumlrst M Driessen A Ultrafast nonlinear all-optical processes in silicon-on-insulator waveguides J Phys D Appl Phys 200740R249ndash71

[27] Lin Q Painter OJ Agrawal GP Nonlinear optical phenomena in silicon waveguides Modeling and applications Opt Express 20071516604ndash44

[28] Tsang HK Liu Y Nonlinear optical properties of silicon waveguides Semicond Sci Technol 2008 23064007

[29] Osgood RM Jr Panoiu NC Dadap JI Liu X Chen X Hsieh I-W Dulkeith E Green WM Vlasov YA Engineering nonlinearities in nanoscalse optical systems Physics and applications in dispersion-engineered silicon nonaphotonics wires Adv Opt Photon 20091162ndash235

[30] Leuthold J Koos C Freude W Nonlinear silicon photonics Nature Photonics 20104535ndash44

[31] Ikeda K Shen Y Fainman Y Enhanced optical nonlinearity in amorphous silicon and its application to waveguide devices Opt Express 20071517761ndash71

[32] Shoji Y Ogasawara T Kamei T Sakakibara Y Suda S Kintaka K Kawashima H Okano M Hasama T Ishikawa H Mori M Ultrafast nonlinear effects in hydrogenated amorphous silicon wire waveguide Opt Express 2010185668ndash73

[33] Narayanan K Preble SF Optical nonlinearities in hydrogenated-amorphous silicon waveguides Opt Express 2010188998ndash9005

[34] Grillet C Carletti L Monat C Grosse P Ben Bakir B Menezo S Fedeli JM Moss DJ Amorphous silicon nanowires combining high nonlinearity FOM and optical stability Opt Express 20122022609ndash15

[35] Matres J Ballesteros GC Gautier P Feacutedeacuteli J-M Martiacute J Oton CJ High nonlinear figure-of-merit amorphous silicon waveguides Opt Express 2013213932ndash40

[36] Hernaacutendez S Pellegrino P Martiacutenez A Lebour Y Garrido B Spano R Cazzanelli M Daldosso N Pavesi L Jordana E Fedeli JM Linear and nonlinear optical properties of Si nanocrystals in SiO2 deposited by plasma-enhanced chemical-vapor deposition J Appl Phys 2008103 064309

[37] Yuan Z Anopchenko A Daldosso N Guider R Navarro-Urrios D Pitanti A Spano R Pavesi L Silicon Nanocrystals as an Enabling Material for Silicon Photonics Proc IEEE 2009971250ndash68

[38] Spano R Daldosso N Cazzanelli M Ferraioli L Tartara L Yu J Degiorgio V Giordana E Fedeli JM Pavesi L Bound electronic and free carrier nonlinearities in Silicon nanocrystals at 1550 nm Opt Express 2009173941ndash50

[39] Rukhlenko ID Zhu W Premaratne M Agrawal GP Effective third-order susceptibility of silicon-nanocrystal-doped silica Opt Express 20122026275ndash84

[40] Loacutepez-Suaacuterez A Torres-Torres C Rangel-Rojo R Reyes-Esqueda JA Santana G Alonso JC Ortiz A Oliver A Modification of the nonlinear optical absorption and optical Kerr response exhibited by nc-Si embedded in a silicon-nitride film Opt Express 20091710056ndash68

[41] Minissale S Yerci S Dal Negro L Nonlinear optical properties of low temperature annealed silicon-rich oxide and silicon-rich nitride materials for silicon photonics Appl Phys Lett 2012100021109

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264emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

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[46] Sun R Dong P Feng N-N Hong C-Y Michel J Lipson M Kimerling L Horizontal single and multiple slot waveguides optical transmission at λ = 1550 nm Opt Express 20071517967ndash72

[47] Fujisawa T Koshiba M Guided modes of nonlinear slot waveguides IEEE Photon Technol Lett 2006181530ndash32

[48] Sanchis P Blasco J Martiacutenez A Martiacute J Design of silicon-based slot waveguide configurations for optimum nonlinear performance J Lightwave Technol 2007251298ndash1305

[49] Koos C Jacome L Poulton C Leuthold J Freude W Nonlinear silicon-on-insulator waveguides for all-optical signal processing Opt Express 2007155976ndash90

[50] Muellner P Wellenzohn M Hainberger R Nonlinearity of optimized silicon photonic slot waveguides Opt Express 2009179282ndash7

[51] Spano R Galan JV Sanchis P Martinez A Martiacute J Pavesi L Group velocity dispersion in horizontal slot waveguides filled by Si nanocrystals International Conf on Group IV Photonics 2008314ndash6

[52] Zheng Z Iqbal M Liu J Dispersion characteristics of SOI-based slot optical waveguides Opt Commun 20082815151ndash5

[53] Zhang L Yue Y Y Xiao-Li Wang J Beausoleil RG Willner AE Flat and low dispersion in highly nonlinear slot waveguides Opt Express 20101813187ndash93

[54] Mas S Caraquitena J Galaacuten JV Sanchis P Martiacute J Tailoring the dispersion behavior of silicon nanophotonic slot waveguides Opt Express 20101820839ndash44

[55] De Leonardis F Passaro VMN Dispersion engineered silicon nanocrystal slot waveguides for soliton ultrafast optical processing Adv Opt Electron 20112011Article ID 751498 9 pages

[56] Liu Q Gao S Li Z Xie Y He S Dispersion engineering of a silicon-nanocrystal-based slot waveguide for broadband wavelength conversion Appl Opt 2011501260ndash5

[57] Ryu H Kim J Jhon YM Lee S Park N Effect of index contrasts in the wide spectral-range control of slot waveguide dispersion Opt Express 20122013189ndash94

[58] Nolte PW Bohley C Schilling J Tuning of zero group velocity dispersion in infiltrated vertical silicon slot waveguides Opt Express 2013211741ndash50

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[60] Zhang L Lin Q Yue Y Yan Y Beausoleil RG Willner AE Silicon waveguide with four zero-dispersion wavelengths and its application in on-chip octave-spanning supercontinuum generation Opt Express 2012201685ndash90

[61] Zhu M Liu H Li X Huang N Sun Q Wen J Wang Z Ultrabroadband flat dispersion tailoring of dual-slot silicon waveguides Opt Express 20122015899ndash907

[62] Wang S Hu J Guo H Zeng X Optical Cherenkov radiation in an As2S3 slot waveguide with four zero-dispersion wavelengths Opt Express 2013213067ndash72

[63] Roy S Biancalana F Formation of quartic solitons and a localized continuum in silicon-based slot waveguides Phys Rev A 201387025801

[64] Monat C de Sterke M Eggleton BJ Slow light enhanced nonlinear optics in periodic structures J Opt 201012104003

[65] Boyd RW Material slow light and structural slow light similarities and differences for nonlinear optics [Invited] J Opt Soc Am B 201128A38ndash44

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[67] Claps R Dimitropoulos D Raghunathan V Han Y Jalali B Observation of stimulated Raman amplification in silicon waveguides Opt Express 2003111731ndash9

[68] Espinola RL Dadap JI Osgood RM Jr McNab SJ Vlasov YA Raman amplification in ultrasmall silicon-on-insulator wire waveguides Opt Express 2004123713ndash8

[69] Xu Q Almeida VR Lipson M Time-resolved study of Raman gain in highly confined silicon-on-insulator waveguides Opt Express 2004124437ndash42

[70] Liu A Rong H Paniccia M Cohen O Hak D Net optical gain in a low loss silicon-on-insulator waveguide by stimulated Raman scattering Opt Express 2004124261ndash8

[71] Rong H Liu A Nicolaescu R Paniccia M Cohen O Hak D Raman gain and nonlinear optical absorption measurement in a low-loss silicon waveguide Appl Phys Lett 2004852196ndash8

[72] Liang TK Tsang HK Efficient Raman amplification in silicon-on-insulator waveguides Appl Phys Lett 2004853343ndash5

[73] Boyraz O Jalali B Demonstration of a silicon Raman laser Opt Express 2004125269ndash73

[74] Krause M Renner H Brinkmeyer E Analysis of Raman lasing characteristics in silicon-on-insulator waveguides Opt Express 2004125703ndash10

[75] Xu Q Almeida VR Lipson M Demonstration of high Raman gain in a submicrometer-size silicon-on-insulator waveguide Opt Lett 20053035ndash7

[76] Rong H Liu A Jones R Cohen O Hak D Nicolaescu R Fang A Paniccia M An all-silicon Raman laser Nature 2005433292ndash4

[77] Rong H Jones R Liu A Cohen O Hak D Fang A Paniccia M A continuous-wave Raman silicon laser Nature 2005433725ndash8

[78] Chen X Panoiu NC Osgood RM Jr Theory of Raman-mediated pulsed amplification in silicon-wire waveguides IEEE J Quantum Electron 200642160ndash70

[79] Rong H Kuo Y-H Xu S Cohen O Raday O Paniccia M Recent development on silicon-based Raman lasers and amplifiers Proc SPIE 6389 638904-1-9 2006

[80] Okawachi Y Foster MA Sharping JE Gaeta AL Xu Q Lipson M All-optical slow-light on a photonic chip Opt Express 2006142317ndash22

[81] Jalali B Raghunathan V Dimitropoulos D Boyraz O Raman-based silicon photonics IEEE J Sel Top Quantum Electron 200612412ndash21

[82] Rong H Xu S Kuo Y Sih V Cohen O Raday O Paniccia M Low-threshold continuous-wave Raman silicon laser Nature Photon 20071232ndash7

[83] De Leonardis F Passaro VMN Ultrafast Raman pulses in SOI waveguides for nonlinear signal processing IEEE J Sel Top Quant 200814739ndash51

[84] Tsang HK Wong CS Liang TK Day IE Roberts SW Harpin A Drake J Asghari M Optical dispersion two-photon absorption and self-phase modulation in silicon waveguides at 15 μm wavelength Appl Phys Lett 200280416ndash8

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp265

[85] Boyraz O Indukuri T Jalali B Self-phase-modulation induced spectral broadening in silicon waveguides Opt Express 200412829ndash34

[86] Rieger GW Virk KS Yong JF Nonlinear propagation of ultrafast 15 μm pulses in high-index-contrast silicon-on-insulator waveguides Appl Phys Lett 200484900ndash2

[87] Dulkeith E Vlasov YA Chen X Panoiu NC Osgood RM Jr Self-phase-modulation in submicron silicon-on-insulator photonic wires Opt Express 2006145524ndash34

[88] Hsieh I-W Chen X Dadap JI Panoiu NC Osgood RM Jr McNab SJ Vlasov YA Ultrafast-pulse self-phase modulation and third-order dispersion in Si photonic wire-waveguides Opt Express 20061412380ndash7

[89] Hsieh I-W Chen X Dadap JI Panoiu NC Osgood RM Jr McNab SJ Vlasov YA Cross phase modulation-induced spectral and temporal effects on co-propagating femtosecond pulses in silicon photonic wires Opt Express 2007151135ndash46

[90] Zhang J Lin Q Piredda G Boyd RW Agrawal GP Fauchet PM Optical solitons in a silicon waveguide Opt Express 2007157682ndash8

[91] Salem R Foster MA Turner AC Geraghty DF Lipson M Gaeta AL All-optical regeneration on a silicon chip Opt Express 2007157802ndash9

[92] Claps R Raghunathan V Dimitropoulos D Jalali B Anti-Sotkes Raman conversion in silicon waveguides Opt Express 2003112862ndash72

[93] Espinola RL Dadap JI Osgood RM Jr McNab SJ Vlasov YA C-band wavelength conversion in silicon photonic wire waveguides Opt Express 2005134341ndash9

[94] Fukuda H Yamada K Shoji T Takahashi M Tsuchizawa T Watanabe T Takahashi J Itabashi S Four-wave mixing in silicon wire waveguides Opt Express 2005134629ndash37

[95] Rong H Kuo Y Liu A Paniccia M Cohen O High efficiency wavelength conversion of 10 Gbs data in silicon waveguides Opt Express 2006141182ndash8

[96] Lin Q Zhang J Fauchet PM Agrawal GP Ultrabroadband parametric generation and wavelength conversion in silicon waveguides Opt Express 2006144786ndash99

[97] Foster MA Turner AC Sharping JE Schmidt BS Lipson M Gaeta AL Broad-band optical parametric gain on a silicon photonic chip Nature 2006441960ndash3

[98] Yamada K Fukuda H Tsuchizawa T Watanabe T Shoji T Itabashi S All-optical efficient wavelength conversion using silicon photonic wire waveguide IEEE Photon Technol Lett 2006181046ndash8

[99] Kuo Y Rong H Sih V Xu S Paniccia M Cohen O Demonstration of wavelength conversion at 40 Gbs data rate in silicon waveguides Opt Express 20061411721ndash6

[100] Foster MA Turner AC Salem R Lipson M Gaeta AL Broad-band continuous-wave parametric wavelength conversion in silicon nanowaveguides Opt Express 20071512949ndash58

[101] Dai Y Chen X Okawachi Y Turner-Foster AC Foster MA Lipson M Gaeta AL Xu C 1 μs tunable delay using parametric mixing and optical phase conjugation in Si waveguides Opt Express 2009177004ndash10

[102] De Leonardis F Passaro VMN Efficient wavelength conversion in optimized SOI waveguides via pulsed four wave mixing IEEE J Lightwave Technol 2011293523ndash35

[103] Yin L Lin Q Agrawal GP Soliton fission and supercontinuum generation in silicon waveguides Opt Lett 200732391ndash3

[104] Koonath P Solli DR Jalali B Continuum generation and carving on a silicon chip Appl Phys Lett 200791061111

[105] Hsieh I-W Chen X Liu X Dadap JI Panoiu NC C-Chou Y Xia F Green WM Vlasov YA Osgood RM Jr Supercontinuum generation in silicon photonic wires Opt Express 20071515242ndash8

[106] Kuyken B Liu X Osgood RM Jr Baets R Roelkens G Green WMJ Mid-infrared to telecom-band supercontinuum generation in highly nonlinear silicon-on-insulator wire waveguides Opt Express 20111920172ndash81

[107] DeVore PTS Solli DR Ropers C Koonath P Jalali B Stimulated supercontinuum generation extends broadening limits in silicon Appl Phys Lett 2012100101111

[108] Zhang L Lin Q Yue Y Yan Y Beausoleil RG Agarwal A Kimerling LC Michel J Wilner AE On-chip octave-spanning supercontinuum in nanostructured silicon waveguides using ultralow pulse energy IEEE J Sel Top Quant 2012181799ndash806

[109] Claps R Raghunathan V Dimitropoulos D Jalali B Influence of nonlinear absorption on Raman amplification in silicon waveguides Opt Express 2004122774ndash80

[110] Yin L Agrawal GP Impact of two-photon absorption on self-phase modulation in silicon waveguides Opt Lett 2007322031ndash3

[111] Ikeda K Saperstein RE Alic N Fainman Y Thermal and Kerr nonlinear properties of plasma-deposited silicon nitridesilicon dioxide waveguides Opt Express 20081612987ndash94

[112] Levy JS Gondarenko A Foster MA Turner-Foster AC Gaeta AL Lipson M CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects Nat Photonics 2010437ndash40

[113] Tan DTH Ikeda K Sun PC Fainman Y Group velocity dispersion and self phase modulation in silicon nitride waveguides Appl Phys Lett 201096061101

[114] Zhang L Yan Y Yue Y Lin Q Painter O Beausoleil RG Willner AE On-chip two-octave supercontinuum generation by enhancing self-steepening of optical pulses Opt Exp 20111911584ndash90

[115] Halir R Okawachi Y Levy JS Foster MA Lipson M Gaeta AL Ultrabroadband supercontinuum generation in a CMOS-compatible platform Opt Lett 2012371685

[116] Ye J Frequency comb spectroscopy from mid-infrared to extreme ultraviolet Conference on Lasers and Electro-Optics (CLEO) 2012 Tutorial CW1J4

[117] Popmintchev T Chen M-C Popmintchev D Arpin P Brown S Alisauskas S Andriukaitis G Balciunas T Mucke OD Pugzlys A Baltuska A Shim B Schrauth SE Gaeta A Hernandez-Garcia C Plaja L Becker A Jaron-Becker A Murnane MM Kapteyn HC Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers Science 20123361287ndash91

[118] Qin GS Yan X Kito C Liao M Chaudhari C Suzuki T Ohishi Y Ultrabroadband supercontinuum generation from ultraviolet to 628 microm in a fluoride fiber Appl Phys Lett 200995 161103ndash1ndash161103-3

[119] Soref RA Emelett SJ Buchwald WR Silicon waveguided components for the long-wave infrared region J Opt A 20068840ndash8

266emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

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[121] Mashanovich GZ Milosevic M Matavulj P Timotijevic B Stankovic S Yang PY Teo EJ Breese MBH Bettiol AA Reed GT Silicon photonic waveguides for different wavelength regions Semiconductor Sci Technol 200823064002

[122] Soref R Mid-infrared photonics in silicon and germanium Nat Photonics 20104495ndash7

[123] Green WMJ Liu X Osgood RM Vlasov YA Mid-infrared nonlinear optics in silicon photonic wire waveguides Photonics Society Summer Topical Meeting Series 201062ndash63

[124] Milosevic MM Nedeljkovic M Masaud T-B Jaberansary E Chong HMH Emerson NG Reed GT Mashanovich GZ Silicon waveguides and devices for the mid-infrared Appl Phys Lett 2012101121105

[125] Soref R Group IV photonics for the mid infrared SPIE Photonics West 2013 Proc of SPIE 20138629paper 862902

[126] Crowder JG Smith SD Vass A Keddie J Infrared methods for gas detection in Mid-Infrared Semiconductor Optoelec-tronics New York Springer-Verlag 2006

[127] George Socrates Infrared and Raman Characteristic Group Frequencies Tables and Charts 3rd Ed Chichester John Wiley amp Sons 2001

[128] Longshore R Raimondi P Lumpkin M Selection of detector peak wavelength for optimum infrared system performance Infrared Phys 197616639ndash47

[129] Findlay GA Cutten DR Comparison of performance of 3ndash5-and 8ndash12-microm infrared systems Appl Opt 1989285029ndash37

[130] Labadie L Wallner O Mid-infrared guided optics a perspective for astronomical instruments Opt Express 2009171947ndash62

[131] Pearl S Rotenberg N van Driel HM Three photon absorption in silicon for 2300ndash3300 nm Appl Phys Lett 200893131102

[132] Wang Z Liu H Huang N Sun Q Wen J Li X Influence of three-photon absorption on Mid-infrared cross-phase modulation in silicon-on-sapphire waveguides Opt Express 2013211840ndash8

[133] Hon NK Soref RA Jalali B The third-order nonlinear optical coefficients of Si Ge and Si1-xGex in the midwave and longwave infrared J Appl Phys 2011110011301

[134] Sheik-Bahae M Hutchings DC Hagan DJ Stryland EWV Dispersion of bound electric nonlinear refraction in solids IEEE J Quant Electron 1991271296ndash1309

[135] Jalali B Raghunathan V Shori R Fathpour S Prospects for silicon mid-IR Raman lasers IEEE J Sel Top Quantum Electron 2006121618ndash27

[136] Raghunathan V Borlaug D Rice RR Jalali B Demonstration of a mid-infrared silicon Raman amplifier Opt Express 20071514355ndash62

[137] Chavez Boggio JM Windmiller JR Knutzen M Jiang R Bres C Alic N Stossel B Rottwitt K Radic S 730-nm optical parametric conversion from near- to short-wave infrared band Opt Express 2008165435ndash43

[138] Lin Q Johnson TJ Perahia R Michael CP Painter OJ A proposal for highly tunable optical parametric oscillation in silicon micro-resonators Opt Express 20081610596ndash610

[139] Turner-Foster AC Foster MA Salem R Gaeta AL Lipson M Frequency conversion over two-thirds of an octave in silicon nanowaveguides Opt Express 2010181904ndash8

[140] Liu X Osgood RM Vlasov YA Green WMJ Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides Nat Photonics 20104557ndash60

[141] Zlatanovic S Park JS Moro S Boggio JMC Divliansky IB Alic N Mookherjea S Radic S Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source Nat Photonics 20104561ndash4

[142] Tien EK Huang YW Gao S Song Q Qian F Kalyoncu SK Boyraz O Discrete parametric band conversion in silicon for mid-infrared applications Opt Exp 20101821981ndash9

[143] Lau RKW Meacutenard M Okawachi Y Foster MA A C Turner-Foster Salem R Lipson M Gaeta AL Continuous-wave mid-infrared frequency conversion in silicon nanowaveguides Opt Lett 2011361263ndash5

[144] Roelkens G Green WMJ Kuyken B Liu X Hattasan N Gassenq A Cerutti L Rodriguez JB Osgood RM Tournie E Baets R III-Vsilicon photonics for short-wave infrared spectroscopy IEEE J Quant Electron 201248292ndash8

[145] Alloatti L Korn D Weimann C Koos C Freude W Leuthold J Second-order nonlinear silicon-organic hybrid waveguides Opt Express 20122020506ndash15

[146] Harris DC Durable 3ndash5 μm transmitting infrared window materials Infrared Phys Technol 199839185ndash201

[147] Carlie N Musgraves JD Zdyrko B Luzinov I Hu J Singh V Agarwal A Kimerling LC Canciamilla A Morichetti F Melloni A Richardson K Integrated chalcogenide waveguide resonators for mid-IR sensing leveraging material properties to meet fabrication challenges Opt Express 20101826728ndash43

[148] Eggleton BJ B Luther-Davies Richardson K Chalcogenide photonics Nat Photonics 20115141ndash8

[149] Madden SJ Vu KT High-Performance Integrated Optics with Tellurite Glasses Status and Prospects Int J Appl Glass Sci 20123289ndash98

[150] Bindra KS Bookey HT Kar AK Wherrett BS Liu X Jha A Nonlinear optical properties of chalcogenide glasses observation of multiphoton absorption App Phys Lett 2001791939ndash41

[151] Zakery A Ruan Y ARode V Samoc M Luther-Davies B Low-loss waveguides in ultrafast laser-deposited As2S3 chalcogenide films J Opt Soc Am B 200391844ndash52

[152] Lenz G Zimmermann J Katsufuji T MLines E Hwang HY Spalter S Slusher RE Cheong SW Sanghera JS Aggarwal ID Large Kerr effect in bulk Se-based chalcogenide glasses Opt Lett 200025254ndash6

[153] Sanghera JS Shaw LB Aggarwal ID Application of chalcogenide glass optical fibers CR Chimie 20025873ndash83

[154] Palik ED Handbook of optical constants of solids San Diego CA Academic 1998

[155] Philipp HR Optical properties of silicon nitride J Electrochem Soc 1973120295ndash300

[156] Malitson IH Interspecimen comparison of the refractive index of fused silica J Opt Soc Am 1965551205ndash8

[157] Barnes NP Piltch MS Temperature-dependent Sellmeier coefficients and nonlinear optics average power limit for germanium J Opt Soc Am 197969178ndash80

[158] Rodney WS Malitson IH King TA Refractive index of arsenic trisulfide J Opt Soc Am 195848633ndash636

[159] Ellipsometry measurement on the thin film samples by our group[160] Bristow AD Rotenberg N van Driel HM Two-photon

absorption and Kerr coefficients of silicon for 850ndash2200 nm Appl Phys Lett 200790191104

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp267

[161] Lin Q Zhang J Piredda G Boyd RW Fauchet PM Agrawal GP Dispersion of silicon nonlinearities in the near infrared region Appl Phys Lett 200791021111

[162] Mizrahi V DeLong KW Stegeman GI Saifi MA Andrejco MJ Two-photon absorption as a limitation to all-optical switching Opt Lett 1989141140ndash2

[163] Guider R NDaldosso APitanti EJordana Fedeli J-M Pavesi L NanoSi low loss horizontal slot waveguides coupled to high Q ring resonators Opt Express 20091720762ndash70 and its erratum

[164] Ferrera M Razzari L Duchesne D Morandotti R Yang Z Liscidini M Sipe JE Chu S Little BE Moss DJ Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures Nat Photonics 20082 737ndash40

[165] Smektala F Quemard C Leneindre L Lucas J Barthelemy A De Angelis C Chalcogenide glasses with large non-linear refractive indices J Non-Crystalline Solids 1998239139ndash42

[166] Boudebs G Sanchez F Troles J Smektala F Nonlinear optical properties of chalcogenide glasses- comparison between Mach-Zehnder interferometry and Z-scan techniques Opt Comm 2001199425ndash33

[167] Asobe M Suzuki K Kanamori T Kubodera K Nonlinear refractive index measurement in chalcogenide-glass fibers by self-phase modulation APL 1992601153ndash4

[168] Asobe M Kanamori T Kubodera K Ultrafast all-optical switching using highly nonlinear chalcogenide glass fiber IEEE Photon Technol Lett 19924362ndash5

[169] Asobe M Kanamori T Kubodera K Applications of highly nonlinear chalcogenide glass fibers in ultrafast all-optical switches IEEE J Quant Electron 1993292325ndash33

[170] Ruan Y Luther-Davies B Li W Rode A Kolev V Madden S Large phase shifts in As2S3 waveguides for all-optical processing devices Opt Lett 2005302605ndash7

[171] Laniel JM Hocirc N Valleacutee R Villeneuve A Nonlinear-refractive-index measurement in As2S3 channel waveguides by asymmetric self-phase modulation J Opt Soc Am B 200522437ndash45

[172] Cerqua-Richardson KA McKinley JM Lawrence B Joshi S Villeneuve A Comparison of nonlinear optical properties of sulfide glasses in bulk and thin film form Opt Mater 199810155ndash9

[173] Harbold JM Ilday FOuml Wise FW Sanghera JS Nguyen VQ Shaw LB Aggarwal ID Highly nonlinear As-S-Se glasses for all-optical switching Opt Lett 200227119ndash121

[174] Ruan YL Li WT Jarvis R Madsen N Rode A Luther-Davies B Fabrication and characterization of low loss rib chalcogenide waveguides made by dry etching Opt Express 2004125140ndash5

[175] Slusher RE Lenz G Hodelin J Sanghera J Shaw LB Aggarwal ID Large Raman gain and nonlinear phase shifts in high-purity As2Se3 chalcogenide fibers J Opt Soc Am B 2004211146ndash55

[176] Jacobsen R Andersen K Borel P Fage-Pedersen J Frandsen L Hansen O Kristensen M Lavrinenko A Moulin G Ou H Peucheret C Zsigri B Bjarklev A Strained silicon as a new electro-optic material Nature 2006441199ndash202

[177] Cazzanelli M Bianco F Borga E Pucker G Ghulinyan M Degoli E Luppi E Veacuteniard V Ossicini S Modotto D Wabnitz S Pierobon R Pavesi L Second-harmonic generation in

silicon waveguides strained by silicon nitride Nat Mater 201111148ndash54

[178] Avrutsky I Soref R Phase-matched sum frequency generation in strained silicon waveguides using their second-order nonlinear optical susceptibility Opt Express 20111921707ndash16

[179] Ghahramani E Moss DJ Sipe JE Second-harmonic generation in odd-period strained (Si)n(Ge)nSi superlattices and at SiGe interfaces Phys Rev Lett 1990642815ndash8

[180] Levy JS Foster MA Gaeta AL Lipson M Harmonic generation in silicon nitride ring resonators Opt Express 20111911415

[181] Zakery A Elliott SR Optical nonlinearities in chalcogenide glasses and their applications Springer Series in Optical Sciences 2007135

[182] Lee KK Lim DR Kimerling LC Shin J Cerrina F Fabrication of ultralow-loss SiSiO2 waveguides by roughness reduction Opt Lett 2001261888ndash90

[183] Cardenas J Poitras CB Robinson JT Preston K Chen L Lipson M Low loss etchless silicon photonic waveguides Opt Express 2009174752ndash7

[184] Biberman A Shaw MJ Timurdogan E Wright JB Watts MR Ultralow-loss silicon ring resonators Opt Lett 2012374236ndash8

[185] Walmsley IA Waxer L Dorrer C The role of dispersion in ultrafast optics Rev Sci Instrum 2001721ndash29

[186] Torres JP MHendrych Valencia A Angular dispersion an enabling tool in nonlinear and quantum optics Adv Opt Photon 20102319ndash69

[187] Yin LH Lin Q Agrawal GP Dispersion tailoring and soliton propagation in silicon waveguides Opt Lett 2006311295ndash7

[188] Dulkeith E Xia FN Schares L Green WMJ Vlasov YA Group index and group velocity dispersion in silicon-on-insulator photonic wires Opt Express 2006143853ndash63

[189] Turner AC Manolatou C Schmidt BS Lipson M Tailored anomalous group-velocity dispersion in silicon channel waveguides Opt Express 2006144357ndash62

[190] Dadap JI Panoiu NC Chen X I-Hsieh W Liu X Chou C-Y Dulkeith E McNab SJ Xia F Green WMJ Sekaric L Vlasov YA Osgood RM Jr Nonlinear-optical phase modification in dispersion-engineered Si photonic wires Opt Express 2008161280ndash99

[191] Milosevic MM Matavulj PS Yang PY Bagolini A Mashanovich GZ Rib waveguides for mid-infrared silicon photonics J Opt Soc Am B 2009261760ndash6

[192] Mashanovich GZ Milošević MM Nedeljkovic M Owens N Xiong B Teo EJ Hu Y Low loss silicon waveguides for the mid-infrared Opt Express 2011197112ndash9

[193] Reimer C Nedeljkovic M Stothard DJM Esnault MOS Reardon C OrsquoFaolain L Dunn M Mashanovich GZ Krauss TF Mid-infrared photonic crystal waveguides in silicon Opt Express 20122029361ndash8

[194] Baehr-Jones T Spott A Ilic R Spott A Penkov B Asher W Hochberg M Silicon-on-sapphire integrated waveguides for the midinfrared Opt Express 20101812127ndash35

[195] Li F Jackson S Grillet C Magi E Hudson D Madden SJ Moghe Y OrsquoBrien C Read A Duvall SG Atanackovic P Eggleton BJ Moss D Low propagation loss silicon-on-sapphire waveguides for the midinfrared Opt Express 20111915212ndash20

268emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

[196] Yue Y Zhang L Huang H Beausoleil RG Willner AE Silicon-on-nitride waveguide with ultralow dispersion over an octave-spanning mid-infared wavelength range IEEE Photonics J 20124126ndash32

[197] Khan S Chiles J Ma J Fathpour S Silicon-on-nitride waveguides for mid-and near-infrared integrated photonics Appl Phys Lett 2013102121104

[198] Cheng Z Chen X Wong CY Xu K Tsang HK Mid-infrared suspended membrane waveguide and ring resonator on silicon-on-insulator IEEE Photonics J 201241510ndash9

[199] Lin P-T Singh V Cai Y Kimerling LC Agarwal A Air-clad silicon pedestal structures for broadband mid-infrared microphotonics Opt Lett 2013381031ndash3

[200] Chang YC Paeder V Hvozdara L Hartmann JM Herzig HP Low-loss germanium strip waveguides on silicon for the mid-infrared Opt Lett 2012372883ndash5

[201] Zhang L Yue Y Y Xiao-Li R G Beausoleil Willner AE Highly dispersive slot waveguides Opt Express 2009177095ndash101

[202] Zhang L Yue Y Beausoleil RG Willner AE Analysis and engineering of chromatic dispersion in silicon waveguide bends and ring resonators Opt Express 2011198102ndash7

[203] Zhang L Mu J Singh V Agarwal A Kimerling LC Michel J Intra-cavity dispersion of microresonators and its engineering for octave-spanning Kerr frequency comb generation to be published

[204] Lin Q Zhang L Generalized nonlinear envelope equation with high-order dispersion of nonlinearity to be published

[205] Wang Y Yue R Han H Liao X Raman study of structural order of a-SiNxH and its change upon thermal annealing J Non-Crystalline Solids 2001291107ndash12

[206] Brida D Marangoni M Manzoni C De Silvestri S Cerullo G Two-optical-cycle pulses in the mid-infrared from an optical parametric amplifier Opt Lett 2008332901ndash3

[207] Brida D Manzoni C Cirmi G Marangoni M Bonora S Villoresi P De Silvestri S Cerullo G Few-optical-cycle pulses tunable from the visible to the mid-infrared by optical parametric amplifiers J Opt 201012013001

[208] Kippenberg TJ Holzwarth R Diddams SA Microresonator-based optical frequency combs Science 2011332555ndash9

[209] Levy JS Gondarenko A Foster MA Turner-Foster AC Gaeta AL Lipson M CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects Nat Photonics 2009437ndash40

[210] DelrsquoHaye P Herr T Gavartin E Gorodetsky ML Holzwarth R Kippenberg TJ Octave spanningtunable frequency comb from a microresonator Phys Rev Lett 2011107063901

[211] Okawachi Y Saha K Levy JS Wen YH Lipson M Gaeta AL Octave-spanning frequency combgeneration in a silicon nitride chip Opt Lett 2011363398ndash400

[212] Matsko AB Savchenkov AA Liang W Ilchenko VS Seidel D Maleki L Mode-locked Kerr frequency combs Opt Lett 2011362845ndash7

[213] Herr T Brasch V Jost JD Wang CY Kondratiev NM Gorodetsky ML Kippenberg TJ Temporal solitons in optical microresonators httparxivorgabs12110733

[214] Saha K Okawachi Y Shim B Levy JS Salem R Johnson AR Foster MA Lamont MR Lipson M Gaeta AL Modelocking and femtosecond pulse generation in chip-based frequency combs Opt Express 2013211335ndash43

[215] Coen S Erkintalo M Universal scaling laws of Kerr frequency combs Opt Lett 2013381790ndash2

[216] Lugiato LA Lefever R Spatial dissipative structures in passive optical-systems Phys Rev Lett 1987582209ndash11

[217] Haelterman M Trillo S Wabnitz S Dissipative modulation instability in a nonlinear dispersive ring cavity Opt Commun 199291401ndash7

[218] Coen S Randle HG Sylvestre T Erkintalo M Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato-Lefever model Opt Lett 20133837ndash9

[219] Chembo YK Menyuk CR Spatiotemporal Lugiato-Lefever formalism for Kerr-comb generation in whispering-gallery-mode resonators Phys Rev A 201387053852

[220] Foltynowicz A Mas1owski P Ban T Adler F Cossel KC Briles TC Ye J Optical frequency comb spectroscopy Faraday Discussion 201115023ndash31

[221] Hartl I Li XD Chudoba C Ghanta RK Ko TH Fujimoto JG Ranka JK Windeler RS Ultrahigh-resolution optical coherence tomography using continuum generation in an air silica microstructure optical fiber Opt Lett 200126608ndash10

[222] Brabec T Krausz F Intense few-cycle laser fields Frontiers of nonlinear optics Rev Mod Phys 200072545ndash91

[223] Hu J Meyer J Richardson K Shah L Feature issue introduction mid-IR photonic materials Opt Mater Express 201331571ndash5

[224] Private communications with Dr Jacob Levy in Prof Lipsonrsquos group and Dr Johann Riemensberger in Prof Kippenbergrsquos group

[225] Zhang J Lin Q Piredda G Boyd RW Agrawal GP Fauchet PM Anisotropic nonlinear response of silicon in the near-infrared region Appl Phys Lett 200791071113

Page 6: Lin Zhang*, Anuradha M. Agarwal, Lionel C. Kimerling and ...

252emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

compatibility in device fabrication On the other hand compared to the material choices device design (mainly on waveguide and resonator) can also produce widely var-iable dispersion and nonlinearity properties In the next section we will discuss enhanced waveguide properties using improved designs

3 DevicesOptical waveguides form the backbone of photonic devices Light propagation properties in a waveguide could be remarkably different from those in corresponding bulk materials especially when there is a high index con-trast between waveguide core and surrounding cladding Therefore understanding and optimizing the waveguide properties including loss dispersion and nonlinearity are essential in nonlinear photonics

Propagation loss in a waveguide includes material loss confinement loss scattering loss and nonlinear loss Working at a transparency window of a material especially beyond the half-bandgap wavelength one can primarily have low material and nonlinear loss caused by TPA Note that benefiting from the wide multi-octave bandwidth in the mid-IR one can even eliminate the impact of 3PA in silicon and germanium by pumping at  gt 33 microm and  gt 48 microm respectively Since the substrate index in a silicon wafer is higher than or equal to that in most of materials we consider for a waveguide core con-finement loss exists due to mode leakage to the silicon substrate This loss can be markedly reduced by increas-ing the spacing between waveguide core and the substrate or choosing low-index material between them In general scattering loss due to sidewall roughness of a waveguide is dominant in high-index-contrast silicon photonics which is mainly caused in device fabrication and can thus be reduced by improving the fabrication processes [182ndash184]

Compared to propagation loss chromatic disper-sion and nonlinearity in integrated waveguides are more de signable Since the dispersion is the second-order deriv-ative of the effective index with respect to wavelength it is particularly tailorable by changing waveguide shape and dimension Moreover dispersion has been recognized to be critical for broadband nonlinear effects [12 14 15 60 61 92ndash108 112ndash115 137ndash145] which is true especially for ultrafast octave-spanning applications [185] Spec-tral characteristics in a dispersion profile including the number and positions of zero-dispersion wavelengths (ZDWs) and dispersion slope greatly affect and often set the limit on the bandwidth of optical spectra the temporal

widths of pulses and conversion efficiency in nonlinear interactions [185] Generally speaking a flat dispersion profile (ie third- and higher-order dispersion terms are small) with low dispersion values is preferred

In conventional ultrafast nonlinear optics in a free-space setup many components were developed to control dispersion over a wide bandwidth [185 186] such as prisms gratings chirped mirrors and so on However in a waveguiding system eg in fiber-based ultrafast optics the dispersion-control toolkit is smaller and engineer-ing waveguide dispersion becomes critical In particular when waveguides are built on a silicon platform with a much higher index contrast than optical fibers dispersion in a highly nonlinear waveguide [187ndash190] often shows strong wavelength dependence which is not preferable for wideband nonlinear applications In [187 190] the ZDW in silicon rib and strip waveguides is mapped by scanning waveguide dimensions It is shown that tight confinement of a guided mode produces a ZDW in its dispersion profile around 12~14 μm close to the bandgap wavelength More-over even if the waveguide size is increased to move the ZDW to longer wavelength the dispersion slope near the ZDW is not small as shown in [187ndash189] causing a limited low-dispersion bandwidth

Recently a dispersion engineering technique for integrated high-index-contrast waveguides has been pro-posed in which an off-center nano-scale slot controls modal distribution at different wavelengths [59 60] The guided mode experiences a transition from strip-mode like to slot-mode like as wavelength increases This approach can produce a very flat dispersion profile over an ultra-wide bandwidth with dispersion flatness improved by 1ndash2 orders in terms of dispersion variation divided by low-dispersion bandwidth More importantly it is applicable to different material combinations and wavelength ranges [59ndash63]

Towards mid-IR applications different types of Group IV waveguides have been reported recently based on silicon-on-insulator (SOI) [191ndash193] silicon-on-sapphire [142 194 195] silicon-on-porous-silicon [192] silicon-on-nitride [196 197] suspended membrane silicon [198] silicon pedestal [199] and germanium-on-silicon [200] Most of the waveguides are not aimed specifically at non-linear applications and little attention has been paid to dispersion engineering [196]

In this section we survey different structures of Group IV waveguides for broadband nonlinear applica-tions from the near- to mid-IR There are three main goals in waveguide designs (i) we consider joint optimization on both dispersion and nonlinearity properties (ii) we tend to fully utilize the available bandwidth brought by

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp253

the materials in Figure 1 and (iii) we emphasize disper-sion engineering naturally as a result of aiming at octave-spanning broadband applications

Figure 4 shows a general illustration of various types of integrated waveguides for nonlinear Group IV photonics Looking at a specific wavelength range one can accord-ingly choose a materials combination for an appropriate index contrast and a desired level of nonlinearity Note that one may need low nonlinearity in some cases when high-power output is required Here we discuss waveguide design at four different wavelength ranges as follows

First we consider SOI waveguides for a wavelength range from the telecom window in the near-IR to the short-wave end in the mid-IR ie roughly from 14 to 25 microm This is the wavelength range that many of the current research efforts have been addressing [60 61 106 108 114 115 135 137 139ndash141 143 144] In this wavelength range a SOI strip waveguide as shown in Figure 4 can be used with air as an upper cladding (see eg [140]) One can change the width of the waveguide to tailor its disper-sion profile while the height of the waveguide is 220 nm set by SOI wafers From Figure 5(A) we note that a rela-tively small width W = 800 nm is corresponding to a dis-persion profile with two ZDWs at 1585 and 2345 microm and a peak value of anomalous dispersion 532 ps(nmmiddotkm) at 205 microm for the quasi-TE mode The anomalous disper-sion is typically useful for parametric amplification and oscillation soliton and soliton-based supercontinuum generation [12] With W  =  900 nm one can have a flatter dispersion profile but the anomalous band is smaller When W is increased to 1000 nm the dispersion is even flatter but no anomalous dispersion occurs Figure 5(A) shows a good example that tight mode confinement in a strip waveguide moves ZDW to short wavelengths and near ZDWs dispersion changes quickly with a large slope

Strip WG

Strip WG suspended

Air Air

Slot

Core

Upper cladding

Slab

Lower cladding

Si substrate

Slot WG suspended

Slot WG Rib WG

Figure 4emspDifferent types of Group IV waveguides (WGs) for disper-sion and nonlinearity engineering in the near- and mid-IR ranges

One can calculate the nonlinear coefficient γ as a function of wavelength with the nonlinear Kerr index n2 given in Tables 1ndash4 in Appendix B We show in Figure 5(B) that the nonlinear coefficient in the silicon strip wave-guide with W = 900 nm first increases to 187 (mmiddotW) with wavelength until 17 μm and then decreases to 56 (mmiddotW) at 25 μm This is caused by both the peaking of the silicon n2 value near 19 μm and the gradual increase of wave-length and mode area beyond that

A silicon stripslot hybrid waveguide exhibits very flat dispersion as presented in Figure 5(A) The SOI waveguide has crystalline silicon at the bottom a thin SRO slot and amorphous silicon at the top The upper cladding is silicon dioxide When setting the lower Si height to Hl = 430 nm slot height to Hs = 54 nm upper Si height to Hu = 160 nm and width to W = 660 nm we obtain an extremely flat disper-sion profile for the quasi-TM mode over a wide bandwidth between two ZDWs at 1545 and 2448 microm From 1605 to 238 microm the value of anomalous dispersion changes between 30 and 46 ps(nmmiddotkm) In this way one can have a flat and low anomalous dispersion between two far apart ZDWs The average dispersion value can be shifted by increasing Hu to move dispersion between normal and anomalous regimes Detailed explanation on how the flat-tened and saddle-shaped dispersion profile is produced is given in [59 60] Briefly the mode transition over wave-length for the quasi-TM mode is responsible for this behav-ior Due to the off-center slot the mode is mostly confined in the crystalline silicon at short wavelengths while the mode becomes more like a slot mode at long wavelengths As shown in Figure 5(C) we plot the mode power distribu-tions at wavelengths of 15 183 217 and 25 microm The mode transition adds negative dispersion in the middle of the low-dispersion bandwidth as explained in [60 201]

Having a slot one has an opportunity to fill the slot with highly nonlinear materials into it [49 51 53 55 56 58 59] which can overcome the decrease of the nonlinear coeffi-cient over wavelength In Figure 5(B) we show the γ value increasing to 306 (mmiddotW) with wavelength from 14 to 25 microm This is because the guided mode extends more to the highly nonlinear thin slot layer Note that the used n2 value in SRO [38] is currently the one measured at 155 microm so the n2 and γ thinspvalues may vary in the mid-IR but the trend is general

Next we explore the short-wavelength end of the near-IR spectrum Silicon-based devices become unus-able for nonlinear photonics as wavelength decreases to 11 microm and we thus look at silicon nitride for near-IR nonlinear applications extending to the visible light spec-trum Again a strip waveguide based on silicon nitride is examined first Figure 6(A) shows dispersion curves of the quasi-TE mode in two waveguides sized to be 1300 times 540

254emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

and 1400 times 800 nm2 The upper cladding is air and the lower cladding is silicon dioxide The anomalous disper-sion region in the dispersion curves shrinks when the waveguide is made smaller This is because of a relatively small index contrast between silicon nitride and silicon dioxide which makes the guided mode leak quickly to the substrate as wavelength increases For the strip waveguide with a cross-section of 1400 times 800 nm2 there are two ZDWs near 10 and 23 microm but one can see a strong dispersion of 250 ps(nmmiddotkm) between the two ZDWs in Figure 6(A) The nonlinear coefficient in the second silicon nitride wave-guide is shown in Figure 6(B) which is much smaller than that in silicon waveguides because of a one-order smaller n2 value and larger Aeff in the silicon nitride waveguide At 16 microm γ is about 123(mW)

One can also use a stripslot hybrid structure to tailor the dispersion profile in silicon nitride waveguides For example the slot and lower cladding are silicon dioxide and the upper cladding is air In Figure 6(A) we show the dispersion curves in two silicon nitride stripslot hybrid waveguides for comparison The waveguide 1 has Hl = 900 nm Hs = 124 nm Hu = 340 nm and W = 1000 nm and the waveguide 2 has Hl = 920 nm Hs = 154 nm Hu = 480 nm and W = 1300 nm These two waveguides produce increasingly flatter dispersion profiles as shown in Figure 6(A) The first waveguide has two ZDWs located at 106 and 22 microm with the peak dispersion of 67 ps(nmmiddotkm) The second waveguide has two ZDWs at 115 and 235 microm with the dispersion varying within 0~20 ps(nmmiddotkm) This octave-spanning dispersion flattening with different levels

1000A

B

C

500

-500

400

300

200

100

0

-100014 16

Strip WG W=800 nmStrip WG W=900 nm

Strip WG W=900 nm

Strip WG W=1000 nm

Slot WG Hu=160 nm

Slot WG Hu=160 nm

Slot WG Hu=163 nmSlot WG Hu=166 nm

18 20 22Wavelength (microm)

Dis

pers

ion

(ps

nmmiddotk

m)

Non

linea

r co

effic

ient

(m

middotW)

24 26

14 16 18 20 22

Wavelength (microm)

24 26

0

Figure 5emspIn a wavelength range from the telecom window in near-IR to the short-wave end in the mid-IR silicon strip and stripslot hybrid waveguides (WGs) are analyzed in terms of (A) dispersion and (B) nonlinearity (C) Mode power distributions at wavelengths of 15 183 217 and 25 microm in the stripslot hybrid waveguide

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp255

of dispersions can be used for multiple applications as detailed in the next section The nonlinear coefficients for the two waveguides are shown in Figure 6(B) We note that the stripslot hybrid waveguides have similar nonlinear coefficients as the strip waveguide which shows that the dispersion profile is much more tailorable by waveguide designs

Then we move to the mid-IR using silicon and silicon nitride for waveguiding A comparison of different types of silicon-on-nitride waveguides have been presented in [196] where rib waveguides were preferred due to the wideband low dispersion over an octave-spanning band-width from 24 to 66 microm for the quasi-TE mode This is a spectral range from siliconrsquos half-bandgap wavelength to the cut-off wavelength of silicon nitride In Figure 7(A) we plot the dispersion curve for a silicon-on-nitride rib waveguide with air as the upper cladding the rib width of 2000 nm the total height of 1200 nm and the slab height of 1000 nm which are the same parameters used in [196] It is shown that less confinement of optical modes reduces the contribution of waveguide dispersion and makes the overall dispersion profile closer to the material dispersion which is flat and low at long wavelengths as in Figure 2(B)

A

B

400

300

200

100

-100

8

6

4

2

0

0

Strip WG 1300times540 nm2

Strip WG 1400times800 nm2

Strip WG 1400times800 nm2

Slot WG 1Slot WG 2

Slot WG 1Slot WG 2

Dis

pers

ion

(ps

nmmiddotk

m)

Non

linea

r co

effic

ient

(m

middotW)

20 3010 15 2505Wavelength (microm)

2010 15 2505

Wavelength (microm)

Figure 6emspIn a wavelength range moved toward the short-wave-length end of near-IR spectrum silicon nitride strip and stripslot hybrid waveguides are designed in terms of (A) dispersion and (B) nonlinearity

Accordingly the nonlinear coefficient is small 285 (mmiddotW) at 3 microm as shown in Figure 7(B)

On the other hand if one needs a small Aeff to enhance nonlinearity additional dispersion tailoring (eg based on stripslot hybrid waveguides) would be beneficial Pursuing a higher nonlinear coefficient we use a 500-nm silicon nitride suspended membrane as illustrated in Figure 4 to support a silicon stripslot hybrid waveguide This helps confine light in the waveguide core Using W = 880 nm Hu = 550 nm Hs = 87 nm and Hl = 840 nm we obtain a saddle-shaped anomalous dispersion from 19 to 449 microm within 0~60 ps(nmmiddotkm) for the quasi-TM mode as shown in Figure 7(A) This structure produces much tighter mode confinement than the rib waveguide and exhibits a 3 times larger nonlinear coefficient in Figure 7(B) while having similar dispersion flatness

Finally we consider germanium-on-silicon wave-guides over a wavelength range from 33 to 85 microm between the half-bandgap wavelength of germanium and the cut-off wavelength of silicon This type of waveguide has been demonstrated with strain-free mono-crystal-line germanium [200] Here we assume that the germa-nium waveguide has a 10-nm silicon nitride layer on its

A

B

200

-200

60

40

20

0

100

-100

0

Rib WGSlot WG

Rib WGSlot WG

Dis

pers

ion

(ps

nmmiddotk

m)

Non

linea

r co

effic

ient

(m

middotW)

1 2 3 4 5 6 7Wavelength (microm)

1 2 3 4 5 6 7

Wavelength (microm)

Figure 7emspIn a wavelength range from the short-wave IR to mid-IR silicon rib waveguide on silicon nitride and stripslot hybrid waveguide on a suspended membrane are analyzed in terms of (A) dispersion and (B) nonlinearity

256emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

surface for passivation The upper cladding could be air or silicon which provides significantly different dispersion properties due to a varied index contrast For comparison only we also have silicon nitride as the upper cladding although silicon nitride becomes lossy for wavelengths longer than 67 microm Figure 8(A) shows the dispersion pro-files of four germanium-on-silicon strip waveguides with equal size 3000 times 1600 nm2 for the quasi-TE mode Air and silicon nitride as an upper cladding result in similar shape and bandwidth in the dispersion profiles Thus the air-cladded waveguide is chosen and discussed further The waveguide with silicon upper cladding has normal dispersion at all wavelengths since there is a relatively small index contrast between germanium and silicon and thus weak mode confinement A germanium strip wave-guide on a 600-nm-thick silicon suspended membrane is also considered to increase light confinement with an air upper cladding to maximize light confinement However as mentioned earlier strong confinement typically causes strong dispersion as shown in Figure 8(A) and therefore the germanium waveguide on a silicon membraneis not chosen for broadband nonlinear applications In contrast the germanium strip waveguide with air upper cladding exhibits a flat and low dispersion

The dimensions of the air-cladded germanium wave-guide are varied by simultaneously changing its height and width with a step of 200 nm for both polarization states It is interesting to see from Figure 8(B) and 8(C) that the dispersion peak value remains nearly unchanged for all the waveguide sizes although we have a widely tunable ZDW at long wavelengths For the quasi-TE mode the right ZDW moves from 605 microm to 841 microm while the left ZDW is always near 4 microm We can thus obtain an octave-spanning anomalous dispersion band with the peak value below 100 ps(nmmiddotkm) For the quasi-TM mode one can see similar dispersion properties but the anomalous disper-sion band is smaller Thus we choose the quasi-TE mode for further discussion in next section

The nonlinear coefficient in the germanium wave-guides for the quasi-TE mode is shown in Figure 8(D) which is about 10(mmiddotW) at 5 microm with a small variation for differ-ent waveguide sizes This is quite high considering that both wavelength and effective mode area become much larger over this wavelength range compared to the near-IR

From above we can see that the stripslot hybrid wave-guides enable unique controllability of dispersion and that this concept is applicable to different wavelength ranges However their performance may be sensitive to fabrication errors especially for inaccuracies in slot height Hs [59 60] A higher yield in device fabrication is expected using advanced fabrication technologies and facilities

A

C

D

B

400

300

200

100

-100

-200

0

Ge WG+air 3000times1600 nm2

Ge WG+air suspended 3000times1600 nm2

Ge WG+Si3N4 3000times1600 nm2

Ge WG+Si 3000times1600 nm2

Ge WG+air 2800times1400 nm2

Ge WG+air 3000times1600 nm2

Ge WG+air 3200times1800 nm2

Ge WG+air 3400times2000 nm2

Ge WG+air 2800times1400 nm2

Ge WG+air 3000times1600 nm2

Ge WG+air 3200times1800 nm2

Ge WG+air 3400times2000 nm2

Ge WG+air 2800times1400 nm2

Ge WG+air 3000times1600 nm2

Ge WG+air 3200times1800 nm2

Ge WG+air 3400times2000 nm2

Dis

pers

ion

(ps

nmmiddotk

m)

400

300

200

100

-100

-200

0

Dis

pers

ion

(ps

nmmiddotk

m)

400

300

200

100

-100

-200

50

40

30

20

10

0

0

Dis

pers

ion

(ps

nmmiddotk

m)

Non

linea

r co

effic

ient

(m

middotW)

3 4 5 6 7 8 9Wavelength (microm)

3 4 5 6 7 8 9Wavelength (microm)

3 4 5 6 7 8 9

Wavelength (microm)

3 4 5 6 7 8 9

Wavelength (microm)

Figure 8emspIn a wavelength range covering the main part of the mid-IR spectrum (A) on silicon substrate or on suspended silicon membrane are analyzed in terms of dispersion Germanium-on-silicon strip waveguides with an air upper cladding and different dimensions are characterized by (B) dispersion for the quasi-TE mode (C) dispersion for the quasi-TM mode and (D) nonlinearity for the quasi-TE mode

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp257

Besides photonic waveguides another important cat-egory of nonlinear devices is integrated resonators In the scope of this paper we consider relatively large resona-tors for frequency comb generation in which the bending radius of a ring resonator is varied from 50 microm to 100 microm depending on free spectral range (FSR) and the group index in the waveguide In these cases the waveguide-bending-induced dispersion is small and we would not discuss intra-cavity dispersion [202 203] in details here

4 ApplicationsBenefiting from the unique dispersion engineering over an octave-spanning bandwidth as described above one can develop ultra-wideband nonlinear applications that could hardly be attained in an integrated platform previously These include octave-spanning supercontinuum genera-tion pulse compression to a few-cycle or even sub-cycle level octave-spanning Kerr frequency comb generation and the associated mode-locked ultrashort pulse genera-tion using microresonators In this section we review our recent work on these topics

First we discuss the supercontinuum generation and pulse compression in a straight waveguide The nonlinear envelope equation used here to simulate supercontinuum generation is the following

βα infin

=

part part+ + = + part part sum

2

( - )( ) ( )

2

m mm

mm

ii A K A R A

z m t (1)

where

2

0 0

- -( ) 1- ( ) 2

n nn

nn

i i iK A A An t tγ δ δ

ω δ δ

infin

=

= sum

and

2shock_R( ) - 1- [ ( - ) | | ]δ

γ τδ minusinfin

= prime prime int

t

R RR A i i A h t t A dtt

We denote A  =  A(zt) as the complex amplitude of an optical pulse Note that its Fourier transform is

-

1( ) ( ) exp( - ) 2

A z A z t i t dtω ωπ

infin

infin

= int

In Eq (1) α is the total propagation loss and βm is the mth-order dispersion coefficient The frequency dependence of nonlinearity parameters including the nonlinear index n2 the TPA coefficient βTPA and the

effective mode area Aeff is included in the nth-order dis-persion coefficient γn of nonlinearity which is defined as γn = ω0middotpartn[γ(ω)ω]partωn where ω0 is the angular frequency of the carrier Therefore we can consider all-order linear dispersion terms and all-order dispersion of the nonlin-ear coefficient in Eq (1) Specifically in the simulations for a silicon and silicon nitride waveguides we have all-order linear dispersion and up to 6th-order and 2nd-order of the nonlinear coefficient dispersion included A detailed derivation of Eq (1) is given in [204] For the quasi-TM mode that experiences the engineered dispersion due to the mode transition SRS in silicon waveguides fabricated on the (001) surface can be ignored [27 96] For silicon nitride waveguide we include the SRS term in Eq (1) where γR = gRΓR(AeffΩR) and gR ΓR and ΩR represent the Raman gain coefficient the full width at half maximum of the gain spectrum and the Raman shift respectively The Raman shock time τshock_R is associated with γRrsquos fre-quency dependence which is 1ω0-[1Aeff(ω0)][dAeff(ω)dω] similarly as in [14] if we ignore frequency dependent gR ΓR and ΩR hR(t) is the Raman response function and it corresponds to the Raman gain spectrum

2

2 20 0

( ) -( - ) 2 ( - )

Ωω

Ω ω ω Γ ω ω=

+R

RR R

Hi

Note that the sign before the imaginary unit is differ-ent from that in [27] to be consistent with the expression of the Fourier transform that we used

We have considered supercontinuum generation in both silicon and silicon nitride waveguides with the slot-assisted dispersion tailoring Octave-spanning supercon-tinua in a silicon-based stripslot hybrid waveguide have been investigated in detail in [108] in which two-cycle optical pulses are obtained The main results in that work are shown in Figure 9 for comparison purposes

Here we mainly focus on the supercontinuum gen-erated in the silicon nitride stripslot hybrid waveguide (ie the slot WG 1 in Section III) whose dispersion and nonlinearity properties are shown in Figure 6 In the non-linear simulations we set the total propagation loss to be 1 dBcm The SRS parameters used here are the following [205] ΩR2π = 143 THz ΓR2π = 172 THz and gR = 1 times 10-12 mW τshock_R is calculated to be  = 156 fs

In our simulations we use a time step of 025 fs which is corresponding to a bandwidth of 4000 THz in the fre-quency domain For a femtosecond input pulse we set the time window length to 50 ps (ie frequency resolution Δf = 20 GHz)

We simulate the nonlinear propagation of a chirp-free hyperbolic secant pulse in the silicon nitride waveguide

258emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

The pulse center wavelength is at 1610 nm and its full width at half-maximum (FWHM) T0 is 120 fs Its peak power is 1200 W corresponding to pulse energy of 016 nJ

Figure 10(A) shows the supercontinua at different propagation distances At 48 mm the spectrum is greatly broadened at the -30 dB level covering a wavelength range from 0585 to 2833 microm which is more than two octaves The spectrum evolution in Figure 10(A) shows a similar spectrum shape as that in Figure 9(A) both featuring a ldquotriangularrdquo central spectrum bounded by two dispersive waves at the edges However it is important to note that the absence of TPA and 3PA in silicon nitride at the telecom window leads to a much more efficient spectrum broad-ening than that in silicon [108] The generated spectrum extends from the visible light to the mid-IR with excellent spectral coherence which is confirmed by the pulse wave-form shown in Figure 10(B) In the time domain the pulse is greatly compressed from 120 to 408 fs corresponding to 076 optical cycles at 161 microm wavelength

We examine the pulsewidth as a function of propa-gation distance Figure 11 shows that the pulse becomes increasingly narrower until the propagation distance reaches 47 mm For longer distances the pulsewidth

A

B

60 mm

48 mm

36 mm

24 mm

12 mm

Input

Spe

ctru

m (

10 d

Bd

iv)

Pow

er (

W)

12

246

24

18

12

6

0

248 250 252 254

14 16 18 20 22 24Wavelength (microm)

Time (ps)

Figure 9emsp(A) The supercontinuum generation in a silicon-based stripslot hybrid waveguide presented in [108] (B) The significant spectrum broadening at 425-mm distance is associated with a temporal compression of an input pulse (dash line) to the output waveform (solid line) with a FWHM of 12 fs

A

B

50 mm

48 mm

46 mm

44 mm

42 mm

Input

Spe

ctru

m (

10 d

Bd

iv)

Pow

er (

W)

8000

6000

4000

2000

0250249 251

06 09 12 15 18 21 24 27

Wavelength (microm)

Time (ps)

Figure 10emsp(A) Spectrum evolution of the pulse over propagation distance A supercontinuum of more than two octaves is achieved at 48 mm distance (B) Generated pulse waveform with a pulse width of 408 fs as short as 076 optical cycles Low pedestals are caused by dispersive waves generated at the two ends of the spectrum

remains almost constant However it is important to mention that after 48 mm the dispersive waves become increasingly stronger as shown in Figure 10(A) causing larger pedestals

Comparing the results in Figures 9 and 10 we note that the mid-IR wavelength range for silicon would be in analogy to the near-IR for silicon nitride in terms of non-linear optics operations Pumping at or beyond 33 microm one can use the waveguide designs shown in Figure 7 to produce very efficient nonlinear interactions without TPA and 3PA in silicon Ultrashort pulses in the mid-IR from parametric amplifiers [206 207] could be used to pump the Group IV waveguides

Another nonlinear application of the dispersion-engi-neered Group IV waveguides is micro-resonator-based Kerr frequency comb generation When such a waveguide is curved to form a microring resonator input CW light travels around the cavity and amplifies the noise in the source located at the frequencies with a high parametric gain As a result of modulation instability and cascaded FWM in the cavity a frequency comb can be generated [208ndash211] Mode-locked frequency combs have been reported pro-ducing low-noise pulse trains in time domain [212ndash214]

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp259

The formation of cavity solitons is identified as the main reason for the mode-locking in the Kerr frequency combs [215] This is instructive because one can thus predict the spectral bandwidth and temporal pulsewidth in the generated low-noise combs The 3-dB comb bandwidth is inversely proportional to the square root of the 2nd-order dispersion coefficient |β2| as given in [213 215] It is desira-ble that all comb lines that constitute the soliton spectrum experience the same |β2| In this sense the stripslot hybrid waveguides with flattened dispersion are preferably suit-able for supporting broadband Kerr comb generation and ultra-short cavity soliton generation

The Kerr frequency comb generation can be modeled using the generalized Lugiato-Lefever equation (LLE) [216ndash219]

20

2

( - )- - | |

2 2

m mm

R inmm

jkt j jl E kE j l E Et m

βαδ γ

τ

infin

=

part part+ + + = part part

sum (2)

where tR is the round-trip time E = E(tτ) and Ein are intra-cavity field and input field (pump power Pin  =  |Ein|2) t and τ are the slow and fast times δ0 is the cavity phase detuning defined as δ0  =  tRmiddot(ωn -ω0) where ω0 and ωn are the pumprsquos angular frequency and the nth angular reso-nance frequency that is pumped Other resonator param-eters include the power loss per round trip α the power coupling coefficient κ the nonlinear coefficient γ and the mth dispersion coefficient βm Since a flattened dispersion profile has a small β2 over a wide bandwidth it is impor-tant to take the influence of higher-order dispersion into account We include all-order dispersion terms in Eq (2) as we did in solving Eq (1)

To enhance the Kerr comb bandwidth in the near-IR we use the ultra-flattened dispersion profile in Figure 6(A) which is obtained in the slot WG 2 based on

Pul

se w

idth

(fs

)

14

12

10

8

6

4

242 44 46 48 50 52

Propagation distance (mm)

Figure 11emspPulse width first decreases with propagation distance and then remains stable After 48 mm dispersive waves get stronger causing more pedestals

Pow

er (

10 d

Bd

iv)

Pow

er (

W)

70A

B

60

50

40

30

20

10

-10

-20

600

400

200

0

80 120

0575 0600 0625 0650

160 200 240 280 320 360

0

Frequency (THz)

Time (ps)

Figure 12emsp(A) Frequency comb generation with a CW pump at 155 microm using a microring resonator based on a silicon stripslot hybrid waveguide Over an octave-spanning bandwidth from 135 to 270 THz the comb lines have a power drop of 20 dB (B) Generated pulse waveform with a pulse width of 82 fs as short as 16 optical cycles

silicon nitride The ring resonator has a bending radius of 104 microm corresponding to a FSR of 200 GHz Pumping near 155 microm with a pump power of 2 W the resonance peak is red-shifted and we need to red-shift the pump wavelength accordingly and tune it into the resonance from the short-wavelength side When the pump is step-by-step tuned by up to 63 resonance linewidths we obtain the comb spectrum and the mode-locked pulse waveform as shown in Figure 12 One can see that over an octave-spanning bandwidth from 133 to 268 THz the comb lines have a power drop by 20 dB from the center of the spectrum The spectral flatness of this comb is relatively good compared to the previously reported results [208ndash211] The comb bandwidth at -40 dB is as wide as two octaves There are two dispersive peaks in normal dispersion regions beyond the low-dispersion band Such a mode-locked broadband comb produces a train of sub-two-cycle optical pulses as shown in Figure 12(B) with one pulse per round trip The peak power of the pulse is up to 600 W Nonlinear conver-sion efficiency is estimated to be -267 dB

To generate frequency combs in the mid-IR the ger-manium-on-silicon strip waveguide is chosen We choose

260emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

a cross-section of 3200 times 1800 nm2 which has an octave-spanning low-dispersion band from 4 to 767 microm as shown in Figure 8(B) A germanium ring resonator is formed with a bending radius of 564 microm corresponding to a FSR of 200 GHz Pumping at 6 microm with a CW power of 14 W and detuning the pump wavelength by 10 resonance linewidth one can see that a mode-locked wideband mid-IR comb is generated from 358 to 644 THz (ie from 466 to 838 microm) at -40 dB level The FWHM of the produced pulses is 69 fs which corresponds to ~35 optical cycles The pulse peak power is 184 W and the nonlinear conversion efficiency is estimated to be -143 dB Since the pumping frequency is not at the center of the low-dispersion band we only see one peak in the comb spectrum caused by the dispersive wave in the normal dispersion region from Figure 13(A) There is another peak at higher frequencies beyond what is shown in the figure

As shown above broadband dispersion engineering is critical for octave-spanning nonlinear applications in both near- and mid-IR wavelength ranges which enables us to fully utilize the bandwidth allowed by the materials transparency windows Generally speaking the nonlinear applications mentioned here such as supercontinuum generation ultrafast pulse compression and frequency comb generation are often the intermediate steps towards higher-level system applications In the frequency domain a wide spectrum can serve as an electromagnetic carrier to acquire high-volume of information eg for sensing [220] and imaging [221] In the time domain an ultrashort pulse can be used as probe to sample ultrafast phenomena [222]

5 Summary and OutlookWe have presented a review of our recent work on nonlin-ear photonics based on silicon and germanium Various types of Group IV waveguides are analyzed and optimized for four different wavelength ranges from near- to mid-IR The recently proposed dispersion engineering technique based on stripslot hybrid waveguide structures is used for different material combinations and wavelength ranges Numerical simulations show that the dispersion-flattened Group IV waveguides are preferably suitable for octave-spanning nonlinear applications including on-chip supercontinuum generation ultrashort pulse compres-sion and mode-locked wideband frequency comb genera-tion based on micro-resonators

The presented approach to achieving octave-span-ning nonlinear applications on an integrated CMOS-compatible Group IV platform holds great potential for realizing chip-scale sensing imaging communications and signal processing system The ultrawide transparency windows in the mid-IR allowed by Group IV elements and compounds potentially together with other materi-als [223] provide an exciting arena for building powerful information acquisition and processing units enabled by nonlinear optics nano-photonics and ultrafast optics

Received June 14 2013 accepted October 29 2013 previously pub-lished online November 27 2013

Pow

er (

10 d

Bd

iv)

A

8030 40 50 60 70Frequency (THz)

Pow

er (

W)

B200

150

100

50

0

21 22 23 24 25Time (ps)

Figure 13emsp(A) Frequency comb generation with a CW pump at 6 microm using a microring resonator based on a germanium strip waveguide with air upper cladding (B) Generated pulse waveform with a pulse width of 69 fs as short as 35 optical cycles

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp261

Appendix

A Material index and dispersion

In this section we give the wavelength-dependent mate-rial index expressed as Sellmeier equations where wave-length λ is in μm

For silicon we use the following material index that is a fit curve from measurement results at room temperature (293 K) with 184 data points in total from 112 to 588 μm [154]

22 1 2 2

2 2 22

( )-

C Cn

λλ ε

λ λ λ= + +

where ε = 116858 C1 = 0939816 μm2 C2 = 000810461 and λ2 = 11071 μm

For silicon nitride the material index is affected by deposition conditions using plasma-enhanced chemical vapor deposition (PECVD) low-pressure chemical vapor deposition (LPCVD) and so on We use the following Sell-meier equation [155] which predicts the material index close to that in LPCVD silicon nitride films measured by a few groups [224]

22 1

2 21

( ) 1-

Cn

λλ

λ λ= +

where C1 = 28939 and λ1 = 013967 μmFor silicon dioxide we use the following Sellmeier

equation for fused silica [156]22 2

2 31 22 2 2 2 2 2

1 2 3

( ) 1- - -

CC Cn

λλ λλ

λ λ λ λ λ λ= + + +

where C1 = 06961663 C2 = 04079426 C3 = 08974794 λ1 = 00684043 μm λ2 = 01162414 μm and λ3 = 9896161 μm

For SRO the material index is affected by deposition conditions such as silicon excess annealing temperature and so on Here we choose the one with silicon excess of 8 and annealed at 1250oC [51]

22 22 31 2

2 2 2 2 2 21 2 3

( ) 1- - -

CC Cn

λλ λλ

λ λ λ λ λ λ= + + +

where C1 = 001 C2 = 196 C3 = 141 λ1 = 03 μm λ2 = 007071 μm and λ3 = 2775968 μm

For germanium the temperature-dependent mate-rial index was measured [157] Here we choose the one for room temperature (293 K)

2 22 1 2

2 2 2 21 2

( )- -

C Cn

λ λλ ε

λ λ λ λ= + +

where ε = 928156 C1 = 67288 C2 = 021307 λ1 = 0664116 μm and λ2 = 6221013 μm

For arsenic sulfide we use the material index pro-vided in [158]

2 2 22 22 3 4 51 2

2 2 2 2 2 2 2 2 2 21 2 3 4 5

( ) 1- - - - -

C C CC Cn

λ λ λλ λλ

λ λ λ λ λ λ λ λ λ λ= + + + + +

where C1 = 18983678 C2 = 19222979 C3 = 08765134 C4 = 01188704 C5 = 09569903 λ1 = 015 μm λ2 = 025 μm λ3 = 035 μm λ4 = 045 μm and λ5 = 27386128 μm

For arsenic selenide we fit ellipsometry measure-ments of our arsenic selenide thin films and the bulk material is provided by Prof Kathleen A Richardson group

22 22 31 2

2 2 2 2 2 21 2 3

( ) 1- - -

CC Cn

λλ λλ

λ λ λ λ λ λ= + + +

where C1 = 298463 C2 = 321011 C3 = 100182 λ1 = 044118 μm λ2 = 0000354953 μm and λ3 = 38413 μm

B Nonlinear Kerr index n2

The third-order nonlinear susceptibility χ(3)1111 for silicon and

germanium is predicted over the mid-IR range [133] based on a two-band model The effective nonlinear susceptibil-ity χ(3) is dependent on polarization and crystallographic orientation [225] For strong nonlinearity we consider a single-polarization incident light aligned to the crystal-lographic axis and we have χ(3) = χ(3)

1111 To investigate the octave-spanning nonlinear phenomena one need to take the wavelength-dependent nonlinear Kerr index n2 and TPA coefficient βTPA into account which are expressed as

( 3 )2 2

0

( 3 )2

0

3( ) ( )4 ( )

3( ) ( )( )

re

TPA im

ncn

cn

λ χ λε λ

πβ λ χ λ

λε λ

=

=

where ε0 and c are the vacuum permittivity and the speed of light in vacuum Using the material index given in Appendix A and χ(3) value from [133] we obtain the n2 and βTPA values tabulated as follows

262emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

Table 1enspNonlinear Kerr index n2 in silicon

λμm

  n2

10-18 m2W  λ

μm  n2

10-18 m2W  λ

μm  n2

10-18 m2W

130   234   310   389   490   312135   305   315   384   495   311140   378   320   379   500   310145   443   325   375   505   309150   501   330   371   510   307155   559   335   368   515   306160   618   340   365   520   304165   671   345   362   525   304170   710   350   360   530   303175   741   355   358   535   302180   766   360   355   540   302185   781   365   352   545   301190   783   370   350   550   300195   778   375   346   555   298200   762   380   343   560   297205   732   385   341   565   296210   699   390   338   570   296215   658   395   336   575   295220   612   400   334   580   295225   576   405   332   585   295230   547   410   331   590   294235   525   415   330   595   293240   508   420   329   600   292245   493   425   328   605   291250   479   430   327   610   290255   467   435   325   615   289260   456   440   324   620   288265   448   445   321   625   288270   440   450   319   630   288275   432   455   317   635   288280   424   460   315   640   288285   417   465   314   645   288290   410   470   313   650   288295   404   475   313   655   288300   398   480   312   660   288305   394   485   312    

Table 2enspTPA coefficient βTPA in silicon

λμm

  βTPA

10-12 mW  λ

μm  βTPA

10-12 mW  λ

μm  βTPA

10-12 mW

130   1334   165   812   200   180135   1284   170   713   205   115140   1222   175   613   210   064145   1154   180   522   215   024150   1079   185   424   220   0003155   995   190   333    160   905   195   254    

Table 3enspNonlinear Kerr index n2 in germanium

λμm

  n2

10-18 m2W  λ

μm  n2

10-18 m2W  λ

μm  n2

10-18 m2W

23  3932  63  1986  103  170524  4994  64  1972  104  169925  6007  65  1959  105  169426  6650  66  1946  106  169027  6772  67  1934  107  168728  6273  68  1923  108  168429  4897  69  1913  109  168230  4403  70  1904  110  168131  3970  71  1895  111  167932  3680  72  1886  112  167733  3470  73  1876  113  167534  3286  74  1868  114  167335  3128  75  1859  115  167036  2998  76  1850  116  166737  2895  77  1841  117  166338  2812  78  1833  118  165939  2737  79  1826  119  165640  2668  80  1819  120  165341  2605  81  1812  121  165142  2550  82  1807  122  164843  2498  83  1801  123  164644  2450  84  1797  124  164445  2406  85  1792  125  164346  2365  86  1787  126  164147  2328  87  1782  127  163948  2295  88  1777  128  163649  2266  89  1772  129  163450  2238  90  1767  130  163251  2212  91  1762  131  163052  2187  92  1758  132  162853  2164  93  1753  133  162654  2141  94  1749  134  162555  2121  95  1744  135  162356  2101  96  1740  136  162157  2083  97  1736  137  162058  2066  98  1731  138  161859  2049  99  1727  139  161760  2032  100  1722  140  161661  2016  101  1716   62  2001  102  1711   

Table 4enspTPA coefficient βTPA in germanium

λμm

  βTPA

10-8 mW  λμm

  βTPA

10-8 mW  λ

μm  βTPA

10-8 mW

23   130   25   088   27   03124   111   26   060   28   006

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp263

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[106] Kuyken B Liu X Osgood RM Jr Baets R Roelkens G Green WMJ Mid-infrared to telecom-band supercontinuum generation in highly nonlinear silicon-on-insulator wire waveguides Opt Express 20111920172ndash81

[107] DeVore PTS Solli DR Ropers C Koonath P Jalali B Stimulated supercontinuum generation extends broadening limits in silicon Appl Phys Lett 2012100101111

[108] Zhang L Lin Q Yue Y Yan Y Beausoleil RG Agarwal A Kimerling LC Michel J Wilner AE On-chip octave-spanning supercontinuum in nanostructured silicon waveguides using ultralow pulse energy IEEE J Sel Top Quant 2012181799ndash806

[109] Claps R Raghunathan V Dimitropoulos D Jalali B Influence of nonlinear absorption on Raman amplification in silicon waveguides Opt Express 2004122774ndash80

[110] Yin L Agrawal GP Impact of two-photon absorption on self-phase modulation in silicon waveguides Opt Lett 2007322031ndash3

[111] Ikeda K Saperstein RE Alic N Fainman Y Thermal and Kerr nonlinear properties of plasma-deposited silicon nitridesilicon dioxide waveguides Opt Express 20081612987ndash94

[112] Levy JS Gondarenko A Foster MA Turner-Foster AC Gaeta AL Lipson M CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects Nat Photonics 2010437ndash40

[113] Tan DTH Ikeda K Sun PC Fainman Y Group velocity dispersion and self phase modulation in silicon nitride waveguides Appl Phys Lett 201096061101

[114] Zhang L Yan Y Yue Y Lin Q Painter O Beausoleil RG Willner AE On-chip two-octave supercontinuum generation by enhancing self-steepening of optical pulses Opt Exp 20111911584ndash90

[115] Halir R Okawachi Y Levy JS Foster MA Lipson M Gaeta AL Ultrabroadband supercontinuum generation in a CMOS-compatible platform Opt Lett 2012371685

[116] Ye J Frequency comb spectroscopy from mid-infrared to extreme ultraviolet Conference on Lasers and Electro-Optics (CLEO) 2012 Tutorial CW1J4

[117] Popmintchev T Chen M-C Popmintchev D Arpin P Brown S Alisauskas S Andriukaitis G Balciunas T Mucke OD Pugzlys A Baltuska A Shim B Schrauth SE Gaeta A Hernandez-Garcia C Plaja L Becker A Jaron-Becker A Murnane MM Kapteyn HC Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers Science 20123361287ndash91

[118] Qin GS Yan X Kito C Liao M Chaudhari C Suzuki T Ohishi Y Ultrabroadband supercontinuum generation from ultraviolet to 628 microm in a fluoride fiber Appl Phys Lett 200995 161103ndash1ndash161103-3

[119] Soref RA Emelett SJ Buchwald WR Silicon waveguided components for the long-wave infrared region J Opt A 20068840ndash8

266emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

[120] Soref R Towards Silicon-based Longwave Integrated Optoelectronics (LIO) SPIE Proceedings 6898 (2008) paper 6898-5 SPIE Photonics West Silicon Photonics III Conference San Jose CA (21 Jan 2008)

[121] Mashanovich GZ Milosevic M Matavulj P Timotijevic B Stankovic S Yang PY Teo EJ Breese MBH Bettiol AA Reed GT Silicon photonic waveguides for different wavelength regions Semiconductor Sci Technol 200823064002

[122] Soref R Mid-infrared photonics in silicon and germanium Nat Photonics 20104495ndash7

[123] Green WMJ Liu X Osgood RM Vlasov YA Mid-infrared nonlinear optics in silicon photonic wire waveguides Photonics Society Summer Topical Meeting Series 201062ndash63

[124] Milosevic MM Nedeljkovic M Masaud T-B Jaberansary E Chong HMH Emerson NG Reed GT Mashanovich GZ Silicon waveguides and devices for the mid-infrared Appl Phys Lett 2012101121105

[125] Soref R Group IV photonics for the mid infrared SPIE Photonics West 2013 Proc of SPIE 20138629paper 862902

[126] Crowder JG Smith SD Vass A Keddie J Infrared methods for gas detection in Mid-Infrared Semiconductor Optoelec-tronics New York Springer-Verlag 2006

[127] George Socrates Infrared and Raman Characteristic Group Frequencies Tables and Charts 3rd Ed Chichester John Wiley amp Sons 2001

[128] Longshore R Raimondi P Lumpkin M Selection of detector peak wavelength for optimum infrared system performance Infrared Phys 197616639ndash47

[129] Findlay GA Cutten DR Comparison of performance of 3ndash5-and 8ndash12-microm infrared systems Appl Opt 1989285029ndash37

[130] Labadie L Wallner O Mid-infrared guided optics a perspective for astronomical instruments Opt Express 2009171947ndash62

[131] Pearl S Rotenberg N van Driel HM Three photon absorption in silicon for 2300ndash3300 nm Appl Phys Lett 200893131102

[132] Wang Z Liu H Huang N Sun Q Wen J Li X Influence of three-photon absorption on Mid-infrared cross-phase modulation in silicon-on-sapphire waveguides Opt Express 2013211840ndash8

[133] Hon NK Soref RA Jalali B The third-order nonlinear optical coefficients of Si Ge and Si1-xGex in the midwave and longwave infrared J Appl Phys 2011110011301

[134] Sheik-Bahae M Hutchings DC Hagan DJ Stryland EWV Dispersion of bound electric nonlinear refraction in solids IEEE J Quant Electron 1991271296ndash1309

[135] Jalali B Raghunathan V Shori R Fathpour S Prospects for silicon mid-IR Raman lasers IEEE J Sel Top Quantum Electron 2006121618ndash27

[136] Raghunathan V Borlaug D Rice RR Jalali B Demonstration of a mid-infrared silicon Raman amplifier Opt Express 20071514355ndash62

[137] Chavez Boggio JM Windmiller JR Knutzen M Jiang R Bres C Alic N Stossel B Rottwitt K Radic S 730-nm optical parametric conversion from near- to short-wave infrared band Opt Express 2008165435ndash43

[138] Lin Q Johnson TJ Perahia R Michael CP Painter OJ A proposal for highly tunable optical parametric oscillation in silicon micro-resonators Opt Express 20081610596ndash610

[139] Turner-Foster AC Foster MA Salem R Gaeta AL Lipson M Frequency conversion over two-thirds of an octave in silicon nanowaveguides Opt Express 2010181904ndash8

[140] Liu X Osgood RM Vlasov YA Green WMJ Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides Nat Photonics 20104557ndash60

[141] Zlatanovic S Park JS Moro S Boggio JMC Divliansky IB Alic N Mookherjea S Radic S Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source Nat Photonics 20104561ndash4

[142] Tien EK Huang YW Gao S Song Q Qian F Kalyoncu SK Boyraz O Discrete parametric band conversion in silicon for mid-infrared applications Opt Exp 20101821981ndash9

[143] Lau RKW Meacutenard M Okawachi Y Foster MA A C Turner-Foster Salem R Lipson M Gaeta AL Continuous-wave mid-infrared frequency conversion in silicon nanowaveguides Opt Lett 2011361263ndash5

[144] Roelkens G Green WMJ Kuyken B Liu X Hattasan N Gassenq A Cerutti L Rodriguez JB Osgood RM Tournie E Baets R III-Vsilicon photonics for short-wave infrared spectroscopy IEEE J Quant Electron 201248292ndash8

[145] Alloatti L Korn D Weimann C Koos C Freude W Leuthold J Second-order nonlinear silicon-organic hybrid waveguides Opt Express 20122020506ndash15

[146] Harris DC Durable 3ndash5 μm transmitting infrared window materials Infrared Phys Technol 199839185ndash201

[147] Carlie N Musgraves JD Zdyrko B Luzinov I Hu J Singh V Agarwal A Kimerling LC Canciamilla A Morichetti F Melloni A Richardson K Integrated chalcogenide waveguide resonators for mid-IR sensing leveraging material properties to meet fabrication challenges Opt Express 20101826728ndash43

[148] Eggleton BJ B Luther-Davies Richardson K Chalcogenide photonics Nat Photonics 20115141ndash8

[149] Madden SJ Vu KT High-Performance Integrated Optics with Tellurite Glasses Status and Prospects Int J Appl Glass Sci 20123289ndash98

[150] Bindra KS Bookey HT Kar AK Wherrett BS Liu X Jha A Nonlinear optical properties of chalcogenide glasses observation of multiphoton absorption App Phys Lett 2001791939ndash41

[151] Zakery A Ruan Y ARode V Samoc M Luther-Davies B Low-loss waveguides in ultrafast laser-deposited As2S3 chalcogenide films J Opt Soc Am B 200391844ndash52

[152] Lenz G Zimmermann J Katsufuji T MLines E Hwang HY Spalter S Slusher RE Cheong SW Sanghera JS Aggarwal ID Large Kerr effect in bulk Se-based chalcogenide glasses Opt Lett 200025254ndash6

[153] Sanghera JS Shaw LB Aggarwal ID Application of chalcogenide glass optical fibers CR Chimie 20025873ndash83

[154] Palik ED Handbook of optical constants of solids San Diego CA Academic 1998

[155] Philipp HR Optical properties of silicon nitride J Electrochem Soc 1973120295ndash300

[156] Malitson IH Interspecimen comparison of the refractive index of fused silica J Opt Soc Am 1965551205ndash8

[157] Barnes NP Piltch MS Temperature-dependent Sellmeier coefficients and nonlinear optics average power limit for germanium J Opt Soc Am 197969178ndash80

[158] Rodney WS Malitson IH King TA Refractive index of arsenic trisulfide J Opt Soc Am 195848633ndash636

[159] Ellipsometry measurement on the thin film samples by our group[160] Bristow AD Rotenberg N van Driel HM Two-photon

absorption and Kerr coefficients of silicon for 850ndash2200 nm Appl Phys Lett 200790191104

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp267

[161] Lin Q Zhang J Piredda G Boyd RW Fauchet PM Agrawal GP Dispersion of silicon nonlinearities in the near infrared region Appl Phys Lett 200791021111

[162] Mizrahi V DeLong KW Stegeman GI Saifi MA Andrejco MJ Two-photon absorption as a limitation to all-optical switching Opt Lett 1989141140ndash2

[163] Guider R NDaldosso APitanti EJordana Fedeli J-M Pavesi L NanoSi low loss horizontal slot waveguides coupled to high Q ring resonators Opt Express 20091720762ndash70 and its erratum

[164] Ferrera M Razzari L Duchesne D Morandotti R Yang Z Liscidini M Sipe JE Chu S Little BE Moss DJ Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures Nat Photonics 20082 737ndash40

[165] Smektala F Quemard C Leneindre L Lucas J Barthelemy A De Angelis C Chalcogenide glasses with large non-linear refractive indices J Non-Crystalline Solids 1998239139ndash42

[166] Boudebs G Sanchez F Troles J Smektala F Nonlinear optical properties of chalcogenide glasses- comparison between Mach-Zehnder interferometry and Z-scan techniques Opt Comm 2001199425ndash33

[167] Asobe M Suzuki K Kanamori T Kubodera K Nonlinear refractive index measurement in chalcogenide-glass fibers by self-phase modulation APL 1992601153ndash4

[168] Asobe M Kanamori T Kubodera K Ultrafast all-optical switching using highly nonlinear chalcogenide glass fiber IEEE Photon Technol Lett 19924362ndash5

[169] Asobe M Kanamori T Kubodera K Applications of highly nonlinear chalcogenide glass fibers in ultrafast all-optical switches IEEE J Quant Electron 1993292325ndash33

[170] Ruan Y Luther-Davies B Li W Rode A Kolev V Madden S Large phase shifts in As2S3 waveguides for all-optical processing devices Opt Lett 2005302605ndash7

[171] Laniel JM Hocirc N Valleacutee R Villeneuve A Nonlinear-refractive-index measurement in As2S3 channel waveguides by asymmetric self-phase modulation J Opt Soc Am B 200522437ndash45

[172] Cerqua-Richardson KA McKinley JM Lawrence B Joshi S Villeneuve A Comparison of nonlinear optical properties of sulfide glasses in bulk and thin film form Opt Mater 199810155ndash9

[173] Harbold JM Ilday FOuml Wise FW Sanghera JS Nguyen VQ Shaw LB Aggarwal ID Highly nonlinear As-S-Se glasses for all-optical switching Opt Lett 200227119ndash121

[174] Ruan YL Li WT Jarvis R Madsen N Rode A Luther-Davies B Fabrication and characterization of low loss rib chalcogenide waveguides made by dry etching Opt Express 2004125140ndash5

[175] Slusher RE Lenz G Hodelin J Sanghera J Shaw LB Aggarwal ID Large Raman gain and nonlinear phase shifts in high-purity As2Se3 chalcogenide fibers J Opt Soc Am B 2004211146ndash55

[176] Jacobsen R Andersen K Borel P Fage-Pedersen J Frandsen L Hansen O Kristensen M Lavrinenko A Moulin G Ou H Peucheret C Zsigri B Bjarklev A Strained silicon as a new electro-optic material Nature 2006441199ndash202

[177] Cazzanelli M Bianco F Borga E Pucker G Ghulinyan M Degoli E Luppi E Veacuteniard V Ossicini S Modotto D Wabnitz S Pierobon R Pavesi L Second-harmonic generation in

silicon waveguides strained by silicon nitride Nat Mater 201111148ndash54

[178] Avrutsky I Soref R Phase-matched sum frequency generation in strained silicon waveguides using their second-order nonlinear optical susceptibility Opt Express 20111921707ndash16

[179] Ghahramani E Moss DJ Sipe JE Second-harmonic generation in odd-period strained (Si)n(Ge)nSi superlattices and at SiGe interfaces Phys Rev Lett 1990642815ndash8

[180] Levy JS Foster MA Gaeta AL Lipson M Harmonic generation in silicon nitride ring resonators Opt Express 20111911415

[181] Zakery A Elliott SR Optical nonlinearities in chalcogenide glasses and their applications Springer Series in Optical Sciences 2007135

[182] Lee KK Lim DR Kimerling LC Shin J Cerrina F Fabrication of ultralow-loss SiSiO2 waveguides by roughness reduction Opt Lett 2001261888ndash90

[183] Cardenas J Poitras CB Robinson JT Preston K Chen L Lipson M Low loss etchless silicon photonic waveguides Opt Express 2009174752ndash7

[184] Biberman A Shaw MJ Timurdogan E Wright JB Watts MR Ultralow-loss silicon ring resonators Opt Lett 2012374236ndash8

[185] Walmsley IA Waxer L Dorrer C The role of dispersion in ultrafast optics Rev Sci Instrum 2001721ndash29

[186] Torres JP MHendrych Valencia A Angular dispersion an enabling tool in nonlinear and quantum optics Adv Opt Photon 20102319ndash69

[187] Yin LH Lin Q Agrawal GP Dispersion tailoring and soliton propagation in silicon waveguides Opt Lett 2006311295ndash7

[188] Dulkeith E Xia FN Schares L Green WMJ Vlasov YA Group index and group velocity dispersion in silicon-on-insulator photonic wires Opt Express 2006143853ndash63

[189] Turner AC Manolatou C Schmidt BS Lipson M Tailored anomalous group-velocity dispersion in silicon channel waveguides Opt Express 2006144357ndash62

[190] Dadap JI Panoiu NC Chen X I-Hsieh W Liu X Chou C-Y Dulkeith E McNab SJ Xia F Green WMJ Sekaric L Vlasov YA Osgood RM Jr Nonlinear-optical phase modification in dispersion-engineered Si photonic wires Opt Express 2008161280ndash99

[191] Milosevic MM Matavulj PS Yang PY Bagolini A Mashanovich GZ Rib waveguides for mid-infrared silicon photonics J Opt Soc Am B 2009261760ndash6

[192] Mashanovich GZ Milošević MM Nedeljkovic M Owens N Xiong B Teo EJ Hu Y Low loss silicon waveguides for the mid-infrared Opt Express 2011197112ndash9

[193] Reimer C Nedeljkovic M Stothard DJM Esnault MOS Reardon C OrsquoFaolain L Dunn M Mashanovich GZ Krauss TF Mid-infrared photonic crystal waveguides in silicon Opt Express 20122029361ndash8

[194] Baehr-Jones T Spott A Ilic R Spott A Penkov B Asher W Hochberg M Silicon-on-sapphire integrated waveguides for the midinfrared Opt Express 20101812127ndash35

[195] Li F Jackson S Grillet C Magi E Hudson D Madden SJ Moghe Y OrsquoBrien C Read A Duvall SG Atanackovic P Eggleton BJ Moss D Low propagation loss silicon-on-sapphire waveguides for the midinfrared Opt Express 20111915212ndash20

268emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

[196] Yue Y Zhang L Huang H Beausoleil RG Willner AE Silicon-on-nitride waveguide with ultralow dispersion over an octave-spanning mid-infared wavelength range IEEE Photonics J 20124126ndash32

[197] Khan S Chiles J Ma J Fathpour S Silicon-on-nitride waveguides for mid-and near-infrared integrated photonics Appl Phys Lett 2013102121104

[198] Cheng Z Chen X Wong CY Xu K Tsang HK Mid-infrared suspended membrane waveguide and ring resonator on silicon-on-insulator IEEE Photonics J 201241510ndash9

[199] Lin P-T Singh V Cai Y Kimerling LC Agarwal A Air-clad silicon pedestal structures for broadband mid-infrared microphotonics Opt Lett 2013381031ndash3

[200] Chang YC Paeder V Hvozdara L Hartmann JM Herzig HP Low-loss germanium strip waveguides on silicon for the mid-infrared Opt Lett 2012372883ndash5

[201] Zhang L Yue Y Y Xiao-Li R G Beausoleil Willner AE Highly dispersive slot waveguides Opt Express 2009177095ndash101

[202] Zhang L Yue Y Beausoleil RG Willner AE Analysis and engineering of chromatic dispersion in silicon waveguide bends and ring resonators Opt Express 2011198102ndash7

[203] Zhang L Mu J Singh V Agarwal A Kimerling LC Michel J Intra-cavity dispersion of microresonators and its engineering for octave-spanning Kerr frequency comb generation to be published

[204] Lin Q Zhang L Generalized nonlinear envelope equation with high-order dispersion of nonlinearity to be published

[205] Wang Y Yue R Han H Liao X Raman study of structural order of a-SiNxH and its change upon thermal annealing J Non-Crystalline Solids 2001291107ndash12

[206] Brida D Marangoni M Manzoni C De Silvestri S Cerullo G Two-optical-cycle pulses in the mid-infrared from an optical parametric amplifier Opt Lett 2008332901ndash3

[207] Brida D Manzoni C Cirmi G Marangoni M Bonora S Villoresi P De Silvestri S Cerullo G Few-optical-cycle pulses tunable from the visible to the mid-infrared by optical parametric amplifiers J Opt 201012013001

[208] Kippenberg TJ Holzwarth R Diddams SA Microresonator-based optical frequency combs Science 2011332555ndash9

[209] Levy JS Gondarenko A Foster MA Turner-Foster AC Gaeta AL Lipson M CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects Nat Photonics 2009437ndash40

[210] DelrsquoHaye P Herr T Gavartin E Gorodetsky ML Holzwarth R Kippenberg TJ Octave spanningtunable frequency comb from a microresonator Phys Rev Lett 2011107063901

[211] Okawachi Y Saha K Levy JS Wen YH Lipson M Gaeta AL Octave-spanning frequency combgeneration in a silicon nitride chip Opt Lett 2011363398ndash400

[212] Matsko AB Savchenkov AA Liang W Ilchenko VS Seidel D Maleki L Mode-locked Kerr frequency combs Opt Lett 2011362845ndash7

[213] Herr T Brasch V Jost JD Wang CY Kondratiev NM Gorodetsky ML Kippenberg TJ Temporal solitons in optical microresonators httparxivorgabs12110733

[214] Saha K Okawachi Y Shim B Levy JS Salem R Johnson AR Foster MA Lamont MR Lipson M Gaeta AL Modelocking and femtosecond pulse generation in chip-based frequency combs Opt Express 2013211335ndash43

[215] Coen S Erkintalo M Universal scaling laws of Kerr frequency combs Opt Lett 2013381790ndash2

[216] Lugiato LA Lefever R Spatial dissipative structures in passive optical-systems Phys Rev Lett 1987582209ndash11

[217] Haelterman M Trillo S Wabnitz S Dissipative modulation instability in a nonlinear dispersive ring cavity Opt Commun 199291401ndash7

[218] Coen S Randle HG Sylvestre T Erkintalo M Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato-Lefever model Opt Lett 20133837ndash9

[219] Chembo YK Menyuk CR Spatiotemporal Lugiato-Lefever formalism for Kerr-comb generation in whispering-gallery-mode resonators Phys Rev A 201387053852

[220] Foltynowicz A Mas1owski P Ban T Adler F Cossel KC Briles TC Ye J Optical frequency comb spectroscopy Faraday Discussion 201115023ndash31

[221] Hartl I Li XD Chudoba C Ghanta RK Ko TH Fujimoto JG Ranka JK Windeler RS Ultrahigh-resolution optical coherence tomography using continuum generation in an air silica microstructure optical fiber Opt Lett 200126608ndash10

[222] Brabec T Krausz F Intense few-cycle laser fields Frontiers of nonlinear optics Rev Mod Phys 200072545ndash91

[223] Hu J Meyer J Richardson K Shah L Feature issue introduction mid-IR photonic materials Opt Mater Express 201331571ndash5

[224] Private communications with Dr Jacob Levy in Prof Lipsonrsquos group and Dr Johann Riemensberger in Prof Kippenbergrsquos group

[225] Zhang J Lin Q Piredda G Boyd RW Agrawal GP Fauchet PM Anisotropic nonlinear response of silicon in the near-infrared region Appl Phys Lett 200791071113

Page 7: Lin Zhang*, Anuradha M. Agarwal, Lionel C. Kimerling and ...

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp253

the materials in Figure 1 and (iii) we emphasize disper-sion engineering naturally as a result of aiming at octave-spanning broadband applications

Figure 4 shows a general illustration of various types of integrated waveguides for nonlinear Group IV photonics Looking at a specific wavelength range one can accord-ingly choose a materials combination for an appropriate index contrast and a desired level of nonlinearity Note that one may need low nonlinearity in some cases when high-power output is required Here we discuss waveguide design at four different wavelength ranges as follows

First we consider SOI waveguides for a wavelength range from the telecom window in the near-IR to the short-wave end in the mid-IR ie roughly from 14 to 25 microm This is the wavelength range that many of the current research efforts have been addressing [60 61 106 108 114 115 135 137 139ndash141 143 144] In this wavelength range a SOI strip waveguide as shown in Figure 4 can be used with air as an upper cladding (see eg [140]) One can change the width of the waveguide to tailor its disper-sion profile while the height of the waveguide is 220 nm set by SOI wafers From Figure 5(A) we note that a rela-tively small width W = 800 nm is corresponding to a dis-persion profile with two ZDWs at 1585 and 2345 microm and a peak value of anomalous dispersion 532 ps(nmmiddotkm) at 205 microm for the quasi-TE mode The anomalous disper-sion is typically useful for parametric amplification and oscillation soliton and soliton-based supercontinuum generation [12] With W  =  900 nm one can have a flatter dispersion profile but the anomalous band is smaller When W is increased to 1000 nm the dispersion is even flatter but no anomalous dispersion occurs Figure 5(A) shows a good example that tight mode confinement in a strip waveguide moves ZDW to short wavelengths and near ZDWs dispersion changes quickly with a large slope

Strip WG

Strip WG suspended

Air Air

Slot

Core

Upper cladding

Slab

Lower cladding

Si substrate

Slot WG suspended

Slot WG Rib WG

Figure 4emspDifferent types of Group IV waveguides (WGs) for disper-sion and nonlinearity engineering in the near- and mid-IR ranges

One can calculate the nonlinear coefficient γ as a function of wavelength with the nonlinear Kerr index n2 given in Tables 1ndash4 in Appendix B We show in Figure 5(B) that the nonlinear coefficient in the silicon strip wave-guide with W = 900 nm first increases to 187 (mmiddotW) with wavelength until 17 μm and then decreases to 56 (mmiddotW) at 25 μm This is caused by both the peaking of the silicon n2 value near 19 μm and the gradual increase of wave-length and mode area beyond that

A silicon stripslot hybrid waveguide exhibits very flat dispersion as presented in Figure 5(A) The SOI waveguide has crystalline silicon at the bottom a thin SRO slot and amorphous silicon at the top The upper cladding is silicon dioxide When setting the lower Si height to Hl = 430 nm slot height to Hs = 54 nm upper Si height to Hu = 160 nm and width to W = 660 nm we obtain an extremely flat disper-sion profile for the quasi-TM mode over a wide bandwidth between two ZDWs at 1545 and 2448 microm From 1605 to 238 microm the value of anomalous dispersion changes between 30 and 46 ps(nmmiddotkm) In this way one can have a flat and low anomalous dispersion between two far apart ZDWs The average dispersion value can be shifted by increasing Hu to move dispersion between normal and anomalous regimes Detailed explanation on how the flat-tened and saddle-shaped dispersion profile is produced is given in [59 60] Briefly the mode transition over wave-length for the quasi-TM mode is responsible for this behav-ior Due to the off-center slot the mode is mostly confined in the crystalline silicon at short wavelengths while the mode becomes more like a slot mode at long wavelengths As shown in Figure 5(C) we plot the mode power distribu-tions at wavelengths of 15 183 217 and 25 microm The mode transition adds negative dispersion in the middle of the low-dispersion bandwidth as explained in [60 201]

Having a slot one has an opportunity to fill the slot with highly nonlinear materials into it [49 51 53 55 56 58 59] which can overcome the decrease of the nonlinear coeffi-cient over wavelength In Figure 5(B) we show the γ value increasing to 306 (mmiddotW) with wavelength from 14 to 25 microm This is because the guided mode extends more to the highly nonlinear thin slot layer Note that the used n2 value in SRO [38] is currently the one measured at 155 microm so the n2 and γ thinspvalues may vary in the mid-IR but the trend is general

Next we explore the short-wavelength end of the near-IR spectrum Silicon-based devices become unus-able for nonlinear photonics as wavelength decreases to 11 microm and we thus look at silicon nitride for near-IR nonlinear applications extending to the visible light spec-trum Again a strip waveguide based on silicon nitride is examined first Figure 6(A) shows dispersion curves of the quasi-TE mode in two waveguides sized to be 1300 times 540

254emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

and 1400 times 800 nm2 The upper cladding is air and the lower cladding is silicon dioxide The anomalous disper-sion region in the dispersion curves shrinks when the waveguide is made smaller This is because of a relatively small index contrast between silicon nitride and silicon dioxide which makes the guided mode leak quickly to the substrate as wavelength increases For the strip waveguide with a cross-section of 1400 times 800 nm2 there are two ZDWs near 10 and 23 microm but one can see a strong dispersion of 250 ps(nmmiddotkm) between the two ZDWs in Figure 6(A) The nonlinear coefficient in the second silicon nitride wave-guide is shown in Figure 6(B) which is much smaller than that in silicon waveguides because of a one-order smaller n2 value and larger Aeff in the silicon nitride waveguide At 16 microm γ is about 123(mW)

One can also use a stripslot hybrid structure to tailor the dispersion profile in silicon nitride waveguides For example the slot and lower cladding are silicon dioxide and the upper cladding is air In Figure 6(A) we show the dispersion curves in two silicon nitride stripslot hybrid waveguides for comparison The waveguide 1 has Hl = 900 nm Hs = 124 nm Hu = 340 nm and W = 1000 nm and the waveguide 2 has Hl = 920 nm Hs = 154 nm Hu = 480 nm and W = 1300 nm These two waveguides produce increasingly flatter dispersion profiles as shown in Figure 6(A) The first waveguide has two ZDWs located at 106 and 22 microm with the peak dispersion of 67 ps(nmmiddotkm) The second waveguide has two ZDWs at 115 and 235 microm with the dispersion varying within 0~20 ps(nmmiddotkm) This octave-spanning dispersion flattening with different levels

1000A

B

C

500

-500

400

300

200

100

0

-100014 16

Strip WG W=800 nmStrip WG W=900 nm

Strip WG W=900 nm

Strip WG W=1000 nm

Slot WG Hu=160 nm

Slot WG Hu=160 nm

Slot WG Hu=163 nmSlot WG Hu=166 nm

18 20 22Wavelength (microm)

Dis

pers

ion

(ps

nmmiddotk

m)

Non

linea

r co

effic

ient

(m

middotW)

24 26

14 16 18 20 22

Wavelength (microm)

24 26

0

Figure 5emspIn a wavelength range from the telecom window in near-IR to the short-wave end in the mid-IR silicon strip and stripslot hybrid waveguides (WGs) are analyzed in terms of (A) dispersion and (B) nonlinearity (C) Mode power distributions at wavelengths of 15 183 217 and 25 microm in the stripslot hybrid waveguide

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp255

of dispersions can be used for multiple applications as detailed in the next section The nonlinear coefficients for the two waveguides are shown in Figure 6(B) We note that the stripslot hybrid waveguides have similar nonlinear coefficients as the strip waveguide which shows that the dispersion profile is much more tailorable by waveguide designs

Then we move to the mid-IR using silicon and silicon nitride for waveguiding A comparison of different types of silicon-on-nitride waveguides have been presented in [196] where rib waveguides were preferred due to the wideband low dispersion over an octave-spanning band-width from 24 to 66 microm for the quasi-TE mode This is a spectral range from siliconrsquos half-bandgap wavelength to the cut-off wavelength of silicon nitride In Figure 7(A) we plot the dispersion curve for a silicon-on-nitride rib waveguide with air as the upper cladding the rib width of 2000 nm the total height of 1200 nm and the slab height of 1000 nm which are the same parameters used in [196] It is shown that less confinement of optical modes reduces the contribution of waveguide dispersion and makes the overall dispersion profile closer to the material dispersion which is flat and low at long wavelengths as in Figure 2(B)

A

B

400

300

200

100

-100

8

6

4

2

0

0

Strip WG 1300times540 nm2

Strip WG 1400times800 nm2

Strip WG 1400times800 nm2

Slot WG 1Slot WG 2

Slot WG 1Slot WG 2

Dis

pers

ion

(ps

nmmiddotk

m)

Non

linea

r co

effic

ient

(m

middotW)

20 3010 15 2505Wavelength (microm)

2010 15 2505

Wavelength (microm)

Figure 6emspIn a wavelength range moved toward the short-wave-length end of near-IR spectrum silicon nitride strip and stripslot hybrid waveguides are designed in terms of (A) dispersion and (B) nonlinearity

Accordingly the nonlinear coefficient is small 285 (mmiddotW) at 3 microm as shown in Figure 7(B)

On the other hand if one needs a small Aeff to enhance nonlinearity additional dispersion tailoring (eg based on stripslot hybrid waveguides) would be beneficial Pursuing a higher nonlinear coefficient we use a 500-nm silicon nitride suspended membrane as illustrated in Figure 4 to support a silicon stripslot hybrid waveguide This helps confine light in the waveguide core Using W = 880 nm Hu = 550 nm Hs = 87 nm and Hl = 840 nm we obtain a saddle-shaped anomalous dispersion from 19 to 449 microm within 0~60 ps(nmmiddotkm) for the quasi-TM mode as shown in Figure 7(A) This structure produces much tighter mode confinement than the rib waveguide and exhibits a 3 times larger nonlinear coefficient in Figure 7(B) while having similar dispersion flatness

Finally we consider germanium-on-silicon wave-guides over a wavelength range from 33 to 85 microm between the half-bandgap wavelength of germanium and the cut-off wavelength of silicon This type of waveguide has been demonstrated with strain-free mono-crystal-line germanium [200] Here we assume that the germa-nium waveguide has a 10-nm silicon nitride layer on its

A

B

200

-200

60

40

20

0

100

-100

0

Rib WGSlot WG

Rib WGSlot WG

Dis

pers

ion

(ps

nmmiddotk

m)

Non

linea

r co

effic

ient

(m

middotW)

1 2 3 4 5 6 7Wavelength (microm)

1 2 3 4 5 6 7

Wavelength (microm)

Figure 7emspIn a wavelength range from the short-wave IR to mid-IR silicon rib waveguide on silicon nitride and stripslot hybrid waveguide on a suspended membrane are analyzed in terms of (A) dispersion and (B) nonlinearity

256emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

surface for passivation The upper cladding could be air or silicon which provides significantly different dispersion properties due to a varied index contrast For comparison only we also have silicon nitride as the upper cladding although silicon nitride becomes lossy for wavelengths longer than 67 microm Figure 8(A) shows the dispersion pro-files of four germanium-on-silicon strip waveguides with equal size 3000 times 1600 nm2 for the quasi-TE mode Air and silicon nitride as an upper cladding result in similar shape and bandwidth in the dispersion profiles Thus the air-cladded waveguide is chosen and discussed further The waveguide with silicon upper cladding has normal dispersion at all wavelengths since there is a relatively small index contrast between germanium and silicon and thus weak mode confinement A germanium strip wave-guide on a 600-nm-thick silicon suspended membrane is also considered to increase light confinement with an air upper cladding to maximize light confinement However as mentioned earlier strong confinement typically causes strong dispersion as shown in Figure 8(A) and therefore the germanium waveguide on a silicon membraneis not chosen for broadband nonlinear applications In contrast the germanium strip waveguide with air upper cladding exhibits a flat and low dispersion

The dimensions of the air-cladded germanium wave-guide are varied by simultaneously changing its height and width with a step of 200 nm for both polarization states It is interesting to see from Figure 8(B) and 8(C) that the dispersion peak value remains nearly unchanged for all the waveguide sizes although we have a widely tunable ZDW at long wavelengths For the quasi-TE mode the right ZDW moves from 605 microm to 841 microm while the left ZDW is always near 4 microm We can thus obtain an octave-spanning anomalous dispersion band with the peak value below 100 ps(nmmiddotkm) For the quasi-TM mode one can see similar dispersion properties but the anomalous disper-sion band is smaller Thus we choose the quasi-TE mode for further discussion in next section

The nonlinear coefficient in the germanium wave-guides for the quasi-TE mode is shown in Figure 8(D) which is about 10(mmiddotW) at 5 microm with a small variation for differ-ent waveguide sizes This is quite high considering that both wavelength and effective mode area become much larger over this wavelength range compared to the near-IR

From above we can see that the stripslot hybrid wave-guides enable unique controllability of dispersion and that this concept is applicable to different wavelength ranges However their performance may be sensitive to fabrication errors especially for inaccuracies in slot height Hs [59 60] A higher yield in device fabrication is expected using advanced fabrication technologies and facilities

A

C

D

B

400

300

200

100

-100

-200

0

Ge WG+air 3000times1600 nm2

Ge WG+air suspended 3000times1600 nm2

Ge WG+Si3N4 3000times1600 nm2

Ge WG+Si 3000times1600 nm2

Ge WG+air 2800times1400 nm2

Ge WG+air 3000times1600 nm2

Ge WG+air 3200times1800 nm2

Ge WG+air 3400times2000 nm2

Ge WG+air 2800times1400 nm2

Ge WG+air 3000times1600 nm2

Ge WG+air 3200times1800 nm2

Ge WG+air 3400times2000 nm2

Ge WG+air 2800times1400 nm2

Ge WG+air 3000times1600 nm2

Ge WG+air 3200times1800 nm2

Ge WG+air 3400times2000 nm2

Dis

pers

ion

(ps

nmmiddotk

m)

400

300

200

100

-100

-200

0

Dis

pers

ion

(ps

nmmiddotk

m)

400

300

200

100

-100

-200

50

40

30

20

10

0

0

Dis

pers

ion

(ps

nmmiddotk

m)

Non

linea

r co

effic

ient

(m

middotW)

3 4 5 6 7 8 9Wavelength (microm)

3 4 5 6 7 8 9Wavelength (microm)

3 4 5 6 7 8 9

Wavelength (microm)

3 4 5 6 7 8 9

Wavelength (microm)

Figure 8emspIn a wavelength range covering the main part of the mid-IR spectrum (A) on silicon substrate or on suspended silicon membrane are analyzed in terms of dispersion Germanium-on-silicon strip waveguides with an air upper cladding and different dimensions are characterized by (B) dispersion for the quasi-TE mode (C) dispersion for the quasi-TM mode and (D) nonlinearity for the quasi-TE mode

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp257

Besides photonic waveguides another important cat-egory of nonlinear devices is integrated resonators In the scope of this paper we consider relatively large resona-tors for frequency comb generation in which the bending radius of a ring resonator is varied from 50 microm to 100 microm depending on free spectral range (FSR) and the group index in the waveguide In these cases the waveguide-bending-induced dispersion is small and we would not discuss intra-cavity dispersion [202 203] in details here

4 ApplicationsBenefiting from the unique dispersion engineering over an octave-spanning bandwidth as described above one can develop ultra-wideband nonlinear applications that could hardly be attained in an integrated platform previously These include octave-spanning supercontinuum genera-tion pulse compression to a few-cycle or even sub-cycle level octave-spanning Kerr frequency comb generation and the associated mode-locked ultrashort pulse genera-tion using microresonators In this section we review our recent work on these topics

First we discuss the supercontinuum generation and pulse compression in a straight waveguide The nonlinear envelope equation used here to simulate supercontinuum generation is the following

βα infin

=

part part+ + = + part part sum

2

( - )( ) ( )

2

m mm

mm

ii A K A R A

z m t (1)

where

2

0 0

- -( ) 1- ( ) 2

n nn

nn

i i iK A A An t tγ δ δ

ω δ δ

infin

=

= sum

and

2shock_R( ) - 1- [ ( - ) | | ]δ

γ τδ minusinfin

= prime prime int

t

R RR A i i A h t t A dtt

We denote A  =  A(zt) as the complex amplitude of an optical pulse Note that its Fourier transform is

-

1( ) ( ) exp( - ) 2

A z A z t i t dtω ωπ

infin

infin

= int

In Eq (1) α is the total propagation loss and βm is the mth-order dispersion coefficient The frequency dependence of nonlinearity parameters including the nonlinear index n2 the TPA coefficient βTPA and the

effective mode area Aeff is included in the nth-order dis-persion coefficient γn of nonlinearity which is defined as γn = ω0middotpartn[γ(ω)ω]partωn where ω0 is the angular frequency of the carrier Therefore we can consider all-order linear dispersion terms and all-order dispersion of the nonlin-ear coefficient in Eq (1) Specifically in the simulations for a silicon and silicon nitride waveguides we have all-order linear dispersion and up to 6th-order and 2nd-order of the nonlinear coefficient dispersion included A detailed derivation of Eq (1) is given in [204] For the quasi-TM mode that experiences the engineered dispersion due to the mode transition SRS in silicon waveguides fabricated on the (001) surface can be ignored [27 96] For silicon nitride waveguide we include the SRS term in Eq (1) where γR = gRΓR(AeffΩR) and gR ΓR and ΩR represent the Raman gain coefficient the full width at half maximum of the gain spectrum and the Raman shift respectively The Raman shock time τshock_R is associated with γRrsquos fre-quency dependence which is 1ω0-[1Aeff(ω0)][dAeff(ω)dω] similarly as in [14] if we ignore frequency dependent gR ΓR and ΩR hR(t) is the Raman response function and it corresponds to the Raman gain spectrum

2

2 20 0

( ) -( - ) 2 ( - )

Ωω

Ω ω ω Γ ω ω=

+R

RR R

Hi

Note that the sign before the imaginary unit is differ-ent from that in [27] to be consistent with the expression of the Fourier transform that we used

We have considered supercontinuum generation in both silicon and silicon nitride waveguides with the slot-assisted dispersion tailoring Octave-spanning supercon-tinua in a silicon-based stripslot hybrid waveguide have been investigated in detail in [108] in which two-cycle optical pulses are obtained The main results in that work are shown in Figure 9 for comparison purposes

Here we mainly focus on the supercontinuum gen-erated in the silicon nitride stripslot hybrid waveguide (ie the slot WG 1 in Section III) whose dispersion and nonlinearity properties are shown in Figure 6 In the non-linear simulations we set the total propagation loss to be 1 dBcm The SRS parameters used here are the following [205] ΩR2π = 143 THz ΓR2π = 172 THz and gR = 1 times 10-12 mW τshock_R is calculated to be  = 156 fs

In our simulations we use a time step of 025 fs which is corresponding to a bandwidth of 4000 THz in the fre-quency domain For a femtosecond input pulse we set the time window length to 50 ps (ie frequency resolution Δf = 20 GHz)

We simulate the nonlinear propagation of a chirp-free hyperbolic secant pulse in the silicon nitride waveguide

258emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

The pulse center wavelength is at 1610 nm and its full width at half-maximum (FWHM) T0 is 120 fs Its peak power is 1200 W corresponding to pulse energy of 016 nJ

Figure 10(A) shows the supercontinua at different propagation distances At 48 mm the spectrum is greatly broadened at the -30 dB level covering a wavelength range from 0585 to 2833 microm which is more than two octaves The spectrum evolution in Figure 10(A) shows a similar spectrum shape as that in Figure 9(A) both featuring a ldquotriangularrdquo central spectrum bounded by two dispersive waves at the edges However it is important to note that the absence of TPA and 3PA in silicon nitride at the telecom window leads to a much more efficient spectrum broad-ening than that in silicon [108] The generated spectrum extends from the visible light to the mid-IR with excellent spectral coherence which is confirmed by the pulse wave-form shown in Figure 10(B) In the time domain the pulse is greatly compressed from 120 to 408 fs corresponding to 076 optical cycles at 161 microm wavelength

We examine the pulsewidth as a function of propa-gation distance Figure 11 shows that the pulse becomes increasingly narrower until the propagation distance reaches 47 mm For longer distances the pulsewidth

A

B

60 mm

48 mm

36 mm

24 mm

12 mm

Input

Spe

ctru

m (

10 d

Bd

iv)

Pow

er (

W)

12

246

24

18

12

6

0

248 250 252 254

14 16 18 20 22 24Wavelength (microm)

Time (ps)

Figure 9emsp(A) The supercontinuum generation in a silicon-based stripslot hybrid waveguide presented in [108] (B) The significant spectrum broadening at 425-mm distance is associated with a temporal compression of an input pulse (dash line) to the output waveform (solid line) with a FWHM of 12 fs

A

B

50 mm

48 mm

46 mm

44 mm

42 mm

Input

Spe

ctru

m (

10 d

Bd

iv)

Pow

er (

W)

8000

6000

4000

2000

0250249 251

06 09 12 15 18 21 24 27

Wavelength (microm)

Time (ps)

Figure 10emsp(A) Spectrum evolution of the pulse over propagation distance A supercontinuum of more than two octaves is achieved at 48 mm distance (B) Generated pulse waveform with a pulse width of 408 fs as short as 076 optical cycles Low pedestals are caused by dispersive waves generated at the two ends of the spectrum

remains almost constant However it is important to mention that after 48 mm the dispersive waves become increasingly stronger as shown in Figure 10(A) causing larger pedestals

Comparing the results in Figures 9 and 10 we note that the mid-IR wavelength range for silicon would be in analogy to the near-IR for silicon nitride in terms of non-linear optics operations Pumping at or beyond 33 microm one can use the waveguide designs shown in Figure 7 to produce very efficient nonlinear interactions without TPA and 3PA in silicon Ultrashort pulses in the mid-IR from parametric amplifiers [206 207] could be used to pump the Group IV waveguides

Another nonlinear application of the dispersion-engi-neered Group IV waveguides is micro-resonator-based Kerr frequency comb generation When such a waveguide is curved to form a microring resonator input CW light travels around the cavity and amplifies the noise in the source located at the frequencies with a high parametric gain As a result of modulation instability and cascaded FWM in the cavity a frequency comb can be generated [208ndash211] Mode-locked frequency combs have been reported pro-ducing low-noise pulse trains in time domain [212ndash214]

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp259

The formation of cavity solitons is identified as the main reason for the mode-locking in the Kerr frequency combs [215] This is instructive because one can thus predict the spectral bandwidth and temporal pulsewidth in the generated low-noise combs The 3-dB comb bandwidth is inversely proportional to the square root of the 2nd-order dispersion coefficient |β2| as given in [213 215] It is desira-ble that all comb lines that constitute the soliton spectrum experience the same |β2| In this sense the stripslot hybrid waveguides with flattened dispersion are preferably suit-able for supporting broadband Kerr comb generation and ultra-short cavity soliton generation

The Kerr frequency comb generation can be modeled using the generalized Lugiato-Lefever equation (LLE) [216ndash219]

20

2

( - )- - | |

2 2

m mm

R inmm

jkt j jl E kE j l E Et m

βαδ γ

τ

infin

=

part part+ + + = part part

sum (2)

where tR is the round-trip time E = E(tτ) and Ein are intra-cavity field and input field (pump power Pin  =  |Ein|2) t and τ are the slow and fast times δ0 is the cavity phase detuning defined as δ0  =  tRmiddot(ωn -ω0) where ω0 and ωn are the pumprsquos angular frequency and the nth angular reso-nance frequency that is pumped Other resonator param-eters include the power loss per round trip α the power coupling coefficient κ the nonlinear coefficient γ and the mth dispersion coefficient βm Since a flattened dispersion profile has a small β2 over a wide bandwidth it is impor-tant to take the influence of higher-order dispersion into account We include all-order dispersion terms in Eq (2) as we did in solving Eq (1)

To enhance the Kerr comb bandwidth in the near-IR we use the ultra-flattened dispersion profile in Figure 6(A) which is obtained in the slot WG 2 based on

Pul

se w

idth

(fs

)

14

12

10

8

6

4

242 44 46 48 50 52

Propagation distance (mm)

Figure 11emspPulse width first decreases with propagation distance and then remains stable After 48 mm dispersive waves get stronger causing more pedestals

Pow

er (

10 d

Bd

iv)

Pow

er (

W)

70A

B

60

50

40

30

20

10

-10

-20

600

400

200

0

80 120

0575 0600 0625 0650

160 200 240 280 320 360

0

Frequency (THz)

Time (ps)

Figure 12emsp(A) Frequency comb generation with a CW pump at 155 microm using a microring resonator based on a silicon stripslot hybrid waveguide Over an octave-spanning bandwidth from 135 to 270 THz the comb lines have a power drop of 20 dB (B) Generated pulse waveform with a pulse width of 82 fs as short as 16 optical cycles

silicon nitride The ring resonator has a bending radius of 104 microm corresponding to a FSR of 200 GHz Pumping near 155 microm with a pump power of 2 W the resonance peak is red-shifted and we need to red-shift the pump wavelength accordingly and tune it into the resonance from the short-wavelength side When the pump is step-by-step tuned by up to 63 resonance linewidths we obtain the comb spectrum and the mode-locked pulse waveform as shown in Figure 12 One can see that over an octave-spanning bandwidth from 133 to 268 THz the comb lines have a power drop by 20 dB from the center of the spectrum The spectral flatness of this comb is relatively good compared to the previously reported results [208ndash211] The comb bandwidth at -40 dB is as wide as two octaves There are two dispersive peaks in normal dispersion regions beyond the low-dispersion band Such a mode-locked broadband comb produces a train of sub-two-cycle optical pulses as shown in Figure 12(B) with one pulse per round trip The peak power of the pulse is up to 600 W Nonlinear conver-sion efficiency is estimated to be -267 dB

To generate frequency combs in the mid-IR the ger-manium-on-silicon strip waveguide is chosen We choose

260emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

a cross-section of 3200 times 1800 nm2 which has an octave-spanning low-dispersion band from 4 to 767 microm as shown in Figure 8(B) A germanium ring resonator is formed with a bending radius of 564 microm corresponding to a FSR of 200 GHz Pumping at 6 microm with a CW power of 14 W and detuning the pump wavelength by 10 resonance linewidth one can see that a mode-locked wideband mid-IR comb is generated from 358 to 644 THz (ie from 466 to 838 microm) at -40 dB level The FWHM of the produced pulses is 69 fs which corresponds to ~35 optical cycles The pulse peak power is 184 W and the nonlinear conversion efficiency is estimated to be -143 dB Since the pumping frequency is not at the center of the low-dispersion band we only see one peak in the comb spectrum caused by the dispersive wave in the normal dispersion region from Figure 13(A) There is another peak at higher frequencies beyond what is shown in the figure

As shown above broadband dispersion engineering is critical for octave-spanning nonlinear applications in both near- and mid-IR wavelength ranges which enables us to fully utilize the bandwidth allowed by the materials transparency windows Generally speaking the nonlinear applications mentioned here such as supercontinuum generation ultrafast pulse compression and frequency comb generation are often the intermediate steps towards higher-level system applications In the frequency domain a wide spectrum can serve as an electromagnetic carrier to acquire high-volume of information eg for sensing [220] and imaging [221] In the time domain an ultrashort pulse can be used as probe to sample ultrafast phenomena [222]

5 Summary and OutlookWe have presented a review of our recent work on nonlin-ear photonics based on silicon and germanium Various types of Group IV waveguides are analyzed and optimized for four different wavelength ranges from near- to mid-IR The recently proposed dispersion engineering technique based on stripslot hybrid waveguide structures is used for different material combinations and wavelength ranges Numerical simulations show that the dispersion-flattened Group IV waveguides are preferably suitable for octave-spanning nonlinear applications including on-chip supercontinuum generation ultrashort pulse compres-sion and mode-locked wideband frequency comb genera-tion based on micro-resonators

The presented approach to achieving octave-span-ning nonlinear applications on an integrated CMOS-compatible Group IV platform holds great potential for realizing chip-scale sensing imaging communications and signal processing system The ultrawide transparency windows in the mid-IR allowed by Group IV elements and compounds potentially together with other materi-als [223] provide an exciting arena for building powerful information acquisition and processing units enabled by nonlinear optics nano-photonics and ultrafast optics

Received June 14 2013 accepted October 29 2013 previously pub-lished online November 27 2013

Pow

er (

10 d

Bd

iv)

A

8030 40 50 60 70Frequency (THz)

Pow

er (

W)

B200

150

100

50

0

21 22 23 24 25Time (ps)

Figure 13emsp(A) Frequency comb generation with a CW pump at 6 microm using a microring resonator based on a germanium strip waveguide with air upper cladding (B) Generated pulse waveform with a pulse width of 69 fs as short as 35 optical cycles

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp261

Appendix

A Material index and dispersion

In this section we give the wavelength-dependent mate-rial index expressed as Sellmeier equations where wave-length λ is in μm

For silicon we use the following material index that is a fit curve from measurement results at room temperature (293 K) with 184 data points in total from 112 to 588 μm [154]

22 1 2 2

2 2 22

( )-

C Cn

λλ ε

λ λ λ= + +

where ε = 116858 C1 = 0939816 μm2 C2 = 000810461 and λ2 = 11071 μm

For silicon nitride the material index is affected by deposition conditions using plasma-enhanced chemical vapor deposition (PECVD) low-pressure chemical vapor deposition (LPCVD) and so on We use the following Sell-meier equation [155] which predicts the material index close to that in LPCVD silicon nitride films measured by a few groups [224]

22 1

2 21

( ) 1-

Cn

λλ

λ λ= +

where C1 = 28939 and λ1 = 013967 μmFor silicon dioxide we use the following Sellmeier

equation for fused silica [156]22 2

2 31 22 2 2 2 2 2

1 2 3

( ) 1- - -

CC Cn

λλ λλ

λ λ λ λ λ λ= + + +

where C1 = 06961663 C2 = 04079426 C3 = 08974794 λ1 = 00684043 μm λ2 = 01162414 μm and λ3 = 9896161 μm

For SRO the material index is affected by deposition conditions such as silicon excess annealing temperature and so on Here we choose the one with silicon excess of 8 and annealed at 1250oC [51]

22 22 31 2

2 2 2 2 2 21 2 3

( ) 1- - -

CC Cn

λλ λλ

λ λ λ λ λ λ= + + +

where C1 = 001 C2 = 196 C3 = 141 λ1 = 03 μm λ2 = 007071 μm and λ3 = 2775968 μm

For germanium the temperature-dependent mate-rial index was measured [157] Here we choose the one for room temperature (293 K)

2 22 1 2

2 2 2 21 2

( )- -

C Cn

λ λλ ε

λ λ λ λ= + +

where ε = 928156 C1 = 67288 C2 = 021307 λ1 = 0664116 μm and λ2 = 6221013 μm

For arsenic sulfide we use the material index pro-vided in [158]

2 2 22 22 3 4 51 2

2 2 2 2 2 2 2 2 2 21 2 3 4 5

( ) 1- - - - -

C C CC Cn

λ λ λλ λλ

λ λ λ λ λ λ λ λ λ λ= + + + + +

where C1 = 18983678 C2 = 19222979 C3 = 08765134 C4 = 01188704 C5 = 09569903 λ1 = 015 μm λ2 = 025 μm λ3 = 035 μm λ4 = 045 μm and λ5 = 27386128 μm

For arsenic selenide we fit ellipsometry measure-ments of our arsenic selenide thin films and the bulk material is provided by Prof Kathleen A Richardson group

22 22 31 2

2 2 2 2 2 21 2 3

( ) 1- - -

CC Cn

λλ λλ

λ λ λ λ λ λ= + + +

where C1 = 298463 C2 = 321011 C3 = 100182 λ1 = 044118 μm λ2 = 0000354953 μm and λ3 = 38413 μm

B Nonlinear Kerr index n2

The third-order nonlinear susceptibility χ(3)1111 for silicon and

germanium is predicted over the mid-IR range [133] based on a two-band model The effective nonlinear susceptibil-ity χ(3) is dependent on polarization and crystallographic orientation [225] For strong nonlinearity we consider a single-polarization incident light aligned to the crystal-lographic axis and we have χ(3) = χ(3)

1111 To investigate the octave-spanning nonlinear phenomena one need to take the wavelength-dependent nonlinear Kerr index n2 and TPA coefficient βTPA into account which are expressed as

( 3 )2 2

0

( 3 )2

0

3( ) ( )4 ( )

3( ) ( )( )

re

TPA im

ncn

cn

λ χ λε λ

πβ λ χ λ

λε λ

=

=

where ε0 and c are the vacuum permittivity and the speed of light in vacuum Using the material index given in Appendix A and χ(3) value from [133] we obtain the n2 and βTPA values tabulated as follows

262emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

Table 1enspNonlinear Kerr index n2 in silicon

λμm

  n2

10-18 m2W  λ

μm  n2

10-18 m2W  λ

μm  n2

10-18 m2W

130   234   310   389   490   312135   305   315   384   495   311140   378   320   379   500   310145   443   325   375   505   309150   501   330   371   510   307155   559   335   368   515   306160   618   340   365   520   304165   671   345   362   525   304170   710   350   360   530   303175   741   355   358   535   302180   766   360   355   540   302185   781   365   352   545   301190   783   370   350   550   300195   778   375   346   555   298200   762   380   343   560   297205   732   385   341   565   296210   699   390   338   570   296215   658   395   336   575   295220   612   400   334   580   295225   576   405   332   585   295230   547   410   331   590   294235   525   415   330   595   293240   508   420   329   600   292245   493   425   328   605   291250   479   430   327   610   290255   467   435   325   615   289260   456   440   324   620   288265   448   445   321   625   288270   440   450   319   630   288275   432   455   317   635   288280   424   460   315   640   288285   417   465   314   645   288290   410   470   313   650   288295   404   475   313   655   288300   398   480   312   660   288305   394   485   312    

Table 2enspTPA coefficient βTPA in silicon

λμm

  βTPA

10-12 mW  λ

μm  βTPA

10-12 mW  λ

μm  βTPA

10-12 mW

130   1334   165   812   200   180135   1284   170   713   205   115140   1222   175   613   210   064145   1154   180   522   215   024150   1079   185   424   220   0003155   995   190   333    160   905   195   254    

Table 3enspNonlinear Kerr index n2 in germanium

λμm

  n2

10-18 m2W  λ

μm  n2

10-18 m2W  λ

μm  n2

10-18 m2W

23  3932  63  1986  103  170524  4994  64  1972  104  169925  6007  65  1959  105  169426  6650  66  1946  106  169027  6772  67  1934  107  168728  6273  68  1923  108  168429  4897  69  1913  109  168230  4403  70  1904  110  168131  3970  71  1895  111  167932  3680  72  1886  112  167733  3470  73  1876  113  167534  3286  74  1868  114  167335  3128  75  1859  115  167036  2998  76  1850  116  166737  2895  77  1841  117  166338  2812  78  1833  118  165939  2737  79  1826  119  165640  2668  80  1819  120  165341  2605  81  1812  121  165142  2550  82  1807  122  164843  2498  83  1801  123  164644  2450  84  1797  124  164445  2406  85  1792  125  164346  2365  86  1787  126  164147  2328  87  1782  127  163948  2295  88  1777  128  163649  2266  89  1772  129  163450  2238  90  1767  130  163251  2212  91  1762  131  163052  2187  92  1758  132  162853  2164  93  1753  133  162654  2141  94  1749  134  162555  2121  95  1744  135  162356  2101  96  1740  136  162157  2083  97  1736  137  162058  2066  98  1731  138  161859  2049  99  1727  139  161760  2032  100  1722  140  161661  2016  101  1716   62  2001  102  1711   

Table 4enspTPA coefficient βTPA in germanium

λμm

  βTPA

10-8 mW  λμm

  βTPA

10-8 mW  λ

μm  βTPA

10-8 mW

23   130   25   088   27   03124   111   26   060   28   006

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp263

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[147] Carlie N Musgraves JD Zdyrko B Luzinov I Hu J Singh V Agarwal A Kimerling LC Canciamilla A Morichetti F Melloni A Richardson K Integrated chalcogenide waveguide resonators for mid-IR sensing leveraging material properties to meet fabrication challenges Opt Express 20101826728ndash43

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absorption and Kerr coefficients of silicon for 850ndash2200 nm Appl Phys Lett 200790191104

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp267

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[168] Asobe M Kanamori T Kubodera K Ultrafast all-optical switching using highly nonlinear chalcogenide glass fiber IEEE Photon Technol Lett 19924362ndash5

[169] Asobe M Kanamori T Kubodera K Applications of highly nonlinear chalcogenide glass fibers in ultrafast all-optical switches IEEE J Quant Electron 1993292325ndash33

[170] Ruan Y Luther-Davies B Li W Rode A Kolev V Madden S Large phase shifts in As2S3 waveguides for all-optical processing devices Opt Lett 2005302605ndash7

[171] Laniel JM Hocirc N Valleacutee R Villeneuve A Nonlinear-refractive-index measurement in As2S3 channel waveguides by asymmetric self-phase modulation J Opt Soc Am B 200522437ndash45

[172] Cerqua-Richardson KA McKinley JM Lawrence B Joshi S Villeneuve A Comparison of nonlinear optical properties of sulfide glasses in bulk and thin film form Opt Mater 199810155ndash9

[173] Harbold JM Ilday FOuml Wise FW Sanghera JS Nguyen VQ Shaw LB Aggarwal ID Highly nonlinear As-S-Se glasses for all-optical switching Opt Lett 200227119ndash121

[174] Ruan YL Li WT Jarvis R Madsen N Rode A Luther-Davies B Fabrication and characterization of low loss rib chalcogenide waveguides made by dry etching Opt Express 2004125140ndash5

[175] Slusher RE Lenz G Hodelin J Sanghera J Shaw LB Aggarwal ID Large Raman gain and nonlinear phase shifts in high-purity As2Se3 chalcogenide fibers J Opt Soc Am B 2004211146ndash55

[176] Jacobsen R Andersen K Borel P Fage-Pedersen J Frandsen L Hansen O Kristensen M Lavrinenko A Moulin G Ou H Peucheret C Zsigri B Bjarklev A Strained silicon as a new electro-optic material Nature 2006441199ndash202

[177] Cazzanelli M Bianco F Borga E Pucker G Ghulinyan M Degoli E Luppi E Veacuteniard V Ossicini S Modotto D Wabnitz S Pierobon R Pavesi L Second-harmonic generation in

silicon waveguides strained by silicon nitride Nat Mater 201111148ndash54

[178] Avrutsky I Soref R Phase-matched sum frequency generation in strained silicon waveguides using their second-order nonlinear optical susceptibility Opt Express 20111921707ndash16

[179] Ghahramani E Moss DJ Sipe JE Second-harmonic generation in odd-period strained (Si)n(Ge)nSi superlattices and at SiGe interfaces Phys Rev Lett 1990642815ndash8

[180] Levy JS Foster MA Gaeta AL Lipson M Harmonic generation in silicon nitride ring resonators Opt Express 20111911415

[181] Zakery A Elliott SR Optical nonlinearities in chalcogenide glasses and their applications Springer Series in Optical Sciences 2007135

[182] Lee KK Lim DR Kimerling LC Shin J Cerrina F Fabrication of ultralow-loss SiSiO2 waveguides by roughness reduction Opt Lett 2001261888ndash90

[183] Cardenas J Poitras CB Robinson JT Preston K Chen L Lipson M Low loss etchless silicon photonic waveguides Opt Express 2009174752ndash7

[184] Biberman A Shaw MJ Timurdogan E Wright JB Watts MR Ultralow-loss silicon ring resonators Opt Lett 2012374236ndash8

[185] Walmsley IA Waxer L Dorrer C The role of dispersion in ultrafast optics Rev Sci Instrum 2001721ndash29

[186] Torres JP MHendrych Valencia A Angular dispersion an enabling tool in nonlinear and quantum optics Adv Opt Photon 20102319ndash69

[187] Yin LH Lin Q Agrawal GP Dispersion tailoring and soliton propagation in silicon waveguides Opt Lett 2006311295ndash7

[188] Dulkeith E Xia FN Schares L Green WMJ Vlasov YA Group index and group velocity dispersion in silicon-on-insulator photonic wires Opt Express 2006143853ndash63

[189] Turner AC Manolatou C Schmidt BS Lipson M Tailored anomalous group-velocity dispersion in silicon channel waveguides Opt Express 2006144357ndash62

[190] Dadap JI Panoiu NC Chen X I-Hsieh W Liu X Chou C-Y Dulkeith E McNab SJ Xia F Green WMJ Sekaric L Vlasov YA Osgood RM Jr Nonlinear-optical phase modification in dispersion-engineered Si photonic wires Opt Express 2008161280ndash99

[191] Milosevic MM Matavulj PS Yang PY Bagolini A Mashanovich GZ Rib waveguides for mid-infrared silicon photonics J Opt Soc Am B 2009261760ndash6

[192] Mashanovich GZ Milošević MM Nedeljkovic M Owens N Xiong B Teo EJ Hu Y Low loss silicon waveguides for the mid-infrared Opt Express 2011197112ndash9

[193] Reimer C Nedeljkovic M Stothard DJM Esnault MOS Reardon C OrsquoFaolain L Dunn M Mashanovich GZ Krauss TF Mid-infrared photonic crystal waveguides in silicon Opt Express 20122029361ndash8

[194] Baehr-Jones T Spott A Ilic R Spott A Penkov B Asher W Hochberg M Silicon-on-sapphire integrated waveguides for the midinfrared Opt Express 20101812127ndash35

[195] Li F Jackson S Grillet C Magi E Hudson D Madden SJ Moghe Y OrsquoBrien C Read A Duvall SG Atanackovic P Eggleton BJ Moss D Low propagation loss silicon-on-sapphire waveguides for the midinfrared Opt Express 20111915212ndash20

268emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

[196] Yue Y Zhang L Huang H Beausoleil RG Willner AE Silicon-on-nitride waveguide with ultralow dispersion over an octave-spanning mid-infared wavelength range IEEE Photonics J 20124126ndash32

[197] Khan S Chiles J Ma J Fathpour S Silicon-on-nitride waveguides for mid-and near-infrared integrated photonics Appl Phys Lett 2013102121104

[198] Cheng Z Chen X Wong CY Xu K Tsang HK Mid-infrared suspended membrane waveguide and ring resonator on silicon-on-insulator IEEE Photonics J 201241510ndash9

[199] Lin P-T Singh V Cai Y Kimerling LC Agarwal A Air-clad silicon pedestal structures for broadband mid-infrared microphotonics Opt Lett 2013381031ndash3

[200] Chang YC Paeder V Hvozdara L Hartmann JM Herzig HP Low-loss germanium strip waveguides on silicon for the mid-infrared Opt Lett 2012372883ndash5

[201] Zhang L Yue Y Y Xiao-Li R G Beausoleil Willner AE Highly dispersive slot waveguides Opt Express 2009177095ndash101

[202] Zhang L Yue Y Beausoleil RG Willner AE Analysis and engineering of chromatic dispersion in silicon waveguide bends and ring resonators Opt Express 2011198102ndash7

[203] Zhang L Mu J Singh V Agarwal A Kimerling LC Michel J Intra-cavity dispersion of microresonators and its engineering for octave-spanning Kerr frequency comb generation to be published

[204] Lin Q Zhang L Generalized nonlinear envelope equation with high-order dispersion of nonlinearity to be published

[205] Wang Y Yue R Han H Liao X Raman study of structural order of a-SiNxH and its change upon thermal annealing J Non-Crystalline Solids 2001291107ndash12

[206] Brida D Marangoni M Manzoni C De Silvestri S Cerullo G Two-optical-cycle pulses in the mid-infrared from an optical parametric amplifier Opt Lett 2008332901ndash3

[207] Brida D Manzoni C Cirmi G Marangoni M Bonora S Villoresi P De Silvestri S Cerullo G Few-optical-cycle pulses tunable from the visible to the mid-infrared by optical parametric amplifiers J Opt 201012013001

[208] Kippenberg TJ Holzwarth R Diddams SA Microresonator-based optical frequency combs Science 2011332555ndash9

[209] Levy JS Gondarenko A Foster MA Turner-Foster AC Gaeta AL Lipson M CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects Nat Photonics 2009437ndash40

[210] DelrsquoHaye P Herr T Gavartin E Gorodetsky ML Holzwarth R Kippenberg TJ Octave spanningtunable frequency comb from a microresonator Phys Rev Lett 2011107063901

[211] Okawachi Y Saha K Levy JS Wen YH Lipson M Gaeta AL Octave-spanning frequency combgeneration in a silicon nitride chip Opt Lett 2011363398ndash400

[212] Matsko AB Savchenkov AA Liang W Ilchenko VS Seidel D Maleki L Mode-locked Kerr frequency combs Opt Lett 2011362845ndash7

[213] Herr T Brasch V Jost JD Wang CY Kondratiev NM Gorodetsky ML Kippenberg TJ Temporal solitons in optical microresonators httparxivorgabs12110733

[214] Saha K Okawachi Y Shim B Levy JS Salem R Johnson AR Foster MA Lamont MR Lipson M Gaeta AL Modelocking and femtosecond pulse generation in chip-based frequency combs Opt Express 2013211335ndash43

[215] Coen S Erkintalo M Universal scaling laws of Kerr frequency combs Opt Lett 2013381790ndash2

[216] Lugiato LA Lefever R Spatial dissipative structures in passive optical-systems Phys Rev Lett 1987582209ndash11

[217] Haelterman M Trillo S Wabnitz S Dissipative modulation instability in a nonlinear dispersive ring cavity Opt Commun 199291401ndash7

[218] Coen S Randle HG Sylvestre T Erkintalo M Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato-Lefever model Opt Lett 20133837ndash9

[219] Chembo YK Menyuk CR Spatiotemporal Lugiato-Lefever formalism for Kerr-comb generation in whispering-gallery-mode resonators Phys Rev A 201387053852

[220] Foltynowicz A Mas1owski P Ban T Adler F Cossel KC Briles TC Ye J Optical frequency comb spectroscopy Faraday Discussion 201115023ndash31

[221] Hartl I Li XD Chudoba C Ghanta RK Ko TH Fujimoto JG Ranka JK Windeler RS Ultrahigh-resolution optical coherence tomography using continuum generation in an air silica microstructure optical fiber Opt Lett 200126608ndash10

[222] Brabec T Krausz F Intense few-cycle laser fields Frontiers of nonlinear optics Rev Mod Phys 200072545ndash91

[223] Hu J Meyer J Richardson K Shah L Feature issue introduction mid-IR photonic materials Opt Mater Express 201331571ndash5

[224] Private communications with Dr Jacob Levy in Prof Lipsonrsquos group and Dr Johann Riemensberger in Prof Kippenbergrsquos group

[225] Zhang J Lin Q Piredda G Boyd RW Agrawal GP Fauchet PM Anisotropic nonlinear response of silicon in the near-infrared region Appl Phys Lett 200791071113

Page 8: Lin Zhang*, Anuradha M. Agarwal, Lionel C. Kimerling and ...

254emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

and 1400 times 800 nm2 The upper cladding is air and the lower cladding is silicon dioxide The anomalous disper-sion region in the dispersion curves shrinks when the waveguide is made smaller This is because of a relatively small index contrast between silicon nitride and silicon dioxide which makes the guided mode leak quickly to the substrate as wavelength increases For the strip waveguide with a cross-section of 1400 times 800 nm2 there are two ZDWs near 10 and 23 microm but one can see a strong dispersion of 250 ps(nmmiddotkm) between the two ZDWs in Figure 6(A) The nonlinear coefficient in the second silicon nitride wave-guide is shown in Figure 6(B) which is much smaller than that in silicon waveguides because of a one-order smaller n2 value and larger Aeff in the silicon nitride waveguide At 16 microm γ is about 123(mW)

One can also use a stripslot hybrid structure to tailor the dispersion profile in silicon nitride waveguides For example the slot and lower cladding are silicon dioxide and the upper cladding is air In Figure 6(A) we show the dispersion curves in two silicon nitride stripslot hybrid waveguides for comparison The waveguide 1 has Hl = 900 nm Hs = 124 nm Hu = 340 nm and W = 1000 nm and the waveguide 2 has Hl = 920 nm Hs = 154 nm Hu = 480 nm and W = 1300 nm These two waveguides produce increasingly flatter dispersion profiles as shown in Figure 6(A) The first waveguide has two ZDWs located at 106 and 22 microm with the peak dispersion of 67 ps(nmmiddotkm) The second waveguide has two ZDWs at 115 and 235 microm with the dispersion varying within 0~20 ps(nmmiddotkm) This octave-spanning dispersion flattening with different levels

1000A

B

C

500

-500

400

300

200

100

0

-100014 16

Strip WG W=800 nmStrip WG W=900 nm

Strip WG W=900 nm

Strip WG W=1000 nm

Slot WG Hu=160 nm

Slot WG Hu=160 nm

Slot WG Hu=163 nmSlot WG Hu=166 nm

18 20 22Wavelength (microm)

Dis

pers

ion

(ps

nmmiddotk

m)

Non

linea

r co

effic

ient

(m

middotW)

24 26

14 16 18 20 22

Wavelength (microm)

24 26

0

Figure 5emspIn a wavelength range from the telecom window in near-IR to the short-wave end in the mid-IR silicon strip and stripslot hybrid waveguides (WGs) are analyzed in terms of (A) dispersion and (B) nonlinearity (C) Mode power distributions at wavelengths of 15 183 217 and 25 microm in the stripslot hybrid waveguide

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp255

of dispersions can be used for multiple applications as detailed in the next section The nonlinear coefficients for the two waveguides are shown in Figure 6(B) We note that the stripslot hybrid waveguides have similar nonlinear coefficients as the strip waveguide which shows that the dispersion profile is much more tailorable by waveguide designs

Then we move to the mid-IR using silicon and silicon nitride for waveguiding A comparison of different types of silicon-on-nitride waveguides have been presented in [196] where rib waveguides were preferred due to the wideband low dispersion over an octave-spanning band-width from 24 to 66 microm for the quasi-TE mode This is a spectral range from siliconrsquos half-bandgap wavelength to the cut-off wavelength of silicon nitride In Figure 7(A) we plot the dispersion curve for a silicon-on-nitride rib waveguide with air as the upper cladding the rib width of 2000 nm the total height of 1200 nm and the slab height of 1000 nm which are the same parameters used in [196] It is shown that less confinement of optical modes reduces the contribution of waveguide dispersion and makes the overall dispersion profile closer to the material dispersion which is flat and low at long wavelengths as in Figure 2(B)

A

B

400

300

200

100

-100

8

6

4

2

0

0

Strip WG 1300times540 nm2

Strip WG 1400times800 nm2

Strip WG 1400times800 nm2

Slot WG 1Slot WG 2

Slot WG 1Slot WG 2

Dis

pers

ion

(ps

nmmiddotk

m)

Non

linea

r co

effic

ient

(m

middotW)

20 3010 15 2505Wavelength (microm)

2010 15 2505

Wavelength (microm)

Figure 6emspIn a wavelength range moved toward the short-wave-length end of near-IR spectrum silicon nitride strip and stripslot hybrid waveguides are designed in terms of (A) dispersion and (B) nonlinearity

Accordingly the nonlinear coefficient is small 285 (mmiddotW) at 3 microm as shown in Figure 7(B)

On the other hand if one needs a small Aeff to enhance nonlinearity additional dispersion tailoring (eg based on stripslot hybrid waveguides) would be beneficial Pursuing a higher nonlinear coefficient we use a 500-nm silicon nitride suspended membrane as illustrated in Figure 4 to support a silicon stripslot hybrid waveguide This helps confine light in the waveguide core Using W = 880 nm Hu = 550 nm Hs = 87 nm and Hl = 840 nm we obtain a saddle-shaped anomalous dispersion from 19 to 449 microm within 0~60 ps(nmmiddotkm) for the quasi-TM mode as shown in Figure 7(A) This structure produces much tighter mode confinement than the rib waveguide and exhibits a 3 times larger nonlinear coefficient in Figure 7(B) while having similar dispersion flatness

Finally we consider germanium-on-silicon wave-guides over a wavelength range from 33 to 85 microm between the half-bandgap wavelength of germanium and the cut-off wavelength of silicon This type of waveguide has been demonstrated with strain-free mono-crystal-line germanium [200] Here we assume that the germa-nium waveguide has a 10-nm silicon nitride layer on its

A

B

200

-200

60

40

20

0

100

-100

0

Rib WGSlot WG

Rib WGSlot WG

Dis

pers

ion

(ps

nmmiddotk

m)

Non

linea

r co

effic

ient

(m

middotW)

1 2 3 4 5 6 7Wavelength (microm)

1 2 3 4 5 6 7

Wavelength (microm)

Figure 7emspIn a wavelength range from the short-wave IR to mid-IR silicon rib waveguide on silicon nitride and stripslot hybrid waveguide on a suspended membrane are analyzed in terms of (A) dispersion and (B) nonlinearity

256emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

surface for passivation The upper cladding could be air or silicon which provides significantly different dispersion properties due to a varied index contrast For comparison only we also have silicon nitride as the upper cladding although silicon nitride becomes lossy for wavelengths longer than 67 microm Figure 8(A) shows the dispersion pro-files of four germanium-on-silicon strip waveguides with equal size 3000 times 1600 nm2 for the quasi-TE mode Air and silicon nitride as an upper cladding result in similar shape and bandwidth in the dispersion profiles Thus the air-cladded waveguide is chosen and discussed further The waveguide with silicon upper cladding has normal dispersion at all wavelengths since there is a relatively small index contrast between germanium and silicon and thus weak mode confinement A germanium strip wave-guide on a 600-nm-thick silicon suspended membrane is also considered to increase light confinement with an air upper cladding to maximize light confinement However as mentioned earlier strong confinement typically causes strong dispersion as shown in Figure 8(A) and therefore the germanium waveguide on a silicon membraneis not chosen for broadband nonlinear applications In contrast the germanium strip waveguide with air upper cladding exhibits a flat and low dispersion

The dimensions of the air-cladded germanium wave-guide are varied by simultaneously changing its height and width with a step of 200 nm for both polarization states It is interesting to see from Figure 8(B) and 8(C) that the dispersion peak value remains nearly unchanged for all the waveguide sizes although we have a widely tunable ZDW at long wavelengths For the quasi-TE mode the right ZDW moves from 605 microm to 841 microm while the left ZDW is always near 4 microm We can thus obtain an octave-spanning anomalous dispersion band with the peak value below 100 ps(nmmiddotkm) For the quasi-TM mode one can see similar dispersion properties but the anomalous disper-sion band is smaller Thus we choose the quasi-TE mode for further discussion in next section

The nonlinear coefficient in the germanium wave-guides for the quasi-TE mode is shown in Figure 8(D) which is about 10(mmiddotW) at 5 microm with a small variation for differ-ent waveguide sizes This is quite high considering that both wavelength and effective mode area become much larger over this wavelength range compared to the near-IR

From above we can see that the stripslot hybrid wave-guides enable unique controllability of dispersion and that this concept is applicable to different wavelength ranges However their performance may be sensitive to fabrication errors especially for inaccuracies in slot height Hs [59 60] A higher yield in device fabrication is expected using advanced fabrication technologies and facilities

A

C

D

B

400

300

200

100

-100

-200

0

Ge WG+air 3000times1600 nm2

Ge WG+air suspended 3000times1600 nm2

Ge WG+Si3N4 3000times1600 nm2

Ge WG+Si 3000times1600 nm2

Ge WG+air 2800times1400 nm2

Ge WG+air 3000times1600 nm2

Ge WG+air 3200times1800 nm2

Ge WG+air 3400times2000 nm2

Ge WG+air 2800times1400 nm2

Ge WG+air 3000times1600 nm2

Ge WG+air 3200times1800 nm2

Ge WG+air 3400times2000 nm2

Ge WG+air 2800times1400 nm2

Ge WG+air 3000times1600 nm2

Ge WG+air 3200times1800 nm2

Ge WG+air 3400times2000 nm2

Dis

pers

ion

(ps

nmmiddotk

m)

400

300

200

100

-100

-200

0

Dis

pers

ion

(ps

nmmiddotk

m)

400

300

200

100

-100

-200

50

40

30

20

10

0

0

Dis

pers

ion

(ps

nmmiddotk

m)

Non

linea

r co

effic

ient

(m

middotW)

3 4 5 6 7 8 9Wavelength (microm)

3 4 5 6 7 8 9Wavelength (microm)

3 4 5 6 7 8 9

Wavelength (microm)

3 4 5 6 7 8 9

Wavelength (microm)

Figure 8emspIn a wavelength range covering the main part of the mid-IR spectrum (A) on silicon substrate or on suspended silicon membrane are analyzed in terms of dispersion Germanium-on-silicon strip waveguides with an air upper cladding and different dimensions are characterized by (B) dispersion for the quasi-TE mode (C) dispersion for the quasi-TM mode and (D) nonlinearity for the quasi-TE mode

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp257

Besides photonic waveguides another important cat-egory of nonlinear devices is integrated resonators In the scope of this paper we consider relatively large resona-tors for frequency comb generation in which the bending radius of a ring resonator is varied from 50 microm to 100 microm depending on free spectral range (FSR) and the group index in the waveguide In these cases the waveguide-bending-induced dispersion is small and we would not discuss intra-cavity dispersion [202 203] in details here

4 ApplicationsBenefiting from the unique dispersion engineering over an octave-spanning bandwidth as described above one can develop ultra-wideband nonlinear applications that could hardly be attained in an integrated platform previously These include octave-spanning supercontinuum genera-tion pulse compression to a few-cycle or even sub-cycle level octave-spanning Kerr frequency comb generation and the associated mode-locked ultrashort pulse genera-tion using microresonators In this section we review our recent work on these topics

First we discuss the supercontinuum generation and pulse compression in a straight waveguide The nonlinear envelope equation used here to simulate supercontinuum generation is the following

βα infin

=

part part+ + = + part part sum

2

( - )( ) ( )

2

m mm

mm

ii A K A R A

z m t (1)

where

2

0 0

- -( ) 1- ( ) 2

n nn

nn

i i iK A A An t tγ δ δ

ω δ δ

infin

=

= sum

and

2shock_R( ) - 1- [ ( - ) | | ]δ

γ τδ minusinfin

= prime prime int

t

R RR A i i A h t t A dtt

We denote A  =  A(zt) as the complex amplitude of an optical pulse Note that its Fourier transform is

-

1( ) ( ) exp( - ) 2

A z A z t i t dtω ωπ

infin

infin

= int

In Eq (1) α is the total propagation loss and βm is the mth-order dispersion coefficient The frequency dependence of nonlinearity parameters including the nonlinear index n2 the TPA coefficient βTPA and the

effective mode area Aeff is included in the nth-order dis-persion coefficient γn of nonlinearity which is defined as γn = ω0middotpartn[γ(ω)ω]partωn where ω0 is the angular frequency of the carrier Therefore we can consider all-order linear dispersion terms and all-order dispersion of the nonlin-ear coefficient in Eq (1) Specifically in the simulations for a silicon and silicon nitride waveguides we have all-order linear dispersion and up to 6th-order and 2nd-order of the nonlinear coefficient dispersion included A detailed derivation of Eq (1) is given in [204] For the quasi-TM mode that experiences the engineered dispersion due to the mode transition SRS in silicon waveguides fabricated on the (001) surface can be ignored [27 96] For silicon nitride waveguide we include the SRS term in Eq (1) where γR = gRΓR(AeffΩR) and gR ΓR and ΩR represent the Raman gain coefficient the full width at half maximum of the gain spectrum and the Raman shift respectively The Raman shock time τshock_R is associated with γRrsquos fre-quency dependence which is 1ω0-[1Aeff(ω0)][dAeff(ω)dω] similarly as in [14] if we ignore frequency dependent gR ΓR and ΩR hR(t) is the Raman response function and it corresponds to the Raman gain spectrum

2

2 20 0

( ) -( - ) 2 ( - )

Ωω

Ω ω ω Γ ω ω=

+R

RR R

Hi

Note that the sign before the imaginary unit is differ-ent from that in [27] to be consistent with the expression of the Fourier transform that we used

We have considered supercontinuum generation in both silicon and silicon nitride waveguides with the slot-assisted dispersion tailoring Octave-spanning supercon-tinua in a silicon-based stripslot hybrid waveguide have been investigated in detail in [108] in which two-cycle optical pulses are obtained The main results in that work are shown in Figure 9 for comparison purposes

Here we mainly focus on the supercontinuum gen-erated in the silicon nitride stripslot hybrid waveguide (ie the slot WG 1 in Section III) whose dispersion and nonlinearity properties are shown in Figure 6 In the non-linear simulations we set the total propagation loss to be 1 dBcm The SRS parameters used here are the following [205] ΩR2π = 143 THz ΓR2π = 172 THz and gR = 1 times 10-12 mW τshock_R is calculated to be  = 156 fs

In our simulations we use a time step of 025 fs which is corresponding to a bandwidth of 4000 THz in the fre-quency domain For a femtosecond input pulse we set the time window length to 50 ps (ie frequency resolution Δf = 20 GHz)

We simulate the nonlinear propagation of a chirp-free hyperbolic secant pulse in the silicon nitride waveguide

258emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

The pulse center wavelength is at 1610 nm and its full width at half-maximum (FWHM) T0 is 120 fs Its peak power is 1200 W corresponding to pulse energy of 016 nJ

Figure 10(A) shows the supercontinua at different propagation distances At 48 mm the spectrum is greatly broadened at the -30 dB level covering a wavelength range from 0585 to 2833 microm which is more than two octaves The spectrum evolution in Figure 10(A) shows a similar spectrum shape as that in Figure 9(A) both featuring a ldquotriangularrdquo central spectrum bounded by two dispersive waves at the edges However it is important to note that the absence of TPA and 3PA in silicon nitride at the telecom window leads to a much more efficient spectrum broad-ening than that in silicon [108] The generated spectrum extends from the visible light to the mid-IR with excellent spectral coherence which is confirmed by the pulse wave-form shown in Figure 10(B) In the time domain the pulse is greatly compressed from 120 to 408 fs corresponding to 076 optical cycles at 161 microm wavelength

We examine the pulsewidth as a function of propa-gation distance Figure 11 shows that the pulse becomes increasingly narrower until the propagation distance reaches 47 mm For longer distances the pulsewidth

A

B

60 mm

48 mm

36 mm

24 mm

12 mm

Input

Spe

ctru

m (

10 d

Bd

iv)

Pow

er (

W)

12

246

24

18

12

6

0

248 250 252 254

14 16 18 20 22 24Wavelength (microm)

Time (ps)

Figure 9emsp(A) The supercontinuum generation in a silicon-based stripslot hybrid waveguide presented in [108] (B) The significant spectrum broadening at 425-mm distance is associated with a temporal compression of an input pulse (dash line) to the output waveform (solid line) with a FWHM of 12 fs

A

B

50 mm

48 mm

46 mm

44 mm

42 mm

Input

Spe

ctru

m (

10 d

Bd

iv)

Pow

er (

W)

8000

6000

4000

2000

0250249 251

06 09 12 15 18 21 24 27

Wavelength (microm)

Time (ps)

Figure 10emsp(A) Spectrum evolution of the pulse over propagation distance A supercontinuum of more than two octaves is achieved at 48 mm distance (B) Generated pulse waveform with a pulse width of 408 fs as short as 076 optical cycles Low pedestals are caused by dispersive waves generated at the two ends of the spectrum

remains almost constant However it is important to mention that after 48 mm the dispersive waves become increasingly stronger as shown in Figure 10(A) causing larger pedestals

Comparing the results in Figures 9 and 10 we note that the mid-IR wavelength range for silicon would be in analogy to the near-IR for silicon nitride in terms of non-linear optics operations Pumping at or beyond 33 microm one can use the waveguide designs shown in Figure 7 to produce very efficient nonlinear interactions without TPA and 3PA in silicon Ultrashort pulses in the mid-IR from parametric amplifiers [206 207] could be used to pump the Group IV waveguides

Another nonlinear application of the dispersion-engi-neered Group IV waveguides is micro-resonator-based Kerr frequency comb generation When such a waveguide is curved to form a microring resonator input CW light travels around the cavity and amplifies the noise in the source located at the frequencies with a high parametric gain As a result of modulation instability and cascaded FWM in the cavity a frequency comb can be generated [208ndash211] Mode-locked frequency combs have been reported pro-ducing low-noise pulse trains in time domain [212ndash214]

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp259

The formation of cavity solitons is identified as the main reason for the mode-locking in the Kerr frequency combs [215] This is instructive because one can thus predict the spectral bandwidth and temporal pulsewidth in the generated low-noise combs The 3-dB comb bandwidth is inversely proportional to the square root of the 2nd-order dispersion coefficient |β2| as given in [213 215] It is desira-ble that all comb lines that constitute the soliton spectrum experience the same |β2| In this sense the stripslot hybrid waveguides with flattened dispersion are preferably suit-able for supporting broadband Kerr comb generation and ultra-short cavity soliton generation

The Kerr frequency comb generation can be modeled using the generalized Lugiato-Lefever equation (LLE) [216ndash219]

20

2

( - )- - | |

2 2

m mm

R inmm

jkt j jl E kE j l E Et m

βαδ γ

τ

infin

=

part part+ + + = part part

sum (2)

where tR is the round-trip time E = E(tτ) and Ein are intra-cavity field and input field (pump power Pin  =  |Ein|2) t and τ are the slow and fast times δ0 is the cavity phase detuning defined as δ0  =  tRmiddot(ωn -ω0) where ω0 and ωn are the pumprsquos angular frequency and the nth angular reso-nance frequency that is pumped Other resonator param-eters include the power loss per round trip α the power coupling coefficient κ the nonlinear coefficient γ and the mth dispersion coefficient βm Since a flattened dispersion profile has a small β2 over a wide bandwidth it is impor-tant to take the influence of higher-order dispersion into account We include all-order dispersion terms in Eq (2) as we did in solving Eq (1)

To enhance the Kerr comb bandwidth in the near-IR we use the ultra-flattened dispersion profile in Figure 6(A) which is obtained in the slot WG 2 based on

Pul

se w

idth

(fs

)

14

12

10

8

6

4

242 44 46 48 50 52

Propagation distance (mm)

Figure 11emspPulse width first decreases with propagation distance and then remains stable After 48 mm dispersive waves get stronger causing more pedestals

Pow

er (

10 d

Bd

iv)

Pow

er (

W)

70A

B

60

50

40

30

20

10

-10

-20

600

400

200

0

80 120

0575 0600 0625 0650

160 200 240 280 320 360

0

Frequency (THz)

Time (ps)

Figure 12emsp(A) Frequency comb generation with a CW pump at 155 microm using a microring resonator based on a silicon stripslot hybrid waveguide Over an octave-spanning bandwidth from 135 to 270 THz the comb lines have a power drop of 20 dB (B) Generated pulse waveform with a pulse width of 82 fs as short as 16 optical cycles

silicon nitride The ring resonator has a bending radius of 104 microm corresponding to a FSR of 200 GHz Pumping near 155 microm with a pump power of 2 W the resonance peak is red-shifted and we need to red-shift the pump wavelength accordingly and tune it into the resonance from the short-wavelength side When the pump is step-by-step tuned by up to 63 resonance linewidths we obtain the comb spectrum and the mode-locked pulse waveform as shown in Figure 12 One can see that over an octave-spanning bandwidth from 133 to 268 THz the comb lines have a power drop by 20 dB from the center of the spectrum The spectral flatness of this comb is relatively good compared to the previously reported results [208ndash211] The comb bandwidth at -40 dB is as wide as two octaves There are two dispersive peaks in normal dispersion regions beyond the low-dispersion band Such a mode-locked broadband comb produces a train of sub-two-cycle optical pulses as shown in Figure 12(B) with one pulse per round trip The peak power of the pulse is up to 600 W Nonlinear conver-sion efficiency is estimated to be -267 dB

To generate frequency combs in the mid-IR the ger-manium-on-silicon strip waveguide is chosen We choose

260emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

a cross-section of 3200 times 1800 nm2 which has an octave-spanning low-dispersion band from 4 to 767 microm as shown in Figure 8(B) A germanium ring resonator is formed with a bending radius of 564 microm corresponding to a FSR of 200 GHz Pumping at 6 microm with a CW power of 14 W and detuning the pump wavelength by 10 resonance linewidth one can see that a mode-locked wideband mid-IR comb is generated from 358 to 644 THz (ie from 466 to 838 microm) at -40 dB level The FWHM of the produced pulses is 69 fs which corresponds to ~35 optical cycles The pulse peak power is 184 W and the nonlinear conversion efficiency is estimated to be -143 dB Since the pumping frequency is not at the center of the low-dispersion band we only see one peak in the comb spectrum caused by the dispersive wave in the normal dispersion region from Figure 13(A) There is another peak at higher frequencies beyond what is shown in the figure

As shown above broadband dispersion engineering is critical for octave-spanning nonlinear applications in both near- and mid-IR wavelength ranges which enables us to fully utilize the bandwidth allowed by the materials transparency windows Generally speaking the nonlinear applications mentioned here such as supercontinuum generation ultrafast pulse compression and frequency comb generation are often the intermediate steps towards higher-level system applications In the frequency domain a wide spectrum can serve as an electromagnetic carrier to acquire high-volume of information eg for sensing [220] and imaging [221] In the time domain an ultrashort pulse can be used as probe to sample ultrafast phenomena [222]

5 Summary and OutlookWe have presented a review of our recent work on nonlin-ear photonics based on silicon and germanium Various types of Group IV waveguides are analyzed and optimized for four different wavelength ranges from near- to mid-IR The recently proposed dispersion engineering technique based on stripslot hybrid waveguide structures is used for different material combinations and wavelength ranges Numerical simulations show that the dispersion-flattened Group IV waveguides are preferably suitable for octave-spanning nonlinear applications including on-chip supercontinuum generation ultrashort pulse compres-sion and mode-locked wideband frequency comb genera-tion based on micro-resonators

The presented approach to achieving octave-span-ning nonlinear applications on an integrated CMOS-compatible Group IV platform holds great potential for realizing chip-scale sensing imaging communications and signal processing system The ultrawide transparency windows in the mid-IR allowed by Group IV elements and compounds potentially together with other materi-als [223] provide an exciting arena for building powerful information acquisition and processing units enabled by nonlinear optics nano-photonics and ultrafast optics

Received June 14 2013 accepted October 29 2013 previously pub-lished online November 27 2013

Pow

er (

10 d

Bd

iv)

A

8030 40 50 60 70Frequency (THz)

Pow

er (

W)

B200

150

100

50

0

21 22 23 24 25Time (ps)

Figure 13emsp(A) Frequency comb generation with a CW pump at 6 microm using a microring resonator based on a germanium strip waveguide with air upper cladding (B) Generated pulse waveform with a pulse width of 69 fs as short as 35 optical cycles

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp261

Appendix

A Material index and dispersion

In this section we give the wavelength-dependent mate-rial index expressed as Sellmeier equations where wave-length λ is in μm

For silicon we use the following material index that is a fit curve from measurement results at room temperature (293 K) with 184 data points in total from 112 to 588 μm [154]

22 1 2 2

2 2 22

( )-

C Cn

λλ ε

λ λ λ= + +

where ε = 116858 C1 = 0939816 μm2 C2 = 000810461 and λ2 = 11071 μm

For silicon nitride the material index is affected by deposition conditions using plasma-enhanced chemical vapor deposition (PECVD) low-pressure chemical vapor deposition (LPCVD) and so on We use the following Sell-meier equation [155] which predicts the material index close to that in LPCVD silicon nitride films measured by a few groups [224]

22 1

2 21

( ) 1-

Cn

λλ

λ λ= +

where C1 = 28939 and λ1 = 013967 μmFor silicon dioxide we use the following Sellmeier

equation for fused silica [156]22 2

2 31 22 2 2 2 2 2

1 2 3

( ) 1- - -

CC Cn

λλ λλ

λ λ λ λ λ λ= + + +

where C1 = 06961663 C2 = 04079426 C3 = 08974794 λ1 = 00684043 μm λ2 = 01162414 μm and λ3 = 9896161 μm

For SRO the material index is affected by deposition conditions such as silicon excess annealing temperature and so on Here we choose the one with silicon excess of 8 and annealed at 1250oC [51]

22 22 31 2

2 2 2 2 2 21 2 3

( ) 1- - -

CC Cn

λλ λλ

λ λ λ λ λ λ= + + +

where C1 = 001 C2 = 196 C3 = 141 λ1 = 03 μm λ2 = 007071 μm and λ3 = 2775968 μm

For germanium the temperature-dependent mate-rial index was measured [157] Here we choose the one for room temperature (293 K)

2 22 1 2

2 2 2 21 2

( )- -

C Cn

λ λλ ε

λ λ λ λ= + +

where ε = 928156 C1 = 67288 C2 = 021307 λ1 = 0664116 μm and λ2 = 6221013 μm

For arsenic sulfide we use the material index pro-vided in [158]

2 2 22 22 3 4 51 2

2 2 2 2 2 2 2 2 2 21 2 3 4 5

( ) 1- - - - -

C C CC Cn

λ λ λλ λλ

λ λ λ λ λ λ λ λ λ λ= + + + + +

where C1 = 18983678 C2 = 19222979 C3 = 08765134 C4 = 01188704 C5 = 09569903 λ1 = 015 μm λ2 = 025 μm λ3 = 035 μm λ4 = 045 μm and λ5 = 27386128 μm

For arsenic selenide we fit ellipsometry measure-ments of our arsenic selenide thin films and the bulk material is provided by Prof Kathleen A Richardson group

22 22 31 2

2 2 2 2 2 21 2 3

( ) 1- - -

CC Cn

λλ λλ

λ λ λ λ λ λ= + + +

where C1 = 298463 C2 = 321011 C3 = 100182 λ1 = 044118 μm λ2 = 0000354953 μm and λ3 = 38413 μm

B Nonlinear Kerr index n2

The third-order nonlinear susceptibility χ(3)1111 for silicon and

germanium is predicted over the mid-IR range [133] based on a two-band model The effective nonlinear susceptibil-ity χ(3) is dependent on polarization and crystallographic orientation [225] For strong nonlinearity we consider a single-polarization incident light aligned to the crystal-lographic axis and we have χ(3) = χ(3)

1111 To investigate the octave-spanning nonlinear phenomena one need to take the wavelength-dependent nonlinear Kerr index n2 and TPA coefficient βTPA into account which are expressed as

( 3 )2 2

0

( 3 )2

0

3( ) ( )4 ( )

3( ) ( )( )

re

TPA im

ncn

cn

λ χ λε λ

πβ λ χ λ

λε λ

=

=

where ε0 and c are the vacuum permittivity and the speed of light in vacuum Using the material index given in Appendix A and χ(3) value from [133] we obtain the n2 and βTPA values tabulated as follows

262emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

Table 1enspNonlinear Kerr index n2 in silicon

λμm

  n2

10-18 m2W  λ

μm  n2

10-18 m2W  λ

μm  n2

10-18 m2W

130   234   310   389   490   312135   305   315   384   495   311140   378   320   379   500   310145   443   325   375   505   309150   501   330   371   510   307155   559   335   368   515   306160   618   340   365   520   304165   671   345   362   525   304170   710   350   360   530   303175   741   355   358   535   302180   766   360   355   540   302185   781   365   352   545   301190   783   370   350   550   300195   778   375   346   555   298200   762   380   343   560   297205   732   385   341   565   296210   699   390   338   570   296215   658   395   336   575   295220   612   400   334   580   295225   576   405   332   585   295230   547   410   331   590   294235   525   415   330   595   293240   508   420   329   600   292245   493   425   328   605   291250   479   430   327   610   290255   467   435   325   615   289260   456   440   324   620   288265   448   445   321   625   288270   440   450   319   630   288275   432   455   317   635   288280   424   460   315   640   288285   417   465   314   645   288290   410   470   313   650   288295   404   475   313   655   288300   398   480   312   660   288305   394   485   312    

Table 2enspTPA coefficient βTPA in silicon

λμm

  βTPA

10-12 mW  λ

μm  βTPA

10-12 mW  λ

μm  βTPA

10-12 mW

130   1334   165   812   200   180135   1284   170   713   205   115140   1222   175   613   210   064145   1154   180   522   215   024150   1079   185   424   220   0003155   995   190   333    160   905   195   254    

Table 3enspNonlinear Kerr index n2 in germanium

λμm

  n2

10-18 m2W  λ

μm  n2

10-18 m2W  λ

μm  n2

10-18 m2W

23  3932  63  1986  103  170524  4994  64  1972  104  169925  6007  65  1959  105  169426  6650  66  1946  106  169027  6772  67  1934  107  168728  6273  68  1923  108  168429  4897  69  1913  109  168230  4403  70  1904  110  168131  3970  71  1895  111  167932  3680  72  1886  112  167733  3470  73  1876  113  167534  3286  74  1868  114  167335  3128  75  1859  115  167036  2998  76  1850  116  166737  2895  77  1841  117  166338  2812  78  1833  118  165939  2737  79  1826  119  165640  2668  80  1819  120  165341  2605  81  1812  121  165142  2550  82  1807  122  164843  2498  83  1801  123  164644  2450  84  1797  124  164445  2406  85  1792  125  164346  2365  86  1787  126  164147  2328  87  1782  127  163948  2295  88  1777  128  163649  2266  89  1772  129  163450  2238  90  1767  130  163251  2212  91  1762  131  163052  2187  92  1758  132  162853  2164  93  1753  133  162654  2141  94  1749  134  162555  2121  95  1744  135  162356  2101  96  1740  136  162157  2083  97  1736  137  162058  2066  98  1731  138  161859  2049  99  1727  139  161760  2032  100  1722  140  161661  2016  101  1716   62  2001  102  1711   

Table 4enspTPA coefficient βTPA in germanium

λμm

  βTPA

10-8 mW  λμm

  βTPA

10-8 mW  λ

μm  βTPA

10-8 mW

23   130   25   088   27   03124   111   26   060   28   006

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp263

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[23] Jalali B Paniccia M Reed G Silicon photonics IEEE Microwave Magazine 2006758ndash68

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[25] Kirchain R Kimerling L A roadmap for nanophotonics Nature Photonics 20071303ndash5

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L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp265

[85] Boyraz O Indukuri T Jalali B Self-phase-modulation induced spectral broadening in silicon waveguides Opt Express 200412829ndash34

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[87] Dulkeith E Vlasov YA Chen X Panoiu NC Osgood RM Jr Self-phase-modulation in submicron silicon-on-insulator photonic wires Opt Express 2006145524ndash34

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[89] Hsieh I-W Chen X Dadap JI Panoiu NC Osgood RM Jr McNab SJ Vlasov YA Cross phase modulation-induced spectral and temporal effects on co-propagating femtosecond pulses in silicon photonic wires Opt Express 2007151135ndash46

[90] Zhang J Lin Q Piredda G Boyd RW Agrawal GP Fauchet PM Optical solitons in a silicon waveguide Opt Express 2007157682ndash8

[91] Salem R Foster MA Turner AC Geraghty DF Lipson M Gaeta AL All-optical regeneration on a silicon chip Opt Express 2007157802ndash9

[92] Claps R Raghunathan V Dimitropoulos D Jalali B Anti-Sotkes Raman conversion in silicon waveguides Opt Express 2003112862ndash72

[93] Espinola RL Dadap JI Osgood RM Jr McNab SJ Vlasov YA C-band wavelength conversion in silicon photonic wire waveguides Opt Express 2005134341ndash9

[94] Fukuda H Yamada K Shoji T Takahashi M Tsuchizawa T Watanabe T Takahashi J Itabashi S Four-wave mixing in silicon wire waveguides Opt Express 2005134629ndash37

[95] Rong H Kuo Y Liu A Paniccia M Cohen O High efficiency wavelength conversion of 10 Gbs data in silicon waveguides Opt Express 2006141182ndash8

[96] Lin Q Zhang J Fauchet PM Agrawal GP Ultrabroadband parametric generation and wavelength conversion in silicon waveguides Opt Express 2006144786ndash99

[97] Foster MA Turner AC Sharping JE Schmidt BS Lipson M Gaeta AL Broad-band optical parametric gain on a silicon photonic chip Nature 2006441960ndash3

[98] Yamada K Fukuda H Tsuchizawa T Watanabe T Shoji T Itabashi S All-optical efficient wavelength conversion using silicon photonic wire waveguide IEEE Photon Technol Lett 2006181046ndash8

[99] Kuo Y Rong H Sih V Xu S Paniccia M Cohen O Demonstration of wavelength conversion at 40 Gbs data rate in silicon waveguides Opt Express 20061411721ndash6

[100] Foster MA Turner AC Salem R Lipson M Gaeta AL Broad-band continuous-wave parametric wavelength conversion in silicon nanowaveguides Opt Express 20071512949ndash58

[101] Dai Y Chen X Okawachi Y Turner-Foster AC Foster MA Lipson M Gaeta AL Xu C 1 μs tunable delay using parametric mixing and optical phase conjugation in Si waveguides Opt Express 2009177004ndash10

[102] De Leonardis F Passaro VMN Efficient wavelength conversion in optimized SOI waveguides via pulsed four wave mixing IEEE J Lightwave Technol 2011293523ndash35

[103] Yin L Lin Q Agrawal GP Soliton fission and supercontinuum generation in silicon waveguides Opt Lett 200732391ndash3

[104] Koonath P Solli DR Jalali B Continuum generation and carving on a silicon chip Appl Phys Lett 200791061111

[105] Hsieh I-W Chen X Liu X Dadap JI Panoiu NC C-Chou Y Xia F Green WM Vlasov YA Osgood RM Jr Supercontinuum generation in silicon photonic wires Opt Express 20071515242ndash8

[106] Kuyken B Liu X Osgood RM Jr Baets R Roelkens G Green WMJ Mid-infrared to telecom-band supercontinuum generation in highly nonlinear silicon-on-insulator wire waveguides Opt Express 20111920172ndash81

[107] DeVore PTS Solli DR Ropers C Koonath P Jalali B Stimulated supercontinuum generation extends broadening limits in silicon Appl Phys Lett 2012100101111

[108] Zhang L Lin Q Yue Y Yan Y Beausoleil RG Agarwal A Kimerling LC Michel J Wilner AE On-chip octave-spanning supercontinuum in nanostructured silicon waveguides using ultralow pulse energy IEEE J Sel Top Quant 2012181799ndash806

[109] Claps R Raghunathan V Dimitropoulos D Jalali B Influence of nonlinear absorption on Raman amplification in silicon waveguides Opt Express 2004122774ndash80

[110] Yin L Agrawal GP Impact of two-photon absorption on self-phase modulation in silicon waveguides Opt Lett 2007322031ndash3

[111] Ikeda K Saperstein RE Alic N Fainman Y Thermal and Kerr nonlinear properties of plasma-deposited silicon nitridesilicon dioxide waveguides Opt Express 20081612987ndash94

[112] Levy JS Gondarenko A Foster MA Turner-Foster AC Gaeta AL Lipson M CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects Nat Photonics 2010437ndash40

[113] Tan DTH Ikeda K Sun PC Fainman Y Group velocity dispersion and self phase modulation in silicon nitride waveguides Appl Phys Lett 201096061101

[114] Zhang L Yan Y Yue Y Lin Q Painter O Beausoleil RG Willner AE On-chip two-octave supercontinuum generation by enhancing self-steepening of optical pulses Opt Exp 20111911584ndash90

[115] Halir R Okawachi Y Levy JS Foster MA Lipson M Gaeta AL Ultrabroadband supercontinuum generation in a CMOS-compatible platform Opt Lett 2012371685

[116] Ye J Frequency comb spectroscopy from mid-infrared to extreme ultraviolet Conference on Lasers and Electro-Optics (CLEO) 2012 Tutorial CW1J4

[117] Popmintchev T Chen M-C Popmintchev D Arpin P Brown S Alisauskas S Andriukaitis G Balciunas T Mucke OD Pugzlys A Baltuska A Shim B Schrauth SE Gaeta A Hernandez-Garcia C Plaja L Becker A Jaron-Becker A Murnane MM Kapteyn HC Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers Science 20123361287ndash91

[118] Qin GS Yan X Kito C Liao M Chaudhari C Suzuki T Ohishi Y Ultrabroadband supercontinuum generation from ultraviolet to 628 microm in a fluoride fiber Appl Phys Lett 200995 161103ndash1ndash161103-3

[119] Soref RA Emelett SJ Buchwald WR Silicon waveguided components for the long-wave infrared region J Opt A 20068840ndash8

266emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

[120] Soref R Towards Silicon-based Longwave Integrated Optoelectronics (LIO) SPIE Proceedings 6898 (2008) paper 6898-5 SPIE Photonics West Silicon Photonics III Conference San Jose CA (21 Jan 2008)

[121] Mashanovich GZ Milosevic M Matavulj P Timotijevic B Stankovic S Yang PY Teo EJ Breese MBH Bettiol AA Reed GT Silicon photonic waveguides for different wavelength regions Semiconductor Sci Technol 200823064002

[122] Soref R Mid-infrared photonics in silicon and germanium Nat Photonics 20104495ndash7

[123] Green WMJ Liu X Osgood RM Vlasov YA Mid-infrared nonlinear optics in silicon photonic wire waveguides Photonics Society Summer Topical Meeting Series 201062ndash63

[124] Milosevic MM Nedeljkovic M Masaud T-B Jaberansary E Chong HMH Emerson NG Reed GT Mashanovich GZ Silicon waveguides and devices for the mid-infrared Appl Phys Lett 2012101121105

[125] Soref R Group IV photonics for the mid infrared SPIE Photonics West 2013 Proc of SPIE 20138629paper 862902

[126] Crowder JG Smith SD Vass A Keddie J Infrared methods for gas detection in Mid-Infrared Semiconductor Optoelec-tronics New York Springer-Verlag 2006

[127] George Socrates Infrared and Raman Characteristic Group Frequencies Tables and Charts 3rd Ed Chichester John Wiley amp Sons 2001

[128] Longshore R Raimondi P Lumpkin M Selection of detector peak wavelength for optimum infrared system performance Infrared Phys 197616639ndash47

[129] Findlay GA Cutten DR Comparison of performance of 3ndash5-and 8ndash12-microm infrared systems Appl Opt 1989285029ndash37

[130] Labadie L Wallner O Mid-infrared guided optics a perspective for astronomical instruments Opt Express 2009171947ndash62

[131] Pearl S Rotenberg N van Driel HM Three photon absorption in silicon for 2300ndash3300 nm Appl Phys Lett 200893131102

[132] Wang Z Liu H Huang N Sun Q Wen J Li X Influence of three-photon absorption on Mid-infrared cross-phase modulation in silicon-on-sapphire waveguides Opt Express 2013211840ndash8

[133] Hon NK Soref RA Jalali B The third-order nonlinear optical coefficients of Si Ge and Si1-xGex in the midwave and longwave infrared J Appl Phys 2011110011301

[134] Sheik-Bahae M Hutchings DC Hagan DJ Stryland EWV Dispersion of bound electric nonlinear refraction in solids IEEE J Quant Electron 1991271296ndash1309

[135] Jalali B Raghunathan V Shori R Fathpour S Prospects for silicon mid-IR Raman lasers IEEE J Sel Top Quantum Electron 2006121618ndash27

[136] Raghunathan V Borlaug D Rice RR Jalali B Demonstration of a mid-infrared silicon Raman amplifier Opt Express 20071514355ndash62

[137] Chavez Boggio JM Windmiller JR Knutzen M Jiang R Bres C Alic N Stossel B Rottwitt K Radic S 730-nm optical parametric conversion from near- to short-wave infrared band Opt Express 2008165435ndash43

[138] Lin Q Johnson TJ Perahia R Michael CP Painter OJ A proposal for highly tunable optical parametric oscillation in silicon micro-resonators Opt Express 20081610596ndash610

[139] Turner-Foster AC Foster MA Salem R Gaeta AL Lipson M Frequency conversion over two-thirds of an octave in silicon nanowaveguides Opt Express 2010181904ndash8

[140] Liu X Osgood RM Vlasov YA Green WMJ Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides Nat Photonics 20104557ndash60

[141] Zlatanovic S Park JS Moro S Boggio JMC Divliansky IB Alic N Mookherjea S Radic S Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source Nat Photonics 20104561ndash4

[142] Tien EK Huang YW Gao S Song Q Qian F Kalyoncu SK Boyraz O Discrete parametric band conversion in silicon for mid-infrared applications Opt Exp 20101821981ndash9

[143] Lau RKW Meacutenard M Okawachi Y Foster MA A C Turner-Foster Salem R Lipson M Gaeta AL Continuous-wave mid-infrared frequency conversion in silicon nanowaveguides Opt Lett 2011361263ndash5

[144] Roelkens G Green WMJ Kuyken B Liu X Hattasan N Gassenq A Cerutti L Rodriguez JB Osgood RM Tournie E Baets R III-Vsilicon photonics for short-wave infrared spectroscopy IEEE J Quant Electron 201248292ndash8

[145] Alloatti L Korn D Weimann C Koos C Freude W Leuthold J Second-order nonlinear silicon-organic hybrid waveguides Opt Express 20122020506ndash15

[146] Harris DC Durable 3ndash5 μm transmitting infrared window materials Infrared Phys Technol 199839185ndash201

[147] Carlie N Musgraves JD Zdyrko B Luzinov I Hu J Singh V Agarwal A Kimerling LC Canciamilla A Morichetti F Melloni A Richardson K Integrated chalcogenide waveguide resonators for mid-IR sensing leveraging material properties to meet fabrication challenges Opt Express 20101826728ndash43

[148] Eggleton BJ B Luther-Davies Richardson K Chalcogenide photonics Nat Photonics 20115141ndash8

[149] Madden SJ Vu KT High-Performance Integrated Optics with Tellurite Glasses Status and Prospects Int J Appl Glass Sci 20123289ndash98

[150] Bindra KS Bookey HT Kar AK Wherrett BS Liu X Jha A Nonlinear optical properties of chalcogenide glasses observation of multiphoton absorption App Phys Lett 2001791939ndash41

[151] Zakery A Ruan Y ARode V Samoc M Luther-Davies B Low-loss waveguides in ultrafast laser-deposited As2S3 chalcogenide films J Opt Soc Am B 200391844ndash52

[152] Lenz G Zimmermann J Katsufuji T MLines E Hwang HY Spalter S Slusher RE Cheong SW Sanghera JS Aggarwal ID Large Kerr effect in bulk Se-based chalcogenide glasses Opt Lett 200025254ndash6

[153] Sanghera JS Shaw LB Aggarwal ID Application of chalcogenide glass optical fibers CR Chimie 20025873ndash83

[154] Palik ED Handbook of optical constants of solids San Diego CA Academic 1998

[155] Philipp HR Optical properties of silicon nitride J Electrochem Soc 1973120295ndash300

[156] Malitson IH Interspecimen comparison of the refractive index of fused silica J Opt Soc Am 1965551205ndash8

[157] Barnes NP Piltch MS Temperature-dependent Sellmeier coefficients and nonlinear optics average power limit for germanium J Opt Soc Am 197969178ndash80

[158] Rodney WS Malitson IH King TA Refractive index of arsenic trisulfide J Opt Soc Am 195848633ndash636

[159] Ellipsometry measurement on the thin film samples by our group[160] Bristow AD Rotenberg N van Driel HM Two-photon

absorption and Kerr coefficients of silicon for 850ndash2200 nm Appl Phys Lett 200790191104

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp267

[161] Lin Q Zhang J Piredda G Boyd RW Fauchet PM Agrawal GP Dispersion of silicon nonlinearities in the near infrared region Appl Phys Lett 200791021111

[162] Mizrahi V DeLong KW Stegeman GI Saifi MA Andrejco MJ Two-photon absorption as a limitation to all-optical switching Opt Lett 1989141140ndash2

[163] Guider R NDaldosso APitanti EJordana Fedeli J-M Pavesi L NanoSi low loss horizontal slot waveguides coupled to high Q ring resonators Opt Express 20091720762ndash70 and its erratum

[164] Ferrera M Razzari L Duchesne D Morandotti R Yang Z Liscidini M Sipe JE Chu S Little BE Moss DJ Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures Nat Photonics 20082 737ndash40

[165] Smektala F Quemard C Leneindre L Lucas J Barthelemy A De Angelis C Chalcogenide glasses with large non-linear refractive indices J Non-Crystalline Solids 1998239139ndash42

[166] Boudebs G Sanchez F Troles J Smektala F Nonlinear optical properties of chalcogenide glasses- comparison between Mach-Zehnder interferometry and Z-scan techniques Opt Comm 2001199425ndash33

[167] Asobe M Suzuki K Kanamori T Kubodera K Nonlinear refractive index measurement in chalcogenide-glass fibers by self-phase modulation APL 1992601153ndash4

[168] Asobe M Kanamori T Kubodera K Ultrafast all-optical switching using highly nonlinear chalcogenide glass fiber IEEE Photon Technol Lett 19924362ndash5

[169] Asobe M Kanamori T Kubodera K Applications of highly nonlinear chalcogenide glass fibers in ultrafast all-optical switches IEEE J Quant Electron 1993292325ndash33

[170] Ruan Y Luther-Davies B Li W Rode A Kolev V Madden S Large phase shifts in As2S3 waveguides for all-optical processing devices Opt Lett 2005302605ndash7

[171] Laniel JM Hocirc N Valleacutee R Villeneuve A Nonlinear-refractive-index measurement in As2S3 channel waveguides by asymmetric self-phase modulation J Opt Soc Am B 200522437ndash45

[172] Cerqua-Richardson KA McKinley JM Lawrence B Joshi S Villeneuve A Comparison of nonlinear optical properties of sulfide glasses in bulk and thin film form Opt Mater 199810155ndash9

[173] Harbold JM Ilday FOuml Wise FW Sanghera JS Nguyen VQ Shaw LB Aggarwal ID Highly nonlinear As-S-Se glasses for all-optical switching Opt Lett 200227119ndash121

[174] Ruan YL Li WT Jarvis R Madsen N Rode A Luther-Davies B Fabrication and characterization of low loss rib chalcogenide waveguides made by dry etching Opt Express 2004125140ndash5

[175] Slusher RE Lenz G Hodelin J Sanghera J Shaw LB Aggarwal ID Large Raman gain and nonlinear phase shifts in high-purity As2Se3 chalcogenide fibers J Opt Soc Am B 2004211146ndash55

[176] Jacobsen R Andersen K Borel P Fage-Pedersen J Frandsen L Hansen O Kristensen M Lavrinenko A Moulin G Ou H Peucheret C Zsigri B Bjarklev A Strained silicon as a new electro-optic material Nature 2006441199ndash202

[177] Cazzanelli M Bianco F Borga E Pucker G Ghulinyan M Degoli E Luppi E Veacuteniard V Ossicini S Modotto D Wabnitz S Pierobon R Pavesi L Second-harmonic generation in

silicon waveguides strained by silicon nitride Nat Mater 201111148ndash54

[178] Avrutsky I Soref R Phase-matched sum frequency generation in strained silicon waveguides using their second-order nonlinear optical susceptibility Opt Express 20111921707ndash16

[179] Ghahramani E Moss DJ Sipe JE Second-harmonic generation in odd-period strained (Si)n(Ge)nSi superlattices and at SiGe interfaces Phys Rev Lett 1990642815ndash8

[180] Levy JS Foster MA Gaeta AL Lipson M Harmonic generation in silicon nitride ring resonators Opt Express 20111911415

[181] Zakery A Elliott SR Optical nonlinearities in chalcogenide glasses and their applications Springer Series in Optical Sciences 2007135

[182] Lee KK Lim DR Kimerling LC Shin J Cerrina F Fabrication of ultralow-loss SiSiO2 waveguides by roughness reduction Opt Lett 2001261888ndash90

[183] Cardenas J Poitras CB Robinson JT Preston K Chen L Lipson M Low loss etchless silicon photonic waveguides Opt Express 2009174752ndash7

[184] Biberman A Shaw MJ Timurdogan E Wright JB Watts MR Ultralow-loss silicon ring resonators Opt Lett 2012374236ndash8

[185] Walmsley IA Waxer L Dorrer C The role of dispersion in ultrafast optics Rev Sci Instrum 2001721ndash29

[186] Torres JP MHendrych Valencia A Angular dispersion an enabling tool in nonlinear and quantum optics Adv Opt Photon 20102319ndash69

[187] Yin LH Lin Q Agrawal GP Dispersion tailoring and soliton propagation in silicon waveguides Opt Lett 2006311295ndash7

[188] Dulkeith E Xia FN Schares L Green WMJ Vlasov YA Group index and group velocity dispersion in silicon-on-insulator photonic wires Opt Express 2006143853ndash63

[189] Turner AC Manolatou C Schmidt BS Lipson M Tailored anomalous group-velocity dispersion in silicon channel waveguides Opt Express 2006144357ndash62

[190] Dadap JI Panoiu NC Chen X I-Hsieh W Liu X Chou C-Y Dulkeith E McNab SJ Xia F Green WMJ Sekaric L Vlasov YA Osgood RM Jr Nonlinear-optical phase modification in dispersion-engineered Si photonic wires Opt Express 2008161280ndash99

[191] Milosevic MM Matavulj PS Yang PY Bagolini A Mashanovich GZ Rib waveguides for mid-infrared silicon photonics J Opt Soc Am B 2009261760ndash6

[192] Mashanovich GZ Milošević MM Nedeljkovic M Owens N Xiong B Teo EJ Hu Y Low loss silicon waveguides for the mid-infrared Opt Express 2011197112ndash9

[193] Reimer C Nedeljkovic M Stothard DJM Esnault MOS Reardon C OrsquoFaolain L Dunn M Mashanovich GZ Krauss TF Mid-infrared photonic crystal waveguides in silicon Opt Express 20122029361ndash8

[194] Baehr-Jones T Spott A Ilic R Spott A Penkov B Asher W Hochberg M Silicon-on-sapphire integrated waveguides for the midinfrared Opt Express 20101812127ndash35

[195] Li F Jackson S Grillet C Magi E Hudson D Madden SJ Moghe Y OrsquoBrien C Read A Duvall SG Atanackovic P Eggleton BJ Moss D Low propagation loss silicon-on-sapphire waveguides for the midinfrared Opt Express 20111915212ndash20

268emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

[196] Yue Y Zhang L Huang H Beausoleil RG Willner AE Silicon-on-nitride waveguide with ultralow dispersion over an octave-spanning mid-infared wavelength range IEEE Photonics J 20124126ndash32

[197] Khan S Chiles J Ma J Fathpour S Silicon-on-nitride waveguides for mid-and near-infrared integrated photonics Appl Phys Lett 2013102121104

[198] Cheng Z Chen X Wong CY Xu K Tsang HK Mid-infrared suspended membrane waveguide and ring resonator on silicon-on-insulator IEEE Photonics J 201241510ndash9

[199] Lin P-T Singh V Cai Y Kimerling LC Agarwal A Air-clad silicon pedestal structures for broadband mid-infrared microphotonics Opt Lett 2013381031ndash3

[200] Chang YC Paeder V Hvozdara L Hartmann JM Herzig HP Low-loss germanium strip waveguides on silicon for the mid-infrared Opt Lett 2012372883ndash5

[201] Zhang L Yue Y Y Xiao-Li R G Beausoleil Willner AE Highly dispersive slot waveguides Opt Express 2009177095ndash101

[202] Zhang L Yue Y Beausoleil RG Willner AE Analysis and engineering of chromatic dispersion in silicon waveguide bends and ring resonators Opt Express 2011198102ndash7

[203] Zhang L Mu J Singh V Agarwal A Kimerling LC Michel J Intra-cavity dispersion of microresonators and its engineering for octave-spanning Kerr frequency comb generation to be published

[204] Lin Q Zhang L Generalized nonlinear envelope equation with high-order dispersion of nonlinearity to be published

[205] Wang Y Yue R Han H Liao X Raman study of structural order of a-SiNxH and its change upon thermal annealing J Non-Crystalline Solids 2001291107ndash12

[206] Brida D Marangoni M Manzoni C De Silvestri S Cerullo G Two-optical-cycle pulses in the mid-infrared from an optical parametric amplifier Opt Lett 2008332901ndash3

[207] Brida D Manzoni C Cirmi G Marangoni M Bonora S Villoresi P De Silvestri S Cerullo G Few-optical-cycle pulses tunable from the visible to the mid-infrared by optical parametric amplifiers J Opt 201012013001

[208] Kippenberg TJ Holzwarth R Diddams SA Microresonator-based optical frequency combs Science 2011332555ndash9

[209] Levy JS Gondarenko A Foster MA Turner-Foster AC Gaeta AL Lipson M CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects Nat Photonics 2009437ndash40

[210] DelrsquoHaye P Herr T Gavartin E Gorodetsky ML Holzwarth R Kippenberg TJ Octave spanningtunable frequency comb from a microresonator Phys Rev Lett 2011107063901

[211] Okawachi Y Saha K Levy JS Wen YH Lipson M Gaeta AL Octave-spanning frequency combgeneration in a silicon nitride chip Opt Lett 2011363398ndash400

[212] Matsko AB Savchenkov AA Liang W Ilchenko VS Seidel D Maleki L Mode-locked Kerr frequency combs Opt Lett 2011362845ndash7

[213] Herr T Brasch V Jost JD Wang CY Kondratiev NM Gorodetsky ML Kippenberg TJ Temporal solitons in optical microresonators httparxivorgabs12110733

[214] Saha K Okawachi Y Shim B Levy JS Salem R Johnson AR Foster MA Lamont MR Lipson M Gaeta AL Modelocking and femtosecond pulse generation in chip-based frequency combs Opt Express 2013211335ndash43

[215] Coen S Erkintalo M Universal scaling laws of Kerr frequency combs Opt Lett 2013381790ndash2

[216] Lugiato LA Lefever R Spatial dissipative structures in passive optical-systems Phys Rev Lett 1987582209ndash11

[217] Haelterman M Trillo S Wabnitz S Dissipative modulation instability in a nonlinear dispersive ring cavity Opt Commun 199291401ndash7

[218] Coen S Randle HG Sylvestre T Erkintalo M Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato-Lefever model Opt Lett 20133837ndash9

[219] Chembo YK Menyuk CR Spatiotemporal Lugiato-Lefever formalism for Kerr-comb generation in whispering-gallery-mode resonators Phys Rev A 201387053852

[220] Foltynowicz A Mas1owski P Ban T Adler F Cossel KC Briles TC Ye J Optical frequency comb spectroscopy Faraday Discussion 201115023ndash31

[221] Hartl I Li XD Chudoba C Ghanta RK Ko TH Fujimoto JG Ranka JK Windeler RS Ultrahigh-resolution optical coherence tomography using continuum generation in an air silica microstructure optical fiber Opt Lett 200126608ndash10

[222] Brabec T Krausz F Intense few-cycle laser fields Frontiers of nonlinear optics Rev Mod Phys 200072545ndash91

[223] Hu J Meyer J Richardson K Shah L Feature issue introduction mid-IR photonic materials Opt Mater Express 201331571ndash5

[224] Private communications with Dr Jacob Levy in Prof Lipsonrsquos group and Dr Johann Riemensberger in Prof Kippenbergrsquos group

[225] Zhang J Lin Q Piredda G Boyd RW Agrawal GP Fauchet PM Anisotropic nonlinear response of silicon in the near-infrared region Appl Phys Lett 200791071113

Page 9: Lin Zhang*, Anuradha M. Agarwal, Lionel C. Kimerling and ...

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp255

of dispersions can be used for multiple applications as detailed in the next section The nonlinear coefficients for the two waveguides are shown in Figure 6(B) We note that the stripslot hybrid waveguides have similar nonlinear coefficients as the strip waveguide which shows that the dispersion profile is much more tailorable by waveguide designs

Then we move to the mid-IR using silicon and silicon nitride for waveguiding A comparison of different types of silicon-on-nitride waveguides have been presented in [196] where rib waveguides were preferred due to the wideband low dispersion over an octave-spanning band-width from 24 to 66 microm for the quasi-TE mode This is a spectral range from siliconrsquos half-bandgap wavelength to the cut-off wavelength of silicon nitride In Figure 7(A) we plot the dispersion curve for a silicon-on-nitride rib waveguide with air as the upper cladding the rib width of 2000 nm the total height of 1200 nm and the slab height of 1000 nm which are the same parameters used in [196] It is shown that less confinement of optical modes reduces the contribution of waveguide dispersion and makes the overall dispersion profile closer to the material dispersion which is flat and low at long wavelengths as in Figure 2(B)

A

B

400

300

200

100

-100

8

6

4

2

0

0

Strip WG 1300times540 nm2

Strip WG 1400times800 nm2

Strip WG 1400times800 nm2

Slot WG 1Slot WG 2

Slot WG 1Slot WG 2

Dis

pers

ion

(ps

nmmiddotk

m)

Non

linea

r co

effic

ient

(m

middotW)

20 3010 15 2505Wavelength (microm)

2010 15 2505

Wavelength (microm)

Figure 6emspIn a wavelength range moved toward the short-wave-length end of near-IR spectrum silicon nitride strip and stripslot hybrid waveguides are designed in terms of (A) dispersion and (B) nonlinearity

Accordingly the nonlinear coefficient is small 285 (mmiddotW) at 3 microm as shown in Figure 7(B)

On the other hand if one needs a small Aeff to enhance nonlinearity additional dispersion tailoring (eg based on stripslot hybrid waveguides) would be beneficial Pursuing a higher nonlinear coefficient we use a 500-nm silicon nitride suspended membrane as illustrated in Figure 4 to support a silicon stripslot hybrid waveguide This helps confine light in the waveguide core Using W = 880 nm Hu = 550 nm Hs = 87 nm and Hl = 840 nm we obtain a saddle-shaped anomalous dispersion from 19 to 449 microm within 0~60 ps(nmmiddotkm) for the quasi-TM mode as shown in Figure 7(A) This structure produces much tighter mode confinement than the rib waveguide and exhibits a 3 times larger nonlinear coefficient in Figure 7(B) while having similar dispersion flatness

Finally we consider germanium-on-silicon wave-guides over a wavelength range from 33 to 85 microm between the half-bandgap wavelength of germanium and the cut-off wavelength of silicon This type of waveguide has been demonstrated with strain-free mono-crystal-line germanium [200] Here we assume that the germa-nium waveguide has a 10-nm silicon nitride layer on its

A

B

200

-200

60

40

20

0

100

-100

0

Rib WGSlot WG

Rib WGSlot WG

Dis

pers

ion

(ps

nmmiddotk

m)

Non

linea

r co

effic

ient

(m

middotW)

1 2 3 4 5 6 7Wavelength (microm)

1 2 3 4 5 6 7

Wavelength (microm)

Figure 7emspIn a wavelength range from the short-wave IR to mid-IR silicon rib waveguide on silicon nitride and stripslot hybrid waveguide on a suspended membrane are analyzed in terms of (A) dispersion and (B) nonlinearity

256emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

surface for passivation The upper cladding could be air or silicon which provides significantly different dispersion properties due to a varied index contrast For comparison only we also have silicon nitride as the upper cladding although silicon nitride becomes lossy for wavelengths longer than 67 microm Figure 8(A) shows the dispersion pro-files of four germanium-on-silicon strip waveguides with equal size 3000 times 1600 nm2 for the quasi-TE mode Air and silicon nitride as an upper cladding result in similar shape and bandwidth in the dispersion profiles Thus the air-cladded waveguide is chosen and discussed further The waveguide with silicon upper cladding has normal dispersion at all wavelengths since there is a relatively small index contrast between germanium and silicon and thus weak mode confinement A germanium strip wave-guide on a 600-nm-thick silicon suspended membrane is also considered to increase light confinement with an air upper cladding to maximize light confinement However as mentioned earlier strong confinement typically causes strong dispersion as shown in Figure 8(A) and therefore the germanium waveguide on a silicon membraneis not chosen for broadband nonlinear applications In contrast the germanium strip waveguide with air upper cladding exhibits a flat and low dispersion

The dimensions of the air-cladded germanium wave-guide are varied by simultaneously changing its height and width with a step of 200 nm for both polarization states It is interesting to see from Figure 8(B) and 8(C) that the dispersion peak value remains nearly unchanged for all the waveguide sizes although we have a widely tunable ZDW at long wavelengths For the quasi-TE mode the right ZDW moves from 605 microm to 841 microm while the left ZDW is always near 4 microm We can thus obtain an octave-spanning anomalous dispersion band with the peak value below 100 ps(nmmiddotkm) For the quasi-TM mode one can see similar dispersion properties but the anomalous disper-sion band is smaller Thus we choose the quasi-TE mode for further discussion in next section

The nonlinear coefficient in the germanium wave-guides for the quasi-TE mode is shown in Figure 8(D) which is about 10(mmiddotW) at 5 microm with a small variation for differ-ent waveguide sizes This is quite high considering that both wavelength and effective mode area become much larger over this wavelength range compared to the near-IR

From above we can see that the stripslot hybrid wave-guides enable unique controllability of dispersion and that this concept is applicable to different wavelength ranges However their performance may be sensitive to fabrication errors especially for inaccuracies in slot height Hs [59 60] A higher yield in device fabrication is expected using advanced fabrication technologies and facilities

A

C

D

B

400

300

200

100

-100

-200

0

Ge WG+air 3000times1600 nm2

Ge WG+air suspended 3000times1600 nm2

Ge WG+Si3N4 3000times1600 nm2

Ge WG+Si 3000times1600 nm2

Ge WG+air 2800times1400 nm2

Ge WG+air 3000times1600 nm2

Ge WG+air 3200times1800 nm2

Ge WG+air 3400times2000 nm2

Ge WG+air 2800times1400 nm2

Ge WG+air 3000times1600 nm2

Ge WG+air 3200times1800 nm2

Ge WG+air 3400times2000 nm2

Ge WG+air 2800times1400 nm2

Ge WG+air 3000times1600 nm2

Ge WG+air 3200times1800 nm2

Ge WG+air 3400times2000 nm2

Dis

pers

ion

(ps

nmmiddotk

m)

400

300

200

100

-100

-200

0

Dis

pers

ion

(ps

nmmiddotk

m)

400

300

200

100

-100

-200

50

40

30

20

10

0

0

Dis

pers

ion

(ps

nmmiddotk

m)

Non

linea

r co

effic

ient

(m

middotW)

3 4 5 6 7 8 9Wavelength (microm)

3 4 5 6 7 8 9Wavelength (microm)

3 4 5 6 7 8 9

Wavelength (microm)

3 4 5 6 7 8 9

Wavelength (microm)

Figure 8emspIn a wavelength range covering the main part of the mid-IR spectrum (A) on silicon substrate or on suspended silicon membrane are analyzed in terms of dispersion Germanium-on-silicon strip waveguides with an air upper cladding and different dimensions are characterized by (B) dispersion for the quasi-TE mode (C) dispersion for the quasi-TM mode and (D) nonlinearity for the quasi-TE mode

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp257

Besides photonic waveguides another important cat-egory of nonlinear devices is integrated resonators In the scope of this paper we consider relatively large resona-tors for frequency comb generation in which the bending radius of a ring resonator is varied from 50 microm to 100 microm depending on free spectral range (FSR) and the group index in the waveguide In these cases the waveguide-bending-induced dispersion is small and we would not discuss intra-cavity dispersion [202 203] in details here

4 ApplicationsBenefiting from the unique dispersion engineering over an octave-spanning bandwidth as described above one can develop ultra-wideband nonlinear applications that could hardly be attained in an integrated platform previously These include octave-spanning supercontinuum genera-tion pulse compression to a few-cycle or even sub-cycle level octave-spanning Kerr frequency comb generation and the associated mode-locked ultrashort pulse genera-tion using microresonators In this section we review our recent work on these topics

First we discuss the supercontinuum generation and pulse compression in a straight waveguide The nonlinear envelope equation used here to simulate supercontinuum generation is the following

βα infin

=

part part+ + = + part part sum

2

( - )( ) ( )

2

m mm

mm

ii A K A R A

z m t (1)

where

2

0 0

- -( ) 1- ( ) 2

n nn

nn

i i iK A A An t tγ δ δ

ω δ δ

infin

=

= sum

and

2shock_R( ) - 1- [ ( - ) | | ]δ

γ τδ minusinfin

= prime prime int

t

R RR A i i A h t t A dtt

We denote A  =  A(zt) as the complex amplitude of an optical pulse Note that its Fourier transform is

-

1( ) ( ) exp( - ) 2

A z A z t i t dtω ωπ

infin

infin

= int

In Eq (1) α is the total propagation loss and βm is the mth-order dispersion coefficient The frequency dependence of nonlinearity parameters including the nonlinear index n2 the TPA coefficient βTPA and the

effective mode area Aeff is included in the nth-order dis-persion coefficient γn of nonlinearity which is defined as γn = ω0middotpartn[γ(ω)ω]partωn where ω0 is the angular frequency of the carrier Therefore we can consider all-order linear dispersion terms and all-order dispersion of the nonlin-ear coefficient in Eq (1) Specifically in the simulations for a silicon and silicon nitride waveguides we have all-order linear dispersion and up to 6th-order and 2nd-order of the nonlinear coefficient dispersion included A detailed derivation of Eq (1) is given in [204] For the quasi-TM mode that experiences the engineered dispersion due to the mode transition SRS in silicon waveguides fabricated on the (001) surface can be ignored [27 96] For silicon nitride waveguide we include the SRS term in Eq (1) where γR = gRΓR(AeffΩR) and gR ΓR and ΩR represent the Raman gain coefficient the full width at half maximum of the gain spectrum and the Raman shift respectively The Raman shock time τshock_R is associated with γRrsquos fre-quency dependence which is 1ω0-[1Aeff(ω0)][dAeff(ω)dω] similarly as in [14] if we ignore frequency dependent gR ΓR and ΩR hR(t) is the Raman response function and it corresponds to the Raman gain spectrum

2

2 20 0

( ) -( - ) 2 ( - )

Ωω

Ω ω ω Γ ω ω=

+R

RR R

Hi

Note that the sign before the imaginary unit is differ-ent from that in [27] to be consistent with the expression of the Fourier transform that we used

We have considered supercontinuum generation in both silicon and silicon nitride waveguides with the slot-assisted dispersion tailoring Octave-spanning supercon-tinua in a silicon-based stripslot hybrid waveguide have been investigated in detail in [108] in which two-cycle optical pulses are obtained The main results in that work are shown in Figure 9 for comparison purposes

Here we mainly focus on the supercontinuum gen-erated in the silicon nitride stripslot hybrid waveguide (ie the slot WG 1 in Section III) whose dispersion and nonlinearity properties are shown in Figure 6 In the non-linear simulations we set the total propagation loss to be 1 dBcm The SRS parameters used here are the following [205] ΩR2π = 143 THz ΓR2π = 172 THz and gR = 1 times 10-12 mW τshock_R is calculated to be  = 156 fs

In our simulations we use a time step of 025 fs which is corresponding to a bandwidth of 4000 THz in the fre-quency domain For a femtosecond input pulse we set the time window length to 50 ps (ie frequency resolution Δf = 20 GHz)

We simulate the nonlinear propagation of a chirp-free hyperbolic secant pulse in the silicon nitride waveguide

258emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

The pulse center wavelength is at 1610 nm and its full width at half-maximum (FWHM) T0 is 120 fs Its peak power is 1200 W corresponding to pulse energy of 016 nJ

Figure 10(A) shows the supercontinua at different propagation distances At 48 mm the spectrum is greatly broadened at the -30 dB level covering a wavelength range from 0585 to 2833 microm which is more than two octaves The spectrum evolution in Figure 10(A) shows a similar spectrum shape as that in Figure 9(A) both featuring a ldquotriangularrdquo central spectrum bounded by two dispersive waves at the edges However it is important to note that the absence of TPA and 3PA in silicon nitride at the telecom window leads to a much more efficient spectrum broad-ening than that in silicon [108] The generated spectrum extends from the visible light to the mid-IR with excellent spectral coherence which is confirmed by the pulse wave-form shown in Figure 10(B) In the time domain the pulse is greatly compressed from 120 to 408 fs corresponding to 076 optical cycles at 161 microm wavelength

We examine the pulsewidth as a function of propa-gation distance Figure 11 shows that the pulse becomes increasingly narrower until the propagation distance reaches 47 mm For longer distances the pulsewidth

A

B

60 mm

48 mm

36 mm

24 mm

12 mm

Input

Spe

ctru

m (

10 d

Bd

iv)

Pow

er (

W)

12

246

24

18

12

6

0

248 250 252 254

14 16 18 20 22 24Wavelength (microm)

Time (ps)

Figure 9emsp(A) The supercontinuum generation in a silicon-based stripslot hybrid waveguide presented in [108] (B) The significant spectrum broadening at 425-mm distance is associated with a temporal compression of an input pulse (dash line) to the output waveform (solid line) with a FWHM of 12 fs

A

B

50 mm

48 mm

46 mm

44 mm

42 mm

Input

Spe

ctru

m (

10 d

Bd

iv)

Pow

er (

W)

8000

6000

4000

2000

0250249 251

06 09 12 15 18 21 24 27

Wavelength (microm)

Time (ps)

Figure 10emsp(A) Spectrum evolution of the pulse over propagation distance A supercontinuum of more than two octaves is achieved at 48 mm distance (B) Generated pulse waveform with a pulse width of 408 fs as short as 076 optical cycles Low pedestals are caused by dispersive waves generated at the two ends of the spectrum

remains almost constant However it is important to mention that after 48 mm the dispersive waves become increasingly stronger as shown in Figure 10(A) causing larger pedestals

Comparing the results in Figures 9 and 10 we note that the mid-IR wavelength range for silicon would be in analogy to the near-IR for silicon nitride in terms of non-linear optics operations Pumping at or beyond 33 microm one can use the waveguide designs shown in Figure 7 to produce very efficient nonlinear interactions without TPA and 3PA in silicon Ultrashort pulses in the mid-IR from parametric amplifiers [206 207] could be used to pump the Group IV waveguides

Another nonlinear application of the dispersion-engi-neered Group IV waveguides is micro-resonator-based Kerr frequency comb generation When such a waveguide is curved to form a microring resonator input CW light travels around the cavity and amplifies the noise in the source located at the frequencies with a high parametric gain As a result of modulation instability and cascaded FWM in the cavity a frequency comb can be generated [208ndash211] Mode-locked frequency combs have been reported pro-ducing low-noise pulse trains in time domain [212ndash214]

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp259

The formation of cavity solitons is identified as the main reason for the mode-locking in the Kerr frequency combs [215] This is instructive because one can thus predict the spectral bandwidth and temporal pulsewidth in the generated low-noise combs The 3-dB comb bandwidth is inversely proportional to the square root of the 2nd-order dispersion coefficient |β2| as given in [213 215] It is desira-ble that all comb lines that constitute the soliton spectrum experience the same |β2| In this sense the stripslot hybrid waveguides with flattened dispersion are preferably suit-able for supporting broadband Kerr comb generation and ultra-short cavity soliton generation

The Kerr frequency comb generation can be modeled using the generalized Lugiato-Lefever equation (LLE) [216ndash219]

20

2

( - )- - | |

2 2

m mm

R inmm

jkt j jl E kE j l E Et m

βαδ γ

τ

infin

=

part part+ + + = part part

sum (2)

where tR is the round-trip time E = E(tτ) and Ein are intra-cavity field and input field (pump power Pin  =  |Ein|2) t and τ are the slow and fast times δ0 is the cavity phase detuning defined as δ0  =  tRmiddot(ωn -ω0) where ω0 and ωn are the pumprsquos angular frequency and the nth angular reso-nance frequency that is pumped Other resonator param-eters include the power loss per round trip α the power coupling coefficient κ the nonlinear coefficient γ and the mth dispersion coefficient βm Since a flattened dispersion profile has a small β2 over a wide bandwidth it is impor-tant to take the influence of higher-order dispersion into account We include all-order dispersion terms in Eq (2) as we did in solving Eq (1)

To enhance the Kerr comb bandwidth in the near-IR we use the ultra-flattened dispersion profile in Figure 6(A) which is obtained in the slot WG 2 based on

Pul

se w

idth

(fs

)

14

12

10

8

6

4

242 44 46 48 50 52

Propagation distance (mm)

Figure 11emspPulse width first decreases with propagation distance and then remains stable After 48 mm dispersive waves get stronger causing more pedestals

Pow

er (

10 d

Bd

iv)

Pow

er (

W)

70A

B

60

50

40

30

20

10

-10

-20

600

400

200

0

80 120

0575 0600 0625 0650

160 200 240 280 320 360

0

Frequency (THz)

Time (ps)

Figure 12emsp(A) Frequency comb generation with a CW pump at 155 microm using a microring resonator based on a silicon stripslot hybrid waveguide Over an octave-spanning bandwidth from 135 to 270 THz the comb lines have a power drop of 20 dB (B) Generated pulse waveform with a pulse width of 82 fs as short as 16 optical cycles

silicon nitride The ring resonator has a bending radius of 104 microm corresponding to a FSR of 200 GHz Pumping near 155 microm with a pump power of 2 W the resonance peak is red-shifted and we need to red-shift the pump wavelength accordingly and tune it into the resonance from the short-wavelength side When the pump is step-by-step tuned by up to 63 resonance linewidths we obtain the comb spectrum and the mode-locked pulse waveform as shown in Figure 12 One can see that over an octave-spanning bandwidth from 133 to 268 THz the comb lines have a power drop by 20 dB from the center of the spectrum The spectral flatness of this comb is relatively good compared to the previously reported results [208ndash211] The comb bandwidth at -40 dB is as wide as two octaves There are two dispersive peaks in normal dispersion regions beyond the low-dispersion band Such a mode-locked broadband comb produces a train of sub-two-cycle optical pulses as shown in Figure 12(B) with one pulse per round trip The peak power of the pulse is up to 600 W Nonlinear conver-sion efficiency is estimated to be -267 dB

To generate frequency combs in the mid-IR the ger-manium-on-silicon strip waveguide is chosen We choose

260emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

a cross-section of 3200 times 1800 nm2 which has an octave-spanning low-dispersion band from 4 to 767 microm as shown in Figure 8(B) A germanium ring resonator is formed with a bending radius of 564 microm corresponding to a FSR of 200 GHz Pumping at 6 microm with a CW power of 14 W and detuning the pump wavelength by 10 resonance linewidth one can see that a mode-locked wideband mid-IR comb is generated from 358 to 644 THz (ie from 466 to 838 microm) at -40 dB level The FWHM of the produced pulses is 69 fs which corresponds to ~35 optical cycles The pulse peak power is 184 W and the nonlinear conversion efficiency is estimated to be -143 dB Since the pumping frequency is not at the center of the low-dispersion band we only see one peak in the comb spectrum caused by the dispersive wave in the normal dispersion region from Figure 13(A) There is another peak at higher frequencies beyond what is shown in the figure

As shown above broadband dispersion engineering is critical for octave-spanning nonlinear applications in both near- and mid-IR wavelength ranges which enables us to fully utilize the bandwidth allowed by the materials transparency windows Generally speaking the nonlinear applications mentioned here such as supercontinuum generation ultrafast pulse compression and frequency comb generation are often the intermediate steps towards higher-level system applications In the frequency domain a wide spectrum can serve as an electromagnetic carrier to acquire high-volume of information eg for sensing [220] and imaging [221] In the time domain an ultrashort pulse can be used as probe to sample ultrafast phenomena [222]

5 Summary and OutlookWe have presented a review of our recent work on nonlin-ear photonics based on silicon and germanium Various types of Group IV waveguides are analyzed and optimized for four different wavelength ranges from near- to mid-IR The recently proposed dispersion engineering technique based on stripslot hybrid waveguide structures is used for different material combinations and wavelength ranges Numerical simulations show that the dispersion-flattened Group IV waveguides are preferably suitable for octave-spanning nonlinear applications including on-chip supercontinuum generation ultrashort pulse compres-sion and mode-locked wideband frequency comb genera-tion based on micro-resonators

The presented approach to achieving octave-span-ning nonlinear applications on an integrated CMOS-compatible Group IV platform holds great potential for realizing chip-scale sensing imaging communications and signal processing system The ultrawide transparency windows in the mid-IR allowed by Group IV elements and compounds potentially together with other materi-als [223] provide an exciting arena for building powerful information acquisition and processing units enabled by nonlinear optics nano-photonics and ultrafast optics

Received June 14 2013 accepted October 29 2013 previously pub-lished online November 27 2013

Pow

er (

10 d

Bd

iv)

A

8030 40 50 60 70Frequency (THz)

Pow

er (

W)

B200

150

100

50

0

21 22 23 24 25Time (ps)

Figure 13emsp(A) Frequency comb generation with a CW pump at 6 microm using a microring resonator based on a germanium strip waveguide with air upper cladding (B) Generated pulse waveform with a pulse width of 69 fs as short as 35 optical cycles

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp261

Appendix

A Material index and dispersion

In this section we give the wavelength-dependent mate-rial index expressed as Sellmeier equations where wave-length λ is in μm

For silicon we use the following material index that is a fit curve from measurement results at room temperature (293 K) with 184 data points in total from 112 to 588 μm [154]

22 1 2 2

2 2 22

( )-

C Cn

λλ ε

λ λ λ= + +

where ε = 116858 C1 = 0939816 μm2 C2 = 000810461 and λ2 = 11071 μm

For silicon nitride the material index is affected by deposition conditions using plasma-enhanced chemical vapor deposition (PECVD) low-pressure chemical vapor deposition (LPCVD) and so on We use the following Sell-meier equation [155] which predicts the material index close to that in LPCVD silicon nitride films measured by a few groups [224]

22 1

2 21

( ) 1-

Cn

λλ

λ λ= +

where C1 = 28939 and λ1 = 013967 μmFor silicon dioxide we use the following Sellmeier

equation for fused silica [156]22 2

2 31 22 2 2 2 2 2

1 2 3

( ) 1- - -

CC Cn

λλ λλ

λ λ λ λ λ λ= + + +

where C1 = 06961663 C2 = 04079426 C3 = 08974794 λ1 = 00684043 μm λ2 = 01162414 μm and λ3 = 9896161 μm

For SRO the material index is affected by deposition conditions such as silicon excess annealing temperature and so on Here we choose the one with silicon excess of 8 and annealed at 1250oC [51]

22 22 31 2

2 2 2 2 2 21 2 3

( ) 1- - -

CC Cn

λλ λλ

λ λ λ λ λ λ= + + +

where C1 = 001 C2 = 196 C3 = 141 λ1 = 03 μm λ2 = 007071 μm and λ3 = 2775968 μm

For germanium the temperature-dependent mate-rial index was measured [157] Here we choose the one for room temperature (293 K)

2 22 1 2

2 2 2 21 2

( )- -

C Cn

λ λλ ε

λ λ λ λ= + +

where ε = 928156 C1 = 67288 C2 = 021307 λ1 = 0664116 μm and λ2 = 6221013 μm

For arsenic sulfide we use the material index pro-vided in [158]

2 2 22 22 3 4 51 2

2 2 2 2 2 2 2 2 2 21 2 3 4 5

( ) 1- - - - -

C C CC Cn

λ λ λλ λλ

λ λ λ λ λ λ λ λ λ λ= + + + + +

where C1 = 18983678 C2 = 19222979 C3 = 08765134 C4 = 01188704 C5 = 09569903 λ1 = 015 μm λ2 = 025 μm λ3 = 035 μm λ4 = 045 μm and λ5 = 27386128 μm

For arsenic selenide we fit ellipsometry measure-ments of our arsenic selenide thin films and the bulk material is provided by Prof Kathleen A Richardson group

22 22 31 2

2 2 2 2 2 21 2 3

( ) 1- - -

CC Cn

λλ λλ

λ λ λ λ λ λ= + + +

where C1 = 298463 C2 = 321011 C3 = 100182 λ1 = 044118 μm λ2 = 0000354953 μm and λ3 = 38413 μm

B Nonlinear Kerr index n2

The third-order nonlinear susceptibility χ(3)1111 for silicon and

germanium is predicted over the mid-IR range [133] based on a two-band model The effective nonlinear susceptibil-ity χ(3) is dependent on polarization and crystallographic orientation [225] For strong nonlinearity we consider a single-polarization incident light aligned to the crystal-lographic axis and we have χ(3) = χ(3)

1111 To investigate the octave-spanning nonlinear phenomena one need to take the wavelength-dependent nonlinear Kerr index n2 and TPA coefficient βTPA into account which are expressed as

( 3 )2 2

0

( 3 )2

0

3( ) ( )4 ( )

3( ) ( )( )

re

TPA im

ncn

cn

λ χ λε λ

πβ λ χ λ

λε λ

=

=

where ε0 and c are the vacuum permittivity and the speed of light in vacuum Using the material index given in Appendix A and χ(3) value from [133] we obtain the n2 and βTPA values tabulated as follows

262emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

Table 1enspNonlinear Kerr index n2 in silicon

λμm

  n2

10-18 m2W  λ

μm  n2

10-18 m2W  λ

μm  n2

10-18 m2W

130   234   310   389   490   312135   305   315   384   495   311140   378   320   379   500   310145   443   325   375   505   309150   501   330   371   510   307155   559   335   368   515   306160   618   340   365   520   304165   671   345   362   525   304170   710   350   360   530   303175   741   355   358   535   302180   766   360   355   540   302185   781   365   352   545   301190   783   370   350   550   300195   778   375   346   555   298200   762   380   343   560   297205   732   385   341   565   296210   699   390   338   570   296215   658   395   336   575   295220   612   400   334   580   295225   576   405   332   585   295230   547   410   331   590   294235   525   415   330   595   293240   508   420   329   600   292245   493   425   328   605   291250   479   430   327   610   290255   467   435   325   615   289260   456   440   324   620   288265   448   445   321   625   288270   440   450   319   630   288275   432   455   317   635   288280   424   460   315   640   288285   417   465   314   645   288290   410   470   313   650   288295   404   475   313   655   288300   398   480   312   660   288305   394   485   312    

Table 2enspTPA coefficient βTPA in silicon

λμm

  βTPA

10-12 mW  λ

μm  βTPA

10-12 mW  λ

μm  βTPA

10-12 mW

130   1334   165   812   200   180135   1284   170   713   205   115140   1222   175   613   210   064145   1154   180   522   215   024150   1079   185   424   220   0003155   995   190   333    160   905   195   254    

Table 3enspNonlinear Kerr index n2 in germanium

λμm

  n2

10-18 m2W  λ

μm  n2

10-18 m2W  λ

μm  n2

10-18 m2W

23  3932  63  1986  103  170524  4994  64  1972  104  169925  6007  65  1959  105  169426  6650  66  1946  106  169027  6772  67  1934  107  168728  6273  68  1923  108  168429  4897  69  1913  109  168230  4403  70  1904  110  168131  3970  71  1895  111  167932  3680  72  1886  112  167733  3470  73  1876  113  167534  3286  74  1868  114  167335  3128  75  1859  115  167036  2998  76  1850  116  166737  2895  77  1841  117  166338  2812  78  1833  118  165939  2737  79  1826  119  165640  2668  80  1819  120  165341  2605  81  1812  121  165142  2550  82  1807  122  164843  2498  83  1801  123  164644  2450  84  1797  124  164445  2406  85  1792  125  164346  2365  86  1787  126  164147  2328  87  1782  127  163948  2295  88  1777  128  163649  2266  89  1772  129  163450  2238  90  1767  130  163251  2212  91  1762  131  163052  2187  92  1758  132  162853  2164  93  1753  133  162654  2141  94  1749  134  162555  2121  95  1744  135  162356  2101  96  1740  136  162157  2083  97  1736  137  162058  2066  98  1731  138  161859  2049  99  1727  139  161760  2032  100  1722  140  161661  2016  101  1716   62  2001  102  1711   

Table 4enspTPA coefficient βTPA in germanium

λμm

  βTPA

10-8 mW  λμm

  βTPA

10-8 mW  λ

μm  βTPA

10-8 mW

23   130   25   088   27   03124   111   26   060   28   006

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp263

References[1] Bloembergen N Nonlinear Optics London World Scientific 1996[2] Yuen-Ron S The Principles of Nonlinear Optics Hoboken New

Jersey Wiley-Interscience 2002[3] Robert B Nonlinear Optics (3rd ed) Amsterdam Boston

Academic Press 2008[4] Franken P Hill A Peters C Weinreich G Generation of optical

harmonics Phys Rev Lett 19617118ndash9[5] Terhune RW Maker PD Savage CM Optical harmonic

generation in calcite Phys Rev Lett 19628404ndash6[6] Kaiser W Garrett CGB Two-photon excitation in CaF2Eu2+

Phys Rev Lett 19617229ndash32[7] Eckhardt G Hellwarth RW McClung FJ Schwarz SE Weiner D

Woodbury EJ Stimulated raman scattering from organic liquids Phys Rev Lett 19629455ndash7

[8] Giordmaine JA Mixing of light beams in crystals Phys Rev Lett 1962819ndash20

[9] Maker PD Terhune RW Nisenoff M Savage CM Effects of dispersion and focusing on the production of optical harmonics Phys Rev Lett 1962821ndash22

[10] Delone NB Kraĭnov VP Fundamentals of nonlinear optics of atomic gases New York Wiley 1987

[11] Nikogosyan DN Nonlinear optical crystals a complete survey Springer Berlin 2005

[12] Govind A Nonlinear fiber optics (4th ed) San Diego California Academic Press 2007

[13] Russell PSTJ Birks TA Lloyd-Lucas FD Photonic Bloch waves and photonic band gaps In lsquoConfined electrons and photons New physics and applicationsrsquo New York Plenum Press 1995

[14] Dudley JM Genty G Coen S Supercontinuum generation in photonic crystal fiber Rev Mod Phys 2006781135ndash1184

[15] Dudley JM Taylor JR Ten years of nonlinear optics in photonic crystal fibre Nature Photonics 2009385ndash90

[16] Soref RA Silicon-based optoelectronics Proceedings of the IEEE 1993811687ndash1706

[17] Kimerling LC Silicon for photonics Proc SPIE 3002 1997192[18] Kimerling LC Silicon materials engineering for the next

millennium Sol St Phen 199970131ndash142[19] Pavesi L Lockwood DJ editors Silicon Photonics New York

Springer 2004[20] Reed GT Knights AP Silicon photonics an introduction Wiley

Hoboken NJ 2004[21] Lipson M Guiding modulating and emitting light on silicon -

challenges and opportunities IEEE J Lightwave Technol 2005 234222

[22] Soref RA The past present and future of silicon photonics IEEE J Sel Top Quantum Electron 2006121678ndash87

[23] Jalali B Paniccia M Reed G Silicon photonics IEEE Microwave Magazine 2006758ndash68

[24] Jalali B Fathpour S Silicon photonics J Lightwave Technol 2006 244600ndash15

[25] Kirchain R Kimerling L A roadmap for nanophotonics Nature Photonics 20071303ndash5

[26] Dekker R Usechak N Foumlrst M Driessen A Ultrafast nonlinear all-optical processes in silicon-on-insulator waveguides J Phys D Appl Phys 200740R249ndash71

[27] Lin Q Painter OJ Agrawal GP Nonlinear optical phenomena in silicon waveguides Modeling and applications Opt Express 20071516604ndash44

[28] Tsang HK Liu Y Nonlinear optical properties of silicon waveguides Semicond Sci Technol 2008 23064007

[29] Osgood RM Jr Panoiu NC Dadap JI Liu X Chen X Hsieh I-W Dulkeith E Green WM Vlasov YA Engineering nonlinearities in nanoscalse optical systems Physics and applications in dispersion-engineered silicon nonaphotonics wires Adv Opt Photon 20091162ndash235

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[141] Zlatanovic S Park JS Moro S Boggio JMC Divliansky IB Alic N Mookherjea S Radic S Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source Nat Photonics 20104561ndash4

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[173] Harbold JM Ilday FOuml Wise FW Sanghera JS Nguyen VQ Shaw LB Aggarwal ID Highly nonlinear As-S-Se glasses for all-optical switching Opt Lett 200227119ndash121

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silicon waveguides strained by silicon nitride Nat Mater 201111148ndash54

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[189] Turner AC Manolatou C Schmidt BS Lipson M Tailored anomalous group-velocity dispersion in silicon channel waveguides Opt Express 2006144357ndash62

[190] Dadap JI Panoiu NC Chen X I-Hsieh W Liu X Chou C-Y Dulkeith E McNab SJ Xia F Green WMJ Sekaric L Vlasov YA Osgood RM Jr Nonlinear-optical phase modification in dispersion-engineered Si photonic wires Opt Express 2008161280ndash99

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[192] Mashanovich GZ Milošević MM Nedeljkovic M Owens N Xiong B Teo EJ Hu Y Low loss silicon waveguides for the mid-infrared Opt Express 2011197112ndash9

[193] Reimer C Nedeljkovic M Stothard DJM Esnault MOS Reardon C OrsquoFaolain L Dunn M Mashanovich GZ Krauss TF Mid-infrared photonic crystal waveguides in silicon Opt Express 20122029361ndash8

[194] Baehr-Jones T Spott A Ilic R Spott A Penkov B Asher W Hochberg M Silicon-on-sapphire integrated waveguides for the midinfrared Opt Express 20101812127ndash35

[195] Li F Jackson S Grillet C Magi E Hudson D Madden SJ Moghe Y OrsquoBrien C Read A Duvall SG Atanackovic P Eggleton BJ Moss D Low propagation loss silicon-on-sapphire waveguides for the midinfrared Opt Express 20111915212ndash20

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[196] Yue Y Zhang L Huang H Beausoleil RG Willner AE Silicon-on-nitride waveguide with ultralow dispersion over an octave-spanning mid-infared wavelength range IEEE Photonics J 20124126ndash32

[197] Khan S Chiles J Ma J Fathpour S Silicon-on-nitride waveguides for mid-and near-infrared integrated photonics Appl Phys Lett 2013102121104

[198] Cheng Z Chen X Wong CY Xu K Tsang HK Mid-infrared suspended membrane waveguide and ring resonator on silicon-on-insulator IEEE Photonics J 201241510ndash9

[199] Lin P-T Singh V Cai Y Kimerling LC Agarwal A Air-clad silicon pedestal structures for broadband mid-infrared microphotonics Opt Lett 2013381031ndash3

[200] Chang YC Paeder V Hvozdara L Hartmann JM Herzig HP Low-loss germanium strip waveguides on silicon for the mid-infrared Opt Lett 2012372883ndash5

[201] Zhang L Yue Y Y Xiao-Li R G Beausoleil Willner AE Highly dispersive slot waveguides Opt Express 2009177095ndash101

[202] Zhang L Yue Y Beausoleil RG Willner AE Analysis and engineering of chromatic dispersion in silicon waveguide bends and ring resonators Opt Express 2011198102ndash7

[203] Zhang L Mu J Singh V Agarwal A Kimerling LC Michel J Intra-cavity dispersion of microresonators and its engineering for octave-spanning Kerr frequency comb generation to be published

[204] Lin Q Zhang L Generalized nonlinear envelope equation with high-order dispersion of nonlinearity to be published

[205] Wang Y Yue R Han H Liao X Raman study of structural order of a-SiNxH and its change upon thermal annealing J Non-Crystalline Solids 2001291107ndash12

[206] Brida D Marangoni M Manzoni C De Silvestri S Cerullo G Two-optical-cycle pulses in the mid-infrared from an optical parametric amplifier Opt Lett 2008332901ndash3

[207] Brida D Manzoni C Cirmi G Marangoni M Bonora S Villoresi P De Silvestri S Cerullo G Few-optical-cycle pulses tunable from the visible to the mid-infrared by optical parametric amplifiers J Opt 201012013001

[208] Kippenberg TJ Holzwarth R Diddams SA Microresonator-based optical frequency combs Science 2011332555ndash9

[209] Levy JS Gondarenko A Foster MA Turner-Foster AC Gaeta AL Lipson M CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects Nat Photonics 2009437ndash40

[210] DelrsquoHaye P Herr T Gavartin E Gorodetsky ML Holzwarth R Kippenberg TJ Octave spanningtunable frequency comb from a microresonator Phys Rev Lett 2011107063901

[211] Okawachi Y Saha K Levy JS Wen YH Lipson M Gaeta AL Octave-spanning frequency combgeneration in a silicon nitride chip Opt Lett 2011363398ndash400

[212] Matsko AB Savchenkov AA Liang W Ilchenko VS Seidel D Maleki L Mode-locked Kerr frequency combs Opt Lett 2011362845ndash7

[213] Herr T Brasch V Jost JD Wang CY Kondratiev NM Gorodetsky ML Kippenberg TJ Temporal solitons in optical microresonators httparxivorgabs12110733

[214] Saha K Okawachi Y Shim B Levy JS Salem R Johnson AR Foster MA Lamont MR Lipson M Gaeta AL Modelocking and femtosecond pulse generation in chip-based frequency combs Opt Express 2013211335ndash43

[215] Coen S Erkintalo M Universal scaling laws of Kerr frequency combs Opt Lett 2013381790ndash2

[216] Lugiato LA Lefever R Spatial dissipative structures in passive optical-systems Phys Rev Lett 1987582209ndash11

[217] Haelterman M Trillo S Wabnitz S Dissipative modulation instability in a nonlinear dispersive ring cavity Opt Commun 199291401ndash7

[218] Coen S Randle HG Sylvestre T Erkintalo M Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato-Lefever model Opt Lett 20133837ndash9

[219] Chembo YK Menyuk CR Spatiotemporal Lugiato-Lefever formalism for Kerr-comb generation in whispering-gallery-mode resonators Phys Rev A 201387053852

[220] Foltynowicz A Mas1owski P Ban T Adler F Cossel KC Briles TC Ye J Optical frequency comb spectroscopy Faraday Discussion 201115023ndash31

[221] Hartl I Li XD Chudoba C Ghanta RK Ko TH Fujimoto JG Ranka JK Windeler RS Ultrahigh-resolution optical coherence tomography using continuum generation in an air silica microstructure optical fiber Opt Lett 200126608ndash10

[222] Brabec T Krausz F Intense few-cycle laser fields Frontiers of nonlinear optics Rev Mod Phys 200072545ndash91

[223] Hu J Meyer J Richardson K Shah L Feature issue introduction mid-IR photonic materials Opt Mater Express 201331571ndash5

[224] Private communications with Dr Jacob Levy in Prof Lipsonrsquos group and Dr Johann Riemensberger in Prof Kippenbergrsquos group

[225] Zhang J Lin Q Piredda G Boyd RW Agrawal GP Fauchet PM Anisotropic nonlinear response of silicon in the near-infrared region Appl Phys Lett 200791071113

Page 10: Lin Zhang*, Anuradha M. Agarwal, Lionel C. Kimerling and ...

256emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

surface for passivation The upper cladding could be air or silicon which provides significantly different dispersion properties due to a varied index contrast For comparison only we also have silicon nitride as the upper cladding although silicon nitride becomes lossy for wavelengths longer than 67 microm Figure 8(A) shows the dispersion pro-files of four germanium-on-silicon strip waveguides with equal size 3000 times 1600 nm2 for the quasi-TE mode Air and silicon nitride as an upper cladding result in similar shape and bandwidth in the dispersion profiles Thus the air-cladded waveguide is chosen and discussed further The waveguide with silicon upper cladding has normal dispersion at all wavelengths since there is a relatively small index contrast between germanium and silicon and thus weak mode confinement A germanium strip wave-guide on a 600-nm-thick silicon suspended membrane is also considered to increase light confinement with an air upper cladding to maximize light confinement However as mentioned earlier strong confinement typically causes strong dispersion as shown in Figure 8(A) and therefore the germanium waveguide on a silicon membraneis not chosen for broadband nonlinear applications In contrast the germanium strip waveguide with air upper cladding exhibits a flat and low dispersion

The dimensions of the air-cladded germanium wave-guide are varied by simultaneously changing its height and width with a step of 200 nm for both polarization states It is interesting to see from Figure 8(B) and 8(C) that the dispersion peak value remains nearly unchanged for all the waveguide sizes although we have a widely tunable ZDW at long wavelengths For the quasi-TE mode the right ZDW moves from 605 microm to 841 microm while the left ZDW is always near 4 microm We can thus obtain an octave-spanning anomalous dispersion band with the peak value below 100 ps(nmmiddotkm) For the quasi-TM mode one can see similar dispersion properties but the anomalous disper-sion band is smaller Thus we choose the quasi-TE mode for further discussion in next section

The nonlinear coefficient in the germanium wave-guides for the quasi-TE mode is shown in Figure 8(D) which is about 10(mmiddotW) at 5 microm with a small variation for differ-ent waveguide sizes This is quite high considering that both wavelength and effective mode area become much larger over this wavelength range compared to the near-IR

From above we can see that the stripslot hybrid wave-guides enable unique controllability of dispersion and that this concept is applicable to different wavelength ranges However their performance may be sensitive to fabrication errors especially for inaccuracies in slot height Hs [59 60] A higher yield in device fabrication is expected using advanced fabrication technologies and facilities

A

C

D

B

400

300

200

100

-100

-200

0

Ge WG+air 3000times1600 nm2

Ge WG+air suspended 3000times1600 nm2

Ge WG+Si3N4 3000times1600 nm2

Ge WG+Si 3000times1600 nm2

Ge WG+air 2800times1400 nm2

Ge WG+air 3000times1600 nm2

Ge WG+air 3200times1800 nm2

Ge WG+air 3400times2000 nm2

Ge WG+air 2800times1400 nm2

Ge WG+air 3000times1600 nm2

Ge WG+air 3200times1800 nm2

Ge WG+air 3400times2000 nm2

Ge WG+air 2800times1400 nm2

Ge WG+air 3000times1600 nm2

Ge WG+air 3200times1800 nm2

Ge WG+air 3400times2000 nm2

Dis

pers

ion

(ps

nmmiddotk

m)

400

300

200

100

-100

-200

0

Dis

pers

ion

(ps

nmmiddotk

m)

400

300

200

100

-100

-200

50

40

30

20

10

0

0

Dis

pers

ion

(ps

nmmiddotk

m)

Non

linea

r co

effic

ient

(m

middotW)

3 4 5 6 7 8 9Wavelength (microm)

3 4 5 6 7 8 9Wavelength (microm)

3 4 5 6 7 8 9

Wavelength (microm)

3 4 5 6 7 8 9

Wavelength (microm)

Figure 8emspIn a wavelength range covering the main part of the mid-IR spectrum (A) on silicon substrate or on suspended silicon membrane are analyzed in terms of dispersion Germanium-on-silicon strip waveguides with an air upper cladding and different dimensions are characterized by (B) dispersion for the quasi-TE mode (C) dispersion for the quasi-TM mode and (D) nonlinearity for the quasi-TE mode

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp257

Besides photonic waveguides another important cat-egory of nonlinear devices is integrated resonators In the scope of this paper we consider relatively large resona-tors for frequency comb generation in which the bending radius of a ring resonator is varied from 50 microm to 100 microm depending on free spectral range (FSR) and the group index in the waveguide In these cases the waveguide-bending-induced dispersion is small and we would not discuss intra-cavity dispersion [202 203] in details here

4 ApplicationsBenefiting from the unique dispersion engineering over an octave-spanning bandwidth as described above one can develop ultra-wideband nonlinear applications that could hardly be attained in an integrated platform previously These include octave-spanning supercontinuum genera-tion pulse compression to a few-cycle or even sub-cycle level octave-spanning Kerr frequency comb generation and the associated mode-locked ultrashort pulse genera-tion using microresonators In this section we review our recent work on these topics

First we discuss the supercontinuum generation and pulse compression in a straight waveguide The nonlinear envelope equation used here to simulate supercontinuum generation is the following

βα infin

=

part part+ + = + part part sum

2

( - )( ) ( )

2

m mm

mm

ii A K A R A

z m t (1)

where

2

0 0

- -( ) 1- ( ) 2

n nn

nn

i i iK A A An t tγ δ δ

ω δ δ

infin

=

= sum

and

2shock_R( ) - 1- [ ( - ) | | ]δ

γ τδ minusinfin

= prime prime int

t

R RR A i i A h t t A dtt

We denote A  =  A(zt) as the complex amplitude of an optical pulse Note that its Fourier transform is

-

1( ) ( ) exp( - ) 2

A z A z t i t dtω ωπ

infin

infin

= int

In Eq (1) α is the total propagation loss and βm is the mth-order dispersion coefficient The frequency dependence of nonlinearity parameters including the nonlinear index n2 the TPA coefficient βTPA and the

effective mode area Aeff is included in the nth-order dis-persion coefficient γn of nonlinearity which is defined as γn = ω0middotpartn[γ(ω)ω]partωn where ω0 is the angular frequency of the carrier Therefore we can consider all-order linear dispersion terms and all-order dispersion of the nonlin-ear coefficient in Eq (1) Specifically in the simulations for a silicon and silicon nitride waveguides we have all-order linear dispersion and up to 6th-order and 2nd-order of the nonlinear coefficient dispersion included A detailed derivation of Eq (1) is given in [204] For the quasi-TM mode that experiences the engineered dispersion due to the mode transition SRS in silicon waveguides fabricated on the (001) surface can be ignored [27 96] For silicon nitride waveguide we include the SRS term in Eq (1) where γR = gRΓR(AeffΩR) and gR ΓR and ΩR represent the Raman gain coefficient the full width at half maximum of the gain spectrum and the Raman shift respectively The Raman shock time τshock_R is associated with γRrsquos fre-quency dependence which is 1ω0-[1Aeff(ω0)][dAeff(ω)dω] similarly as in [14] if we ignore frequency dependent gR ΓR and ΩR hR(t) is the Raman response function and it corresponds to the Raman gain spectrum

2

2 20 0

( ) -( - ) 2 ( - )

Ωω

Ω ω ω Γ ω ω=

+R

RR R

Hi

Note that the sign before the imaginary unit is differ-ent from that in [27] to be consistent with the expression of the Fourier transform that we used

We have considered supercontinuum generation in both silicon and silicon nitride waveguides with the slot-assisted dispersion tailoring Octave-spanning supercon-tinua in a silicon-based stripslot hybrid waveguide have been investigated in detail in [108] in which two-cycle optical pulses are obtained The main results in that work are shown in Figure 9 for comparison purposes

Here we mainly focus on the supercontinuum gen-erated in the silicon nitride stripslot hybrid waveguide (ie the slot WG 1 in Section III) whose dispersion and nonlinearity properties are shown in Figure 6 In the non-linear simulations we set the total propagation loss to be 1 dBcm The SRS parameters used here are the following [205] ΩR2π = 143 THz ΓR2π = 172 THz and gR = 1 times 10-12 mW τshock_R is calculated to be  = 156 fs

In our simulations we use a time step of 025 fs which is corresponding to a bandwidth of 4000 THz in the fre-quency domain For a femtosecond input pulse we set the time window length to 50 ps (ie frequency resolution Δf = 20 GHz)

We simulate the nonlinear propagation of a chirp-free hyperbolic secant pulse in the silicon nitride waveguide

258emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

The pulse center wavelength is at 1610 nm and its full width at half-maximum (FWHM) T0 is 120 fs Its peak power is 1200 W corresponding to pulse energy of 016 nJ

Figure 10(A) shows the supercontinua at different propagation distances At 48 mm the spectrum is greatly broadened at the -30 dB level covering a wavelength range from 0585 to 2833 microm which is more than two octaves The spectrum evolution in Figure 10(A) shows a similar spectrum shape as that in Figure 9(A) both featuring a ldquotriangularrdquo central spectrum bounded by two dispersive waves at the edges However it is important to note that the absence of TPA and 3PA in silicon nitride at the telecom window leads to a much more efficient spectrum broad-ening than that in silicon [108] The generated spectrum extends from the visible light to the mid-IR with excellent spectral coherence which is confirmed by the pulse wave-form shown in Figure 10(B) In the time domain the pulse is greatly compressed from 120 to 408 fs corresponding to 076 optical cycles at 161 microm wavelength

We examine the pulsewidth as a function of propa-gation distance Figure 11 shows that the pulse becomes increasingly narrower until the propagation distance reaches 47 mm For longer distances the pulsewidth

A

B

60 mm

48 mm

36 mm

24 mm

12 mm

Input

Spe

ctru

m (

10 d

Bd

iv)

Pow

er (

W)

12

246

24

18

12

6

0

248 250 252 254

14 16 18 20 22 24Wavelength (microm)

Time (ps)

Figure 9emsp(A) The supercontinuum generation in a silicon-based stripslot hybrid waveguide presented in [108] (B) The significant spectrum broadening at 425-mm distance is associated with a temporal compression of an input pulse (dash line) to the output waveform (solid line) with a FWHM of 12 fs

A

B

50 mm

48 mm

46 mm

44 mm

42 mm

Input

Spe

ctru

m (

10 d

Bd

iv)

Pow

er (

W)

8000

6000

4000

2000

0250249 251

06 09 12 15 18 21 24 27

Wavelength (microm)

Time (ps)

Figure 10emsp(A) Spectrum evolution of the pulse over propagation distance A supercontinuum of more than two octaves is achieved at 48 mm distance (B) Generated pulse waveform with a pulse width of 408 fs as short as 076 optical cycles Low pedestals are caused by dispersive waves generated at the two ends of the spectrum

remains almost constant However it is important to mention that after 48 mm the dispersive waves become increasingly stronger as shown in Figure 10(A) causing larger pedestals

Comparing the results in Figures 9 and 10 we note that the mid-IR wavelength range for silicon would be in analogy to the near-IR for silicon nitride in terms of non-linear optics operations Pumping at or beyond 33 microm one can use the waveguide designs shown in Figure 7 to produce very efficient nonlinear interactions without TPA and 3PA in silicon Ultrashort pulses in the mid-IR from parametric amplifiers [206 207] could be used to pump the Group IV waveguides

Another nonlinear application of the dispersion-engi-neered Group IV waveguides is micro-resonator-based Kerr frequency comb generation When such a waveguide is curved to form a microring resonator input CW light travels around the cavity and amplifies the noise in the source located at the frequencies with a high parametric gain As a result of modulation instability and cascaded FWM in the cavity a frequency comb can be generated [208ndash211] Mode-locked frequency combs have been reported pro-ducing low-noise pulse trains in time domain [212ndash214]

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp259

The formation of cavity solitons is identified as the main reason for the mode-locking in the Kerr frequency combs [215] This is instructive because one can thus predict the spectral bandwidth and temporal pulsewidth in the generated low-noise combs The 3-dB comb bandwidth is inversely proportional to the square root of the 2nd-order dispersion coefficient |β2| as given in [213 215] It is desira-ble that all comb lines that constitute the soliton spectrum experience the same |β2| In this sense the stripslot hybrid waveguides with flattened dispersion are preferably suit-able for supporting broadband Kerr comb generation and ultra-short cavity soliton generation

The Kerr frequency comb generation can be modeled using the generalized Lugiato-Lefever equation (LLE) [216ndash219]

20

2

( - )- - | |

2 2

m mm

R inmm

jkt j jl E kE j l E Et m

βαδ γ

τ

infin

=

part part+ + + = part part

sum (2)

where tR is the round-trip time E = E(tτ) and Ein are intra-cavity field and input field (pump power Pin  =  |Ein|2) t and τ are the slow and fast times δ0 is the cavity phase detuning defined as δ0  =  tRmiddot(ωn -ω0) where ω0 and ωn are the pumprsquos angular frequency and the nth angular reso-nance frequency that is pumped Other resonator param-eters include the power loss per round trip α the power coupling coefficient κ the nonlinear coefficient γ and the mth dispersion coefficient βm Since a flattened dispersion profile has a small β2 over a wide bandwidth it is impor-tant to take the influence of higher-order dispersion into account We include all-order dispersion terms in Eq (2) as we did in solving Eq (1)

To enhance the Kerr comb bandwidth in the near-IR we use the ultra-flattened dispersion profile in Figure 6(A) which is obtained in the slot WG 2 based on

Pul

se w

idth

(fs

)

14

12

10

8

6

4

242 44 46 48 50 52

Propagation distance (mm)

Figure 11emspPulse width first decreases with propagation distance and then remains stable After 48 mm dispersive waves get stronger causing more pedestals

Pow

er (

10 d

Bd

iv)

Pow

er (

W)

70A

B

60

50

40

30

20

10

-10

-20

600

400

200

0

80 120

0575 0600 0625 0650

160 200 240 280 320 360

0

Frequency (THz)

Time (ps)

Figure 12emsp(A) Frequency comb generation with a CW pump at 155 microm using a microring resonator based on a silicon stripslot hybrid waveguide Over an octave-spanning bandwidth from 135 to 270 THz the comb lines have a power drop of 20 dB (B) Generated pulse waveform with a pulse width of 82 fs as short as 16 optical cycles

silicon nitride The ring resonator has a bending radius of 104 microm corresponding to a FSR of 200 GHz Pumping near 155 microm with a pump power of 2 W the resonance peak is red-shifted and we need to red-shift the pump wavelength accordingly and tune it into the resonance from the short-wavelength side When the pump is step-by-step tuned by up to 63 resonance linewidths we obtain the comb spectrum and the mode-locked pulse waveform as shown in Figure 12 One can see that over an octave-spanning bandwidth from 133 to 268 THz the comb lines have a power drop by 20 dB from the center of the spectrum The spectral flatness of this comb is relatively good compared to the previously reported results [208ndash211] The comb bandwidth at -40 dB is as wide as two octaves There are two dispersive peaks in normal dispersion regions beyond the low-dispersion band Such a mode-locked broadband comb produces a train of sub-two-cycle optical pulses as shown in Figure 12(B) with one pulse per round trip The peak power of the pulse is up to 600 W Nonlinear conver-sion efficiency is estimated to be -267 dB

To generate frequency combs in the mid-IR the ger-manium-on-silicon strip waveguide is chosen We choose

260emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

a cross-section of 3200 times 1800 nm2 which has an octave-spanning low-dispersion band from 4 to 767 microm as shown in Figure 8(B) A germanium ring resonator is formed with a bending radius of 564 microm corresponding to a FSR of 200 GHz Pumping at 6 microm with a CW power of 14 W and detuning the pump wavelength by 10 resonance linewidth one can see that a mode-locked wideband mid-IR comb is generated from 358 to 644 THz (ie from 466 to 838 microm) at -40 dB level The FWHM of the produced pulses is 69 fs which corresponds to ~35 optical cycles The pulse peak power is 184 W and the nonlinear conversion efficiency is estimated to be -143 dB Since the pumping frequency is not at the center of the low-dispersion band we only see one peak in the comb spectrum caused by the dispersive wave in the normal dispersion region from Figure 13(A) There is another peak at higher frequencies beyond what is shown in the figure

As shown above broadband dispersion engineering is critical for octave-spanning nonlinear applications in both near- and mid-IR wavelength ranges which enables us to fully utilize the bandwidth allowed by the materials transparency windows Generally speaking the nonlinear applications mentioned here such as supercontinuum generation ultrafast pulse compression and frequency comb generation are often the intermediate steps towards higher-level system applications In the frequency domain a wide spectrum can serve as an electromagnetic carrier to acquire high-volume of information eg for sensing [220] and imaging [221] In the time domain an ultrashort pulse can be used as probe to sample ultrafast phenomena [222]

5 Summary and OutlookWe have presented a review of our recent work on nonlin-ear photonics based on silicon and germanium Various types of Group IV waveguides are analyzed and optimized for four different wavelength ranges from near- to mid-IR The recently proposed dispersion engineering technique based on stripslot hybrid waveguide structures is used for different material combinations and wavelength ranges Numerical simulations show that the dispersion-flattened Group IV waveguides are preferably suitable for octave-spanning nonlinear applications including on-chip supercontinuum generation ultrashort pulse compres-sion and mode-locked wideband frequency comb genera-tion based on micro-resonators

The presented approach to achieving octave-span-ning nonlinear applications on an integrated CMOS-compatible Group IV platform holds great potential for realizing chip-scale sensing imaging communications and signal processing system The ultrawide transparency windows in the mid-IR allowed by Group IV elements and compounds potentially together with other materi-als [223] provide an exciting arena for building powerful information acquisition and processing units enabled by nonlinear optics nano-photonics and ultrafast optics

Received June 14 2013 accepted October 29 2013 previously pub-lished online November 27 2013

Pow

er (

10 d

Bd

iv)

A

8030 40 50 60 70Frequency (THz)

Pow

er (

W)

B200

150

100

50

0

21 22 23 24 25Time (ps)

Figure 13emsp(A) Frequency comb generation with a CW pump at 6 microm using a microring resonator based on a germanium strip waveguide with air upper cladding (B) Generated pulse waveform with a pulse width of 69 fs as short as 35 optical cycles

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp261

Appendix

A Material index and dispersion

In this section we give the wavelength-dependent mate-rial index expressed as Sellmeier equations where wave-length λ is in μm

For silicon we use the following material index that is a fit curve from measurement results at room temperature (293 K) with 184 data points in total from 112 to 588 μm [154]

22 1 2 2

2 2 22

( )-

C Cn

λλ ε

λ λ λ= + +

where ε = 116858 C1 = 0939816 μm2 C2 = 000810461 and λ2 = 11071 μm

For silicon nitride the material index is affected by deposition conditions using plasma-enhanced chemical vapor deposition (PECVD) low-pressure chemical vapor deposition (LPCVD) and so on We use the following Sell-meier equation [155] which predicts the material index close to that in LPCVD silicon nitride films measured by a few groups [224]

22 1

2 21

( ) 1-

Cn

λλ

λ λ= +

where C1 = 28939 and λ1 = 013967 μmFor silicon dioxide we use the following Sellmeier

equation for fused silica [156]22 2

2 31 22 2 2 2 2 2

1 2 3

( ) 1- - -

CC Cn

λλ λλ

λ λ λ λ λ λ= + + +

where C1 = 06961663 C2 = 04079426 C3 = 08974794 λ1 = 00684043 μm λ2 = 01162414 μm and λ3 = 9896161 μm

For SRO the material index is affected by deposition conditions such as silicon excess annealing temperature and so on Here we choose the one with silicon excess of 8 and annealed at 1250oC [51]

22 22 31 2

2 2 2 2 2 21 2 3

( ) 1- - -

CC Cn

λλ λλ

λ λ λ λ λ λ= + + +

where C1 = 001 C2 = 196 C3 = 141 λ1 = 03 μm λ2 = 007071 μm and λ3 = 2775968 μm

For germanium the temperature-dependent mate-rial index was measured [157] Here we choose the one for room temperature (293 K)

2 22 1 2

2 2 2 21 2

( )- -

C Cn

λ λλ ε

λ λ λ λ= + +

where ε = 928156 C1 = 67288 C2 = 021307 λ1 = 0664116 μm and λ2 = 6221013 μm

For arsenic sulfide we use the material index pro-vided in [158]

2 2 22 22 3 4 51 2

2 2 2 2 2 2 2 2 2 21 2 3 4 5

( ) 1- - - - -

C C CC Cn

λ λ λλ λλ

λ λ λ λ λ λ λ λ λ λ= + + + + +

where C1 = 18983678 C2 = 19222979 C3 = 08765134 C4 = 01188704 C5 = 09569903 λ1 = 015 μm λ2 = 025 μm λ3 = 035 μm λ4 = 045 μm and λ5 = 27386128 μm

For arsenic selenide we fit ellipsometry measure-ments of our arsenic selenide thin films and the bulk material is provided by Prof Kathleen A Richardson group

22 22 31 2

2 2 2 2 2 21 2 3

( ) 1- - -

CC Cn

λλ λλ

λ λ λ λ λ λ= + + +

where C1 = 298463 C2 = 321011 C3 = 100182 λ1 = 044118 μm λ2 = 0000354953 μm and λ3 = 38413 μm

B Nonlinear Kerr index n2

The third-order nonlinear susceptibility χ(3)1111 for silicon and

germanium is predicted over the mid-IR range [133] based on a two-band model The effective nonlinear susceptibil-ity χ(3) is dependent on polarization and crystallographic orientation [225] For strong nonlinearity we consider a single-polarization incident light aligned to the crystal-lographic axis and we have χ(3) = χ(3)

1111 To investigate the octave-spanning nonlinear phenomena one need to take the wavelength-dependent nonlinear Kerr index n2 and TPA coefficient βTPA into account which are expressed as

( 3 )2 2

0

( 3 )2

0

3( ) ( )4 ( )

3( ) ( )( )

re

TPA im

ncn

cn

λ χ λε λ

πβ λ χ λ

λε λ

=

=

where ε0 and c are the vacuum permittivity and the speed of light in vacuum Using the material index given in Appendix A and χ(3) value from [133] we obtain the n2 and βTPA values tabulated as follows

262emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

Table 1enspNonlinear Kerr index n2 in silicon

λμm

  n2

10-18 m2W  λ

μm  n2

10-18 m2W  λ

μm  n2

10-18 m2W

130   234   310   389   490   312135   305   315   384   495   311140   378   320   379   500   310145   443   325   375   505   309150   501   330   371   510   307155   559   335   368   515   306160   618   340   365   520   304165   671   345   362   525   304170   710   350   360   530   303175   741   355   358   535   302180   766   360   355   540   302185   781   365   352   545   301190   783   370   350   550   300195   778   375   346   555   298200   762   380   343   560   297205   732   385   341   565   296210   699   390   338   570   296215   658   395   336   575   295220   612   400   334   580   295225   576   405   332   585   295230   547   410   331   590   294235   525   415   330   595   293240   508   420   329   600   292245   493   425   328   605   291250   479   430   327   610   290255   467   435   325   615   289260   456   440   324   620   288265   448   445   321   625   288270   440   450   319   630   288275   432   455   317   635   288280   424   460   315   640   288285   417   465   314   645   288290   410   470   313   650   288295   404   475   313   655   288300   398   480   312   660   288305   394   485   312    

Table 2enspTPA coefficient βTPA in silicon

λμm

  βTPA

10-12 mW  λ

μm  βTPA

10-12 mW  λ

μm  βTPA

10-12 mW

130   1334   165   812   200   180135   1284   170   713   205   115140   1222   175   613   210   064145   1154   180   522   215   024150   1079   185   424   220   0003155   995   190   333    160   905   195   254    

Table 3enspNonlinear Kerr index n2 in germanium

λμm

  n2

10-18 m2W  λ

μm  n2

10-18 m2W  λ

μm  n2

10-18 m2W

23  3932  63  1986  103  170524  4994  64  1972  104  169925  6007  65  1959  105  169426  6650  66  1946  106  169027  6772  67  1934  107  168728  6273  68  1923  108  168429  4897  69  1913  109  168230  4403  70  1904  110  168131  3970  71  1895  111  167932  3680  72  1886  112  167733  3470  73  1876  113  167534  3286  74  1868  114  167335  3128  75  1859  115  167036  2998  76  1850  116  166737  2895  77  1841  117  166338  2812  78  1833  118  165939  2737  79  1826  119  165640  2668  80  1819  120  165341  2605  81  1812  121  165142  2550  82  1807  122  164843  2498  83  1801  123  164644  2450  84  1797  124  164445  2406  85  1792  125  164346  2365  86  1787  126  164147  2328  87  1782  127  163948  2295  88  1777  128  163649  2266  89  1772  129  163450  2238  90  1767  130  163251  2212  91  1762  131  163052  2187  92  1758  132  162853  2164  93  1753  133  162654  2141  94  1749  134  162555  2121  95  1744  135  162356  2101  96  1740  136  162157  2083  97  1736  137  162058  2066  98  1731  138  161859  2049  99  1727  139  161760  2032  100  1722  140  161661  2016  101  1716   62  2001  102  1711   

Table 4enspTPA coefficient βTPA in germanium

λμm

  βTPA

10-8 mW  λμm

  βTPA

10-8 mW  λ

μm  βTPA

10-8 mW

23   130   25   088   27   03124   111   26   060   28   006

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp263

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[137] Chavez Boggio JM Windmiller JR Knutzen M Jiang R Bres C Alic N Stossel B Rottwitt K Radic S 730-nm optical parametric conversion from near- to short-wave infrared band Opt Express 2008165435ndash43

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[140] Liu X Osgood RM Vlasov YA Green WMJ Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides Nat Photonics 20104557ndash60

[141] Zlatanovic S Park JS Moro S Boggio JMC Divliansky IB Alic N Mookherjea S Radic S Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source Nat Photonics 20104561ndash4

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[144] Roelkens G Green WMJ Kuyken B Liu X Hattasan N Gassenq A Cerutti L Rodriguez JB Osgood RM Tournie E Baets R III-Vsilicon photonics for short-wave infrared spectroscopy IEEE J Quant Electron 201248292ndash8

[145] Alloatti L Korn D Weimann C Koos C Freude W Leuthold J Second-order nonlinear silicon-organic hybrid waveguides Opt Express 20122020506ndash15

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[147] Carlie N Musgraves JD Zdyrko B Luzinov I Hu J Singh V Agarwal A Kimerling LC Canciamilla A Morichetti F Melloni A Richardson K Integrated chalcogenide waveguide resonators for mid-IR sensing leveraging material properties to meet fabrication challenges Opt Express 20101826728ndash43

[148] Eggleton BJ B Luther-Davies Richardson K Chalcogenide photonics Nat Photonics 20115141ndash8

[149] Madden SJ Vu KT High-Performance Integrated Optics with Tellurite Glasses Status and Prospects Int J Appl Glass Sci 20123289ndash98

[150] Bindra KS Bookey HT Kar AK Wherrett BS Liu X Jha A Nonlinear optical properties of chalcogenide glasses observation of multiphoton absorption App Phys Lett 2001791939ndash41

[151] Zakery A Ruan Y ARode V Samoc M Luther-Davies B Low-loss waveguides in ultrafast laser-deposited As2S3 chalcogenide films J Opt Soc Am B 200391844ndash52

[152] Lenz G Zimmermann J Katsufuji T MLines E Hwang HY Spalter S Slusher RE Cheong SW Sanghera JS Aggarwal ID Large Kerr effect in bulk Se-based chalcogenide glasses Opt Lett 200025254ndash6

[153] Sanghera JS Shaw LB Aggarwal ID Application of chalcogenide glass optical fibers CR Chimie 20025873ndash83

[154] Palik ED Handbook of optical constants of solids San Diego CA Academic 1998

[155] Philipp HR Optical properties of silicon nitride J Electrochem Soc 1973120295ndash300

[156] Malitson IH Interspecimen comparison of the refractive index of fused silica J Opt Soc Am 1965551205ndash8

[157] Barnes NP Piltch MS Temperature-dependent Sellmeier coefficients and nonlinear optics average power limit for germanium J Opt Soc Am 197969178ndash80

[158] Rodney WS Malitson IH King TA Refractive index of arsenic trisulfide J Opt Soc Am 195848633ndash636

[159] Ellipsometry measurement on the thin film samples by our group[160] Bristow AD Rotenberg N van Driel HM Two-photon

absorption and Kerr coefficients of silicon for 850ndash2200 nm Appl Phys Lett 200790191104

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp267

[161] Lin Q Zhang J Piredda G Boyd RW Fauchet PM Agrawal GP Dispersion of silicon nonlinearities in the near infrared region Appl Phys Lett 200791021111

[162] Mizrahi V DeLong KW Stegeman GI Saifi MA Andrejco MJ Two-photon absorption as a limitation to all-optical switching Opt Lett 1989141140ndash2

[163] Guider R NDaldosso APitanti EJordana Fedeli J-M Pavesi L NanoSi low loss horizontal slot waveguides coupled to high Q ring resonators Opt Express 20091720762ndash70 and its erratum

[164] Ferrera M Razzari L Duchesne D Morandotti R Yang Z Liscidini M Sipe JE Chu S Little BE Moss DJ Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures Nat Photonics 20082 737ndash40

[165] Smektala F Quemard C Leneindre L Lucas J Barthelemy A De Angelis C Chalcogenide glasses with large non-linear refractive indices J Non-Crystalline Solids 1998239139ndash42

[166] Boudebs G Sanchez F Troles J Smektala F Nonlinear optical properties of chalcogenide glasses- comparison between Mach-Zehnder interferometry and Z-scan techniques Opt Comm 2001199425ndash33

[167] Asobe M Suzuki K Kanamori T Kubodera K Nonlinear refractive index measurement in chalcogenide-glass fibers by self-phase modulation APL 1992601153ndash4

[168] Asobe M Kanamori T Kubodera K Ultrafast all-optical switching using highly nonlinear chalcogenide glass fiber IEEE Photon Technol Lett 19924362ndash5

[169] Asobe M Kanamori T Kubodera K Applications of highly nonlinear chalcogenide glass fibers in ultrafast all-optical switches IEEE J Quant Electron 1993292325ndash33

[170] Ruan Y Luther-Davies B Li W Rode A Kolev V Madden S Large phase shifts in As2S3 waveguides for all-optical processing devices Opt Lett 2005302605ndash7

[171] Laniel JM Hocirc N Valleacutee R Villeneuve A Nonlinear-refractive-index measurement in As2S3 channel waveguides by asymmetric self-phase modulation J Opt Soc Am B 200522437ndash45

[172] Cerqua-Richardson KA McKinley JM Lawrence B Joshi S Villeneuve A Comparison of nonlinear optical properties of sulfide glasses in bulk and thin film form Opt Mater 199810155ndash9

[173] Harbold JM Ilday FOuml Wise FW Sanghera JS Nguyen VQ Shaw LB Aggarwal ID Highly nonlinear As-S-Se glasses for all-optical switching Opt Lett 200227119ndash121

[174] Ruan YL Li WT Jarvis R Madsen N Rode A Luther-Davies B Fabrication and characterization of low loss rib chalcogenide waveguides made by dry etching Opt Express 2004125140ndash5

[175] Slusher RE Lenz G Hodelin J Sanghera J Shaw LB Aggarwal ID Large Raman gain and nonlinear phase shifts in high-purity As2Se3 chalcogenide fibers J Opt Soc Am B 2004211146ndash55

[176] Jacobsen R Andersen K Borel P Fage-Pedersen J Frandsen L Hansen O Kristensen M Lavrinenko A Moulin G Ou H Peucheret C Zsigri B Bjarklev A Strained silicon as a new electro-optic material Nature 2006441199ndash202

[177] Cazzanelli M Bianco F Borga E Pucker G Ghulinyan M Degoli E Luppi E Veacuteniard V Ossicini S Modotto D Wabnitz S Pierobon R Pavesi L Second-harmonic generation in

silicon waveguides strained by silicon nitride Nat Mater 201111148ndash54

[178] Avrutsky I Soref R Phase-matched sum frequency generation in strained silicon waveguides using their second-order nonlinear optical susceptibility Opt Express 20111921707ndash16

[179] Ghahramani E Moss DJ Sipe JE Second-harmonic generation in odd-period strained (Si)n(Ge)nSi superlattices and at SiGe interfaces Phys Rev Lett 1990642815ndash8

[180] Levy JS Foster MA Gaeta AL Lipson M Harmonic generation in silicon nitride ring resonators Opt Express 20111911415

[181] Zakery A Elliott SR Optical nonlinearities in chalcogenide glasses and their applications Springer Series in Optical Sciences 2007135

[182] Lee KK Lim DR Kimerling LC Shin J Cerrina F Fabrication of ultralow-loss SiSiO2 waveguides by roughness reduction Opt Lett 2001261888ndash90

[183] Cardenas J Poitras CB Robinson JT Preston K Chen L Lipson M Low loss etchless silicon photonic waveguides Opt Express 2009174752ndash7

[184] Biberman A Shaw MJ Timurdogan E Wright JB Watts MR Ultralow-loss silicon ring resonators Opt Lett 2012374236ndash8

[185] Walmsley IA Waxer L Dorrer C The role of dispersion in ultrafast optics Rev Sci Instrum 2001721ndash29

[186] Torres JP MHendrych Valencia A Angular dispersion an enabling tool in nonlinear and quantum optics Adv Opt Photon 20102319ndash69

[187] Yin LH Lin Q Agrawal GP Dispersion tailoring and soliton propagation in silicon waveguides Opt Lett 2006311295ndash7

[188] Dulkeith E Xia FN Schares L Green WMJ Vlasov YA Group index and group velocity dispersion in silicon-on-insulator photonic wires Opt Express 2006143853ndash63

[189] Turner AC Manolatou C Schmidt BS Lipson M Tailored anomalous group-velocity dispersion in silicon channel waveguides Opt Express 2006144357ndash62

[190] Dadap JI Panoiu NC Chen X I-Hsieh W Liu X Chou C-Y Dulkeith E McNab SJ Xia F Green WMJ Sekaric L Vlasov YA Osgood RM Jr Nonlinear-optical phase modification in dispersion-engineered Si photonic wires Opt Express 2008161280ndash99

[191] Milosevic MM Matavulj PS Yang PY Bagolini A Mashanovich GZ Rib waveguides for mid-infrared silicon photonics J Opt Soc Am B 2009261760ndash6

[192] Mashanovich GZ Milošević MM Nedeljkovic M Owens N Xiong B Teo EJ Hu Y Low loss silicon waveguides for the mid-infrared Opt Express 2011197112ndash9

[193] Reimer C Nedeljkovic M Stothard DJM Esnault MOS Reardon C OrsquoFaolain L Dunn M Mashanovich GZ Krauss TF Mid-infrared photonic crystal waveguides in silicon Opt Express 20122029361ndash8

[194] Baehr-Jones T Spott A Ilic R Spott A Penkov B Asher W Hochberg M Silicon-on-sapphire integrated waveguides for the midinfrared Opt Express 20101812127ndash35

[195] Li F Jackson S Grillet C Magi E Hudson D Madden SJ Moghe Y OrsquoBrien C Read A Duvall SG Atanackovic P Eggleton BJ Moss D Low propagation loss silicon-on-sapphire waveguides for the midinfrared Opt Express 20111915212ndash20

268emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

[196] Yue Y Zhang L Huang H Beausoleil RG Willner AE Silicon-on-nitride waveguide with ultralow dispersion over an octave-spanning mid-infared wavelength range IEEE Photonics J 20124126ndash32

[197] Khan S Chiles J Ma J Fathpour S Silicon-on-nitride waveguides for mid-and near-infrared integrated photonics Appl Phys Lett 2013102121104

[198] Cheng Z Chen X Wong CY Xu K Tsang HK Mid-infrared suspended membrane waveguide and ring resonator on silicon-on-insulator IEEE Photonics J 201241510ndash9

[199] Lin P-T Singh V Cai Y Kimerling LC Agarwal A Air-clad silicon pedestal structures for broadband mid-infrared microphotonics Opt Lett 2013381031ndash3

[200] Chang YC Paeder V Hvozdara L Hartmann JM Herzig HP Low-loss germanium strip waveguides on silicon for the mid-infrared Opt Lett 2012372883ndash5

[201] Zhang L Yue Y Y Xiao-Li R G Beausoleil Willner AE Highly dispersive slot waveguides Opt Express 2009177095ndash101

[202] Zhang L Yue Y Beausoleil RG Willner AE Analysis and engineering of chromatic dispersion in silicon waveguide bends and ring resonators Opt Express 2011198102ndash7

[203] Zhang L Mu J Singh V Agarwal A Kimerling LC Michel J Intra-cavity dispersion of microresonators and its engineering for octave-spanning Kerr frequency comb generation to be published

[204] Lin Q Zhang L Generalized nonlinear envelope equation with high-order dispersion of nonlinearity to be published

[205] Wang Y Yue R Han H Liao X Raman study of structural order of a-SiNxH and its change upon thermal annealing J Non-Crystalline Solids 2001291107ndash12

[206] Brida D Marangoni M Manzoni C De Silvestri S Cerullo G Two-optical-cycle pulses in the mid-infrared from an optical parametric amplifier Opt Lett 2008332901ndash3

[207] Brida D Manzoni C Cirmi G Marangoni M Bonora S Villoresi P De Silvestri S Cerullo G Few-optical-cycle pulses tunable from the visible to the mid-infrared by optical parametric amplifiers J Opt 201012013001

[208] Kippenberg TJ Holzwarth R Diddams SA Microresonator-based optical frequency combs Science 2011332555ndash9

[209] Levy JS Gondarenko A Foster MA Turner-Foster AC Gaeta AL Lipson M CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects Nat Photonics 2009437ndash40

[210] DelrsquoHaye P Herr T Gavartin E Gorodetsky ML Holzwarth R Kippenberg TJ Octave spanningtunable frequency comb from a microresonator Phys Rev Lett 2011107063901

[211] Okawachi Y Saha K Levy JS Wen YH Lipson M Gaeta AL Octave-spanning frequency combgeneration in a silicon nitride chip Opt Lett 2011363398ndash400

[212] Matsko AB Savchenkov AA Liang W Ilchenko VS Seidel D Maleki L Mode-locked Kerr frequency combs Opt Lett 2011362845ndash7

[213] Herr T Brasch V Jost JD Wang CY Kondratiev NM Gorodetsky ML Kippenberg TJ Temporal solitons in optical microresonators httparxivorgabs12110733

[214] Saha K Okawachi Y Shim B Levy JS Salem R Johnson AR Foster MA Lamont MR Lipson M Gaeta AL Modelocking and femtosecond pulse generation in chip-based frequency combs Opt Express 2013211335ndash43

[215] Coen S Erkintalo M Universal scaling laws of Kerr frequency combs Opt Lett 2013381790ndash2

[216] Lugiato LA Lefever R Spatial dissipative structures in passive optical-systems Phys Rev Lett 1987582209ndash11

[217] Haelterman M Trillo S Wabnitz S Dissipative modulation instability in a nonlinear dispersive ring cavity Opt Commun 199291401ndash7

[218] Coen S Randle HG Sylvestre T Erkintalo M Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato-Lefever model Opt Lett 20133837ndash9

[219] Chembo YK Menyuk CR Spatiotemporal Lugiato-Lefever formalism for Kerr-comb generation in whispering-gallery-mode resonators Phys Rev A 201387053852

[220] Foltynowicz A Mas1owski P Ban T Adler F Cossel KC Briles TC Ye J Optical frequency comb spectroscopy Faraday Discussion 201115023ndash31

[221] Hartl I Li XD Chudoba C Ghanta RK Ko TH Fujimoto JG Ranka JK Windeler RS Ultrahigh-resolution optical coherence tomography using continuum generation in an air silica microstructure optical fiber Opt Lett 200126608ndash10

[222] Brabec T Krausz F Intense few-cycle laser fields Frontiers of nonlinear optics Rev Mod Phys 200072545ndash91

[223] Hu J Meyer J Richardson K Shah L Feature issue introduction mid-IR photonic materials Opt Mater Express 201331571ndash5

[224] Private communications with Dr Jacob Levy in Prof Lipsonrsquos group and Dr Johann Riemensberger in Prof Kippenbergrsquos group

[225] Zhang J Lin Q Piredda G Boyd RW Agrawal GP Fauchet PM Anisotropic nonlinear response of silicon in the near-infrared region Appl Phys Lett 200791071113

Page 11: Lin Zhang*, Anuradha M. Agarwal, Lionel C. Kimerling and ...

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp257

Besides photonic waveguides another important cat-egory of nonlinear devices is integrated resonators In the scope of this paper we consider relatively large resona-tors for frequency comb generation in which the bending radius of a ring resonator is varied from 50 microm to 100 microm depending on free spectral range (FSR) and the group index in the waveguide In these cases the waveguide-bending-induced dispersion is small and we would not discuss intra-cavity dispersion [202 203] in details here

4 ApplicationsBenefiting from the unique dispersion engineering over an octave-spanning bandwidth as described above one can develop ultra-wideband nonlinear applications that could hardly be attained in an integrated platform previously These include octave-spanning supercontinuum genera-tion pulse compression to a few-cycle or even sub-cycle level octave-spanning Kerr frequency comb generation and the associated mode-locked ultrashort pulse genera-tion using microresonators In this section we review our recent work on these topics

First we discuss the supercontinuum generation and pulse compression in a straight waveguide The nonlinear envelope equation used here to simulate supercontinuum generation is the following

βα infin

=

part part+ + = + part part sum

2

( - )( ) ( )

2

m mm

mm

ii A K A R A

z m t (1)

where

2

0 0

- -( ) 1- ( ) 2

n nn

nn

i i iK A A An t tγ δ δ

ω δ δ

infin

=

= sum

and

2shock_R( ) - 1- [ ( - ) | | ]δ

γ τδ minusinfin

= prime prime int

t

R RR A i i A h t t A dtt

We denote A  =  A(zt) as the complex amplitude of an optical pulse Note that its Fourier transform is

-

1( ) ( ) exp( - ) 2

A z A z t i t dtω ωπ

infin

infin

= int

In Eq (1) α is the total propagation loss and βm is the mth-order dispersion coefficient The frequency dependence of nonlinearity parameters including the nonlinear index n2 the TPA coefficient βTPA and the

effective mode area Aeff is included in the nth-order dis-persion coefficient γn of nonlinearity which is defined as γn = ω0middotpartn[γ(ω)ω]partωn where ω0 is the angular frequency of the carrier Therefore we can consider all-order linear dispersion terms and all-order dispersion of the nonlin-ear coefficient in Eq (1) Specifically in the simulations for a silicon and silicon nitride waveguides we have all-order linear dispersion and up to 6th-order and 2nd-order of the nonlinear coefficient dispersion included A detailed derivation of Eq (1) is given in [204] For the quasi-TM mode that experiences the engineered dispersion due to the mode transition SRS in silicon waveguides fabricated on the (001) surface can be ignored [27 96] For silicon nitride waveguide we include the SRS term in Eq (1) where γR = gRΓR(AeffΩR) and gR ΓR and ΩR represent the Raman gain coefficient the full width at half maximum of the gain spectrum and the Raman shift respectively The Raman shock time τshock_R is associated with γRrsquos fre-quency dependence which is 1ω0-[1Aeff(ω0)][dAeff(ω)dω] similarly as in [14] if we ignore frequency dependent gR ΓR and ΩR hR(t) is the Raman response function and it corresponds to the Raman gain spectrum

2

2 20 0

( ) -( - ) 2 ( - )

Ωω

Ω ω ω Γ ω ω=

+R

RR R

Hi

Note that the sign before the imaginary unit is differ-ent from that in [27] to be consistent with the expression of the Fourier transform that we used

We have considered supercontinuum generation in both silicon and silicon nitride waveguides with the slot-assisted dispersion tailoring Octave-spanning supercon-tinua in a silicon-based stripslot hybrid waveguide have been investigated in detail in [108] in which two-cycle optical pulses are obtained The main results in that work are shown in Figure 9 for comparison purposes

Here we mainly focus on the supercontinuum gen-erated in the silicon nitride stripslot hybrid waveguide (ie the slot WG 1 in Section III) whose dispersion and nonlinearity properties are shown in Figure 6 In the non-linear simulations we set the total propagation loss to be 1 dBcm The SRS parameters used here are the following [205] ΩR2π = 143 THz ΓR2π = 172 THz and gR = 1 times 10-12 mW τshock_R is calculated to be  = 156 fs

In our simulations we use a time step of 025 fs which is corresponding to a bandwidth of 4000 THz in the fre-quency domain For a femtosecond input pulse we set the time window length to 50 ps (ie frequency resolution Δf = 20 GHz)

We simulate the nonlinear propagation of a chirp-free hyperbolic secant pulse in the silicon nitride waveguide

258emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

The pulse center wavelength is at 1610 nm and its full width at half-maximum (FWHM) T0 is 120 fs Its peak power is 1200 W corresponding to pulse energy of 016 nJ

Figure 10(A) shows the supercontinua at different propagation distances At 48 mm the spectrum is greatly broadened at the -30 dB level covering a wavelength range from 0585 to 2833 microm which is more than two octaves The spectrum evolution in Figure 10(A) shows a similar spectrum shape as that in Figure 9(A) both featuring a ldquotriangularrdquo central spectrum bounded by two dispersive waves at the edges However it is important to note that the absence of TPA and 3PA in silicon nitride at the telecom window leads to a much more efficient spectrum broad-ening than that in silicon [108] The generated spectrum extends from the visible light to the mid-IR with excellent spectral coherence which is confirmed by the pulse wave-form shown in Figure 10(B) In the time domain the pulse is greatly compressed from 120 to 408 fs corresponding to 076 optical cycles at 161 microm wavelength

We examine the pulsewidth as a function of propa-gation distance Figure 11 shows that the pulse becomes increasingly narrower until the propagation distance reaches 47 mm For longer distances the pulsewidth

A

B

60 mm

48 mm

36 mm

24 mm

12 mm

Input

Spe

ctru

m (

10 d

Bd

iv)

Pow

er (

W)

12

246

24

18

12

6

0

248 250 252 254

14 16 18 20 22 24Wavelength (microm)

Time (ps)

Figure 9emsp(A) The supercontinuum generation in a silicon-based stripslot hybrid waveguide presented in [108] (B) The significant spectrum broadening at 425-mm distance is associated with a temporal compression of an input pulse (dash line) to the output waveform (solid line) with a FWHM of 12 fs

A

B

50 mm

48 mm

46 mm

44 mm

42 mm

Input

Spe

ctru

m (

10 d

Bd

iv)

Pow

er (

W)

8000

6000

4000

2000

0250249 251

06 09 12 15 18 21 24 27

Wavelength (microm)

Time (ps)

Figure 10emsp(A) Spectrum evolution of the pulse over propagation distance A supercontinuum of more than two octaves is achieved at 48 mm distance (B) Generated pulse waveform with a pulse width of 408 fs as short as 076 optical cycles Low pedestals are caused by dispersive waves generated at the two ends of the spectrum

remains almost constant However it is important to mention that after 48 mm the dispersive waves become increasingly stronger as shown in Figure 10(A) causing larger pedestals

Comparing the results in Figures 9 and 10 we note that the mid-IR wavelength range for silicon would be in analogy to the near-IR for silicon nitride in terms of non-linear optics operations Pumping at or beyond 33 microm one can use the waveguide designs shown in Figure 7 to produce very efficient nonlinear interactions without TPA and 3PA in silicon Ultrashort pulses in the mid-IR from parametric amplifiers [206 207] could be used to pump the Group IV waveguides

Another nonlinear application of the dispersion-engi-neered Group IV waveguides is micro-resonator-based Kerr frequency comb generation When such a waveguide is curved to form a microring resonator input CW light travels around the cavity and amplifies the noise in the source located at the frequencies with a high parametric gain As a result of modulation instability and cascaded FWM in the cavity a frequency comb can be generated [208ndash211] Mode-locked frequency combs have been reported pro-ducing low-noise pulse trains in time domain [212ndash214]

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp259

The formation of cavity solitons is identified as the main reason for the mode-locking in the Kerr frequency combs [215] This is instructive because one can thus predict the spectral bandwidth and temporal pulsewidth in the generated low-noise combs The 3-dB comb bandwidth is inversely proportional to the square root of the 2nd-order dispersion coefficient |β2| as given in [213 215] It is desira-ble that all comb lines that constitute the soliton spectrum experience the same |β2| In this sense the stripslot hybrid waveguides with flattened dispersion are preferably suit-able for supporting broadband Kerr comb generation and ultra-short cavity soliton generation

The Kerr frequency comb generation can be modeled using the generalized Lugiato-Lefever equation (LLE) [216ndash219]

20

2

( - )- - | |

2 2

m mm

R inmm

jkt j jl E kE j l E Et m

βαδ γ

τ

infin

=

part part+ + + = part part

sum (2)

where tR is the round-trip time E = E(tτ) and Ein are intra-cavity field and input field (pump power Pin  =  |Ein|2) t and τ are the slow and fast times δ0 is the cavity phase detuning defined as δ0  =  tRmiddot(ωn -ω0) where ω0 and ωn are the pumprsquos angular frequency and the nth angular reso-nance frequency that is pumped Other resonator param-eters include the power loss per round trip α the power coupling coefficient κ the nonlinear coefficient γ and the mth dispersion coefficient βm Since a flattened dispersion profile has a small β2 over a wide bandwidth it is impor-tant to take the influence of higher-order dispersion into account We include all-order dispersion terms in Eq (2) as we did in solving Eq (1)

To enhance the Kerr comb bandwidth in the near-IR we use the ultra-flattened dispersion profile in Figure 6(A) which is obtained in the slot WG 2 based on

Pul

se w

idth

(fs

)

14

12

10

8

6

4

242 44 46 48 50 52

Propagation distance (mm)

Figure 11emspPulse width first decreases with propagation distance and then remains stable After 48 mm dispersive waves get stronger causing more pedestals

Pow

er (

10 d

Bd

iv)

Pow

er (

W)

70A

B

60

50

40

30

20

10

-10

-20

600

400

200

0

80 120

0575 0600 0625 0650

160 200 240 280 320 360

0

Frequency (THz)

Time (ps)

Figure 12emsp(A) Frequency comb generation with a CW pump at 155 microm using a microring resonator based on a silicon stripslot hybrid waveguide Over an octave-spanning bandwidth from 135 to 270 THz the comb lines have a power drop of 20 dB (B) Generated pulse waveform with a pulse width of 82 fs as short as 16 optical cycles

silicon nitride The ring resonator has a bending radius of 104 microm corresponding to a FSR of 200 GHz Pumping near 155 microm with a pump power of 2 W the resonance peak is red-shifted and we need to red-shift the pump wavelength accordingly and tune it into the resonance from the short-wavelength side When the pump is step-by-step tuned by up to 63 resonance linewidths we obtain the comb spectrum and the mode-locked pulse waveform as shown in Figure 12 One can see that over an octave-spanning bandwidth from 133 to 268 THz the comb lines have a power drop by 20 dB from the center of the spectrum The spectral flatness of this comb is relatively good compared to the previously reported results [208ndash211] The comb bandwidth at -40 dB is as wide as two octaves There are two dispersive peaks in normal dispersion regions beyond the low-dispersion band Such a mode-locked broadband comb produces a train of sub-two-cycle optical pulses as shown in Figure 12(B) with one pulse per round trip The peak power of the pulse is up to 600 W Nonlinear conver-sion efficiency is estimated to be -267 dB

To generate frequency combs in the mid-IR the ger-manium-on-silicon strip waveguide is chosen We choose

260emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

a cross-section of 3200 times 1800 nm2 which has an octave-spanning low-dispersion band from 4 to 767 microm as shown in Figure 8(B) A germanium ring resonator is formed with a bending radius of 564 microm corresponding to a FSR of 200 GHz Pumping at 6 microm with a CW power of 14 W and detuning the pump wavelength by 10 resonance linewidth one can see that a mode-locked wideband mid-IR comb is generated from 358 to 644 THz (ie from 466 to 838 microm) at -40 dB level The FWHM of the produced pulses is 69 fs which corresponds to ~35 optical cycles The pulse peak power is 184 W and the nonlinear conversion efficiency is estimated to be -143 dB Since the pumping frequency is not at the center of the low-dispersion band we only see one peak in the comb spectrum caused by the dispersive wave in the normal dispersion region from Figure 13(A) There is another peak at higher frequencies beyond what is shown in the figure

As shown above broadband dispersion engineering is critical for octave-spanning nonlinear applications in both near- and mid-IR wavelength ranges which enables us to fully utilize the bandwidth allowed by the materials transparency windows Generally speaking the nonlinear applications mentioned here such as supercontinuum generation ultrafast pulse compression and frequency comb generation are often the intermediate steps towards higher-level system applications In the frequency domain a wide spectrum can serve as an electromagnetic carrier to acquire high-volume of information eg for sensing [220] and imaging [221] In the time domain an ultrashort pulse can be used as probe to sample ultrafast phenomena [222]

5 Summary and OutlookWe have presented a review of our recent work on nonlin-ear photonics based on silicon and germanium Various types of Group IV waveguides are analyzed and optimized for four different wavelength ranges from near- to mid-IR The recently proposed dispersion engineering technique based on stripslot hybrid waveguide structures is used for different material combinations and wavelength ranges Numerical simulations show that the dispersion-flattened Group IV waveguides are preferably suitable for octave-spanning nonlinear applications including on-chip supercontinuum generation ultrashort pulse compres-sion and mode-locked wideband frequency comb genera-tion based on micro-resonators

The presented approach to achieving octave-span-ning nonlinear applications on an integrated CMOS-compatible Group IV platform holds great potential for realizing chip-scale sensing imaging communications and signal processing system The ultrawide transparency windows in the mid-IR allowed by Group IV elements and compounds potentially together with other materi-als [223] provide an exciting arena for building powerful information acquisition and processing units enabled by nonlinear optics nano-photonics and ultrafast optics

Received June 14 2013 accepted October 29 2013 previously pub-lished online November 27 2013

Pow

er (

10 d

Bd

iv)

A

8030 40 50 60 70Frequency (THz)

Pow

er (

W)

B200

150

100

50

0

21 22 23 24 25Time (ps)

Figure 13emsp(A) Frequency comb generation with a CW pump at 6 microm using a microring resonator based on a germanium strip waveguide with air upper cladding (B) Generated pulse waveform with a pulse width of 69 fs as short as 35 optical cycles

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp261

Appendix

A Material index and dispersion

In this section we give the wavelength-dependent mate-rial index expressed as Sellmeier equations where wave-length λ is in μm

For silicon we use the following material index that is a fit curve from measurement results at room temperature (293 K) with 184 data points in total from 112 to 588 μm [154]

22 1 2 2

2 2 22

( )-

C Cn

λλ ε

λ λ λ= + +

where ε = 116858 C1 = 0939816 μm2 C2 = 000810461 and λ2 = 11071 μm

For silicon nitride the material index is affected by deposition conditions using plasma-enhanced chemical vapor deposition (PECVD) low-pressure chemical vapor deposition (LPCVD) and so on We use the following Sell-meier equation [155] which predicts the material index close to that in LPCVD silicon nitride films measured by a few groups [224]

22 1

2 21

( ) 1-

Cn

λλ

λ λ= +

where C1 = 28939 and λ1 = 013967 μmFor silicon dioxide we use the following Sellmeier

equation for fused silica [156]22 2

2 31 22 2 2 2 2 2

1 2 3

( ) 1- - -

CC Cn

λλ λλ

λ λ λ λ λ λ= + + +

where C1 = 06961663 C2 = 04079426 C3 = 08974794 λ1 = 00684043 μm λ2 = 01162414 μm and λ3 = 9896161 μm

For SRO the material index is affected by deposition conditions such as silicon excess annealing temperature and so on Here we choose the one with silicon excess of 8 and annealed at 1250oC [51]

22 22 31 2

2 2 2 2 2 21 2 3

( ) 1- - -

CC Cn

λλ λλ

λ λ λ λ λ λ= + + +

where C1 = 001 C2 = 196 C3 = 141 λ1 = 03 μm λ2 = 007071 μm and λ3 = 2775968 μm

For germanium the temperature-dependent mate-rial index was measured [157] Here we choose the one for room temperature (293 K)

2 22 1 2

2 2 2 21 2

( )- -

C Cn

λ λλ ε

λ λ λ λ= + +

where ε = 928156 C1 = 67288 C2 = 021307 λ1 = 0664116 μm and λ2 = 6221013 μm

For arsenic sulfide we use the material index pro-vided in [158]

2 2 22 22 3 4 51 2

2 2 2 2 2 2 2 2 2 21 2 3 4 5

( ) 1- - - - -

C C CC Cn

λ λ λλ λλ

λ λ λ λ λ λ λ λ λ λ= + + + + +

where C1 = 18983678 C2 = 19222979 C3 = 08765134 C4 = 01188704 C5 = 09569903 λ1 = 015 μm λ2 = 025 μm λ3 = 035 μm λ4 = 045 μm and λ5 = 27386128 μm

For arsenic selenide we fit ellipsometry measure-ments of our arsenic selenide thin films and the bulk material is provided by Prof Kathleen A Richardson group

22 22 31 2

2 2 2 2 2 21 2 3

( ) 1- - -

CC Cn

λλ λλ

λ λ λ λ λ λ= + + +

where C1 = 298463 C2 = 321011 C3 = 100182 λ1 = 044118 μm λ2 = 0000354953 μm and λ3 = 38413 μm

B Nonlinear Kerr index n2

The third-order nonlinear susceptibility χ(3)1111 for silicon and

germanium is predicted over the mid-IR range [133] based on a two-band model The effective nonlinear susceptibil-ity χ(3) is dependent on polarization and crystallographic orientation [225] For strong nonlinearity we consider a single-polarization incident light aligned to the crystal-lographic axis and we have χ(3) = χ(3)

1111 To investigate the octave-spanning nonlinear phenomena one need to take the wavelength-dependent nonlinear Kerr index n2 and TPA coefficient βTPA into account which are expressed as

( 3 )2 2

0

( 3 )2

0

3( ) ( )4 ( )

3( ) ( )( )

re

TPA im

ncn

cn

λ χ λε λ

πβ λ χ λ

λε λ

=

=

where ε0 and c are the vacuum permittivity and the speed of light in vacuum Using the material index given in Appendix A and χ(3) value from [133] we obtain the n2 and βTPA values tabulated as follows

262emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

Table 1enspNonlinear Kerr index n2 in silicon

λμm

  n2

10-18 m2W  λ

μm  n2

10-18 m2W  λ

μm  n2

10-18 m2W

130   234   310   389   490   312135   305   315   384   495   311140   378   320   379   500   310145   443   325   375   505   309150   501   330   371   510   307155   559   335   368   515   306160   618   340   365   520   304165   671   345   362   525   304170   710   350   360   530   303175   741   355   358   535   302180   766   360   355   540   302185   781   365   352   545   301190   783   370   350   550   300195   778   375   346   555   298200   762   380   343   560   297205   732   385   341   565   296210   699   390   338   570   296215   658   395   336   575   295220   612   400   334   580   295225   576   405   332   585   295230   547   410   331   590   294235   525   415   330   595   293240   508   420   329   600   292245   493   425   328   605   291250   479   430   327   610   290255   467   435   325   615   289260   456   440   324   620   288265   448   445   321   625   288270   440   450   319   630   288275   432   455   317   635   288280   424   460   315   640   288285   417   465   314   645   288290   410   470   313   650   288295   404   475   313   655   288300   398   480   312   660   288305   394   485   312    

Table 2enspTPA coefficient βTPA in silicon

λμm

  βTPA

10-12 mW  λ

μm  βTPA

10-12 mW  λ

μm  βTPA

10-12 mW

130   1334   165   812   200   180135   1284   170   713   205   115140   1222   175   613   210   064145   1154   180   522   215   024150   1079   185   424   220   0003155   995   190   333    160   905   195   254    

Table 3enspNonlinear Kerr index n2 in germanium

λμm

  n2

10-18 m2W  λ

μm  n2

10-18 m2W  λ

μm  n2

10-18 m2W

23  3932  63  1986  103  170524  4994  64  1972  104  169925  6007  65  1959  105  169426  6650  66  1946  106  169027  6772  67  1934  107  168728  6273  68  1923  108  168429  4897  69  1913  109  168230  4403  70  1904  110  168131  3970  71  1895  111  167932  3680  72  1886  112  167733  3470  73  1876  113  167534  3286  74  1868  114  167335  3128  75  1859  115  167036  2998  76  1850  116  166737  2895  77  1841  117  166338  2812  78  1833  118  165939  2737  79  1826  119  165640  2668  80  1819  120  165341  2605  81  1812  121  165142  2550  82  1807  122  164843  2498  83  1801  123  164644  2450  84  1797  124  164445  2406  85  1792  125  164346  2365  86  1787  126  164147  2328  87  1782  127  163948  2295  88  1777  128  163649  2266  89  1772  129  163450  2238  90  1767  130  163251  2212  91  1762  131  163052  2187  92  1758  132  162853  2164  93  1753  133  162654  2141  94  1749  134  162555  2121  95  1744  135  162356  2101  96  1740  136  162157  2083  97  1736  137  162058  2066  98  1731  138  161859  2049  99  1727  139  161760  2032  100  1722  140  161661  2016  101  1716   62  2001  102  1711   

Table 4enspTPA coefficient βTPA in germanium

λμm

  βTPA

10-8 mW  λμm

  βTPA

10-8 mW  λ

μm  βTPA

10-8 mW

23   130   25   088   27   03124   111   26   060   28   006

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp263

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[135] Jalali B Raghunathan V Shori R Fathpour S Prospects for silicon mid-IR Raman lasers IEEE J Sel Top Quantum Electron 2006121618ndash27

[136] Raghunathan V Borlaug D Rice RR Jalali B Demonstration of a mid-infrared silicon Raman amplifier Opt Express 20071514355ndash62

[137] Chavez Boggio JM Windmiller JR Knutzen M Jiang R Bres C Alic N Stossel B Rottwitt K Radic S 730-nm optical parametric conversion from near- to short-wave infrared band Opt Express 2008165435ndash43

[138] Lin Q Johnson TJ Perahia R Michael CP Painter OJ A proposal for highly tunable optical parametric oscillation in silicon micro-resonators Opt Express 20081610596ndash610

[139] Turner-Foster AC Foster MA Salem R Gaeta AL Lipson M Frequency conversion over two-thirds of an octave in silicon nanowaveguides Opt Express 2010181904ndash8

[140] Liu X Osgood RM Vlasov YA Green WMJ Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides Nat Photonics 20104557ndash60

[141] Zlatanovic S Park JS Moro S Boggio JMC Divliansky IB Alic N Mookherjea S Radic S Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source Nat Photonics 20104561ndash4

[142] Tien EK Huang YW Gao S Song Q Qian F Kalyoncu SK Boyraz O Discrete parametric band conversion in silicon for mid-infrared applications Opt Exp 20101821981ndash9

[143] Lau RKW Meacutenard M Okawachi Y Foster MA A C Turner-Foster Salem R Lipson M Gaeta AL Continuous-wave mid-infrared frequency conversion in silicon nanowaveguides Opt Lett 2011361263ndash5

[144] Roelkens G Green WMJ Kuyken B Liu X Hattasan N Gassenq A Cerutti L Rodriguez JB Osgood RM Tournie E Baets R III-Vsilicon photonics for short-wave infrared spectroscopy IEEE J Quant Electron 201248292ndash8

[145] Alloatti L Korn D Weimann C Koos C Freude W Leuthold J Second-order nonlinear silicon-organic hybrid waveguides Opt Express 20122020506ndash15

[146] Harris DC Durable 3ndash5 μm transmitting infrared window materials Infrared Phys Technol 199839185ndash201

[147] Carlie N Musgraves JD Zdyrko B Luzinov I Hu J Singh V Agarwal A Kimerling LC Canciamilla A Morichetti F Melloni A Richardson K Integrated chalcogenide waveguide resonators for mid-IR sensing leveraging material properties to meet fabrication challenges Opt Express 20101826728ndash43

[148] Eggleton BJ B Luther-Davies Richardson K Chalcogenide photonics Nat Photonics 20115141ndash8

[149] Madden SJ Vu KT High-Performance Integrated Optics with Tellurite Glasses Status and Prospects Int J Appl Glass Sci 20123289ndash98

[150] Bindra KS Bookey HT Kar AK Wherrett BS Liu X Jha A Nonlinear optical properties of chalcogenide glasses observation of multiphoton absorption App Phys Lett 2001791939ndash41

[151] Zakery A Ruan Y ARode V Samoc M Luther-Davies B Low-loss waveguides in ultrafast laser-deposited As2S3 chalcogenide films J Opt Soc Am B 200391844ndash52

[152] Lenz G Zimmermann J Katsufuji T MLines E Hwang HY Spalter S Slusher RE Cheong SW Sanghera JS Aggarwal ID Large Kerr effect in bulk Se-based chalcogenide glasses Opt Lett 200025254ndash6

[153] Sanghera JS Shaw LB Aggarwal ID Application of chalcogenide glass optical fibers CR Chimie 20025873ndash83

[154] Palik ED Handbook of optical constants of solids San Diego CA Academic 1998

[155] Philipp HR Optical properties of silicon nitride J Electrochem Soc 1973120295ndash300

[156] Malitson IH Interspecimen comparison of the refractive index of fused silica J Opt Soc Am 1965551205ndash8

[157] Barnes NP Piltch MS Temperature-dependent Sellmeier coefficients and nonlinear optics average power limit for germanium J Opt Soc Am 197969178ndash80

[158] Rodney WS Malitson IH King TA Refractive index of arsenic trisulfide J Opt Soc Am 195848633ndash636

[159] Ellipsometry measurement on the thin film samples by our group[160] Bristow AD Rotenberg N van Driel HM Two-photon

absorption and Kerr coefficients of silicon for 850ndash2200 nm Appl Phys Lett 200790191104

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp267

[161] Lin Q Zhang J Piredda G Boyd RW Fauchet PM Agrawal GP Dispersion of silicon nonlinearities in the near infrared region Appl Phys Lett 200791021111

[162] Mizrahi V DeLong KW Stegeman GI Saifi MA Andrejco MJ Two-photon absorption as a limitation to all-optical switching Opt Lett 1989141140ndash2

[163] Guider R NDaldosso APitanti EJordana Fedeli J-M Pavesi L NanoSi low loss horizontal slot waveguides coupled to high Q ring resonators Opt Express 20091720762ndash70 and its erratum

[164] Ferrera M Razzari L Duchesne D Morandotti R Yang Z Liscidini M Sipe JE Chu S Little BE Moss DJ Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures Nat Photonics 20082 737ndash40

[165] Smektala F Quemard C Leneindre L Lucas J Barthelemy A De Angelis C Chalcogenide glasses with large non-linear refractive indices J Non-Crystalline Solids 1998239139ndash42

[166] Boudebs G Sanchez F Troles J Smektala F Nonlinear optical properties of chalcogenide glasses- comparison between Mach-Zehnder interferometry and Z-scan techniques Opt Comm 2001199425ndash33

[167] Asobe M Suzuki K Kanamori T Kubodera K Nonlinear refractive index measurement in chalcogenide-glass fibers by self-phase modulation APL 1992601153ndash4

[168] Asobe M Kanamori T Kubodera K Ultrafast all-optical switching using highly nonlinear chalcogenide glass fiber IEEE Photon Technol Lett 19924362ndash5

[169] Asobe M Kanamori T Kubodera K Applications of highly nonlinear chalcogenide glass fibers in ultrafast all-optical switches IEEE J Quant Electron 1993292325ndash33

[170] Ruan Y Luther-Davies B Li W Rode A Kolev V Madden S Large phase shifts in As2S3 waveguides for all-optical processing devices Opt Lett 2005302605ndash7

[171] Laniel JM Hocirc N Valleacutee R Villeneuve A Nonlinear-refractive-index measurement in As2S3 channel waveguides by asymmetric self-phase modulation J Opt Soc Am B 200522437ndash45

[172] Cerqua-Richardson KA McKinley JM Lawrence B Joshi S Villeneuve A Comparison of nonlinear optical properties of sulfide glasses in bulk and thin film form Opt Mater 199810155ndash9

[173] Harbold JM Ilday FOuml Wise FW Sanghera JS Nguyen VQ Shaw LB Aggarwal ID Highly nonlinear As-S-Se glasses for all-optical switching Opt Lett 200227119ndash121

[174] Ruan YL Li WT Jarvis R Madsen N Rode A Luther-Davies B Fabrication and characterization of low loss rib chalcogenide waveguides made by dry etching Opt Express 2004125140ndash5

[175] Slusher RE Lenz G Hodelin J Sanghera J Shaw LB Aggarwal ID Large Raman gain and nonlinear phase shifts in high-purity As2Se3 chalcogenide fibers J Opt Soc Am B 2004211146ndash55

[176] Jacobsen R Andersen K Borel P Fage-Pedersen J Frandsen L Hansen O Kristensen M Lavrinenko A Moulin G Ou H Peucheret C Zsigri B Bjarklev A Strained silicon as a new electro-optic material Nature 2006441199ndash202

[177] Cazzanelli M Bianco F Borga E Pucker G Ghulinyan M Degoli E Luppi E Veacuteniard V Ossicini S Modotto D Wabnitz S Pierobon R Pavesi L Second-harmonic generation in

silicon waveguides strained by silicon nitride Nat Mater 201111148ndash54

[178] Avrutsky I Soref R Phase-matched sum frequency generation in strained silicon waveguides using their second-order nonlinear optical susceptibility Opt Express 20111921707ndash16

[179] Ghahramani E Moss DJ Sipe JE Second-harmonic generation in odd-period strained (Si)n(Ge)nSi superlattices and at SiGe interfaces Phys Rev Lett 1990642815ndash8

[180] Levy JS Foster MA Gaeta AL Lipson M Harmonic generation in silicon nitride ring resonators Opt Express 20111911415

[181] Zakery A Elliott SR Optical nonlinearities in chalcogenide glasses and their applications Springer Series in Optical Sciences 2007135

[182] Lee KK Lim DR Kimerling LC Shin J Cerrina F Fabrication of ultralow-loss SiSiO2 waveguides by roughness reduction Opt Lett 2001261888ndash90

[183] Cardenas J Poitras CB Robinson JT Preston K Chen L Lipson M Low loss etchless silicon photonic waveguides Opt Express 2009174752ndash7

[184] Biberman A Shaw MJ Timurdogan E Wright JB Watts MR Ultralow-loss silicon ring resonators Opt Lett 2012374236ndash8

[185] Walmsley IA Waxer L Dorrer C The role of dispersion in ultrafast optics Rev Sci Instrum 2001721ndash29

[186] Torres JP MHendrych Valencia A Angular dispersion an enabling tool in nonlinear and quantum optics Adv Opt Photon 20102319ndash69

[187] Yin LH Lin Q Agrawal GP Dispersion tailoring and soliton propagation in silicon waveguides Opt Lett 2006311295ndash7

[188] Dulkeith E Xia FN Schares L Green WMJ Vlasov YA Group index and group velocity dispersion in silicon-on-insulator photonic wires Opt Express 2006143853ndash63

[189] Turner AC Manolatou C Schmidt BS Lipson M Tailored anomalous group-velocity dispersion in silicon channel waveguides Opt Express 2006144357ndash62

[190] Dadap JI Panoiu NC Chen X I-Hsieh W Liu X Chou C-Y Dulkeith E McNab SJ Xia F Green WMJ Sekaric L Vlasov YA Osgood RM Jr Nonlinear-optical phase modification in dispersion-engineered Si photonic wires Opt Express 2008161280ndash99

[191] Milosevic MM Matavulj PS Yang PY Bagolini A Mashanovich GZ Rib waveguides for mid-infrared silicon photonics J Opt Soc Am B 2009261760ndash6

[192] Mashanovich GZ Milošević MM Nedeljkovic M Owens N Xiong B Teo EJ Hu Y Low loss silicon waveguides for the mid-infrared Opt Express 2011197112ndash9

[193] Reimer C Nedeljkovic M Stothard DJM Esnault MOS Reardon C OrsquoFaolain L Dunn M Mashanovich GZ Krauss TF Mid-infrared photonic crystal waveguides in silicon Opt Express 20122029361ndash8

[194] Baehr-Jones T Spott A Ilic R Spott A Penkov B Asher W Hochberg M Silicon-on-sapphire integrated waveguides for the midinfrared Opt Express 20101812127ndash35

[195] Li F Jackson S Grillet C Magi E Hudson D Madden SJ Moghe Y OrsquoBrien C Read A Duvall SG Atanackovic P Eggleton BJ Moss D Low propagation loss silicon-on-sapphire waveguides for the midinfrared Opt Express 20111915212ndash20

268emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

[196] Yue Y Zhang L Huang H Beausoleil RG Willner AE Silicon-on-nitride waveguide with ultralow dispersion over an octave-spanning mid-infared wavelength range IEEE Photonics J 20124126ndash32

[197] Khan S Chiles J Ma J Fathpour S Silicon-on-nitride waveguides for mid-and near-infrared integrated photonics Appl Phys Lett 2013102121104

[198] Cheng Z Chen X Wong CY Xu K Tsang HK Mid-infrared suspended membrane waveguide and ring resonator on silicon-on-insulator IEEE Photonics J 201241510ndash9

[199] Lin P-T Singh V Cai Y Kimerling LC Agarwal A Air-clad silicon pedestal structures for broadband mid-infrared microphotonics Opt Lett 2013381031ndash3

[200] Chang YC Paeder V Hvozdara L Hartmann JM Herzig HP Low-loss germanium strip waveguides on silicon for the mid-infrared Opt Lett 2012372883ndash5

[201] Zhang L Yue Y Y Xiao-Li R G Beausoleil Willner AE Highly dispersive slot waveguides Opt Express 2009177095ndash101

[202] Zhang L Yue Y Beausoleil RG Willner AE Analysis and engineering of chromatic dispersion in silicon waveguide bends and ring resonators Opt Express 2011198102ndash7

[203] Zhang L Mu J Singh V Agarwal A Kimerling LC Michel J Intra-cavity dispersion of microresonators and its engineering for octave-spanning Kerr frequency comb generation to be published

[204] Lin Q Zhang L Generalized nonlinear envelope equation with high-order dispersion of nonlinearity to be published

[205] Wang Y Yue R Han H Liao X Raman study of structural order of a-SiNxH and its change upon thermal annealing J Non-Crystalline Solids 2001291107ndash12

[206] Brida D Marangoni M Manzoni C De Silvestri S Cerullo G Two-optical-cycle pulses in the mid-infrared from an optical parametric amplifier Opt Lett 2008332901ndash3

[207] Brida D Manzoni C Cirmi G Marangoni M Bonora S Villoresi P De Silvestri S Cerullo G Few-optical-cycle pulses tunable from the visible to the mid-infrared by optical parametric amplifiers J Opt 201012013001

[208] Kippenberg TJ Holzwarth R Diddams SA Microresonator-based optical frequency combs Science 2011332555ndash9

[209] Levy JS Gondarenko A Foster MA Turner-Foster AC Gaeta AL Lipson M CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects Nat Photonics 2009437ndash40

[210] DelrsquoHaye P Herr T Gavartin E Gorodetsky ML Holzwarth R Kippenberg TJ Octave spanningtunable frequency comb from a microresonator Phys Rev Lett 2011107063901

[211] Okawachi Y Saha K Levy JS Wen YH Lipson M Gaeta AL Octave-spanning frequency combgeneration in a silicon nitride chip Opt Lett 2011363398ndash400

[212] Matsko AB Savchenkov AA Liang W Ilchenko VS Seidel D Maleki L Mode-locked Kerr frequency combs Opt Lett 2011362845ndash7

[213] Herr T Brasch V Jost JD Wang CY Kondratiev NM Gorodetsky ML Kippenberg TJ Temporal solitons in optical microresonators httparxivorgabs12110733

[214] Saha K Okawachi Y Shim B Levy JS Salem R Johnson AR Foster MA Lamont MR Lipson M Gaeta AL Modelocking and femtosecond pulse generation in chip-based frequency combs Opt Express 2013211335ndash43

[215] Coen S Erkintalo M Universal scaling laws of Kerr frequency combs Opt Lett 2013381790ndash2

[216] Lugiato LA Lefever R Spatial dissipative structures in passive optical-systems Phys Rev Lett 1987582209ndash11

[217] Haelterman M Trillo S Wabnitz S Dissipative modulation instability in a nonlinear dispersive ring cavity Opt Commun 199291401ndash7

[218] Coen S Randle HG Sylvestre T Erkintalo M Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato-Lefever model Opt Lett 20133837ndash9

[219] Chembo YK Menyuk CR Spatiotemporal Lugiato-Lefever formalism for Kerr-comb generation in whispering-gallery-mode resonators Phys Rev A 201387053852

[220] Foltynowicz A Mas1owski P Ban T Adler F Cossel KC Briles TC Ye J Optical frequency comb spectroscopy Faraday Discussion 201115023ndash31

[221] Hartl I Li XD Chudoba C Ghanta RK Ko TH Fujimoto JG Ranka JK Windeler RS Ultrahigh-resolution optical coherence tomography using continuum generation in an air silica microstructure optical fiber Opt Lett 200126608ndash10

[222] Brabec T Krausz F Intense few-cycle laser fields Frontiers of nonlinear optics Rev Mod Phys 200072545ndash91

[223] Hu J Meyer J Richardson K Shah L Feature issue introduction mid-IR photonic materials Opt Mater Express 201331571ndash5

[224] Private communications with Dr Jacob Levy in Prof Lipsonrsquos group and Dr Johann Riemensberger in Prof Kippenbergrsquos group

[225] Zhang J Lin Q Piredda G Boyd RW Agrawal GP Fauchet PM Anisotropic nonlinear response of silicon in the near-infrared region Appl Phys Lett 200791071113

Page 12: Lin Zhang*, Anuradha M. Agarwal, Lionel C. Kimerling and ...

258emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

The pulse center wavelength is at 1610 nm and its full width at half-maximum (FWHM) T0 is 120 fs Its peak power is 1200 W corresponding to pulse energy of 016 nJ

Figure 10(A) shows the supercontinua at different propagation distances At 48 mm the spectrum is greatly broadened at the -30 dB level covering a wavelength range from 0585 to 2833 microm which is more than two octaves The spectrum evolution in Figure 10(A) shows a similar spectrum shape as that in Figure 9(A) both featuring a ldquotriangularrdquo central spectrum bounded by two dispersive waves at the edges However it is important to note that the absence of TPA and 3PA in silicon nitride at the telecom window leads to a much more efficient spectrum broad-ening than that in silicon [108] The generated spectrum extends from the visible light to the mid-IR with excellent spectral coherence which is confirmed by the pulse wave-form shown in Figure 10(B) In the time domain the pulse is greatly compressed from 120 to 408 fs corresponding to 076 optical cycles at 161 microm wavelength

We examine the pulsewidth as a function of propa-gation distance Figure 11 shows that the pulse becomes increasingly narrower until the propagation distance reaches 47 mm For longer distances the pulsewidth

A

B

60 mm

48 mm

36 mm

24 mm

12 mm

Input

Spe

ctru

m (

10 d

Bd

iv)

Pow

er (

W)

12

246

24

18

12

6

0

248 250 252 254

14 16 18 20 22 24Wavelength (microm)

Time (ps)

Figure 9emsp(A) The supercontinuum generation in a silicon-based stripslot hybrid waveguide presented in [108] (B) The significant spectrum broadening at 425-mm distance is associated with a temporal compression of an input pulse (dash line) to the output waveform (solid line) with a FWHM of 12 fs

A

B

50 mm

48 mm

46 mm

44 mm

42 mm

Input

Spe

ctru

m (

10 d

Bd

iv)

Pow

er (

W)

8000

6000

4000

2000

0250249 251

06 09 12 15 18 21 24 27

Wavelength (microm)

Time (ps)

Figure 10emsp(A) Spectrum evolution of the pulse over propagation distance A supercontinuum of more than two octaves is achieved at 48 mm distance (B) Generated pulse waveform with a pulse width of 408 fs as short as 076 optical cycles Low pedestals are caused by dispersive waves generated at the two ends of the spectrum

remains almost constant However it is important to mention that after 48 mm the dispersive waves become increasingly stronger as shown in Figure 10(A) causing larger pedestals

Comparing the results in Figures 9 and 10 we note that the mid-IR wavelength range for silicon would be in analogy to the near-IR for silicon nitride in terms of non-linear optics operations Pumping at or beyond 33 microm one can use the waveguide designs shown in Figure 7 to produce very efficient nonlinear interactions without TPA and 3PA in silicon Ultrashort pulses in the mid-IR from parametric amplifiers [206 207] could be used to pump the Group IV waveguides

Another nonlinear application of the dispersion-engi-neered Group IV waveguides is micro-resonator-based Kerr frequency comb generation When such a waveguide is curved to form a microring resonator input CW light travels around the cavity and amplifies the noise in the source located at the frequencies with a high parametric gain As a result of modulation instability and cascaded FWM in the cavity a frequency comb can be generated [208ndash211] Mode-locked frequency combs have been reported pro-ducing low-noise pulse trains in time domain [212ndash214]

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp259

The formation of cavity solitons is identified as the main reason for the mode-locking in the Kerr frequency combs [215] This is instructive because one can thus predict the spectral bandwidth and temporal pulsewidth in the generated low-noise combs The 3-dB comb bandwidth is inversely proportional to the square root of the 2nd-order dispersion coefficient |β2| as given in [213 215] It is desira-ble that all comb lines that constitute the soliton spectrum experience the same |β2| In this sense the stripslot hybrid waveguides with flattened dispersion are preferably suit-able for supporting broadband Kerr comb generation and ultra-short cavity soliton generation

The Kerr frequency comb generation can be modeled using the generalized Lugiato-Lefever equation (LLE) [216ndash219]

20

2

( - )- - | |

2 2

m mm

R inmm

jkt j jl E kE j l E Et m

βαδ γ

τ

infin

=

part part+ + + = part part

sum (2)

where tR is the round-trip time E = E(tτ) and Ein are intra-cavity field and input field (pump power Pin  =  |Ein|2) t and τ are the slow and fast times δ0 is the cavity phase detuning defined as δ0  =  tRmiddot(ωn -ω0) where ω0 and ωn are the pumprsquos angular frequency and the nth angular reso-nance frequency that is pumped Other resonator param-eters include the power loss per round trip α the power coupling coefficient κ the nonlinear coefficient γ and the mth dispersion coefficient βm Since a flattened dispersion profile has a small β2 over a wide bandwidth it is impor-tant to take the influence of higher-order dispersion into account We include all-order dispersion terms in Eq (2) as we did in solving Eq (1)

To enhance the Kerr comb bandwidth in the near-IR we use the ultra-flattened dispersion profile in Figure 6(A) which is obtained in the slot WG 2 based on

Pul

se w

idth

(fs

)

14

12

10

8

6

4

242 44 46 48 50 52

Propagation distance (mm)

Figure 11emspPulse width first decreases with propagation distance and then remains stable After 48 mm dispersive waves get stronger causing more pedestals

Pow

er (

10 d

Bd

iv)

Pow

er (

W)

70A

B

60

50

40

30

20

10

-10

-20

600

400

200

0

80 120

0575 0600 0625 0650

160 200 240 280 320 360

0

Frequency (THz)

Time (ps)

Figure 12emsp(A) Frequency comb generation with a CW pump at 155 microm using a microring resonator based on a silicon stripslot hybrid waveguide Over an octave-spanning bandwidth from 135 to 270 THz the comb lines have a power drop of 20 dB (B) Generated pulse waveform with a pulse width of 82 fs as short as 16 optical cycles

silicon nitride The ring resonator has a bending radius of 104 microm corresponding to a FSR of 200 GHz Pumping near 155 microm with a pump power of 2 W the resonance peak is red-shifted and we need to red-shift the pump wavelength accordingly and tune it into the resonance from the short-wavelength side When the pump is step-by-step tuned by up to 63 resonance linewidths we obtain the comb spectrum and the mode-locked pulse waveform as shown in Figure 12 One can see that over an octave-spanning bandwidth from 133 to 268 THz the comb lines have a power drop by 20 dB from the center of the spectrum The spectral flatness of this comb is relatively good compared to the previously reported results [208ndash211] The comb bandwidth at -40 dB is as wide as two octaves There are two dispersive peaks in normal dispersion regions beyond the low-dispersion band Such a mode-locked broadband comb produces a train of sub-two-cycle optical pulses as shown in Figure 12(B) with one pulse per round trip The peak power of the pulse is up to 600 W Nonlinear conver-sion efficiency is estimated to be -267 dB

To generate frequency combs in the mid-IR the ger-manium-on-silicon strip waveguide is chosen We choose

260emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

a cross-section of 3200 times 1800 nm2 which has an octave-spanning low-dispersion band from 4 to 767 microm as shown in Figure 8(B) A germanium ring resonator is formed with a bending radius of 564 microm corresponding to a FSR of 200 GHz Pumping at 6 microm with a CW power of 14 W and detuning the pump wavelength by 10 resonance linewidth one can see that a mode-locked wideband mid-IR comb is generated from 358 to 644 THz (ie from 466 to 838 microm) at -40 dB level The FWHM of the produced pulses is 69 fs which corresponds to ~35 optical cycles The pulse peak power is 184 W and the nonlinear conversion efficiency is estimated to be -143 dB Since the pumping frequency is not at the center of the low-dispersion band we only see one peak in the comb spectrum caused by the dispersive wave in the normal dispersion region from Figure 13(A) There is another peak at higher frequencies beyond what is shown in the figure

As shown above broadband dispersion engineering is critical for octave-spanning nonlinear applications in both near- and mid-IR wavelength ranges which enables us to fully utilize the bandwidth allowed by the materials transparency windows Generally speaking the nonlinear applications mentioned here such as supercontinuum generation ultrafast pulse compression and frequency comb generation are often the intermediate steps towards higher-level system applications In the frequency domain a wide spectrum can serve as an electromagnetic carrier to acquire high-volume of information eg for sensing [220] and imaging [221] In the time domain an ultrashort pulse can be used as probe to sample ultrafast phenomena [222]

5 Summary and OutlookWe have presented a review of our recent work on nonlin-ear photonics based on silicon and germanium Various types of Group IV waveguides are analyzed and optimized for four different wavelength ranges from near- to mid-IR The recently proposed dispersion engineering technique based on stripslot hybrid waveguide structures is used for different material combinations and wavelength ranges Numerical simulations show that the dispersion-flattened Group IV waveguides are preferably suitable for octave-spanning nonlinear applications including on-chip supercontinuum generation ultrashort pulse compres-sion and mode-locked wideband frequency comb genera-tion based on micro-resonators

The presented approach to achieving octave-span-ning nonlinear applications on an integrated CMOS-compatible Group IV platform holds great potential for realizing chip-scale sensing imaging communications and signal processing system The ultrawide transparency windows in the mid-IR allowed by Group IV elements and compounds potentially together with other materi-als [223] provide an exciting arena for building powerful information acquisition and processing units enabled by nonlinear optics nano-photonics and ultrafast optics

Received June 14 2013 accepted October 29 2013 previously pub-lished online November 27 2013

Pow

er (

10 d

Bd

iv)

A

8030 40 50 60 70Frequency (THz)

Pow

er (

W)

B200

150

100

50

0

21 22 23 24 25Time (ps)

Figure 13emsp(A) Frequency comb generation with a CW pump at 6 microm using a microring resonator based on a germanium strip waveguide with air upper cladding (B) Generated pulse waveform with a pulse width of 69 fs as short as 35 optical cycles

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp261

Appendix

A Material index and dispersion

In this section we give the wavelength-dependent mate-rial index expressed as Sellmeier equations where wave-length λ is in μm

For silicon we use the following material index that is a fit curve from measurement results at room temperature (293 K) with 184 data points in total from 112 to 588 μm [154]

22 1 2 2

2 2 22

( )-

C Cn

λλ ε

λ λ λ= + +

where ε = 116858 C1 = 0939816 μm2 C2 = 000810461 and λ2 = 11071 μm

For silicon nitride the material index is affected by deposition conditions using plasma-enhanced chemical vapor deposition (PECVD) low-pressure chemical vapor deposition (LPCVD) and so on We use the following Sell-meier equation [155] which predicts the material index close to that in LPCVD silicon nitride films measured by a few groups [224]

22 1

2 21

( ) 1-

Cn

λλ

λ λ= +

where C1 = 28939 and λ1 = 013967 μmFor silicon dioxide we use the following Sellmeier

equation for fused silica [156]22 2

2 31 22 2 2 2 2 2

1 2 3

( ) 1- - -

CC Cn

λλ λλ

λ λ λ λ λ λ= + + +

where C1 = 06961663 C2 = 04079426 C3 = 08974794 λ1 = 00684043 μm λ2 = 01162414 μm and λ3 = 9896161 μm

For SRO the material index is affected by deposition conditions such as silicon excess annealing temperature and so on Here we choose the one with silicon excess of 8 and annealed at 1250oC [51]

22 22 31 2

2 2 2 2 2 21 2 3

( ) 1- - -

CC Cn

λλ λλ

λ λ λ λ λ λ= + + +

where C1 = 001 C2 = 196 C3 = 141 λ1 = 03 μm λ2 = 007071 μm and λ3 = 2775968 μm

For germanium the temperature-dependent mate-rial index was measured [157] Here we choose the one for room temperature (293 K)

2 22 1 2

2 2 2 21 2

( )- -

C Cn

λ λλ ε

λ λ λ λ= + +

where ε = 928156 C1 = 67288 C2 = 021307 λ1 = 0664116 μm and λ2 = 6221013 μm

For arsenic sulfide we use the material index pro-vided in [158]

2 2 22 22 3 4 51 2

2 2 2 2 2 2 2 2 2 21 2 3 4 5

( ) 1- - - - -

C C CC Cn

λ λ λλ λλ

λ λ λ λ λ λ λ λ λ λ= + + + + +

where C1 = 18983678 C2 = 19222979 C3 = 08765134 C4 = 01188704 C5 = 09569903 λ1 = 015 μm λ2 = 025 μm λ3 = 035 μm λ4 = 045 μm and λ5 = 27386128 μm

For arsenic selenide we fit ellipsometry measure-ments of our arsenic selenide thin films and the bulk material is provided by Prof Kathleen A Richardson group

22 22 31 2

2 2 2 2 2 21 2 3

( ) 1- - -

CC Cn

λλ λλ

λ λ λ λ λ λ= + + +

where C1 = 298463 C2 = 321011 C3 = 100182 λ1 = 044118 μm λ2 = 0000354953 μm and λ3 = 38413 μm

B Nonlinear Kerr index n2

The third-order nonlinear susceptibility χ(3)1111 for silicon and

germanium is predicted over the mid-IR range [133] based on a two-band model The effective nonlinear susceptibil-ity χ(3) is dependent on polarization and crystallographic orientation [225] For strong nonlinearity we consider a single-polarization incident light aligned to the crystal-lographic axis and we have χ(3) = χ(3)

1111 To investigate the octave-spanning nonlinear phenomena one need to take the wavelength-dependent nonlinear Kerr index n2 and TPA coefficient βTPA into account which are expressed as

( 3 )2 2

0

( 3 )2

0

3( ) ( )4 ( )

3( ) ( )( )

re

TPA im

ncn

cn

λ χ λε λ

πβ λ χ λ

λε λ

=

=

where ε0 and c are the vacuum permittivity and the speed of light in vacuum Using the material index given in Appendix A and χ(3) value from [133] we obtain the n2 and βTPA values tabulated as follows

262emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

Table 1enspNonlinear Kerr index n2 in silicon

λμm

  n2

10-18 m2W  λ

μm  n2

10-18 m2W  λ

μm  n2

10-18 m2W

130   234   310   389   490   312135   305   315   384   495   311140   378   320   379   500   310145   443   325   375   505   309150   501   330   371   510   307155   559   335   368   515   306160   618   340   365   520   304165   671   345   362   525   304170   710   350   360   530   303175   741   355   358   535   302180   766   360   355   540   302185   781   365   352   545   301190   783   370   350   550   300195   778   375   346   555   298200   762   380   343   560   297205   732   385   341   565   296210   699   390   338   570   296215   658   395   336   575   295220   612   400   334   580   295225   576   405   332   585   295230   547   410   331   590   294235   525   415   330   595   293240   508   420   329   600   292245   493   425   328   605   291250   479   430   327   610   290255   467   435   325   615   289260   456   440   324   620   288265   448   445   321   625   288270   440   450   319   630   288275   432   455   317   635   288280   424   460   315   640   288285   417   465   314   645   288290   410   470   313   650   288295   404   475   313   655   288300   398   480   312   660   288305   394   485   312    

Table 2enspTPA coefficient βTPA in silicon

λμm

  βTPA

10-12 mW  λ

μm  βTPA

10-12 mW  λ

μm  βTPA

10-12 mW

130   1334   165   812   200   180135   1284   170   713   205   115140   1222   175   613   210   064145   1154   180   522   215   024150   1079   185   424   220   0003155   995   190   333    160   905   195   254    

Table 3enspNonlinear Kerr index n2 in germanium

λμm

  n2

10-18 m2W  λ

μm  n2

10-18 m2W  λ

μm  n2

10-18 m2W

23  3932  63  1986  103  170524  4994  64  1972  104  169925  6007  65  1959  105  169426  6650  66  1946  106  169027  6772  67  1934  107  168728  6273  68  1923  108  168429  4897  69  1913  109  168230  4403  70  1904  110  168131  3970  71  1895  111  167932  3680  72  1886  112  167733  3470  73  1876  113  167534  3286  74  1868  114  167335  3128  75  1859  115  167036  2998  76  1850  116  166737  2895  77  1841  117  166338  2812  78  1833  118  165939  2737  79  1826  119  165640  2668  80  1819  120  165341  2605  81  1812  121  165142  2550  82  1807  122  164843  2498  83  1801  123  164644  2450  84  1797  124  164445  2406  85  1792  125  164346  2365  86  1787  126  164147  2328  87  1782  127  163948  2295  88  1777  128  163649  2266  89  1772  129  163450  2238  90  1767  130  163251  2212  91  1762  131  163052  2187  92  1758  132  162853  2164  93  1753  133  162654  2141  94  1749  134  162555  2121  95  1744  135  162356  2101  96  1740  136  162157  2083  97  1736  137  162058  2066  98  1731  138  161859  2049  99  1727  139  161760  2032  100  1722  140  161661  2016  101  1716   62  2001  102  1711   

Table 4enspTPA coefficient βTPA in germanium

λμm

  βTPA

10-8 mW  λμm

  βTPA

10-8 mW  λ

μm  βTPA

10-8 mW

23   130   25   088   27   03124   111   26   060   28   006

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp263

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[140] Liu X Osgood RM Vlasov YA Green WMJ Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides Nat Photonics 20104557ndash60

[141] Zlatanovic S Park JS Moro S Boggio JMC Divliansky IB Alic N Mookherjea S Radic S Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source Nat Photonics 20104561ndash4

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[145] Alloatti L Korn D Weimann C Koos C Freude W Leuthold J Second-order nonlinear silicon-organic hybrid waveguides Opt Express 20122020506ndash15

[146] Harris DC Durable 3ndash5 μm transmitting infrared window materials Infrared Phys Technol 199839185ndash201

[147] Carlie N Musgraves JD Zdyrko B Luzinov I Hu J Singh V Agarwal A Kimerling LC Canciamilla A Morichetti F Melloni A Richardson K Integrated chalcogenide waveguide resonators for mid-IR sensing leveraging material properties to meet fabrication challenges Opt Express 20101826728ndash43

[148] Eggleton BJ B Luther-Davies Richardson K Chalcogenide photonics Nat Photonics 20115141ndash8

[149] Madden SJ Vu KT High-Performance Integrated Optics with Tellurite Glasses Status and Prospects Int J Appl Glass Sci 20123289ndash98

[150] Bindra KS Bookey HT Kar AK Wherrett BS Liu X Jha A Nonlinear optical properties of chalcogenide glasses observation of multiphoton absorption App Phys Lett 2001791939ndash41

[151] Zakery A Ruan Y ARode V Samoc M Luther-Davies B Low-loss waveguides in ultrafast laser-deposited As2S3 chalcogenide films J Opt Soc Am B 200391844ndash52

[152] Lenz G Zimmermann J Katsufuji T MLines E Hwang HY Spalter S Slusher RE Cheong SW Sanghera JS Aggarwal ID Large Kerr effect in bulk Se-based chalcogenide glasses Opt Lett 200025254ndash6

[153] Sanghera JS Shaw LB Aggarwal ID Application of chalcogenide glass optical fibers CR Chimie 20025873ndash83

[154] Palik ED Handbook of optical constants of solids San Diego CA Academic 1998

[155] Philipp HR Optical properties of silicon nitride J Electrochem Soc 1973120295ndash300

[156] Malitson IH Interspecimen comparison of the refractive index of fused silica J Opt Soc Am 1965551205ndash8

[157] Barnes NP Piltch MS Temperature-dependent Sellmeier coefficients and nonlinear optics average power limit for germanium J Opt Soc Am 197969178ndash80

[158] Rodney WS Malitson IH King TA Refractive index of arsenic trisulfide J Opt Soc Am 195848633ndash636

[159] Ellipsometry measurement on the thin film samples by our group[160] Bristow AD Rotenberg N van Driel HM Two-photon

absorption and Kerr coefficients of silicon for 850ndash2200 nm Appl Phys Lett 200790191104

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp267

[161] Lin Q Zhang J Piredda G Boyd RW Fauchet PM Agrawal GP Dispersion of silicon nonlinearities in the near infrared region Appl Phys Lett 200791021111

[162] Mizrahi V DeLong KW Stegeman GI Saifi MA Andrejco MJ Two-photon absorption as a limitation to all-optical switching Opt Lett 1989141140ndash2

[163] Guider R NDaldosso APitanti EJordana Fedeli J-M Pavesi L NanoSi low loss horizontal slot waveguides coupled to high Q ring resonators Opt Express 20091720762ndash70 and its erratum

[164] Ferrera M Razzari L Duchesne D Morandotti R Yang Z Liscidini M Sipe JE Chu S Little BE Moss DJ Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures Nat Photonics 20082 737ndash40

[165] Smektala F Quemard C Leneindre L Lucas J Barthelemy A De Angelis C Chalcogenide glasses with large non-linear refractive indices J Non-Crystalline Solids 1998239139ndash42

[166] Boudebs G Sanchez F Troles J Smektala F Nonlinear optical properties of chalcogenide glasses- comparison between Mach-Zehnder interferometry and Z-scan techniques Opt Comm 2001199425ndash33

[167] Asobe M Suzuki K Kanamori T Kubodera K Nonlinear refractive index measurement in chalcogenide-glass fibers by self-phase modulation APL 1992601153ndash4

[168] Asobe M Kanamori T Kubodera K Ultrafast all-optical switching using highly nonlinear chalcogenide glass fiber IEEE Photon Technol Lett 19924362ndash5

[169] Asobe M Kanamori T Kubodera K Applications of highly nonlinear chalcogenide glass fibers in ultrafast all-optical switches IEEE J Quant Electron 1993292325ndash33

[170] Ruan Y Luther-Davies B Li W Rode A Kolev V Madden S Large phase shifts in As2S3 waveguides for all-optical processing devices Opt Lett 2005302605ndash7

[171] Laniel JM Hocirc N Valleacutee R Villeneuve A Nonlinear-refractive-index measurement in As2S3 channel waveguides by asymmetric self-phase modulation J Opt Soc Am B 200522437ndash45

[172] Cerqua-Richardson KA McKinley JM Lawrence B Joshi S Villeneuve A Comparison of nonlinear optical properties of sulfide glasses in bulk and thin film form Opt Mater 199810155ndash9

[173] Harbold JM Ilday FOuml Wise FW Sanghera JS Nguyen VQ Shaw LB Aggarwal ID Highly nonlinear As-S-Se glasses for all-optical switching Opt Lett 200227119ndash121

[174] Ruan YL Li WT Jarvis R Madsen N Rode A Luther-Davies B Fabrication and characterization of low loss rib chalcogenide waveguides made by dry etching Opt Express 2004125140ndash5

[175] Slusher RE Lenz G Hodelin J Sanghera J Shaw LB Aggarwal ID Large Raman gain and nonlinear phase shifts in high-purity As2Se3 chalcogenide fibers J Opt Soc Am B 2004211146ndash55

[176] Jacobsen R Andersen K Borel P Fage-Pedersen J Frandsen L Hansen O Kristensen M Lavrinenko A Moulin G Ou H Peucheret C Zsigri B Bjarklev A Strained silicon as a new electro-optic material Nature 2006441199ndash202

[177] Cazzanelli M Bianco F Borga E Pucker G Ghulinyan M Degoli E Luppi E Veacuteniard V Ossicini S Modotto D Wabnitz S Pierobon R Pavesi L Second-harmonic generation in

silicon waveguides strained by silicon nitride Nat Mater 201111148ndash54

[178] Avrutsky I Soref R Phase-matched sum frequency generation in strained silicon waveguides using their second-order nonlinear optical susceptibility Opt Express 20111921707ndash16

[179] Ghahramani E Moss DJ Sipe JE Second-harmonic generation in odd-period strained (Si)n(Ge)nSi superlattices and at SiGe interfaces Phys Rev Lett 1990642815ndash8

[180] Levy JS Foster MA Gaeta AL Lipson M Harmonic generation in silicon nitride ring resonators Opt Express 20111911415

[181] Zakery A Elliott SR Optical nonlinearities in chalcogenide glasses and their applications Springer Series in Optical Sciences 2007135

[182] Lee KK Lim DR Kimerling LC Shin J Cerrina F Fabrication of ultralow-loss SiSiO2 waveguides by roughness reduction Opt Lett 2001261888ndash90

[183] Cardenas J Poitras CB Robinson JT Preston K Chen L Lipson M Low loss etchless silicon photonic waveguides Opt Express 2009174752ndash7

[184] Biberman A Shaw MJ Timurdogan E Wright JB Watts MR Ultralow-loss silicon ring resonators Opt Lett 2012374236ndash8

[185] Walmsley IA Waxer L Dorrer C The role of dispersion in ultrafast optics Rev Sci Instrum 2001721ndash29

[186] Torres JP MHendrych Valencia A Angular dispersion an enabling tool in nonlinear and quantum optics Adv Opt Photon 20102319ndash69

[187] Yin LH Lin Q Agrawal GP Dispersion tailoring and soliton propagation in silicon waveguides Opt Lett 2006311295ndash7

[188] Dulkeith E Xia FN Schares L Green WMJ Vlasov YA Group index and group velocity dispersion in silicon-on-insulator photonic wires Opt Express 2006143853ndash63

[189] Turner AC Manolatou C Schmidt BS Lipson M Tailored anomalous group-velocity dispersion in silicon channel waveguides Opt Express 2006144357ndash62

[190] Dadap JI Panoiu NC Chen X I-Hsieh W Liu X Chou C-Y Dulkeith E McNab SJ Xia F Green WMJ Sekaric L Vlasov YA Osgood RM Jr Nonlinear-optical phase modification in dispersion-engineered Si photonic wires Opt Express 2008161280ndash99

[191] Milosevic MM Matavulj PS Yang PY Bagolini A Mashanovich GZ Rib waveguides for mid-infrared silicon photonics J Opt Soc Am B 2009261760ndash6

[192] Mashanovich GZ Milošević MM Nedeljkovic M Owens N Xiong B Teo EJ Hu Y Low loss silicon waveguides for the mid-infrared Opt Express 2011197112ndash9

[193] Reimer C Nedeljkovic M Stothard DJM Esnault MOS Reardon C OrsquoFaolain L Dunn M Mashanovich GZ Krauss TF Mid-infrared photonic crystal waveguides in silicon Opt Express 20122029361ndash8

[194] Baehr-Jones T Spott A Ilic R Spott A Penkov B Asher W Hochberg M Silicon-on-sapphire integrated waveguides for the midinfrared Opt Express 20101812127ndash35

[195] Li F Jackson S Grillet C Magi E Hudson D Madden SJ Moghe Y OrsquoBrien C Read A Duvall SG Atanackovic P Eggleton BJ Moss D Low propagation loss silicon-on-sapphire waveguides for the midinfrared Opt Express 20111915212ndash20

268emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

[196] Yue Y Zhang L Huang H Beausoleil RG Willner AE Silicon-on-nitride waveguide with ultralow dispersion over an octave-spanning mid-infared wavelength range IEEE Photonics J 20124126ndash32

[197] Khan S Chiles J Ma J Fathpour S Silicon-on-nitride waveguides for mid-and near-infrared integrated photonics Appl Phys Lett 2013102121104

[198] Cheng Z Chen X Wong CY Xu K Tsang HK Mid-infrared suspended membrane waveguide and ring resonator on silicon-on-insulator IEEE Photonics J 201241510ndash9

[199] Lin P-T Singh V Cai Y Kimerling LC Agarwal A Air-clad silicon pedestal structures for broadband mid-infrared microphotonics Opt Lett 2013381031ndash3

[200] Chang YC Paeder V Hvozdara L Hartmann JM Herzig HP Low-loss germanium strip waveguides on silicon for the mid-infrared Opt Lett 2012372883ndash5

[201] Zhang L Yue Y Y Xiao-Li R G Beausoleil Willner AE Highly dispersive slot waveguides Opt Express 2009177095ndash101

[202] Zhang L Yue Y Beausoleil RG Willner AE Analysis and engineering of chromatic dispersion in silicon waveguide bends and ring resonators Opt Express 2011198102ndash7

[203] Zhang L Mu J Singh V Agarwal A Kimerling LC Michel J Intra-cavity dispersion of microresonators and its engineering for octave-spanning Kerr frequency comb generation to be published

[204] Lin Q Zhang L Generalized nonlinear envelope equation with high-order dispersion of nonlinearity to be published

[205] Wang Y Yue R Han H Liao X Raman study of structural order of a-SiNxH and its change upon thermal annealing J Non-Crystalline Solids 2001291107ndash12

[206] Brida D Marangoni M Manzoni C De Silvestri S Cerullo G Two-optical-cycle pulses in the mid-infrared from an optical parametric amplifier Opt Lett 2008332901ndash3

[207] Brida D Manzoni C Cirmi G Marangoni M Bonora S Villoresi P De Silvestri S Cerullo G Few-optical-cycle pulses tunable from the visible to the mid-infrared by optical parametric amplifiers J Opt 201012013001

[208] Kippenberg TJ Holzwarth R Diddams SA Microresonator-based optical frequency combs Science 2011332555ndash9

[209] Levy JS Gondarenko A Foster MA Turner-Foster AC Gaeta AL Lipson M CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects Nat Photonics 2009437ndash40

[210] DelrsquoHaye P Herr T Gavartin E Gorodetsky ML Holzwarth R Kippenberg TJ Octave spanningtunable frequency comb from a microresonator Phys Rev Lett 2011107063901

[211] Okawachi Y Saha K Levy JS Wen YH Lipson M Gaeta AL Octave-spanning frequency combgeneration in a silicon nitride chip Opt Lett 2011363398ndash400

[212] Matsko AB Savchenkov AA Liang W Ilchenko VS Seidel D Maleki L Mode-locked Kerr frequency combs Opt Lett 2011362845ndash7

[213] Herr T Brasch V Jost JD Wang CY Kondratiev NM Gorodetsky ML Kippenberg TJ Temporal solitons in optical microresonators httparxivorgabs12110733

[214] Saha K Okawachi Y Shim B Levy JS Salem R Johnson AR Foster MA Lamont MR Lipson M Gaeta AL Modelocking and femtosecond pulse generation in chip-based frequency combs Opt Express 2013211335ndash43

[215] Coen S Erkintalo M Universal scaling laws of Kerr frequency combs Opt Lett 2013381790ndash2

[216] Lugiato LA Lefever R Spatial dissipative structures in passive optical-systems Phys Rev Lett 1987582209ndash11

[217] Haelterman M Trillo S Wabnitz S Dissipative modulation instability in a nonlinear dispersive ring cavity Opt Commun 199291401ndash7

[218] Coen S Randle HG Sylvestre T Erkintalo M Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato-Lefever model Opt Lett 20133837ndash9

[219] Chembo YK Menyuk CR Spatiotemporal Lugiato-Lefever formalism for Kerr-comb generation in whispering-gallery-mode resonators Phys Rev A 201387053852

[220] Foltynowicz A Mas1owski P Ban T Adler F Cossel KC Briles TC Ye J Optical frequency comb spectroscopy Faraday Discussion 201115023ndash31

[221] Hartl I Li XD Chudoba C Ghanta RK Ko TH Fujimoto JG Ranka JK Windeler RS Ultrahigh-resolution optical coherence tomography using continuum generation in an air silica microstructure optical fiber Opt Lett 200126608ndash10

[222] Brabec T Krausz F Intense few-cycle laser fields Frontiers of nonlinear optics Rev Mod Phys 200072545ndash91

[223] Hu J Meyer J Richardson K Shah L Feature issue introduction mid-IR photonic materials Opt Mater Express 201331571ndash5

[224] Private communications with Dr Jacob Levy in Prof Lipsonrsquos group and Dr Johann Riemensberger in Prof Kippenbergrsquos group

[225] Zhang J Lin Q Piredda G Boyd RW Agrawal GP Fauchet PM Anisotropic nonlinear response of silicon in the near-infrared region Appl Phys Lett 200791071113

Page 13: Lin Zhang*, Anuradha M. Agarwal, Lionel C. Kimerling and ...

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp259

The formation of cavity solitons is identified as the main reason for the mode-locking in the Kerr frequency combs [215] This is instructive because one can thus predict the spectral bandwidth and temporal pulsewidth in the generated low-noise combs The 3-dB comb bandwidth is inversely proportional to the square root of the 2nd-order dispersion coefficient |β2| as given in [213 215] It is desira-ble that all comb lines that constitute the soliton spectrum experience the same |β2| In this sense the stripslot hybrid waveguides with flattened dispersion are preferably suit-able for supporting broadband Kerr comb generation and ultra-short cavity soliton generation

The Kerr frequency comb generation can be modeled using the generalized Lugiato-Lefever equation (LLE) [216ndash219]

20

2

( - )- - | |

2 2

m mm

R inmm

jkt j jl E kE j l E Et m

βαδ γ

τ

infin

=

part part+ + + = part part

sum (2)

where tR is the round-trip time E = E(tτ) and Ein are intra-cavity field and input field (pump power Pin  =  |Ein|2) t and τ are the slow and fast times δ0 is the cavity phase detuning defined as δ0  =  tRmiddot(ωn -ω0) where ω0 and ωn are the pumprsquos angular frequency and the nth angular reso-nance frequency that is pumped Other resonator param-eters include the power loss per round trip α the power coupling coefficient κ the nonlinear coefficient γ and the mth dispersion coefficient βm Since a flattened dispersion profile has a small β2 over a wide bandwidth it is impor-tant to take the influence of higher-order dispersion into account We include all-order dispersion terms in Eq (2) as we did in solving Eq (1)

To enhance the Kerr comb bandwidth in the near-IR we use the ultra-flattened dispersion profile in Figure 6(A) which is obtained in the slot WG 2 based on

Pul

se w

idth

(fs

)

14

12

10

8

6

4

242 44 46 48 50 52

Propagation distance (mm)

Figure 11emspPulse width first decreases with propagation distance and then remains stable After 48 mm dispersive waves get stronger causing more pedestals

Pow

er (

10 d

Bd

iv)

Pow

er (

W)

70A

B

60

50

40

30

20

10

-10

-20

600

400

200

0

80 120

0575 0600 0625 0650

160 200 240 280 320 360

0

Frequency (THz)

Time (ps)

Figure 12emsp(A) Frequency comb generation with a CW pump at 155 microm using a microring resonator based on a silicon stripslot hybrid waveguide Over an octave-spanning bandwidth from 135 to 270 THz the comb lines have a power drop of 20 dB (B) Generated pulse waveform with a pulse width of 82 fs as short as 16 optical cycles

silicon nitride The ring resonator has a bending radius of 104 microm corresponding to a FSR of 200 GHz Pumping near 155 microm with a pump power of 2 W the resonance peak is red-shifted and we need to red-shift the pump wavelength accordingly and tune it into the resonance from the short-wavelength side When the pump is step-by-step tuned by up to 63 resonance linewidths we obtain the comb spectrum and the mode-locked pulse waveform as shown in Figure 12 One can see that over an octave-spanning bandwidth from 133 to 268 THz the comb lines have a power drop by 20 dB from the center of the spectrum The spectral flatness of this comb is relatively good compared to the previously reported results [208ndash211] The comb bandwidth at -40 dB is as wide as two octaves There are two dispersive peaks in normal dispersion regions beyond the low-dispersion band Such a mode-locked broadband comb produces a train of sub-two-cycle optical pulses as shown in Figure 12(B) with one pulse per round trip The peak power of the pulse is up to 600 W Nonlinear conver-sion efficiency is estimated to be -267 dB

To generate frequency combs in the mid-IR the ger-manium-on-silicon strip waveguide is chosen We choose

260emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

a cross-section of 3200 times 1800 nm2 which has an octave-spanning low-dispersion band from 4 to 767 microm as shown in Figure 8(B) A germanium ring resonator is formed with a bending radius of 564 microm corresponding to a FSR of 200 GHz Pumping at 6 microm with a CW power of 14 W and detuning the pump wavelength by 10 resonance linewidth one can see that a mode-locked wideband mid-IR comb is generated from 358 to 644 THz (ie from 466 to 838 microm) at -40 dB level The FWHM of the produced pulses is 69 fs which corresponds to ~35 optical cycles The pulse peak power is 184 W and the nonlinear conversion efficiency is estimated to be -143 dB Since the pumping frequency is not at the center of the low-dispersion band we only see one peak in the comb spectrum caused by the dispersive wave in the normal dispersion region from Figure 13(A) There is another peak at higher frequencies beyond what is shown in the figure

As shown above broadband dispersion engineering is critical for octave-spanning nonlinear applications in both near- and mid-IR wavelength ranges which enables us to fully utilize the bandwidth allowed by the materials transparency windows Generally speaking the nonlinear applications mentioned here such as supercontinuum generation ultrafast pulse compression and frequency comb generation are often the intermediate steps towards higher-level system applications In the frequency domain a wide spectrum can serve as an electromagnetic carrier to acquire high-volume of information eg for sensing [220] and imaging [221] In the time domain an ultrashort pulse can be used as probe to sample ultrafast phenomena [222]

5 Summary and OutlookWe have presented a review of our recent work on nonlin-ear photonics based on silicon and germanium Various types of Group IV waveguides are analyzed and optimized for four different wavelength ranges from near- to mid-IR The recently proposed dispersion engineering technique based on stripslot hybrid waveguide structures is used for different material combinations and wavelength ranges Numerical simulations show that the dispersion-flattened Group IV waveguides are preferably suitable for octave-spanning nonlinear applications including on-chip supercontinuum generation ultrashort pulse compres-sion and mode-locked wideband frequency comb genera-tion based on micro-resonators

The presented approach to achieving octave-span-ning nonlinear applications on an integrated CMOS-compatible Group IV platform holds great potential for realizing chip-scale sensing imaging communications and signal processing system The ultrawide transparency windows in the mid-IR allowed by Group IV elements and compounds potentially together with other materi-als [223] provide an exciting arena for building powerful information acquisition and processing units enabled by nonlinear optics nano-photonics and ultrafast optics

Received June 14 2013 accepted October 29 2013 previously pub-lished online November 27 2013

Pow

er (

10 d

Bd

iv)

A

8030 40 50 60 70Frequency (THz)

Pow

er (

W)

B200

150

100

50

0

21 22 23 24 25Time (ps)

Figure 13emsp(A) Frequency comb generation with a CW pump at 6 microm using a microring resonator based on a germanium strip waveguide with air upper cladding (B) Generated pulse waveform with a pulse width of 69 fs as short as 35 optical cycles

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp261

Appendix

A Material index and dispersion

In this section we give the wavelength-dependent mate-rial index expressed as Sellmeier equations where wave-length λ is in μm

For silicon we use the following material index that is a fit curve from measurement results at room temperature (293 K) with 184 data points in total from 112 to 588 μm [154]

22 1 2 2

2 2 22

( )-

C Cn

λλ ε

λ λ λ= + +

where ε = 116858 C1 = 0939816 μm2 C2 = 000810461 and λ2 = 11071 μm

For silicon nitride the material index is affected by deposition conditions using plasma-enhanced chemical vapor deposition (PECVD) low-pressure chemical vapor deposition (LPCVD) and so on We use the following Sell-meier equation [155] which predicts the material index close to that in LPCVD silicon nitride films measured by a few groups [224]

22 1

2 21

( ) 1-

Cn

λλ

λ λ= +

where C1 = 28939 and λ1 = 013967 μmFor silicon dioxide we use the following Sellmeier

equation for fused silica [156]22 2

2 31 22 2 2 2 2 2

1 2 3

( ) 1- - -

CC Cn

λλ λλ

λ λ λ λ λ λ= + + +

where C1 = 06961663 C2 = 04079426 C3 = 08974794 λ1 = 00684043 μm λ2 = 01162414 μm and λ3 = 9896161 μm

For SRO the material index is affected by deposition conditions such as silicon excess annealing temperature and so on Here we choose the one with silicon excess of 8 and annealed at 1250oC [51]

22 22 31 2

2 2 2 2 2 21 2 3

( ) 1- - -

CC Cn

λλ λλ

λ λ λ λ λ λ= + + +

where C1 = 001 C2 = 196 C3 = 141 λ1 = 03 μm λ2 = 007071 μm and λ3 = 2775968 μm

For germanium the temperature-dependent mate-rial index was measured [157] Here we choose the one for room temperature (293 K)

2 22 1 2

2 2 2 21 2

( )- -

C Cn

λ λλ ε

λ λ λ λ= + +

where ε = 928156 C1 = 67288 C2 = 021307 λ1 = 0664116 μm and λ2 = 6221013 μm

For arsenic sulfide we use the material index pro-vided in [158]

2 2 22 22 3 4 51 2

2 2 2 2 2 2 2 2 2 21 2 3 4 5

( ) 1- - - - -

C C CC Cn

λ λ λλ λλ

λ λ λ λ λ λ λ λ λ λ= + + + + +

where C1 = 18983678 C2 = 19222979 C3 = 08765134 C4 = 01188704 C5 = 09569903 λ1 = 015 μm λ2 = 025 μm λ3 = 035 μm λ4 = 045 μm and λ5 = 27386128 μm

For arsenic selenide we fit ellipsometry measure-ments of our arsenic selenide thin films and the bulk material is provided by Prof Kathleen A Richardson group

22 22 31 2

2 2 2 2 2 21 2 3

( ) 1- - -

CC Cn

λλ λλ

λ λ λ λ λ λ= + + +

where C1 = 298463 C2 = 321011 C3 = 100182 λ1 = 044118 μm λ2 = 0000354953 μm and λ3 = 38413 μm

B Nonlinear Kerr index n2

The third-order nonlinear susceptibility χ(3)1111 for silicon and

germanium is predicted over the mid-IR range [133] based on a two-band model The effective nonlinear susceptibil-ity χ(3) is dependent on polarization and crystallographic orientation [225] For strong nonlinearity we consider a single-polarization incident light aligned to the crystal-lographic axis and we have χ(3) = χ(3)

1111 To investigate the octave-spanning nonlinear phenomena one need to take the wavelength-dependent nonlinear Kerr index n2 and TPA coefficient βTPA into account which are expressed as

( 3 )2 2

0

( 3 )2

0

3( ) ( )4 ( )

3( ) ( )( )

re

TPA im

ncn

cn

λ χ λε λ

πβ λ χ λ

λε λ

=

=

where ε0 and c are the vacuum permittivity and the speed of light in vacuum Using the material index given in Appendix A and χ(3) value from [133] we obtain the n2 and βTPA values tabulated as follows

262emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

Table 1enspNonlinear Kerr index n2 in silicon

λμm

  n2

10-18 m2W  λ

μm  n2

10-18 m2W  λ

μm  n2

10-18 m2W

130   234   310   389   490   312135   305   315   384   495   311140   378   320   379   500   310145   443   325   375   505   309150   501   330   371   510   307155   559   335   368   515   306160   618   340   365   520   304165   671   345   362   525   304170   710   350   360   530   303175   741   355   358   535   302180   766   360   355   540   302185   781   365   352   545   301190   783   370   350   550   300195   778   375   346   555   298200   762   380   343   560   297205   732   385   341   565   296210   699   390   338   570   296215   658   395   336   575   295220   612   400   334   580   295225   576   405   332   585   295230   547   410   331   590   294235   525   415   330   595   293240   508   420   329   600   292245   493   425   328   605   291250   479   430   327   610   290255   467   435   325   615   289260   456   440   324   620   288265   448   445   321   625   288270   440   450   319   630   288275   432   455   317   635   288280   424   460   315   640   288285   417   465   314   645   288290   410   470   313   650   288295   404   475   313   655   288300   398   480   312   660   288305   394   485   312    

Table 2enspTPA coefficient βTPA in silicon

λμm

  βTPA

10-12 mW  λ

μm  βTPA

10-12 mW  λ

μm  βTPA

10-12 mW

130   1334   165   812   200   180135   1284   170   713   205   115140   1222   175   613   210   064145   1154   180   522   215   024150   1079   185   424   220   0003155   995   190   333    160   905   195   254    

Table 3enspNonlinear Kerr index n2 in germanium

λμm

  n2

10-18 m2W  λ

μm  n2

10-18 m2W  λ

μm  n2

10-18 m2W

23  3932  63  1986  103  170524  4994  64  1972  104  169925  6007  65  1959  105  169426  6650  66  1946  106  169027  6772  67  1934  107  168728  6273  68  1923  108  168429  4897  69  1913  109  168230  4403  70  1904  110  168131  3970  71  1895  111  167932  3680  72  1886  112  167733  3470  73  1876  113  167534  3286  74  1868  114  167335  3128  75  1859  115  167036  2998  76  1850  116  166737  2895  77  1841  117  166338  2812  78  1833  118  165939  2737  79  1826  119  165640  2668  80  1819  120  165341  2605  81  1812  121  165142  2550  82  1807  122  164843  2498  83  1801  123  164644  2450  84  1797  124  164445  2406  85  1792  125  164346  2365  86  1787  126  164147  2328  87  1782  127  163948  2295  88  1777  128  163649  2266  89  1772  129  163450  2238  90  1767  130  163251  2212  91  1762  131  163052  2187  92  1758  132  162853  2164  93  1753  133  162654  2141  94  1749  134  162555  2121  95  1744  135  162356  2101  96  1740  136  162157  2083  97  1736  137  162058  2066  98  1731  138  161859  2049  99  1727  139  161760  2032  100  1722  140  161661  2016  101  1716   62  2001  102  1711   

Table 4enspTPA coefficient βTPA in germanium

λμm

  βTPA

10-8 mW  λμm

  βTPA

10-8 mW  λ

μm  βTPA

10-8 mW

23   130   25   088   27   03124   111   26   060   28   006

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp263

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[147] Carlie N Musgraves JD Zdyrko B Luzinov I Hu J Singh V Agarwal A Kimerling LC Canciamilla A Morichetti F Melloni A Richardson K Integrated chalcogenide waveguide resonators for mid-IR sensing leveraging material properties to meet fabrication challenges Opt Express 20101826728ndash43

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absorption and Kerr coefficients of silicon for 850ndash2200 nm Appl Phys Lett 200790191104

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp267

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[168] Asobe M Kanamori T Kubodera K Ultrafast all-optical switching using highly nonlinear chalcogenide glass fiber IEEE Photon Technol Lett 19924362ndash5

[169] Asobe M Kanamori T Kubodera K Applications of highly nonlinear chalcogenide glass fibers in ultrafast all-optical switches IEEE J Quant Electron 1993292325ndash33

[170] Ruan Y Luther-Davies B Li W Rode A Kolev V Madden S Large phase shifts in As2S3 waveguides for all-optical processing devices Opt Lett 2005302605ndash7

[171] Laniel JM Hocirc N Valleacutee R Villeneuve A Nonlinear-refractive-index measurement in As2S3 channel waveguides by asymmetric self-phase modulation J Opt Soc Am B 200522437ndash45

[172] Cerqua-Richardson KA McKinley JM Lawrence B Joshi S Villeneuve A Comparison of nonlinear optical properties of sulfide glasses in bulk and thin film form Opt Mater 199810155ndash9

[173] Harbold JM Ilday FOuml Wise FW Sanghera JS Nguyen VQ Shaw LB Aggarwal ID Highly nonlinear As-S-Se glasses for all-optical switching Opt Lett 200227119ndash121

[174] Ruan YL Li WT Jarvis R Madsen N Rode A Luther-Davies B Fabrication and characterization of low loss rib chalcogenide waveguides made by dry etching Opt Express 2004125140ndash5

[175] Slusher RE Lenz G Hodelin J Sanghera J Shaw LB Aggarwal ID Large Raman gain and nonlinear phase shifts in high-purity As2Se3 chalcogenide fibers J Opt Soc Am B 2004211146ndash55

[176] Jacobsen R Andersen K Borel P Fage-Pedersen J Frandsen L Hansen O Kristensen M Lavrinenko A Moulin G Ou H Peucheret C Zsigri B Bjarklev A Strained silicon as a new electro-optic material Nature 2006441199ndash202

[177] Cazzanelli M Bianco F Borga E Pucker G Ghulinyan M Degoli E Luppi E Veacuteniard V Ossicini S Modotto D Wabnitz S Pierobon R Pavesi L Second-harmonic generation in

silicon waveguides strained by silicon nitride Nat Mater 201111148ndash54

[178] Avrutsky I Soref R Phase-matched sum frequency generation in strained silicon waveguides using their second-order nonlinear optical susceptibility Opt Express 20111921707ndash16

[179] Ghahramani E Moss DJ Sipe JE Second-harmonic generation in odd-period strained (Si)n(Ge)nSi superlattices and at SiGe interfaces Phys Rev Lett 1990642815ndash8

[180] Levy JS Foster MA Gaeta AL Lipson M Harmonic generation in silicon nitride ring resonators Opt Express 20111911415

[181] Zakery A Elliott SR Optical nonlinearities in chalcogenide glasses and their applications Springer Series in Optical Sciences 2007135

[182] Lee KK Lim DR Kimerling LC Shin J Cerrina F Fabrication of ultralow-loss SiSiO2 waveguides by roughness reduction Opt Lett 2001261888ndash90

[183] Cardenas J Poitras CB Robinson JT Preston K Chen L Lipson M Low loss etchless silicon photonic waveguides Opt Express 2009174752ndash7

[184] Biberman A Shaw MJ Timurdogan E Wright JB Watts MR Ultralow-loss silicon ring resonators Opt Lett 2012374236ndash8

[185] Walmsley IA Waxer L Dorrer C The role of dispersion in ultrafast optics Rev Sci Instrum 2001721ndash29

[186] Torres JP MHendrych Valencia A Angular dispersion an enabling tool in nonlinear and quantum optics Adv Opt Photon 20102319ndash69

[187] Yin LH Lin Q Agrawal GP Dispersion tailoring and soliton propagation in silicon waveguides Opt Lett 2006311295ndash7

[188] Dulkeith E Xia FN Schares L Green WMJ Vlasov YA Group index and group velocity dispersion in silicon-on-insulator photonic wires Opt Express 2006143853ndash63

[189] Turner AC Manolatou C Schmidt BS Lipson M Tailored anomalous group-velocity dispersion in silicon channel waveguides Opt Express 2006144357ndash62

[190] Dadap JI Panoiu NC Chen X I-Hsieh W Liu X Chou C-Y Dulkeith E McNab SJ Xia F Green WMJ Sekaric L Vlasov YA Osgood RM Jr Nonlinear-optical phase modification in dispersion-engineered Si photonic wires Opt Express 2008161280ndash99

[191] Milosevic MM Matavulj PS Yang PY Bagolini A Mashanovich GZ Rib waveguides for mid-infrared silicon photonics J Opt Soc Am B 2009261760ndash6

[192] Mashanovich GZ Milošević MM Nedeljkovic M Owens N Xiong B Teo EJ Hu Y Low loss silicon waveguides for the mid-infrared Opt Express 2011197112ndash9

[193] Reimer C Nedeljkovic M Stothard DJM Esnault MOS Reardon C OrsquoFaolain L Dunn M Mashanovich GZ Krauss TF Mid-infrared photonic crystal waveguides in silicon Opt Express 20122029361ndash8

[194] Baehr-Jones T Spott A Ilic R Spott A Penkov B Asher W Hochberg M Silicon-on-sapphire integrated waveguides for the midinfrared Opt Express 20101812127ndash35

[195] Li F Jackson S Grillet C Magi E Hudson D Madden SJ Moghe Y OrsquoBrien C Read A Duvall SG Atanackovic P Eggleton BJ Moss D Low propagation loss silicon-on-sapphire waveguides for the midinfrared Opt Express 20111915212ndash20

268emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

[196] Yue Y Zhang L Huang H Beausoleil RG Willner AE Silicon-on-nitride waveguide with ultralow dispersion over an octave-spanning mid-infared wavelength range IEEE Photonics J 20124126ndash32

[197] Khan S Chiles J Ma J Fathpour S Silicon-on-nitride waveguides for mid-and near-infrared integrated photonics Appl Phys Lett 2013102121104

[198] Cheng Z Chen X Wong CY Xu K Tsang HK Mid-infrared suspended membrane waveguide and ring resonator on silicon-on-insulator IEEE Photonics J 201241510ndash9

[199] Lin P-T Singh V Cai Y Kimerling LC Agarwal A Air-clad silicon pedestal structures for broadband mid-infrared microphotonics Opt Lett 2013381031ndash3

[200] Chang YC Paeder V Hvozdara L Hartmann JM Herzig HP Low-loss germanium strip waveguides on silicon for the mid-infrared Opt Lett 2012372883ndash5

[201] Zhang L Yue Y Y Xiao-Li R G Beausoleil Willner AE Highly dispersive slot waveguides Opt Express 2009177095ndash101

[202] Zhang L Yue Y Beausoleil RG Willner AE Analysis and engineering of chromatic dispersion in silicon waveguide bends and ring resonators Opt Express 2011198102ndash7

[203] Zhang L Mu J Singh V Agarwal A Kimerling LC Michel J Intra-cavity dispersion of microresonators and its engineering for octave-spanning Kerr frequency comb generation to be published

[204] Lin Q Zhang L Generalized nonlinear envelope equation with high-order dispersion of nonlinearity to be published

[205] Wang Y Yue R Han H Liao X Raman study of structural order of a-SiNxH and its change upon thermal annealing J Non-Crystalline Solids 2001291107ndash12

[206] Brida D Marangoni M Manzoni C De Silvestri S Cerullo G Two-optical-cycle pulses in the mid-infrared from an optical parametric amplifier Opt Lett 2008332901ndash3

[207] Brida D Manzoni C Cirmi G Marangoni M Bonora S Villoresi P De Silvestri S Cerullo G Few-optical-cycle pulses tunable from the visible to the mid-infrared by optical parametric amplifiers J Opt 201012013001

[208] Kippenberg TJ Holzwarth R Diddams SA Microresonator-based optical frequency combs Science 2011332555ndash9

[209] Levy JS Gondarenko A Foster MA Turner-Foster AC Gaeta AL Lipson M CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects Nat Photonics 2009437ndash40

[210] DelrsquoHaye P Herr T Gavartin E Gorodetsky ML Holzwarth R Kippenberg TJ Octave spanningtunable frequency comb from a microresonator Phys Rev Lett 2011107063901

[211] Okawachi Y Saha K Levy JS Wen YH Lipson M Gaeta AL Octave-spanning frequency combgeneration in a silicon nitride chip Opt Lett 2011363398ndash400

[212] Matsko AB Savchenkov AA Liang W Ilchenko VS Seidel D Maleki L Mode-locked Kerr frequency combs Opt Lett 2011362845ndash7

[213] Herr T Brasch V Jost JD Wang CY Kondratiev NM Gorodetsky ML Kippenberg TJ Temporal solitons in optical microresonators httparxivorgabs12110733

[214] Saha K Okawachi Y Shim B Levy JS Salem R Johnson AR Foster MA Lamont MR Lipson M Gaeta AL Modelocking and femtosecond pulse generation in chip-based frequency combs Opt Express 2013211335ndash43

[215] Coen S Erkintalo M Universal scaling laws of Kerr frequency combs Opt Lett 2013381790ndash2

[216] Lugiato LA Lefever R Spatial dissipative structures in passive optical-systems Phys Rev Lett 1987582209ndash11

[217] Haelterman M Trillo S Wabnitz S Dissipative modulation instability in a nonlinear dispersive ring cavity Opt Commun 199291401ndash7

[218] Coen S Randle HG Sylvestre T Erkintalo M Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato-Lefever model Opt Lett 20133837ndash9

[219] Chembo YK Menyuk CR Spatiotemporal Lugiato-Lefever formalism for Kerr-comb generation in whispering-gallery-mode resonators Phys Rev A 201387053852

[220] Foltynowicz A Mas1owski P Ban T Adler F Cossel KC Briles TC Ye J Optical frequency comb spectroscopy Faraday Discussion 201115023ndash31

[221] Hartl I Li XD Chudoba C Ghanta RK Ko TH Fujimoto JG Ranka JK Windeler RS Ultrahigh-resolution optical coherence tomography using continuum generation in an air silica microstructure optical fiber Opt Lett 200126608ndash10

[222] Brabec T Krausz F Intense few-cycle laser fields Frontiers of nonlinear optics Rev Mod Phys 200072545ndash91

[223] Hu J Meyer J Richardson K Shah L Feature issue introduction mid-IR photonic materials Opt Mater Express 201331571ndash5

[224] Private communications with Dr Jacob Levy in Prof Lipsonrsquos group and Dr Johann Riemensberger in Prof Kippenbergrsquos group

[225] Zhang J Lin Q Piredda G Boyd RW Agrawal GP Fauchet PM Anisotropic nonlinear response of silicon in the near-infrared region Appl Phys Lett 200791071113

Page 14: Lin Zhang*, Anuradha M. Agarwal, Lionel C. Kimerling and ...

260emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

a cross-section of 3200 times 1800 nm2 which has an octave-spanning low-dispersion band from 4 to 767 microm as shown in Figure 8(B) A germanium ring resonator is formed with a bending radius of 564 microm corresponding to a FSR of 200 GHz Pumping at 6 microm with a CW power of 14 W and detuning the pump wavelength by 10 resonance linewidth one can see that a mode-locked wideband mid-IR comb is generated from 358 to 644 THz (ie from 466 to 838 microm) at -40 dB level The FWHM of the produced pulses is 69 fs which corresponds to ~35 optical cycles The pulse peak power is 184 W and the nonlinear conversion efficiency is estimated to be -143 dB Since the pumping frequency is not at the center of the low-dispersion band we only see one peak in the comb spectrum caused by the dispersive wave in the normal dispersion region from Figure 13(A) There is another peak at higher frequencies beyond what is shown in the figure

As shown above broadband dispersion engineering is critical for octave-spanning nonlinear applications in both near- and mid-IR wavelength ranges which enables us to fully utilize the bandwidth allowed by the materials transparency windows Generally speaking the nonlinear applications mentioned here such as supercontinuum generation ultrafast pulse compression and frequency comb generation are often the intermediate steps towards higher-level system applications In the frequency domain a wide spectrum can serve as an electromagnetic carrier to acquire high-volume of information eg for sensing [220] and imaging [221] In the time domain an ultrashort pulse can be used as probe to sample ultrafast phenomena [222]

5 Summary and OutlookWe have presented a review of our recent work on nonlin-ear photonics based on silicon and germanium Various types of Group IV waveguides are analyzed and optimized for four different wavelength ranges from near- to mid-IR The recently proposed dispersion engineering technique based on stripslot hybrid waveguide structures is used for different material combinations and wavelength ranges Numerical simulations show that the dispersion-flattened Group IV waveguides are preferably suitable for octave-spanning nonlinear applications including on-chip supercontinuum generation ultrashort pulse compres-sion and mode-locked wideband frequency comb genera-tion based on micro-resonators

The presented approach to achieving octave-span-ning nonlinear applications on an integrated CMOS-compatible Group IV platform holds great potential for realizing chip-scale sensing imaging communications and signal processing system The ultrawide transparency windows in the mid-IR allowed by Group IV elements and compounds potentially together with other materi-als [223] provide an exciting arena for building powerful information acquisition and processing units enabled by nonlinear optics nano-photonics and ultrafast optics

Received June 14 2013 accepted October 29 2013 previously pub-lished online November 27 2013

Pow

er (

10 d

Bd

iv)

A

8030 40 50 60 70Frequency (THz)

Pow

er (

W)

B200

150

100

50

0

21 22 23 24 25Time (ps)

Figure 13emsp(A) Frequency comb generation with a CW pump at 6 microm using a microring resonator based on a germanium strip waveguide with air upper cladding (B) Generated pulse waveform with a pulse width of 69 fs as short as 35 optical cycles

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp261

Appendix

A Material index and dispersion

In this section we give the wavelength-dependent mate-rial index expressed as Sellmeier equations where wave-length λ is in μm

For silicon we use the following material index that is a fit curve from measurement results at room temperature (293 K) with 184 data points in total from 112 to 588 μm [154]

22 1 2 2

2 2 22

( )-

C Cn

λλ ε

λ λ λ= + +

where ε = 116858 C1 = 0939816 μm2 C2 = 000810461 and λ2 = 11071 μm

For silicon nitride the material index is affected by deposition conditions using plasma-enhanced chemical vapor deposition (PECVD) low-pressure chemical vapor deposition (LPCVD) and so on We use the following Sell-meier equation [155] which predicts the material index close to that in LPCVD silicon nitride films measured by a few groups [224]

22 1

2 21

( ) 1-

Cn

λλ

λ λ= +

where C1 = 28939 and λ1 = 013967 μmFor silicon dioxide we use the following Sellmeier

equation for fused silica [156]22 2

2 31 22 2 2 2 2 2

1 2 3

( ) 1- - -

CC Cn

λλ λλ

λ λ λ λ λ λ= + + +

where C1 = 06961663 C2 = 04079426 C3 = 08974794 λ1 = 00684043 μm λ2 = 01162414 μm and λ3 = 9896161 μm

For SRO the material index is affected by deposition conditions such as silicon excess annealing temperature and so on Here we choose the one with silicon excess of 8 and annealed at 1250oC [51]

22 22 31 2

2 2 2 2 2 21 2 3

( ) 1- - -

CC Cn

λλ λλ

λ λ λ λ λ λ= + + +

where C1 = 001 C2 = 196 C3 = 141 λ1 = 03 μm λ2 = 007071 μm and λ3 = 2775968 μm

For germanium the temperature-dependent mate-rial index was measured [157] Here we choose the one for room temperature (293 K)

2 22 1 2

2 2 2 21 2

( )- -

C Cn

λ λλ ε

λ λ λ λ= + +

where ε = 928156 C1 = 67288 C2 = 021307 λ1 = 0664116 μm and λ2 = 6221013 μm

For arsenic sulfide we use the material index pro-vided in [158]

2 2 22 22 3 4 51 2

2 2 2 2 2 2 2 2 2 21 2 3 4 5

( ) 1- - - - -

C C CC Cn

λ λ λλ λλ

λ λ λ λ λ λ λ λ λ λ= + + + + +

where C1 = 18983678 C2 = 19222979 C3 = 08765134 C4 = 01188704 C5 = 09569903 λ1 = 015 μm λ2 = 025 μm λ3 = 035 μm λ4 = 045 μm and λ5 = 27386128 μm

For arsenic selenide we fit ellipsometry measure-ments of our arsenic selenide thin films and the bulk material is provided by Prof Kathleen A Richardson group

22 22 31 2

2 2 2 2 2 21 2 3

( ) 1- - -

CC Cn

λλ λλ

λ λ λ λ λ λ= + + +

where C1 = 298463 C2 = 321011 C3 = 100182 λ1 = 044118 μm λ2 = 0000354953 μm and λ3 = 38413 μm

B Nonlinear Kerr index n2

The third-order nonlinear susceptibility χ(3)1111 for silicon and

germanium is predicted over the mid-IR range [133] based on a two-band model The effective nonlinear susceptibil-ity χ(3) is dependent on polarization and crystallographic orientation [225] For strong nonlinearity we consider a single-polarization incident light aligned to the crystal-lographic axis and we have χ(3) = χ(3)

1111 To investigate the octave-spanning nonlinear phenomena one need to take the wavelength-dependent nonlinear Kerr index n2 and TPA coefficient βTPA into account which are expressed as

( 3 )2 2

0

( 3 )2

0

3( ) ( )4 ( )

3( ) ( )( )

re

TPA im

ncn

cn

λ χ λε λ

πβ λ χ λ

λε λ

=

=

where ε0 and c are the vacuum permittivity and the speed of light in vacuum Using the material index given in Appendix A and χ(3) value from [133] we obtain the n2 and βTPA values tabulated as follows

262emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

Table 1enspNonlinear Kerr index n2 in silicon

λμm

  n2

10-18 m2W  λ

μm  n2

10-18 m2W  λ

μm  n2

10-18 m2W

130   234   310   389   490   312135   305   315   384   495   311140   378   320   379   500   310145   443   325   375   505   309150   501   330   371   510   307155   559   335   368   515   306160   618   340   365   520   304165   671   345   362   525   304170   710   350   360   530   303175   741   355   358   535   302180   766   360   355   540   302185   781   365   352   545   301190   783   370   350   550   300195   778   375   346   555   298200   762   380   343   560   297205   732   385   341   565   296210   699   390   338   570   296215   658   395   336   575   295220   612   400   334   580   295225   576   405   332   585   295230   547   410   331   590   294235   525   415   330   595   293240   508   420   329   600   292245   493   425   328   605   291250   479   430   327   610   290255   467   435   325   615   289260   456   440   324   620   288265   448   445   321   625   288270   440   450   319   630   288275   432   455   317   635   288280   424   460   315   640   288285   417   465   314   645   288290   410   470   313   650   288295   404   475   313   655   288300   398   480   312   660   288305   394   485   312    

Table 2enspTPA coefficient βTPA in silicon

λμm

  βTPA

10-12 mW  λ

μm  βTPA

10-12 mW  λ

μm  βTPA

10-12 mW

130   1334   165   812   200   180135   1284   170   713   205   115140   1222   175   613   210   064145   1154   180   522   215   024150   1079   185   424   220   0003155   995   190   333    160   905   195   254    

Table 3enspNonlinear Kerr index n2 in germanium

λμm

  n2

10-18 m2W  λ

μm  n2

10-18 m2W  λ

μm  n2

10-18 m2W

23  3932  63  1986  103  170524  4994  64  1972  104  169925  6007  65  1959  105  169426  6650  66  1946  106  169027  6772  67  1934  107  168728  6273  68  1923  108  168429  4897  69  1913  109  168230  4403  70  1904  110  168131  3970  71  1895  111  167932  3680  72  1886  112  167733  3470  73  1876  113  167534  3286  74  1868  114  167335  3128  75  1859  115  167036  2998  76  1850  116  166737  2895  77  1841  117  166338  2812  78  1833  118  165939  2737  79  1826  119  165640  2668  80  1819  120  165341  2605  81  1812  121  165142  2550  82  1807  122  164843  2498  83  1801  123  164644  2450  84  1797  124  164445  2406  85  1792  125  164346  2365  86  1787  126  164147  2328  87  1782  127  163948  2295  88  1777  128  163649  2266  89  1772  129  163450  2238  90  1767  130  163251  2212  91  1762  131  163052  2187  92  1758  132  162853  2164  93  1753  133  162654  2141  94  1749  134  162555  2121  95  1744  135  162356  2101  96  1740  136  162157  2083  97  1736  137  162058  2066  98  1731  138  161859  2049  99  1727  139  161760  2032  100  1722  140  161661  2016  101  1716   62  2001  102  1711   

Table 4enspTPA coefficient βTPA in germanium

λμm

  βTPA

10-8 mW  λμm

  βTPA

10-8 mW  λ

μm  βTPA

10-8 mW

23   130   25   088   27   03124   111   26   060   28   006

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp263

References[1] Bloembergen N Nonlinear Optics London World Scientific 1996[2] Yuen-Ron S The Principles of Nonlinear Optics Hoboken New

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Woodbury EJ Stimulated raman scattering from organic liquids Phys Rev Lett 19629455ndash7

[8] Giordmaine JA Mixing of light beams in crystals Phys Rev Lett 1962819ndash20

[9] Maker PD Terhune RW Nisenoff M Savage CM Effects of dispersion and focusing on the production of optical harmonics Phys Rev Lett 1962821ndash22

[10] Delone NB Kraĭnov VP Fundamentals of nonlinear optics of atomic gases New York Wiley 1987

[11] Nikogosyan DN Nonlinear optical crystals a complete survey Springer Berlin 2005

[12] Govind A Nonlinear fiber optics (4th ed) San Diego California Academic Press 2007

[13] Russell PSTJ Birks TA Lloyd-Lucas FD Photonic Bloch waves and photonic band gaps In lsquoConfined electrons and photons New physics and applicationsrsquo New York Plenum Press 1995

[14] Dudley JM Genty G Coen S Supercontinuum generation in photonic crystal fiber Rev Mod Phys 2006781135ndash1184

[15] Dudley JM Taylor JR Ten years of nonlinear optics in photonic crystal fibre Nature Photonics 2009385ndash90

[16] Soref RA Silicon-based optoelectronics Proceedings of the IEEE 1993811687ndash1706

[17] Kimerling LC Silicon for photonics Proc SPIE 3002 1997192[18] Kimerling LC Silicon materials engineering for the next

millennium Sol St Phen 199970131ndash142[19] Pavesi L Lockwood DJ editors Silicon Photonics New York

Springer 2004[20] Reed GT Knights AP Silicon photonics an introduction Wiley

Hoboken NJ 2004[21] Lipson M Guiding modulating and emitting light on silicon -

challenges and opportunities IEEE J Lightwave Technol 2005 234222

[22] Soref RA The past present and future of silicon photonics IEEE J Sel Top Quantum Electron 2006121678ndash87

[23] Jalali B Paniccia M Reed G Silicon photonics IEEE Microwave Magazine 2006758ndash68

[24] Jalali B Fathpour S Silicon photonics J Lightwave Technol 2006 244600ndash15

[25] Kirchain R Kimerling L A roadmap for nanophotonics Nature Photonics 20071303ndash5

[26] Dekker R Usechak N Foumlrst M Driessen A Ultrafast nonlinear all-optical processes in silicon-on-insulator waveguides J Phys D Appl Phys 200740R249ndash71

[27] Lin Q Painter OJ Agrawal GP Nonlinear optical phenomena in silicon waveguides Modeling and applications Opt Express 20071516604ndash44

[28] Tsang HK Liu Y Nonlinear optical properties of silicon waveguides Semicond Sci Technol 2008 23064007

[29] Osgood RM Jr Panoiu NC Dadap JI Liu X Chen X Hsieh I-W Dulkeith E Green WM Vlasov YA Engineering nonlinearities in nanoscalse optical systems Physics and applications in dispersion-engineered silicon nonaphotonics wires Adv Opt Photon 20091162ndash235

[30] Leuthold J Koos C Freude W Nonlinear silicon photonics Nature Photonics 20104535ndash44

[31] Ikeda K Shen Y Fainman Y Enhanced optical nonlinearity in amorphous silicon and its application to waveguide devices Opt Express 20071517761ndash71

[32] Shoji Y Ogasawara T Kamei T Sakakibara Y Suda S Kintaka K Kawashima H Okano M Hasama T Ishikawa H Mori M Ultrafast nonlinear effects in hydrogenated amorphous silicon wire waveguide Opt Express 2010185668ndash73

[33] Narayanan K Preble SF Optical nonlinearities in hydrogenated-amorphous silicon waveguides Opt Express 2010188998ndash9005

[34] Grillet C Carletti L Monat C Grosse P Ben Bakir B Menezo S Fedeli JM Moss DJ Amorphous silicon nanowires combining high nonlinearity FOM and optical stability Opt Express 20122022609ndash15

[35] Matres J Ballesteros GC Gautier P Feacutedeacuteli J-M Martiacute J Oton CJ High nonlinear figure-of-merit amorphous silicon waveguides Opt Express 2013213932ndash40

[36] Hernaacutendez S Pellegrino P Martiacutenez A Lebour Y Garrido B Spano R Cazzanelli M Daldosso N Pavesi L Jordana E Fedeli JM Linear and nonlinear optical properties of Si nanocrystals in SiO2 deposited by plasma-enhanced chemical-vapor deposition J Appl Phys 2008103 064309

[37] Yuan Z Anopchenko A Daldosso N Guider R Navarro-Urrios D Pitanti A Spano R Pavesi L Silicon Nanocrystals as an Enabling Material for Silicon Photonics Proc IEEE 2009971250ndash68

[38] Spano R Daldosso N Cazzanelli M Ferraioli L Tartara L Yu J Degiorgio V Giordana E Fedeli JM Pavesi L Bound electronic and free carrier nonlinearities in Silicon nanocrystals at 1550 nm Opt Express 2009173941ndash50

[39] Rukhlenko ID Zhu W Premaratne M Agrawal GP Effective third-order susceptibility of silicon-nanocrystal-doped silica Opt Express 20122026275ndash84

[40] Loacutepez-Suaacuterez A Torres-Torres C Rangel-Rojo R Reyes-Esqueda JA Santana G Alonso JC Ortiz A Oliver A Modification of the nonlinear optical absorption and optical Kerr response exhibited by nc-Si embedded in a silicon-nitride film Opt Express 20091710056ndash68

[41] Minissale S Yerci S Dal Negro L Nonlinear optical properties of low temperature annealed silicon-rich oxide and silicon-rich nitride materials for silicon photonics Appl Phys Lett 2012100021109

[42] Yamada H Shirane M Chu T Yokoyama H Ishida S Arakawa Y Nonlinear-optic silicon-nanowire waveguides Japanese J Appl Phys 2005446541ndash5

[43] Almeida VR Xu QF Barrios CA Lipson M Guiding and confining light in void nanostructure Opt Lett 2004291209ndash11

264emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

[44] Xu Q Almeida VR Panepucci RR Lipson M Experimental demonstration of guiding and confining light in nanometer-size low-refractive-index material Opt Lett 2004291626ndash8

[45] Baehr-Jones T Hochberg M Walker C Scherer A High-Q optical resonators in silicon-on-insulator based slot waveguides Appl Phys Lett 200586081101

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[141] Zlatanovic S Park JS Moro S Boggio JMC Divliansky IB Alic N Mookherjea S Radic S Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source Nat Photonics 20104561ndash4

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silicon waveguides strained by silicon nitride Nat Mater 201111148ndash54

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[188] Dulkeith E Xia FN Schares L Green WMJ Vlasov YA Group index and group velocity dispersion in silicon-on-insulator photonic wires Opt Express 2006143853ndash63

[189] Turner AC Manolatou C Schmidt BS Lipson M Tailored anomalous group-velocity dispersion in silicon channel waveguides Opt Express 2006144357ndash62

[190] Dadap JI Panoiu NC Chen X I-Hsieh W Liu X Chou C-Y Dulkeith E McNab SJ Xia F Green WMJ Sekaric L Vlasov YA Osgood RM Jr Nonlinear-optical phase modification in dispersion-engineered Si photonic wires Opt Express 2008161280ndash99

[191] Milosevic MM Matavulj PS Yang PY Bagolini A Mashanovich GZ Rib waveguides for mid-infrared silicon photonics J Opt Soc Am B 2009261760ndash6

[192] Mashanovich GZ Milošević MM Nedeljkovic M Owens N Xiong B Teo EJ Hu Y Low loss silicon waveguides for the mid-infrared Opt Express 2011197112ndash9

[193] Reimer C Nedeljkovic M Stothard DJM Esnault MOS Reardon C OrsquoFaolain L Dunn M Mashanovich GZ Krauss TF Mid-infrared photonic crystal waveguides in silicon Opt Express 20122029361ndash8

[194] Baehr-Jones T Spott A Ilic R Spott A Penkov B Asher W Hochberg M Silicon-on-sapphire integrated waveguides for the midinfrared Opt Express 20101812127ndash35

[195] Li F Jackson S Grillet C Magi E Hudson D Madden SJ Moghe Y OrsquoBrien C Read A Duvall SG Atanackovic P Eggleton BJ Moss D Low propagation loss silicon-on-sapphire waveguides for the midinfrared Opt Express 20111915212ndash20

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[196] Yue Y Zhang L Huang H Beausoleil RG Willner AE Silicon-on-nitride waveguide with ultralow dispersion over an octave-spanning mid-infared wavelength range IEEE Photonics J 20124126ndash32

[197] Khan S Chiles J Ma J Fathpour S Silicon-on-nitride waveguides for mid-and near-infrared integrated photonics Appl Phys Lett 2013102121104

[198] Cheng Z Chen X Wong CY Xu K Tsang HK Mid-infrared suspended membrane waveguide and ring resonator on silicon-on-insulator IEEE Photonics J 201241510ndash9

[199] Lin P-T Singh V Cai Y Kimerling LC Agarwal A Air-clad silicon pedestal structures for broadband mid-infrared microphotonics Opt Lett 2013381031ndash3

[200] Chang YC Paeder V Hvozdara L Hartmann JM Herzig HP Low-loss germanium strip waveguides on silicon for the mid-infrared Opt Lett 2012372883ndash5

[201] Zhang L Yue Y Y Xiao-Li R G Beausoleil Willner AE Highly dispersive slot waveguides Opt Express 2009177095ndash101

[202] Zhang L Yue Y Beausoleil RG Willner AE Analysis and engineering of chromatic dispersion in silicon waveguide bends and ring resonators Opt Express 2011198102ndash7

[203] Zhang L Mu J Singh V Agarwal A Kimerling LC Michel J Intra-cavity dispersion of microresonators and its engineering for octave-spanning Kerr frequency comb generation to be published

[204] Lin Q Zhang L Generalized nonlinear envelope equation with high-order dispersion of nonlinearity to be published

[205] Wang Y Yue R Han H Liao X Raman study of structural order of a-SiNxH and its change upon thermal annealing J Non-Crystalline Solids 2001291107ndash12

[206] Brida D Marangoni M Manzoni C De Silvestri S Cerullo G Two-optical-cycle pulses in the mid-infrared from an optical parametric amplifier Opt Lett 2008332901ndash3

[207] Brida D Manzoni C Cirmi G Marangoni M Bonora S Villoresi P De Silvestri S Cerullo G Few-optical-cycle pulses tunable from the visible to the mid-infrared by optical parametric amplifiers J Opt 201012013001

[208] Kippenberg TJ Holzwarth R Diddams SA Microresonator-based optical frequency combs Science 2011332555ndash9

[209] Levy JS Gondarenko A Foster MA Turner-Foster AC Gaeta AL Lipson M CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects Nat Photonics 2009437ndash40

[210] DelrsquoHaye P Herr T Gavartin E Gorodetsky ML Holzwarth R Kippenberg TJ Octave spanningtunable frequency comb from a microresonator Phys Rev Lett 2011107063901

[211] Okawachi Y Saha K Levy JS Wen YH Lipson M Gaeta AL Octave-spanning frequency combgeneration in a silicon nitride chip Opt Lett 2011363398ndash400

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[213] Herr T Brasch V Jost JD Wang CY Kondratiev NM Gorodetsky ML Kippenberg TJ Temporal solitons in optical microresonators httparxivorgabs12110733

[214] Saha K Okawachi Y Shim B Levy JS Salem R Johnson AR Foster MA Lamont MR Lipson M Gaeta AL Modelocking and femtosecond pulse generation in chip-based frequency combs Opt Express 2013211335ndash43

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[216] Lugiato LA Lefever R Spatial dissipative structures in passive optical-systems Phys Rev Lett 1987582209ndash11

[217] Haelterman M Trillo S Wabnitz S Dissipative modulation instability in a nonlinear dispersive ring cavity Opt Commun 199291401ndash7

[218] Coen S Randle HG Sylvestre T Erkintalo M Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato-Lefever model Opt Lett 20133837ndash9

[219] Chembo YK Menyuk CR Spatiotemporal Lugiato-Lefever formalism for Kerr-comb generation in whispering-gallery-mode resonators Phys Rev A 201387053852

[220] Foltynowicz A Mas1owski P Ban T Adler F Cossel KC Briles TC Ye J Optical frequency comb spectroscopy Faraday Discussion 201115023ndash31

[221] Hartl I Li XD Chudoba C Ghanta RK Ko TH Fujimoto JG Ranka JK Windeler RS Ultrahigh-resolution optical coherence tomography using continuum generation in an air silica microstructure optical fiber Opt Lett 200126608ndash10

[222] Brabec T Krausz F Intense few-cycle laser fields Frontiers of nonlinear optics Rev Mod Phys 200072545ndash91

[223] Hu J Meyer J Richardson K Shah L Feature issue introduction mid-IR photonic materials Opt Mater Express 201331571ndash5

[224] Private communications with Dr Jacob Levy in Prof Lipsonrsquos group and Dr Johann Riemensberger in Prof Kippenbergrsquos group

[225] Zhang J Lin Q Piredda G Boyd RW Agrawal GP Fauchet PM Anisotropic nonlinear response of silicon in the near-infrared region Appl Phys Lett 200791071113

Page 15: Lin Zhang*, Anuradha M. Agarwal, Lionel C. Kimerling and ...

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp261

Appendix

A Material index and dispersion

In this section we give the wavelength-dependent mate-rial index expressed as Sellmeier equations where wave-length λ is in μm

For silicon we use the following material index that is a fit curve from measurement results at room temperature (293 K) with 184 data points in total from 112 to 588 μm [154]

22 1 2 2

2 2 22

( )-

C Cn

λλ ε

λ λ λ= + +

where ε = 116858 C1 = 0939816 μm2 C2 = 000810461 and λ2 = 11071 μm

For silicon nitride the material index is affected by deposition conditions using plasma-enhanced chemical vapor deposition (PECVD) low-pressure chemical vapor deposition (LPCVD) and so on We use the following Sell-meier equation [155] which predicts the material index close to that in LPCVD silicon nitride films measured by a few groups [224]

22 1

2 21

( ) 1-

Cn

λλ

λ λ= +

where C1 = 28939 and λ1 = 013967 μmFor silicon dioxide we use the following Sellmeier

equation for fused silica [156]22 2

2 31 22 2 2 2 2 2

1 2 3

( ) 1- - -

CC Cn

λλ λλ

λ λ λ λ λ λ= + + +

where C1 = 06961663 C2 = 04079426 C3 = 08974794 λ1 = 00684043 μm λ2 = 01162414 μm and λ3 = 9896161 μm

For SRO the material index is affected by deposition conditions such as silicon excess annealing temperature and so on Here we choose the one with silicon excess of 8 and annealed at 1250oC [51]

22 22 31 2

2 2 2 2 2 21 2 3

( ) 1- - -

CC Cn

λλ λλ

λ λ λ λ λ λ= + + +

where C1 = 001 C2 = 196 C3 = 141 λ1 = 03 μm λ2 = 007071 μm and λ3 = 2775968 μm

For germanium the temperature-dependent mate-rial index was measured [157] Here we choose the one for room temperature (293 K)

2 22 1 2

2 2 2 21 2

( )- -

C Cn

λ λλ ε

λ λ λ λ= + +

where ε = 928156 C1 = 67288 C2 = 021307 λ1 = 0664116 μm and λ2 = 6221013 μm

For arsenic sulfide we use the material index pro-vided in [158]

2 2 22 22 3 4 51 2

2 2 2 2 2 2 2 2 2 21 2 3 4 5

( ) 1- - - - -

C C CC Cn

λ λ λλ λλ

λ λ λ λ λ λ λ λ λ λ= + + + + +

where C1 = 18983678 C2 = 19222979 C3 = 08765134 C4 = 01188704 C5 = 09569903 λ1 = 015 μm λ2 = 025 μm λ3 = 035 μm λ4 = 045 μm and λ5 = 27386128 μm

For arsenic selenide we fit ellipsometry measure-ments of our arsenic selenide thin films and the bulk material is provided by Prof Kathleen A Richardson group

22 22 31 2

2 2 2 2 2 21 2 3

( ) 1- - -

CC Cn

λλ λλ

λ λ λ λ λ λ= + + +

where C1 = 298463 C2 = 321011 C3 = 100182 λ1 = 044118 μm λ2 = 0000354953 μm and λ3 = 38413 μm

B Nonlinear Kerr index n2

The third-order nonlinear susceptibility χ(3)1111 for silicon and

germanium is predicted over the mid-IR range [133] based on a two-band model The effective nonlinear susceptibil-ity χ(3) is dependent on polarization and crystallographic orientation [225] For strong nonlinearity we consider a single-polarization incident light aligned to the crystal-lographic axis and we have χ(3) = χ(3)

1111 To investigate the octave-spanning nonlinear phenomena one need to take the wavelength-dependent nonlinear Kerr index n2 and TPA coefficient βTPA into account which are expressed as

( 3 )2 2

0

( 3 )2

0

3( ) ( )4 ( )

3( ) ( )( )

re

TPA im

ncn

cn

λ χ λε λ

πβ λ χ λ

λε λ

=

=

where ε0 and c are the vacuum permittivity and the speed of light in vacuum Using the material index given in Appendix A and χ(3) value from [133] we obtain the n2 and βTPA values tabulated as follows

262emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

Table 1enspNonlinear Kerr index n2 in silicon

λμm

  n2

10-18 m2W  λ

μm  n2

10-18 m2W  λ

μm  n2

10-18 m2W

130   234   310   389   490   312135   305   315   384   495   311140   378   320   379   500   310145   443   325   375   505   309150   501   330   371   510   307155   559   335   368   515   306160   618   340   365   520   304165   671   345   362   525   304170   710   350   360   530   303175   741   355   358   535   302180   766   360   355   540   302185   781   365   352   545   301190   783   370   350   550   300195   778   375   346   555   298200   762   380   343   560   297205   732   385   341   565   296210   699   390   338   570   296215   658   395   336   575   295220   612   400   334   580   295225   576   405   332   585   295230   547   410   331   590   294235   525   415   330   595   293240   508   420   329   600   292245   493   425   328   605   291250   479   430   327   610   290255   467   435   325   615   289260   456   440   324   620   288265   448   445   321   625   288270   440   450   319   630   288275   432   455   317   635   288280   424   460   315   640   288285   417   465   314   645   288290   410   470   313   650   288295   404   475   313   655   288300   398   480   312   660   288305   394   485   312    

Table 2enspTPA coefficient βTPA in silicon

λμm

  βTPA

10-12 mW  λ

μm  βTPA

10-12 mW  λ

μm  βTPA

10-12 mW

130   1334   165   812   200   180135   1284   170   713   205   115140   1222   175   613   210   064145   1154   180   522   215   024150   1079   185   424   220   0003155   995   190   333    160   905   195   254    

Table 3enspNonlinear Kerr index n2 in germanium

λμm

  n2

10-18 m2W  λ

μm  n2

10-18 m2W  λ

μm  n2

10-18 m2W

23  3932  63  1986  103  170524  4994  64  1972  104  169925  6007  65  1959  105  169426  6650  66  1946  106  169027  6772  67  1934  107  168728  6273  68  1923  108  168429  4897  69  1913  109  168230  4403  70  1904  110  168131  3970  71  1895  111  167932  3680  72  1886  112  167733  3470  73  1876  113  167534  3286  74  1868  114  167335  3128  75  1859  115  167036  2998  76  1850  116  166737  2895  77  1841  117  166338  2812  78  1833  118  165939  2737  79  1826  119  165640  2668  80  1819  120  165341  2605  81  1812  121  165142  2550  82  1807  122  164843  2498  83  1801  123  164644  2450  84  1797  124  164445  2406  85  1792  125  164346  2365  86  1787  126  164147  2328  87  1782  127  163948  2295  88  1777  128  163649  2266  89  1772  129  163450  2238  90  1767  130  163251  2212  91  1762  131  163052  2187  92  1758  132  162853  2164  93  1753  133  162654  2141  94  1749  134  162555  2121  95  1744  135  162356  2101  96  1740  136  162157  2083  97  1736  137  162058  2066  98  1731  138  161859  2049  99  1727  139  161760  2032  100  1722  140  161661  2016  101  1716   62  2001  102  1711   

Table 4enspTPA coefficient βTPA in germanium

λμm

  βTPA

10-8 mW  λμm

  βTPA

10-8 mW  λ

μm  βTPA

10-8 mW

23   130   25   088   27   03124   111   26   060   28   006

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp263

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[105] Hsieh I-W Chen X Liu X Dadap JI Panoiu NC C-Chou Y Xia F Green WM Vlasov YA Osgood RM Jr Supercontinuum generation in silicon photonic wires Opt Express 20071515242ndash8

[106] Kuyken B Liu X Osgood RM Jr Baets R Roelkens G Green WMJ Mid-infrared to telecom-band supercontinuum generation in highly nonlinear silicon-on-insulator wire waveguides Opt Express 20111920172ndash81

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[109] Claps R Raghunathan V Dimitropoulos D Jalali B Influence of nonlinear absorption on Raman amplification in silicon waveguides Opt Express 2004122774ndash80

[110] Yin L Agrawal GP Impact of two-photon absorption on self-phase modulation in silicon waveguides Opt Lett 2007322031ndash3

[111] Ikeda K Saperstein RE Alic N Fainman Y Thermal and Kerr nonlinear properties of plasma-deposited silicon nitridesilicon dioxide waveguides Opt Express 20081612987ndash94

[112] Levy JS Gondarenko A Foster MA Turner-Foster AC Gaeta AL Lipson M CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects Nat Photonics 2010437ndash40

[113] Tan DTH Ikeda K Sun PC Fainman Y Group velocity dispersion and self phase modulation in silicon nitride waveguides Appl Phys Lett 201096061101

[114] Zhang L Yan Y Yue Y Lin Q Painter O Beausoleil RG Willner AE On-chip two-octave supercontinuum generation by enhancing self-steepening of optical pulses Opt Exp 20111911584ndash90

[115] Halir R Okawachi Y Levy JS Foster MA Lipson M Gaeta AL Ultrabroadband supercontinuum generation in a CMOS-compatible platform Opt Lett 2012371685

[116] Ye J Frequency comb spectroscopy from mid-infrared to extreme ultraviolet Conference on Lasers and Electro-Optics (CLEO) 2012 Tutorial CW1J4

[117] Popmintchev T Chen M-C Popmintchev D Arpin P Brown S Alisauskas S Andriukaitis G Balciunas T Mucke OD Pugzlys A Baltuska A Shim B Schrauth SE Gaeta A Hernandez-Garcia C Plaja L Becker A Jaron-Becker A Murnane MM Kapteyn HC Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers Science 20123361287ndash91

[118] Qin GS Yan X Kito C Liao M Chaudhari C Suzuki T Ohishi Y Ultrabroadband supercontinuum generation from ultraviolet to 628 microm in a fluoride fiber Appl Phys Lett 200995 161103ndash1ndash161103-3

[119] Soref RA Emelett SJ Buchwald WR Silicon waveguided components for the long-wave infrared region J Opt A 20068840ndash8

266emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

[120] Soref R Towards Silicon-based Longwave Integrated Optoelectronics (LIO) SPIE Proceedings 6898 (2008) paper 6898-5 SPIE Photonics West Silicon Photonics III Conference San Jose CA (21 Jan 2008)

[121] Mashanovich GZ Milosevic M Matavulj P Timotijevic B Stankovic S Yang PY Teo EJ Breese MBH Bettiol AA Reed GT Silicon photonic waveguides for different wavelength regions Semiconductor Sci Technol 200823064002

[122] Soref R Mid-infrared photonics in silicon and germanium Nat Photonics 20104495ndash7

[123] Green WMJ Liu X Osgood RM Vlasov YA Mid-infrared nonlinear optics in silicon photonic wire waveguides Photonics Society Summer Topical Meeting Series 201062ndash63

[124] Milosevic MM Nedeljkovic M Masaud T-B Jaberansary E Chong HMH Emerson NG Reed GT Mashanovich GZ Silicon waveguides and devices for the mid-infrared Appl Phys Lett 2012101121105

[125] Soref R Group IV photonics for the mid infrared SPIE Photonics West 2013 Proc of SPIE 20138629paper 862902

[126] Crowder JG Smith SD Vass A Keddie J Infrared methods for gas detection in Mid-Infrared Semiconductor Optoelec-tronics New York Springer-Verlag 2006

[127] George Socrates Infrared and Raman Characteristic Group Frequencies Tables and Charts 3rd Ed Chichester John Wiley amp Sons 2001

[128] Longshore R Raimondi P Lumpkin M Selection of detector peak wavelength for optimum infrared system performance Infrared Phys 197616639ndash47

[129] Findlay GA Cutten DR Comparison of performance of 3ndash5-and 8ndash12-microm infrared systems Appl Opt 1989285029ndash37

[130] Labadie L Wallner O Mid-infrared guided optics a perspective for astronomical instruments Opt Express 2009171947ndash62

[131] Pearl S Rotenberg N van Driel HM Three photon absorption in silicon for 2300ndash3300 nm Appl Phys Lett 200893131102

[132] Wang Z Liu H Huang N Sun Q Wen J Li X Influence of three-photon absorption on Mid-infrared cross-phase modulation in silicon-on-sapphire waveguides Opt Express 2013211840ndash8

[133] Hon NK Soref RA Jalali B The third-order nonlinear optical coefficients of Si Ge and Si1-xGex in the midwave and longwave infrared J Appl Phys 2011110011301

[134] Sheik-Bahae M Hutchings DC Hagan DJ Stryland EWV Dispersion of bound electric nonlinear refraction in solids IEEE J Quant Electron 1991271296ndash1309

[135] Jalali B Raghunathan V Shori R Fathpour S Prospects for silicon mid-IR Raman lasers IEEE J Sel Top Quantum Electron 2006121618ndash27

[136] Raghunathan V Borlaug D Rice RR Jalali B Demonstration of a mid-infrared silicon Raman amplifier Opt Express 20071514355ndash62

[137] Chavez Boggio JM Windmiller JR Knutzen M Jiang R Bres C Alic N Stossel B Rottwitt K Radic S 730-nm optical parametric conversion from near- to short-wave infrared band Opt Express 2008165435ndash43

[138] Lin Q Johnson TJ Perahia R Michael CP Painter OJ A proposal for highly tunable optical parametric oscillation in silicon micro-resonators Opt Express 20081610596ndash610

[139] Turner-Foster AC Foster MA Salem R Gaeta AL Lipson M Frequency conversion over two-thirds of an octave in silicon nanowaveguides Opt Express 2010181904ndash8

[140] Liu X Osgood RM Vlasov YA Green WMJ Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides Nat Photonics 20104557ndash60

[141] Zlatanovic S Park JS Moro S Boggio JMC Divliansky IB Alic N Mookherjea S Radic S Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source Nat Photonics 20104561ndash4

[142] Tien EK Huang YW Gao S Song Q Qian F Kalyoncu SK Boyraz O Discrete parametric band conversion in silicon for mid-infrared applications Opt Exp 20101821981ndash9

[143] Lau RKW Meacutenard M Okawachi Y Foster MA A C Turner-Foster Salem R Lipson M Gaeta AL Continuous-wave mid-infrared frequency conversion in silicon nanowaveguides Opt Lett 2011361263ndash5

[144] Roelkens G Green WMJ Kuyken B Liu X Hattasan N Gassenq A Cerutti L Rodriguez JB Osgood RM Tournie E Baets R III-Vsilicon photonics for short-wave infrared spectroscopy IEEE J Quant Electron 201248292ndash8

[145] Alloatti L Korn D Weimann C Koos C Freude W Leuthold J Second-order nonlinear silicon-organic hybrid waveguides Opt Express 20122020506ndash15

[146] Harris DC Durable 3ndash5 μm transmitting infrared window materials Infrared Phys Technol 199839185ndash201

[147] Carlie N Musgraves JD Zdyrko B Luzinov I Hu J Singh V Agarwal A Kimerling LC Canciamilla A Morichetti F Melloni A Richardson K Integrated chalcogenide waveguide resonators for mid-IR sensing leveraging material properties to meet fabrication challenges Opt Express 20101826728ndash43

[148] Eggleton BJ B Luther-Davies Richardson K Chalcogenide photonics Nat Photonics 20115141ndash8

[149] Madden SJ Vu KT High-Performance Integrated Optics with Tellurite Glasses Status and Prospects Int J Appl Glass Sci 20123289ndash98

[150] Bindra KS Bookey HT Kar AK Wherrett BS Liu X Jha A Nonlinear optical properties of chalcogenide glasses observation of multiphoton absorption App Phys Lett 2001791939ndash41

[151] Zakery A Ruan Y ARode V Samoc M Luther-Davies B Low-loss waveguides in ultrafast laser-deposited As2S3 chalcogenide films J Opt Soc Am B 200391844ndash52

[152] Lenz G Zimmermann J Katsufuji T MLines E Hwang HY Spalter S Slusher RE Cheong SW Sanghera JS Aggarwal ID Large Kerr effect in bulk Se-based chalcogenide glasses Opt Lett 200025254ndash6

[153] Sanghera JS Shaw LB Aggarwal ID Application of chalcogenide glass optical fibers CR Chimie 20025873ndash83

[154] Palik ED Handbook of optical constants of solids San Diego CA Academic 1998

[155] Philipp HR Optical properties of silicon nitride J Electrochem Soc 1973120295ndash300

[156] Malitson IH Interspecimen comparison of the refractive index of fused silica J Opt Soc Am 1965551205ndash8

[157] Barnes NP Piltch MS Temperature-dependent Sellmeier coefficients and nonlinear optics average power limit for germanium J Opt Soc Am 197969178ndash80

[158] Rodney WS Malitson IH King TA Refractive index of arsenic trisulfide J Opt Soc Am 195848633ndash636

[159] Ellipsometry measurement on the thin film samples by our group[160] Bristow AD Rotenberg N van Driel HM Two-photon

absorption and Kerr coefficients of silicon for 850ndash2200 nm Appl Phys Lett 200790191104

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp267

[161] Lin Q Zhang J Piredda G Boyd RW Fauchet PM Agrawal GP Dispersion of silicon nonlinearities in the near infrared region Appl Phys Lett 200791021111

[162] Mizrahi V DeLong KW Stegeman GI Saifi MA Andrejco MJ Two-photon absorption as a limitation to all-optical switching Opt Lett 1989141140ndash2

[163] Guider R NDaldosso APitanti EJordana Fedeli J-M Pavesi L NanoSi low loss horizontal slot waveguides coupled to high Q ring resonators Opt Express 20091720762ndash70 and its erratum

[164] Ferrera M Razzari L Duchesne D Morandotti R Yang Z Liscidini M Sipe JE Chu S Little BE Moss DJ Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures Nat Photonics 20082 737ndash40

[165] Smektala F Quemard C Leneindre L Lucas J Barthelemy A De Angelis C Chalcogenide glasses with large non-linear refractive indices J Non-Crystalline Solids 1998239139ndash42

[166] Boudebs G Sanchez F Troles J Smektala F Nonlinear optical properties of chalcogenide glasses- comparison between Mach-Zehnder interferometry and Z-scan techniques Opt Comm 2001199425ndash33

[167] Asobe M Suzuki K Kanamori T Kubodera K Nonlinear refractive index measurement in chalcogenide-glass fibers by self-phase modulation APL 1992601153ndash4

[168] Asobe M Kanamori T Kubodera K Ultrafast all-optical switching using highly nonlinear chalcogenide glass fiber IEEE Photon Technol Lett 19924362ndash5

[169] Asobe M Kanamori T Kubodera K Applications of highly nonlinear chalcogenide glass fibers in ultrafast all-optical switches IEEE J Quant Electron 1993292325ndash33

[170] Ruan Y Luther-Davies B Li W Rode A Kolev V Madden S Large phase shifts in As2S3 waveguides for all-optical processing devices Opt Lett 2005302605ndash7

[171] Laniel JM Hocirc N Valleacutee R Villeneuve A Nonlinear-refractive-index measurement in As2S3 channel waveguides by asymmetric self-phase modulation J Opt Soc Am B 200522437ndash45

[172] Cerqua-Richardson KA McKinley JM Lawrence B Joshi S Villeneuve A Comparison of nonlinear optical properties of sulfide glasses in bulk and thin film form Opt Mater 199810155ndash9

[173] Harbold JM Ilday FOuml Wise FW Sanghera JS Nguyen VQ Shaw LB Aggarwal ID Highly nonlinear As-S-Se glasses for all-optical switching Opt Lett 200227119ndash121

[174] Ruan YL Li WT Jarvis R Madsen N Rode A Luther-Davies B Fabrication and characterization of low loss rib chalcogenide waveguides made by dry etching Opt Express 2004125140ndash5

[175] Slusher RE Lenz G Hodelin J Sanghera J Shaw LB Aggarwal ID Large Raman gain and nonlinear phase shifts in high-purity As2Se3 chalcogenide fibers J Opt Soc Am B 2004211146ndash55

[176] Jacobsen R Andersen K Borel P Fage-Pedersen J Frandsen L Hansen O Kristensen M Lavrinenko A Moulin G Ou H Peucheret C Zsigri B Bjarklev A Strained silicon as a new electro-optic material Nature 2006441199ndash202

[177] Cazzanelli M Bianco F Borga E Pucker G Ghulinyan M Degoli E Luppi E Veacuteniard V Ossicini S Modotto D Wabnitz S Pierobon R Pavesi L Second-harmonic generation in

silicon waveguides strained by silicon nitride Nat Mater 201111148ndash54

[178] Avrutsky I Soref R Phase-matched sum frequency generation in strained silicon waveguides using their second-order nonlinear optical susceptibility Opt Express 20111921707ndash16

[179] Ghahramani E Moss DJ Sipe JE Second-harmonic generation in odd-period strained (Si)n(Ge)nSi superlattices and at SiGe interfaces Phys Rev Lett 1990642815ndash8

[180] Levy JS Foster MA Gaeta AL Lipson M Harmonic generation in silicon nitride ring resonators Opt Express 20111911415

[181] Zakery A Elliott SR Optical nonlinearities in chalcogenide glasses and their applications Springer Series in Optical Sciences 2007135

[182] Lee KK Lim DR Kimerling LC Shin J Cerrina F Fabrication of ultralow-loss SiSiO2 waveguides by roughness reduction Opt Lett 2001261888ndash90

[183] Cardenas J Poitras CB Robinson JT Preston K Chen L Lipson M Low loss etchless silicon photonic waveguides Opt Express 2009174752ndash7

[184] Biberman A Shaw MJ Timurdogan E Wright JB Watts MR Ultralow-loss silicon ring resonators Opt Lett 2012374236ndash8

[185] Walmsley IA Waxer L Dorrer C The role of dispersion in ultrafast optics Rev Sci Instrum 2001721ndash29

[186] Torres JP MHendrych Valencia A Angular dispersion an enabling tool in nonlinear and quantum optics Adv Opt Photon 20102319ndash69

[187] Yin LH Lin Q Agrawal GP Dispersion tailoring and soliton propagation in silicon waveguides Opt Lett 2006311295ndash7

[188] Dulkeith E Xia FN Schares L Green WMJ Vlasov YA Group index and group velocity dispersion in silicon-on-insulator photonic wires Opt Express 2006143853ndash63

[189] Turner AC Manolatou C Schmidt BS Lipson M Tailored anomalous group-velocity dispersion in silicon channel waveguides Opt Express 2006144357ndash62

[190] Dadap JI Panoiu NC Chen X I-Hsieh W Liu X Chou C-Y Dulkeith E McNab SJ Xia F Green WMJ Sekaric L Vlasov YA Osgood RM Jr Nonlinear-optical phase modification in dispersion-engineered Si photonic wires Opt Express 2008161280ndash99

[191] Milosevic MM Matavulj PS Yang PY Bagolini A Mashanovich GZ Rib waveguides for mid-infrared silicon photonics J Opt Soc Am B 2009261760ndash6

[192] Mashanovich GZ Milošević MM Nedeljkovic M Owens N Xiong B Teo EJ Hu Y Low loss silicon waveguides for the mid-infrared Opt Express 2011197112ndash9

[193] Reimer C Nedeljkovic M Stothard DJM Esnault MOS Reardon C OrsquoFaolain L Dunn M Mashanovich GZ Krauss TF Mid-infrared photonic crystal waveguides in silicon Opt Express 20122029361ndash8

[194] Baehr-Jones T Spott A Ilic R Spott A Penkov B Asher W Hochberg M Silicon-on-sapphire integrated waveguides for the midinfrared Opt Express 20101812127ndash35

[195] Li F Jackson S Grillet C Magi E Hudson D Madden SJ Moghe Y OrsquoBrien C Read A Duvall SG Atanackovic P Eggleton BJ Moss D Low propagation loss silicon-on-sapphire waveguides for the midinfrared Opt Express 20111915212ndash20

268emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

[196] Yue Y Zhang L Huang H Beausoleil RG Willner AE Silicon-on-nitride waveguide with ultralow dispersion over an octave-spanning mid-infared wavelength range IEEE Photonics J 20124126ndash32

[197] Khan S Chiles J Ma J Fathpour S Silicon-on-nitride waveguides for mid-and near-infrared integrated photonics Appl Phys Lett 2013102121104

[198] Cheng Z Chen X Wong CY Xu K Tsang HK Mid-infrared suspended membrane waveguide and ring resonator on silicon-on-insulator IEEE Photonics J 201241510ndash9

[199] Lin P-T Singh V Cai Y Kimerling LC Agarwal A Air-clad silicon pedestal structures for broadband mid-infrared microphotonics Opt Lett 2013381031ndash3

[200] Chang YC Paeder V Hvozdara L Hartmann JM Herzig HP Low-loss germanium strip waveguides on silicon for the mid-infrared Opt Lett 2012372883ndash5

[201] Zhang L Yue Y Y Xiao-Li R G Beausoleil Willner AE Highly dispersive slot waveguides Opt Express 2009177095ndash101

[202] Zhang L Yue Y Beausoleil RG Willner AE Analysis and engineering of chromatic dispersion in silicon waveguide bends and ring resonators Opt Express 2011198102ndash7

[203] Zhang L Mu J Singh V Agarwal A Kimerling LC Michel J Intra-cavity dispersion of microresonators and its engineering for octave-spanning Kerr frequency comb generation to be published

[204] Lin Q Zhang L Generalized nonlinear envelope equation with high-order dispersion of nonlinearity to be published

[205] Wang Y Yue R Han H Liao X Raman study of structural order of a-SiNxH and its change upon thermal annealing J Non-Crystalline Solids 2001291107ndash12

[206] Brida D Marangoni M Manzoni C De Silvestri S Cerullo G Two-optical-cycle pulses in the mid-infrared from an optical parametric amplifier Opt Lett 2008332901ndash3

[207] Brida D Manzoni C Cirmi G Marangoni M Bonora S Villoresi P De Silvestri S Cerullo G Few-optical-cycle pulses tunable from the visible to the mid-infrared by optical parametric amplifiers J Opt 201012013001

[208] Kippenberg TJ Holzwarth R Diddams SA Microresonator-based optical frequency combs Science 2011332555ndash9

[209] Levy JS Gondarenko A Foster MA Turner-Foster AC Gaeta AL Lipson M CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects Nat Photonics 2009437ndash40

[210] DelrsquoHaye P Herr T Gavartin E Gorodetsky ML Holzwarth R Kippenberg TJ Octave spanningtunable frequency comb from a microresonator Phys Rev Lett 2011107063901

[211] Okawachi Y Saha K Levy JS Wen YH Lipson M Gaeta AL Octave-spanning frequency combgeneration in a silicon nitride chip Opt Lett 2011363398ndash400

[212] Matsko AB Savchenkov AA Liang W Ilchenko VS Seidel D Maleki L Mode-locked Kerr frequency combs Opt Lett 2011362845ndash7

[213] Herr T Brasch V Jost JD Wang CY Kondratiev NM Gorodetsky ML Kippenberg TJ Temporal solitons in optical microresonators httparxivorgabs12110733

[214] Saha K Okawachi Y Shim B Levy JS Salem R Johnson AR Foster MA Lamont MR Lipson M Gaeta AL Modelocking and femtosecond pulse generation in chip-based frequency combs Opt Express 2013211335ndash43

[215] Coen S Erkintalo M Universal scaling laws of Kerr frequency combs Opt Lett 2013381790ndash2

[216] Lugiato LA Lefever R Spatial dissipative structures in passive optical-systems Phys Rev Lett 1987582209ndash11

[217] Haelterman M Trillo S Wabnitz S Dissipative modulation instability in a nonlinear dispersive ring cavity Opt Commun 199291401ndash7

[218] Coen S Randle HG Sylvestre T Erkintalo M Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato-Lefever model Opt Lett 20133837ndash9

[219] Chembo YK Menyuk CR Spatiotemporal Lugiato-Lefever formalism for Kerr-comb generation in whispering-gallery-mode resonators Phys Rev A 201387053852

[220] Foltynowicz A Mas1owski P Ban T Adler F Cossel KC Briles TC Ye J Optical frequency comb spectroscopy Faraday Discussion 201115023ndash31

[221] Hartl I Li XD Chudoba C Ghanta RK Ko TH Fujimoto JG Ranka JK Windeler RS Ultrahigh-resolution optical coherence tomography using continuum generation in an air silica microstructure optical fiber Opt Lett 200126608ndash10

[222] Brabec T Krausz F Intense few-cycle laser fields Frontiers of nonlinear optics Rev Mod Phys 200072545ndash91

[223] Hu J Meyer J Richardson K Shah L Feature issue introduction mid-IR photonic materials Opt Mater Express 201331571ndash5

[224] Private communications with Dr Jacob Levy in Prof Lipsonrsquos group and Dr Johann Riemensberger in Prof Kippenbergrsquos group

[225] Zhang J Lin Q Piredda G Boyd RW Agrawal GP Fauchet PM Anisotropic nonlinear response of silicon in the near-infrared region Appl Phys Lett 200791071113

Page 16: Lin Zhang*, Anuradha M. Agarwal, Lionel C. Kimerling and ...

262emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

Table 1enspNonlinear Kerr index n2 in silicon

λμm

  n2

10-18 m2W  λ

μm  n2

10-18 m2W  λ

μm  n2

10-18 m2W

130   234   310   389   490   312135   305   315   384   495   311140   378   320   379   500   310145   443   325   375   505   309150   501   330   371   510   307155   559   335   368   515   306160   618   340   365   520   304165   671   345   362   525   304170   710   350   360   530   303175   741   355   358   535   302180   766   360   355   540   302185   781   365   352   545   301190   783   370   350   550   300195   778   375   346   555   298200   762   380   343   560   297205   732   385   341   565   296210   699   390   338   570   296215   658   395   336   575   295220   612   400   334   580   295225   576   405   332   585   295230   547   410   331   590   294235   525   415   330   595   293240   508   420   329   600   292245   493   425   328   605   291250   479   430   327   610   290255   467   435   325   615   289260   456   440   324   620   288265   448   445   321   625   288270   440   450   319   630   288275   432   455   317   635   288280   424   460   315   640   288285   417   465   314   645   288290   410   470   313   650   288295   404   475   313   655   288300   398   480   312   660   288305   394   485   312    

Table 2enspTPA coefficient βTPA in silicon

λμm

  βTPA

10-12 mW  λ

μm  βTPA

10-12 mW  λ

μm  βTPA

10-12 mW

130   1334   165   812   200   180135   1284   170   713   205   115140   1222   175   613   210   064145   1154   180   522   215   024150   1079   185   424   220   0003155   995   190   333    160   905   195   254    

Table 3enspNonlinear Kerr index n2 in germanium

λμm

  n2

10-18 m2W  λ

μm  n2

10-18 m2W  λ

μm  n2

10-18 m2W

23  3932  63  1986  103  170524  4994  64  1972  104  169925  6007  65  1959  105  169426  6650  66  1946  106  169027  6772  67  1934  107  168728  6273  68  1923  108  168429  4897  69  1913  109  168230  4403  70  1904  110  168131  3970  71  1895  111  167932  3680  72  1886  112  167733  3470  73  1876  113  167534  3286  74  1868  114  167335  3128  75  1859  115  167036  2998  76  1850  116  166737  2895  77  1841  117  166338  2812  78  1833  118  165939  2737  79  1826  119  165640  2668  80  1819  120  165341  2605  81  1812  121  165142  2550  82  1807  122  164843  2498  83  1801  123  164644  2450  84  1797  124  164445  2406  85  1792  125  164346  2365  86  1787  126  164147  2328  87  1782  127  163948  2295  88  1777  128  163649  2266  89  1772  129  163450  2238  90  1767  130  163251  2212  91  1762  131  163052  2187  92  1758  132  162853  2164  93  1753  133  162654  2141  94  1749  134  162555  2121  95  1744  135  162356  2101  96  1740  136  162157  2083  97  1736  137  162058  2066  98  1731  138  161859  2049  99  1727  139  161760  2032  100  1722  140  161661  2016  101  1716   62  2001  102  1711   

Table 4enspTPA coefficient βTPA in germanium

λμm

  βTPA

10-8 mW  λμm

  βTPA

10-8 mW  λ

μm  βTPA

10-8 mW

23   130   25   088   27   03124   111   26   060   28   006

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp263

References[1] Bloembergen N Nonlinear Optics London World Scientific 1996[2] Yuen-Ron S The Principles of Nonlinear Optics Hoboken New

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Woodbury EJ Stimulated raman scattering from organic liquids Phys Rev Lett 19629455ndash7

[8] Giordmaine JA Mixing of light beams in crystals Phys Rev Lett 1962819ndash20

[9] Maker PD Terhune RW Nisenoff M Savage CM Effects of dispersion and focusing on the production of optical harmonics Phys Rev Lett 1962821ndash22

[10] Delone NB Kraĭnov VP Fundamentals of nonlinear optics of atomic gases New York Wiley 1987

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[12] Govind A Nonlinear fiber optics (4th ed) San Diego California Academic Press 2007

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[14] Dudley JM Genty G Coen S Supercontinuum generation in photonic crystal fiber Rev Mod Phys 2006781135ndash1184

[15] Dudley JM Taylor JR Ten years of nonlinear optics in photonic crystal fibre Nature Photonics 2009385ndash90

[16] Soref RA Silicon-based optoelectronics Proceedings of the IEEE 1993811687ndash1706

[17] Kimerling LC Silicon for photonics Proc SPIE 3002 1997192[18] Kimerling LC Silicon materials engineering for the next

millennium Sol St Phen 199970131ndash142[19] Pavesi L Lockwood DJ editors Silicon Photonics New York

Springer 2004[20] Reed GT Knights AP Silicon photonics an introduction Wiley

Hoboken NJ 2004[21] Lipson M Guiding modulating and emitting light on silicon -

challenges and opportunities IEEE J Lightwave Technol 2005 234222

[22] Soref RA The past present and future of silicon photonics IEEE J Sel Top Quantum Electron 2006121678ndash87

[23] Jalali B Paniccia M Reed G Silicon photonics IEEE Microwave Magazine 2006758ndash68

[24] Jalali B Fathpour S Silicon photonics J Lightwave Technol 2006 244600ndash15

[25] Kirchain R Kimerling L A roadmap for nanophotonics Nature Photonics 20071303ndash5

[26] Dekker R Usechak N Foumlrst M Driessen A Ultrafast nonlinear all-optical processes in silicon-on-insulator waveguides J Phys D Appl Phys 200740R249ndash71

[27] Lin Q Painter OJ Agrawal GP Nonlinear optical phenomena in silicon waveguides Modeling and applications Opt Express 20071516604ndash44

[28] Tsang HK Liu Y Nonlinear optical properties of silicon waveguides Semicond Sci Technol 2008 23064007

[29] Osgood RM Jr Panoiu NC Dadap JI Liu X Chen X Hsieh I-W Dulkeith E Green WM Vlasov YA Engineering nonlinearities in nanoscalse optical systems Physics and applications in dispersion-engineered silicon nonaphotonics wires Adv Opt Photon 20091162ndash235

[30] Leuthold J Koos C Freude W Nonlinear silicon photonics Nature Photonics 20104535ndash44

[31] Ikeda K Shen Y Fainman Y Enhanced optical nonlinearity in amorphous silicon and its application to waveguide devices Opt Express 20071517761ndash71

[32] Shoji Y Ogasawara T Kamei T Sakakibara Y Suda S Kintaka K Kawashima H Okano M Hasama T Ishikawa H Mori M Ultrafast nonlinear effects in hydrogenated amorphous silicon wire waveguide Opt Express 2010185668ndash73

[33] Narayanan K Preble SF Optical nonlinearities in hydrogenated-amorphous silicon waveguides Opt Express 2010188998ndash9005

[34] Grillet C Carletti L Monat C Grosse P Ben Bakir B Menezo S Fedeli JM Moss DJ Amorphous silicon nanowires combining high nonlinearity FOM and optical stability Opt Express 20122022609ndash15

[35] Matres J Ballesteros GC Gautier P Feacutedeacuteli J-M Martiacute J Oton CJ High nonlinear figure-of-merit amorphous silicon waveguides Opt Express 2013213932ndash40

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[141] Zlatanovic S Park JS Moro S Boggio JMC Divliansky IB Alic N Mookherjea S Radic S Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source Nat Photonics 20104561ndash4

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[173] Harbold JM Ilday FOuml Wise FW Sanghera JS Nguyen VQ Shaw LB Aggarwal ID Highly nonlinear As-S-Se glasses for all-optical switching Opt Lett 200227119ndash121

[174] Ruan YL Li WT Jarvis R Madsen N Rode A Luther-Davies B Fabrication and characterization of low loss rib chalcogenide waveguides made by dry etching Opt Express 2004125140ndash5

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[176] Jacobsen R Andersen K Borel P Fage-Pedersen J Frandsen L Hansen O Kristensen M Lavrinenko A Moulin G Ou H Peucheret C Zsigri B Bjarklev A Strained silicon as a new electro-optic material Nature 2006441199ndash202

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silicon waveguides strained by silicon nitride Nat Mater 201111148ndash54

[178] Avrutsky I Soref R Phase-matched sum frequency generation in strained silicon waveguides using their second-order nonlinear optical susceptibility Opt Express 20111921707ndash16

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[181] Zakery A Elliott SR Optical nonlinearities in chalcogenide glasses and their applications Springer Series in Optical Sciences 2007135

[182] Lee KK Lim DR Kimerling LC Shin J Cerrina F Fabrication of ultralow-loss SiSiO2 waveguides by roughness reduction Opt Lett 2001261888ndash90

[183] Cardenas J Poitras CB Robinson JT Preston K Chen L Lipson M Low loss etchless silicon photonic waveguides Opt Express 2009174752ndash7

[184] Biberman A Shaw MJ Timurdogan E Wright JB Watts MR Ultralow-loss silicon ring resonators Opt Lett 2012374236ndash8

[185] Walmsley IA Waxer L Dorrer C The role of dispersion in ultrafast optics Rev Sci Instrum 2001721ndash29

[186] Torres JP MHendrych Valencia A Angular dispersion an enabling tool in nonlinear and quantum optics Adv Opt Photon 20102319ndash69

[187] Yin LH Lin Q Agrawal GP Dispersion tailoring and soliton propagation in silicon waveguides Opt Lett 2006311295ndash7

[188] Dulkeith E Xia FN Schares L Green WMJ Vlasov YA Group index and group velocity dispersion in silicon-on-insulator photonic wires Opt Express 2006143853ndash63

[189] Turner AC Manolatou C Schmidt BS Lipson M Tailored anomalous group-velocity dispersion in silicon channel waveguides Opt Express 2006144357ndash62

[190] Dadap JI Panoiu NC Chen X I-Hsieh W Liu X Chou C-Y Dulkeith E McNab SJ Xia F Green WMJ Sekaric L Vlasov YA Osgood RM Jr Nonlinear-optical phase modification in dispersion-engineered Si photonic wires Opt Express 2008161280ndash99

[191] Milosevic MM Matavulj PS Yang PY Bagolini A Mashanovich GZ Rib waveguides for mid-infrared silicon photonics J Opt Soc Am B 2009261760ndash6

[192] Mashanovich GZ Milošević MM Nedeljkovic M Owens N Xiong B Teo EJ Hu Y Low loss silicon waveguides for the mid-infrared Opt Express 2011197112ndash9

[193] Reimer C Nedeljkovic M Stothard DJM Esnault MOS Reardon C OrsquoFaolain L Dunn M Mashanovich GZ Krauss TF Mid-infrared photonic crystal waveguides in silicon Opt Express 20122029361ndash8

[194] Baehr-Jones T Spott A Ilic R Spott A Penkov B Asher W Hochberg M Silicon-on-sapphire integrated waveguides for the midinfrared Opt Express 20101812127ndash35

[195] Li F Jackson S Grillet C Magi E Hudson D Madden SJ Moghe Y OrsquoBrien C Read A Duvall SG Atanackovic P Eggleton BJ Moss D Low propagation loss silicon-on-sapphire waveguides for the midinfrared Opt Express 20111915212ndash20

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[196] Yue Y Zhang L Huang H Beausoleil RG Willner AE Silicon-on-nitride waveguide with ultralow dispersion over an octave-spanning mid-infared wavelength range IEEE Photonics J 20124126ndash32

[197] Khan S Chiles J Ma J Fathpour S Silicon-on-nitride waveguides for mid-and near-infrared integrated photonics Appl Phys Lett 2013102121104

[198] Cheng Z Chen X Wong CY Xu K Tsang HK Mid-infrared suspended membrane waveguide and ring resonator on silicon-on-insulator IEEE Photonics J 201241510ndash9

[199] Lin P-T Singh V Cai Y Kimerling LC Agarwal A Air-clad silicon pedestal structures for broadband mid-infrared microphotonics Opt Lett 2013381031ndash3

[200] Chang YC Paeder V Hvozdara L Hartmann JM Herzig HP Low-loss germanium strip waveguides on silicon for the mid-infrared Opt Lett 2012372883ndash5

[201] Zhang L Yue Y Y Xiao-Li R G Beausoleil Willner AE Highly dispersive slot waveguides Opt Express 2009177095ndash101

[202] Zhang L Yue Y Beausoleil RG Willner AE Analysis and engineering of chromatic dispersion in silicon waveguide bends and ring resonators Opt Express 2011198102ndash7

[203] Zhang L Mu J Singh V Agarwal A Kimerling LC Michel J Intra-cavity dispersion of microresonators and its engineering for octave-spanning Kerr frequency comb generation to be published

[204] Lin Q Zhang L Generalized nonlinear envelope equation with high-order dispersion of nonlinearity to be published

[205] Wang Y Yue R Han H Liao X Raman study of structural order of a-SiNxH and its change upon thermal annealing J Non-Crystalline Solids 2001291107ndash12

[206] Brida D Marangoni M Manzoni C De Silvestri S Cerullo G Two-optical-cycle pulses in the mid-infrared from an optical parametric amplifier Opt Lett 2008332901ndash3

[207] Brida D Manzoni C Cirmi G Marangoni M Bonora S Villoresi P De Silvestri S Cerullo G Few-optical-cycle pulses tunable from the visible to the mid-infrared by optical parametric amplifiers J Opt 201012013001

[208] Kippenberg TJ Holzwarth R Diddams SA Microresonator-based optical frequency combs Science 2011332555ndash9

[209] Levy JS Gondarenko A Foster MA Turner-Foster AC Gaeta AL Lipson M CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects Nat Photonics 2009437ndash40

[210] DelrsquoHaye P Herr T Gavartin E Gorodetsky ML Holzwarth R Kippenberg TJ Octave spanningtunable frequency comb from a microresonator Phys Rev Lett 2011107063901

[211] Okawachi Y Saha K Levy JS Wen YH Lipson M Gaeta AL Octave-spanning frequency combgeneration in a silicon nitride chip Opt Lett 2011363398ndash400

[212] Matsko AB Savchenkov AA Liang W Ilchenko VS Seidel D Maleki L Mode-locked Kerr frequency combs Opt Lett 2011362845ndash7

[213] Herr T Brasch V Jost JD Wang CY Kondratiev NM Gorodetsky ML Kippenberg TJ Temporal solitons in optical microresonators httparxivorgabs12110733

[214] Saha K Okawachi Y Shim B Levy JS Salem R Johnson AR Foster MA Lamont MR Lipson M Gaeta AL Modelocking and femtosecond pulse generation in chip-based frequency combs Opt Express 2013211335ndash43

[215] Coen S Erkintalo M Universal scaling laws of Kerr frequency combs Opt Lett 2013381790ndash2

[216] Lugiato LA Lefever R Spatial dissipative structures in passive optical-systems Phys Rev Lett 1987582209ndash11

[217] Haelterman M Trillo S Wabnitz S Dissipative modulation instability in a nonlinear dispersive ring cavity Opt Commun 199291401ndash7

[218] Coen S Randle HG Sylvestre T Erkintalo M Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato-Lefever model Opt Lett 20133837ndash9

[219] Chembo YK Menyuk CR Spatiotemporal Lugiato-Lefever formalism for Kerr-comb generation in whispering-gallery-mode resonators Phys Rev A 201387053852

[220] Foltynowicz A Mas1owski P Ban T Adler F Cossel KC Briles TC Ye J Optical frequency comb spectroscopy Faraday Discussion 201115023ndash31

[221] Hartl I Li XD Chudoba C Ghanta RK Ko TH Fujimoto JG Ranka JK Windeler RS Ultrahigh-resolution optical coherence tomography using continuum generation in an air silica microstructure optical fiber Opt Lett 200126608ndash10

[222] Brabec T Krausz F Intense few-cycle laser fields Frontiers of nonlinear optics Rev Mod Phys 200072545ndash91

[223] Hu J Meyer J Richardson K Shah L Feature issue introduction mid-IR photonic materials Opt Mater Express 201331571ndash5

[224] Private communications with Dr Jacob Levy in Prof Lipsonrsquos group and Dr Johann Riemensberger in Prof Kippenbergrsquos group

[225] Zhang J Lin Q Piredda G Boyd RW Agrawal GP Fauchet PM Anisotropic nonlinear response of silicon in the near-infrared region Appl Phys Lett 200791071113

Page 17: Lin Zhang*, Anuradha M. Agarwal, Lionel C. Kimerling and ...

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp263

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[100] Foster MA Turner AC Salem R Lipson M Gaeta AL Broad-band continuous-wave parametric wavelength conversion in silicon nanowaveguides Opt Express 20071512949ndash58

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[103] Yin L Lin Q Agrawal GP Soliton fission and supercontinuum generation in silicon waveguides Opt Lett 200732391ndash3

[104] Koonath P Solli DR Jalali B Continuum generation and carving on a silicon chip Appl Phys Lett 200791061111

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[106] Kuyken B Liu X Osgood RM Jr Baets R Roelkens G Green WMJ Mid-infrared to telecom-band supercontinuum generation in highly nonlinear silicon-on-insulator wire waveguides Opt Express 20111920172ndash81

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[111] Ikeda K Saperstein RE Alic N Fainman Y Thermal and Kerr nonlinear properties of plasma-deposited silicon nitridesilicon dioxide waveguides Opt Express 20081612987ndash94

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[113] Tan DTH Ikeda K Sun PC Fainman Y Group velocity dispersion and self phase modulation in silicon nitride waveguides Appl Phys Lett 201096061101

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[147] Carlie N Musgraves JD Zdyrko B Luzinov I Hu J Singh V Agarwal A Kimerling LC Canciamilla A Morichetti F Melloni A Richardson K Integrated chalcogenide waveguide resonators for mid-IR sensing leveraging material properties to meet fabrication challenges Opt Express 20101826728ndash43

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[159] Ellipsometry measurement on the thin film samples by our group[160] Bristow AD Rotenberg N van Driel HM Two-photon

absorption and Kerr coefficients of silicon for 850ndash2200 nm Appl Phys Lett 200790191104

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp267

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[163] Guider R NDaldosso APitanti EJordana Fedeli J-M Pavesi L NanoSi low loss horizontal slot waveguides coupled to high Q ring resonators Opt Express 20091720762ndash70 and its erratum

[164] Ferrera M Razzari L Duchesne D Morandotti R Yang Z Liscidini M Sipe JE Chu S Little BE Moss DJ Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures Nat Photonics 20082 737ndash40

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[169] Asobe M Kanamori T Kubodera K Applications of highly nonlinear chalcogenide glass fibers in ultrafast all-optical switches IEEE J Quant Electron 1993292325ndash33

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[173] Harbold JM Ilday FOuml Wise FW Sanghera JS Nguyen VQ Shaw LB Aggarwal ID Highly nonlinear As-S-Se glasses for all-optical switching Opt Lett 200227119ndash121

[174] Ruan YL Li WT Jarvis R Madsen N Rode A Luther-Davies B Fabrication and characterization of low loss rib chalcogenide waveguides made by dry etching Opt Express 2004125140ndash5

[175] Slusher RE Lenz G Hodelin J Sanghera J Shaw LB Aggarwal ID Large Raman gain and nonlinear phase shifts in high-purity As2Se3 chalcogenide fibers J Opt Soc Am B 2004211146ndash55

[176] Jacobsen R Andersen K Borel P Fage-Pedersen J Frandsen L Hansen O Kristensen M Lavrinenko A Moulin G Ou H Peucheret C Zsigri B Bjarklev A Strained silicon as a new electro-optic material Nature 2006441199ndash202

[177] Cazzanelli M Bianco F Borga E Pucker G Ghulinyan M Degoli E Luppi E Veacuteniard V Ossicini S Modotto D Wabnitz S Pierobon R Pavesi L Second-harmonic generation in

silicon waveguides strained by silicon nitride Nat Mater 201111148ndash54

[178] Avrutsky I Soref R Phase-matched sum frequency generation in strained silicon waveguides using their second-order nonlinear optical susceptibility Opt Express 20111921707ndash16

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[181] Zakery A Elliott SR Optical nonlinearities in chalcogenide glasses and their applications Springer Series in Optical Sciences 2007135

[182] Lee KK Lim DR Kimerling LC Shin J Cerrina F Fabrication of ultralow-loss SiSiO2 waveguides by roughness reduction Opt Lett 2001261888ndash90

[183] Cardenas J Poitras CB Robinson JT Preston K Chen L Lipson M Low loss etchless silicon photonic waveguides Opt Express 2009174752ndash7

[184] Biberman A Shaw MJ Timurdogan E Wright JB Watts MR Ultralow-loss silicon ring resonators Opt Lett 2012374236ndash8

[185] Walmsley IA Waxer L Dorrer C The role of dispersion in ultrafast optics Rev Sci Instrum 2001721ndash29

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[187] Yin LH Lin Q Agrawal GP Dispersion tailoring and soliton propagation in silicon waveguides Opt Lett 2006311295ndash7

[188] Dulkeith E Xia FN Schares L Green WMJ Vlasov YA Group index and group velocity dispersion in silicon-on-insulator photonic wires Opt Express 2006143853ndash63

[189] Turner AC Manolatou C Schmidt BS Lipson M Tailored anomalous group-velocity dispersion in silicon channel waveguides Opt Express 2006144357ndash62

[190] Dadap JI Panoiu NC Chen X I-Hsieh W Liu X Chou C-Y Dulkeith E McNab SJ Xia F Green WMJ Sekaric L Vlasov YA Osgood RM Jr Nonlinear-optical phase modification in dispersion-engineered Si photonic wires Opt Express 2008161280ndash99

[191] Milosevic MM Matavulj PS Yang PY Bagolini A Mashanovich GZ Rib waveguides for mid-infrared silicon photonics J Opt Soc Am B 2009261760ndash6

[192] Mashanovich GZ Milošević MM Nedeljkovic M Owens N Xiong B Teo EJ Hu Y Low loss silicon waveguides for the mid-infrared Opt Express 2011197112ndash9

[193] Reimer C Nedeljkovic M Stothard DJM Esnault MOS Reardon C OrsquoFaolain L Dunn M Mashanovich GZ Krauss TF Mid-infrared photonic crystal waveguides in silicon Opt Express 20122029361ndash8

[194] Baehr-Jones T Spott A Ilic R Spott A Penkov B Asher W Hochberg M Silicon-on-sapphire integrated waveguides for the midinfrared Opt Express 20101812127ndash35

[195] Li F Jackson S Grillet C Magi E Hudson D Madden SJ Moghe Y OrsquoBrien C Read A Duvall SG Atanackovic P Eggleton BJ Moss D Low propagation loss silicon-on-sapphire waveguides for the midinfrared Opt Express 20111915212ndash20

268emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

[196] Yue Y Zhang L Huang H Beausoleil RG Willner AE Silicon-on-nitride waveguide with ultralow dispersion over an octave-spanning mid-infared wavelength range IEEE Photonics J 20124126ndash32

[197] Khan S Chiles J Ma J Fathpour S Silicon-on-nitride waveguides for mid-and near-infrared integrated photonics Appl Phys Lett 2013102121104

[198] Cheng Z Chen X Wong CY Xu K Tsang HK Mid-infrared suspended membrane waveguide and ring resonator on silicon-on-insulator IEEE Photonics J 201241510ndash9

[199] Lin P-T Singh V Cai Y Kimerling LC Agarwal A Air-clad silicon pedestal structures for broadband mid-infrared microphotonics Opt Lett 2013381031ndash3

[200] Chang YC Paeder V Hvozdara L Hartmann JM Herzig HP Low-loss germanium strip waveguides on silicon for the mid-infrared Opt Lett 2012372883ndash5

[201] Zhang L Yue Y Y Xiao-Li R G Beausoleil Willner AE Highly dispersive slot waveguides Opt Express 2009177095ndash101

[202] Zhang L Yue Y Beausoleil RG Willner AE Analysis and engineering of chromatic dispersion in silicon waveguide bends and ring resonators Opt Express 2011198102ndash7

[203] Zhang L Mu J Singh V Agarwal A Kimerling LC Michel J Intra-cavity dispersion of microresonators and its engineering for octave-spanning Kerr frequency comb generation to be published

[204] Lin Q Zhang L Generalized nonlinear envelope equation with high-order dispersion of nonlinearity to be published

[205] Wang Y Yue R Han H Liao X Raman study of structural order of a-SiNxH and its change upon thermal annealing J Non-Crystalline Solids 2001291107ndash12

[206] Brida D Marangoni M Manzoni C De Silvestri S Cerullo G Two-optical-cycle pulses in the mid-infrared from an optical parametric amplifier Opt Lett 2008332901ndash3

[207] Brida D Manzoni C Cirmi G Marangoni M Bonora S Villoresi P De Silvestri S Cerullo G Few-optical-cycle pulses tunable from the visible to the mid-infrared by optical parametric amplifiers J Opt 201012013001

[208] Kippenberg TJ Holzwarth R Diddams SA Microresonator-based optical frequency combs Science 2011332555ndash9

[209] Levy JS Gondarenko A Foster MA Turner-Foster AC Gaeta AL Lipson M CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects Nat Photonics 2009437ndash40

[210] DelrsquoHaye P Herr T Gavartin E Gorodetsky ML Holzwarth R Kippenberg TJ Octave spanningtunable frequency comb from a microresonator Phys Rev Lett 2011107063901

[211] Okawachi Y Saha K Levy JS Wen YH Lipson M Gaeta AL Octave-spanning frequency combgeneration in a silicon nitride chip Opt Lett 2011363398ndash400

[212] Matsko AB Savchenkov AA Liang W Ilchenko VS Seidel D Maleki L Mode-locked Kerr frequency combs Opt Lett 2011362845ndash7

[213] Herr T Brasch V Jost JD Wang CY Kondratiev NM Gorodetsky ML Kippenberg TJ Temporal solitons in optical microresonators httparxivorgabs12110733

[214] Saha K Okawachi Y Shim B Levy JS Salem R Johnson AR Foster MA Lamont MR Lipson M Gaeta AL Modelocking and femtosecond pulse generation in chip-based frequency combs Opt Express 2013211335ndash43

[215] Coen S Erkintalo M Universal scaling laws of Kerr frequency combs Opt Lett 2013381790ndash2

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[218] Coen S Randle HG Sylvestre T Erkintalo M Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato-Lefever model Opt Lett 20133837ndash9

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[223] Hu J Meyer J Richardson K Shah L Feature issue introduction mid-IR photonic materials Opt Mater Express 201331571ndash5

[224] Private communications with Dr Jacob Levy in Prof Lipsonrsquos group and Dr Johann Riemensberger in Prof Kippenbergrsquos group

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Page 18: Lin Zhang*, Anuradha M. Agarwal, Lionel C. Kimerling and ...

264emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

[44] Xu Q Almeida VR Panepucci RR Lipson M Experimental demonstration of guiding and confining light in nanometer-size low-refractive-index material Opt Lett 2004291626ndash8

[45] Baehr-Jones T Hochberg M Walker C Scherer A High-Q optical resonators in silicon-on-insulator based slot waveguides Appl Phys Lett 200586081101

[46] Sun R Dong P Feng N-N Hong C-Y Michel J Lipson M Kimerling L Horizontal single and multiple slot waveguides optical transmission at λ = 1550 nm Opt Express 20071517967ndash72

[47] Fujisawa T Koshiba M Guided modes of nonlinear slot waveguides IEEE Photon Technol Lett 2006181530ndash32

[48] Sanchis P Blasco J Martiacutenez A Martiacute J Design of silicon-based slot waveguide configurations for optimum nonlinear performance J Lightwave Technol 2007251298ndash1305

[49] Koos C Jacome L Poulton C Leuthold J Freude W Nonlinear silicon-on-insulator waveguides for all-optical signal processing Opt Express 2007155976ndash90

[50] Muellner P Wellenzohn M Hainberger R Nonlinearity of optimized silicon photonic slot waveguides Opt Express 2009179282ndash7

[51] Spano R Galan JV Sanchis P Martinez A Martiacute J Pavesi L Group velocity dispersion in horizontal slot waveguides filled by Si nanocrystals International Conf on Group IV Photonics 2008314ndash6

[52] Zheng Z Iqbal M Liu J Dispersion characteristics of SOI-based slot optical waveguides Opt Commun 20082815151ndash5

[53] Zhang L Yue Y Y Xiao-Li Wang J Beausoleil RG Willner AE Flat and low dispersion in highly nonlinear slot waveguides Opt Express 20101813187ndash93

[54] Mas S Caraquitena J Galaacuten JV Sanchis P Martiacute J Tailoring the dispersion behavior of silicon nanophotonic slot waveguides Opt Express 20101820839ndash44

[55] De Leonardis F Passaro VMN Dispersion engineered silicon nanocrystal slot waveguides for soliton ultrafast optical processing Adv Opt Electron 20112011Article ID 751498 9 pages

[56] Liu Q Gao S Li Z Xie Y He S Dispersion engineering of a silicon-nanocrystal-based slot waveguide for broadband wavelength conversion Appl Opt 2011501260ndash5

[57] Ryu H Kim J Jhon YM Lee S Park N Effect of index contrasts in the wide spectral-range control of slot waveguide dispersion Opt Express 20122013189ndash94

[58] Nolte PW Bohley C Schilling J Tuning of zero group velocity dispersion in infiltrated vertical silicon slot waveguides Opt Express 2013211741ndash50

[59] Zhang L Yue Y Beausoleil RG Willner AE Flattened dispersion in silicon slot waveguides Opt Express 20101820529ndash34

[60] Zhang L Lin Q Yue Y Yan Y Beausoleil RG Willner AE Silicon waveguide with four zero-dispersion wavelengths and its application in on-chip octave-spanning supercontinuum generation Opt Express 2012201685ndash90

[61] Zhu M Liu H Li X Huang N Sun Q Wen J Wang Z Ultrabroadband flat dispersion tailoring of dual-slot silicon waveguides Opt Express 20122015899ndash907

[62] Wang S Hu J Guo H Zeng X Optical Cherenkov radiation in an As2S3 slot waveguide with four zero-dispersion wavelengths Opt Express 2013213067ndash72

[63] Roy S Biancalana F Formation of quartic solitons and a localized continuum in silicon-based slot waveguides Phys Rev A 201387025801

[64] Monat C de Sterke M Eggleton BJ Slow light enhanced nonlinear optics in periodic structures J Opt 201012104003

[65] Boyd RW Material slow light and structural slow light similarities and differences for nonlinear optics [Invited] J Opt Soc Am B 201128A38ndash44

[66] Bao C Hou J Wu H Zhou X Cassan E Gao X Zhang D Low dispersion slow light in slot waveguide grating IEEE Photon Technol Lett 2011231700ndash2

[67] Claps R Dimitropoulos D Raghunathan V Han Y Jalali B Observation of stimulated Raman amplification in silicon waveguides Opt Express 2003111731ndash9

[68] Espinola RL Dadap JI Osgood RM Jr McNab SJ Vlasov YA Raman amplification in ultrasmall silicon-on-insulator wire waveguides Opt Express 2004123713ndash8

[69] Xu Q Almeida VR Lipson M Time-resolved study of Raman gain in highly confined silicon-on-insulator waveguides Opt Express 2004124437ndash42

[70] Liu A Rong H Paniccia M Cohen O Hak D Net optical gain in a low loss silicon-on-insulator waveguide by stimulated Raman scattering Opt Express 2004124261ndash8

[71] Rong H Liu A Nicolaescu R Paniccia M Cohen O Hak D Raman gain and nonlinear optical absorption measurement in a low-loss silicon waveguide Appl Phys Lett 2004852196ndash8

[72] Liang TK Tsang HK Efficient Raman amplification in silicon-on-insulator waveguides Appl Phys Lett 2004853343ndash5

[73] Boyraz O Jalali B Demonstration of a silicon Raman laser Opt Express 2004125269ndash73

[74] Krause M Renner H Brinkmeyer E Analysis of Raman lasing characteristics in silicon-on-insulator waveguides Opt Express 2004125703ndash10

[75] Xu Q Almeida VR Lipson M Demonstration of high Raman gain in a submicrometer-size silicon-on-insulator waveguide Opt Lett 20053035ndash7

[76] Rong H Liu A Jones R Cohen O Hak D Nicolaescu R Fang A Paniccia M An all-silicon Raman laser Nature 2005433292ndash4

[77] Rong H Jones R Liu A Cohen O Hak D Fang A Paniccia M A continuous-wave Raman silicon laser Nature 2005433725ndash8

[78] Chen X Panoiu NC Osgood RM Jr Theory of Raman-mediated pulsed amplification in silicon-wire waveguides IEEE J Quantum Electron 200642160ndash70

[79] Rong H Kuo Y-H Xu S Cohen O Raday O Paniccia M Recent development on silicon-based Raman lasers and amplifiers Proc SPIE 6389 638904-1-9 2006

[80] Okawachi Y Foster MA Sharping JE Gaeta AL Xu Q Lipson M All-optical slow-light on a photonic chip Opt Express 2006142317ndash22

[81] Jalali B Raghunathan V Dimitropoulos D Boyraz O Raman-based silicon photonics IEEE J Sel Top Quantum Electron 200612412ndash21

[82] Rong H Xu S Kuo Y Sih V Cohen O Raday O Paniccia M Low-threshold continuous-wave Raman silicon laser Nature Photon 20071232ndash7

[83] De Leonardis F Passaro VMN Ultrafast Raman pulses in SOI waveguides for nonlinear signal processing IEEE J Sel Top Quant 200814739ndash51

[84] Tsang HK Wong CS Liang TK Day IE Roberts SW Harpin A Drake J Asghari M Optical dispersion two-photon absorption and self-phase modulation in silicon waveguides at 15 μm wavelength Appl Phys Lett 200280416ndash8

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp265

[85] Boyraz O Indukuri T Jalali B Self-phase-modulation induced spectral broadening in silicon waveguides Opt Express 200412829ndash34

[86] Rieger GW Virk KS Yong JF Nonlinear propagation of ultrafast 15 μm pulses in high-index-contrast silicon-on-insulator waveguides Appl Phys Lett 200484900ndash2

[87] Dulkeith E Vlasov YA Chen X Panoiu NC Osgood RM Jr Self-phase-modulation in submicron silicon-on-insulator photonic wires Opt Express 2006145524ndash34

[88] Hsieh I-W Chen X Dadap JI Panoiu NC Osgood RM Jr McNab SJ Vlasov YA Ultrafast-pulse self-phase modulation and third-order dispersion in Si photonic wire-waveguides Opt Express 20061412380ndash7

[89] Hsieh I-W Chen X Dadap JI Panoiu NC Osgood RM Jr McNab SJ Vlasov YA Cross phase modulation-induced spectral and temporal effects on co-propagating femtosecond pulses in silicon photonic wires Opt Express 2007151135ndash46

[90] Zhang J Lin Q Piredda G Boyd RW Agrawal GP Fauchet PM Optical solitons in a silicon waveguide Opt Express 2007157682ndash8

[91] Salem R Foster MA Turner AC Geraghty DF Lipson M Gaeta AL All-optical regeneration on a silicon chip Opt Express 2007157802ndash9

[92] Claps R Raghunathan V Dimitropoulos D Jalali B Anti-Sotkes Raman conversion in silicon waveguides Opt Express 2003112862ndash72

[93] Espinola RL Dadap JI Osgood RM Jr McNab SJ Vlasov YA C-band wavelength conversion in silicon photonic wire waveguides Opt Express 2005134341ndash9

[94] Fukuda H Yamada K Shoji T Takahashi M Tsuchizawa T Watanabe T Takahashi J Itabashi S Four-wave mixing in silicon wire waveguides Opt Express 2005134629ndash37

[95] Rong H Kuo Y Liu A Paniccia M Cohen O High efficiency wavelength conversion of 10 Gbs data in silicon waveguides Opt Express 2006141182ndash8

[96] Lin Q Zhang J Fauchet PM Agrawal GP Ultrabroadband parametric generation and wavelength conversion in silicon waveguides Opt Express 2006144786ndash99

[97] Foster MA Turner AC Sharping JE Schmidt BS Lipson M Gaeta AL Broad-band optical parametric gain on a silicon photonic chip Nature 2006441960ndash3

[98] Yamada K Fukuda H Tsuchizawa T Watanabe T Shoji T Itabashi S All-optical efficient wavelength conversion using silicon photonic wire waveguide IEEE Photon Technol Lett 2006181046ndash8

[99] Kuo Y Rong H Sih V Xu S Paniccia M Cohen O Demonstration of wavelength conversion at 40 Gbs data rate in silicon waveguides Opt Express 20061411721ndash6

[100] Foster MA Turner AC Salem R Lipson M Gaeta AL Broad-band continuous-wave parametric wavelength conversion in silicon nanowaveguides Opt Express 20071512949ndash58

[101] Dai Y Chen X Okawachi Y Turner-Foster AC Foster MA Lipson M Gaeta AL Xu C 1 μs tunable delay using parametric mixing and optical phase conjugation in Si waveguides Opt Express 2009177004ndash10

[102] De Leonardis F Passaro VMN Efficient wavelength conversion in optimized SOI waveguides via pulsed four wave mixing IEEE J Lightwave Technol 2011293523ndash35

[103] Yin L Lin Q Agrawal GP Soliton fission and supercontinuum generation in silicon waveguides Opt Lett 200732391ndash3

[104] Koonath P Solli DR Jalali B Continuum generation and carving on a silicon chip Appl Phys Lett 200791061111

[105] Hsieh I-W Chen X Liu X Dadap JI Panoiu NC C-Chou Y Xia F Green WM Vlasov YA Osgood RM Jr Supercontinuum generation in silicon photonic wires Opt Express 20071515242ndash8

[106] Kuyken B Liu X Osgood RM Jr Baets R Roelkens G Green WMJ Mid-infrared to telecom-band supercontinuum generation in highly nonlinear silicon-on-insulator wire waveguides Opt Express 20111920172ndash81

[107] DeVore PTS Solli DR Ropers C Koonath P Jalali B Stimulated supercontinuum generation extends broadening limits in silicon Appl Phys Lett 2012100101111

[108] Zhang L Lin Q Yue Y Yan Y Beausoleil RG Agarwal A Kimerling LC Michel J Wilner AE On-chip octave-spanning supercontinuum in nanostructured silicon waveguides using ultralow pulse energy IEEE J Sel Top Quant 2012181799ndash806

[109] Claps R Raghunathan V Dimitropoulos D Jalali B Influence of nonlinear absorption on Raman amplification in silicon waveguides Opt Express 2004122774ndash80

[110] Yin L Agrawal GP Impact of two-photon absorption on self-phase modulation in silicon waveguides Opt Lett 2007322031ndash3

[111] Ikeda K Saperstein RE Alic N Fainman Y Thermal and Kerr nonlinear properties of plasma-deposited silicon nitridesilicon dioxide waveguides Opt Express 20081612987ndash94

[112] Levy JS Gondarenko A Foster MA Turner-Foster AC Gaeta AL Lipson M CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects Nat Photonics 2010437ndash40

[113] Tan DTH Ikeda K Sun PC Fainman Y Group velocity dispersion and self phase modulation in silicon nitride waveguides Appl Phys Lett 201096061101

[114] Zhang L Yan Y Yue Y Lin Q Painter O Beausoleil RG Willner AE On-chip two-octave supercontinuum generation by enhancing self-steepening of optical pulses Opt Exp 20111911584ndash90

[115] Halir R Okawachi Y Levy JS Foster MA Lipson M Gaeta AL Ultrabroadband supercontinuum generation in a CMOS-compatible platform Opt Lett 2012371685

[116] Ye J Frequency comb spectroscopy from mid-infrared to extreme ultraviolet Conference on Lasers and Electro-Optics (CLEO) 2012 Tutorial CW1J4

[117] Popmintchev T Chen M-C Popmintchev D Arpin P Brown S Alisauskas S Andriukaitis G Balciunas T Mucke OD Pugzlys A Baltuska A Shim B Schrauth SE Gaeta A Hernandez-Garcia C Plaja L Becker A Jaron-Becker A Murnane MM Kapteyn HC Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers Science 20123361287ndash91

[118] Qin GS Yan X Kito C Liao M Chaudhari C Suzuki T Ohishi Y Ultrabroadband supercontinuum generation from ultraviolet to 628 microm in a fluoride fiber Appl Phys Lett 200995 161103ndash1ndash161103-3

[119] Soref RA Emelett SJ Buchwald WR Silicon waveguided components for the long-wave infrared region J Opt A 20068840ndash8

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[120] Soref R Towards Silicon-based Longwave Integrated Optoelectronics (LIO) SPIE Proceedings 6898 (2008) paper 6898-5 SPIE Photonics West Silicon Photonics III Conference San Jose CA (21 Jan 2008)

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[122] Soref R Mid-infrared photonics in silicon and germanium Nat Photonics 20104495ndash7

[123] Green WMJ Liu X Osgood RM Vlasov YA Mid-infrared nonlinear optics in silicon photonic wire waveguides Photonics Society Summer Topical Meeting Series 201062ndash63

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[125] Soref R Group IV photonics for the mid infrared SPIE Photonics West 2013 Proc of SPIE 20138629paper 862902

[126] Crowder JG Smith SD Vass A Keddie J Infrared methods for gas detection in Mid-Infrared Semiconductor Optoelec-tronics New York Springer-Verlag 2006

[127] George Socrates Infrared and Raman Characteristic Group Frequencies Tables and Charts 3rd Ed Chichester John Wiley amp Sons 2001

[128] Longshore R Raimondi P Lumpkin M Selection of detector peak wavelength for optimum infrared system performance Infrared Phys 197616639ndash47

[129] Findlay GA Cutten DR Comparison of performance of 3ndash5-and 8ndash12-microm infrared systems Appl Opt 1989285029ndash37

[130] Labadie L Wallner O Mid-infrared guided optics a perspective for astronomical instruments Opt Express 2009171947ndash62

[131] Pearl S Rotenberg N van Driel HM Three photon absorption in silicon for 2300ndash3300 nm Appl Phys Lett 200893131102

[132] Wang Z Liu H Huang N Sun Q Wen J Li X Influence of three-photon absorption on Mid-infrared cross-phase modulation in silicon-on-sapphire waveguides Opt Express 2013211840ndash8

[133] Hon NK Soref RA Jalali B The third-order nonlinear optical coefficients of Si Ge and Si1-xGex in the midwave and longwave infrared J Appl Phys 2011110011301

[134] Sheik-Bahae M Hutchings DC Hagan DJ Stryland EWV Dispersion of bound electric nonlinear refraction in solids IEEE J Quant Electron 1991271296ndash1309

[135] Jalali B Raghunathan V Shori R Fathpour S Prospects for silicon mid-IR Raman lasers IEEE J Sel Top Quantum Electron 2006121618ndash27

[136] Raghunathan V Borlaug D Rice RR Jalali B Demonstration of a mid-infrared silicon Raman amplifier Opt Express 20071514355ndash62

[137] Chavez Boggio JM Windmiller JR Knutzen M Jiang R Bres C Alic N Stossel B Rottwitt K Radic S 730-nm optical parametric conversion from near- to short-wave infrared band Opt Express 2008165435ndash43

[138] Lin Q Johnson TJ Perahia R Michael CP Painter OJ A proposal for highly tunable optical parametric oscillation in silicon micro-resonators Opt Express 20081610596ndash610

[139] Turner-Foster AC Foster MA Salem R Gaeta AL Lipson M Frequency conversion over two-thirds of an octave in silicon nanowaveguides Opt Express 2010181904ndash8

[140] Liu X Osgood RM Vlasov YA Green WMJ Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides Nat Photonics 20104557ndash60

[141] Zlatanovic S Park JS Moro S Boggio JMC Divliansky IB Alic N Mookherjea S Radic S Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source Nat Photonics 20104561ndash4

[142] Tien EK Huang YW Gao S Song Q Qian F Kalyoncu SK Boyraz O Discrete parametric band conversion in silicon for mid-infrared applications Opt Exp 20101821981ndash9

[143] Lau RKW Meacutenard M Okawachi Y Foster MA A C Turner-Foster Salem R Lipson M Gaeta AL Continuous-wave mid-infrared frequency conversion in silicon nanowaveguides Opt Lett 2011361263ndash5

[144] Roelkens G Green WMJ Kuyken B Liu X Hattasan N Gassenq A Cerutti L Rodriguez JB Osgood RM Tournie E Baets R III-Vsilicon photonics for short-wave infrared spectroscopy IEEE J Quant Electron 201248292ndash8

[145] Alloatti L Korn D Weimann C Koos C Freude W Leuthold J Second-order nonlinear silicon-organic hybrid waveguides Opt Express 20122020506ndash15

[146] Harris DC Durable 3ndash5 μm transmitting infrared window materials Infrared Phys Technol 199839185ndash201

[147] Carlie N Musgraves JD Zdyrko B Luzinov I Hu J Singh V Agarwal A Kimerling LC Canciamilla A Morichetti F Melloni A Richardson K Integrated chalcogenide waveguide resonators for mid-IR sensing leveraging material properties to meet fabrication challenges Opt Express 20101826728ndash43

[148] Eggleton BJ B Luther-Davies Richardson K Chalcogenide photonics Nat Photonics 20115141ndash8

[149] Madden SJ Vu KT High-Performance Integrated Optics with Tellurite Glasses Status and Prospects Int J Appl Glass Sci 20123289ndash98

[150] Bindra KS Bookey HT Kar AK Wherrett BS Liu X Jha A Nonlinear optical properties of chalcogenide glasses observation of multiphoton absorption App Phys Lett 2001791939ndash41

[151] Zakery A Ruan Y ARode V Samoc M Luther-Davies B Low-loss waveguides in ultrafast laser-deposited As2S3 chalcogenide films J Opt Soc Am B 200391844ndash52

[152] Lenz G Zimmermann J Katsufuji T MLines E Hwang HY Spalter S Slusher RE Cheong SW Sanghera JS Aggarwal ID Large Kerr effect in bulk Se-based chalcogenide glasses Opt Lett 200025254ndash6

[153] Sanghera JS Shaw LB Aggarwal ID Application of chalcogenide glass optical fibers CR Chimie 20025873ndash83

[154] Palik ED Handbook of optical constants of solids San Diego CA Academic 1998

[155] Philipp HR Optical properties of silicon nitride J Electrochem Soc 1973120295ndash300

[156] Malitson IH Interspecimen comparison of the refractive index of fused silica J Opt Soc Am 1965551205ndash8

[157] Barnes NP Piltch MS Temperature-dependent Sellmeier coefficients and nonlinear optics average power limit for germanium J Opt Soc Am 197969178ndash80

[158] Rodney WS Malitson IH King TA Refractive index of arsenic trisulfide J Opt Soc Am 195848633ndash636

[159] Ellipsometry measurement on the thin film samples by our group[160] Bristow AD Rotenberg N van Driel HM Two-photon

absorption and Kerr coefficients of silicon for 850ndash2200 nm Appl Phys Lett 200790191104

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp267

[161] Lin Q Zhang J Piredda G Boyd RW Fauchet PM Agrawal GP Dispersion of silicon nonlinearities in the near infrared region Appl Phys Lett 200791021111

[162] Mizrahi V DeLong KW Stegeman GI Saifi MA Andrejco MJ Two-photon absorption as a limitation to all-optical switching Opt Lett 1989141140ndash2

[163] Guider R NDaldosso APitanti EJordana Fedeli J-M Pavesi L NanoSi low loss horizontal slot waveguides coupled to high Q ring resonators Opt Express 20091720762ndash70 and its erratum

[164] Ferrera M Razzari L Duchesne D Morandotti R Yang Z Liscidini M Sipe JE Chu S Little BE Moss DJ Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures Nat Photonics 20082 737ndash40

[165] Smektala F Quemard C Leneindre L Lucas J Barthelemy A De Angelis C Chalcogenide glasses with large non-linear refractive indices J Non-Crystalline Solids 1998239139ndash42

[166] Boudebs G Sanchez F Troles J Smektala F Nonlinear optical properties of chalcogenide glasses- comparison between Mach-Zehnder interferometry and Z-scan techniques Opt Comm 2001199425ndash33

[167] Asobe M Suzuki K Kanamori T Kubodera K Nonlinear refractive index measurement in chalcogenide-glass fibers by self-phase modulation APL 1992601153ndash4

[168] Asobe M Kanamori T Kubodera K Ultrafast all-optical switching using highly nonlinear chalcogenide glass fiber IEEE Photon Technol Lett 19924362ndash5

[169] Asobe M Kanamori T Kubodera K Applications of highly nonlinear chalcogenide glass fibers in ultrafast all-optical switches IEEE J Quant Electron 1993292325ndash33

[170] Ruan Y Luther-Davies B Li W Rode A Kolev V Madden S Large phase shifts in As2S3 waveguides for all-optical processing devices Opt Lett 2005302605ndash7

[171] Laniel JM Hocirc N Valleacutee R Villeneuve A Nonlinear-refractive-index measurement in As2S3 channel waveguides by asymmetric self-phase modulation J Opt Soc Am B 200522437ndash45

[172] Cerqua-Richardson KA McKinley JM Lawrence B Joshi S Villeneuve A Comparison of nonlinear optical properties of sulfide glasses in bulk and thin film form Opt Mater 199810155ndash9

[173] Harbold JM Ilday FOuml Wise FW Sanghera JS Nguyen VQ Shaw LB Aggarwal ID Highly nonlinear As-S-Se glasses for all-optical switching Opt Lett 200227119ndash121

[174] Ruan YL Li WT Jarvis R Madsen N Rode A Luther-Davies B Fabrication and characterization of low loss rib chalcogenide waveguides made by dry etching Opt Express 2004125140ndash5

[175] Slusher RE Lenz G Hodelin J Sanghera J Shaw LB Aggarwal ID Large Raman gain and nonlinear phase shifts in high-purity As2Se3 chalcogenide fibers J Opt Soc Am B 2004211146ndash55

[176] Jacobsen R Andersen K Borel P Fage-Pedersen J Frandsen L Hansen O Kristensen M Lavrinenko A Moulin G Ou H Peucheret C Zsigri B Bjarklev A Strained silicon as a new electro-optic material Nature 2006441199ndash202

[177] Cazzanelli M Bianco F Borga E Pucker G Ghulinyan M Degoli E Luppi E Veacuteniard V Ossicini S Modotto D Wabnitz S Pierobon R Pavesi L Second-harmonic generation in

silicon waveguides strained by silicon nitride Nat Mater 201111148ndash54

[178] Avrutsky I Soref R Phase-matched sum frequency generation in strained silicon waveguides using their second-order nonlinear optical susceptibility Opt Express 20111921707ndash16

[179] Ghahramani E Moss DJ Sipe JE Second-harmonic generation in odd-period strained (Si)n(Ge)nSi superlattices and at SiGe interfaces Phys Rev Lett 1990642815ndash8

[180] Levy JS Foster MA Gaeta AL Lipson M Harmonic generation in silicon nitride ring resonators Opt Express 20111911415

[181] Zakery A Elliott SR Optical nonlinearities in chalcogenide glasses and their applications Springer Series in Optical Sciences 2007135

[182] Lee KK Lim DR Kimerling LC Shin J Cerrina F Fabrication of ultralow-loss SiSiO2 waveguides by roughness reduction Opt Lett 2001261888ndash90

[183] Cardenas J Poitras CB Robinson JT Preston K Chen L Lipson M Low loss etchless silicon photonic waveguides Opt Express 2009174752ndash7

[184] Biberman A Shaw MJ Timurdogan E Wright JB Watts MR Ultralow-loss silicon ring resonators Opt Lett 2012374236ndash8

[185] Walmsley IA Waxer L Dorrer C The role of dispersion in ultrafast optics Rev Sci Instrum 2001721ndash29

[186] Torres JP MHendrych Valencia A Angular dispersion an enabling tool in nonlinear and quantum optics Adv Opt Photon 20102319ndash69

[187] Yin LH Lin Q Agrawal GP Dispersion tailoring and soliton propagation in silicon waveguides Opt Lett 2006311295ndash7

[188] Dulkeith E Xia FN Schares L Green WMJ Vlasov YA Group index and group velocity dispersion in silicon-on-insulator photonic wires Opt Express 2006143853ndash63

[189] Turner AC Manolatou C Schmidt BS Lipson M Tailored anomalous group-velocity dispersion in silicon channel waveguides Opt Express 2006144357ndash62

[190] Dadap JI Panoiu NC Chen X I-Hsieh W Liu X Chou C-Y Dulkeith E McNab SJ Xia F Green WMJ Sekaric L Vlasov YA Osgood RM Jr Nonlinear-optical phase modification in dispersion-engineered Si photonic wires Opt Express 2008161280ndash99

[191] Milosevic MM Matavulj PS Yang PY Bagolini A Mashanovich GZ Rib waveguides for mid-infrared silicon photonics J Opt Soc Am B 2009261760ndash6

[192] Mashanovich GZ Milošević MM Nedeljkovic M Owens N Xiong B Teo EJ Hu Y Low loss silicon waveguides for the mid-infrared Opt Express 2011197112ndash9

[193] Reimer C Nedeljkovic M Stothard DJM Esnault MOS Reardon C OrsquoFaolain L Dunn M Mashanovich GZ Krauss TF Mid-infrared photonic crystal waveguides in silicon Opt Express 20122029361ndash8

[194] Baehr-Jones T Spott A Ilic R Spott A Penkov B Asher W Hochberg M Silicon-on-sapphire integrated waveguides for the midinfrared Opt Express 20101812127ndash35

[195] Li F Jackson S Grillet C Magi E Hudson D Madden SJ Moghe Y OrsquoBrien C Read A Duvall SG Atanackovic P Eggleton BJ Moss D Low propagation loss silicon-on-sapphire waveguides for the midinfrared Opt Express 20111915212ndash20

268emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

[196] Yue Y Zhang L Huang H Beausoleil RG Willner AE Silicon-on-nitride waveguide with ultralow dispersion over an octave-spanning mid-infared wavelength range IEEE Photonics J 20124126ndash32

[197] Khan S Chiles J Ma J Fathpour S Silicon-on-nitride waveguides for mid-and near-infrared integrated photonics Appl Phys Lett 2013102121104

[198] Cheng Z Chen X Wong CY Xu K Tsang HK Mid-infrared suspended membrane waveguide and ring resonator on silicon-on-insulator IEEE Photonics J 201241510ndash9

[199] Lin P-T Singh V Cai Y Kimerling LC Agarwal A Air-clad silicon pedestal structures for broadband mid-infrared microphotonics Opt Lett 2013381031ndash3

[200] Chang YC Paeder V Hvozdara L Hartmann JM Herzig HP Low-loss germanium strip waveguides on silicon for the mid-infrared Opt Lett 2012372883ndash5

[201] Zhang L Yue Y Y Xiao-Li R G Beausoleil Willner AE Highly dispersive slot waveguides Opt Express 2009177095ndash101

[202] Zhang L Yue Y Beausoleil RG Willner AE Analysis and engineering of chromatic dispersion in silicon waveguide bends and ring resonators Opt Express 2011198102ndash7

[203] Zhang L Mu J Singh V Agarwal A Kimerling LC Michel J Intra-cavity dispersion of microresonators and its engineering for octave-spanning Kerr frequency comb generation to be published

[204] Lin Q Zhang L Generalized nonlinear envelope equation with high-order dispersion of nonlinearity to be published

[205] Wang Y Yue R Han H Liao X Raman study of structural order of a-SiNxH and its change upon thermal annealing J Non-Crystalline Solids 2001291107ndash12

[206] Brida D Marangoni M Manzoni C De Silvestri S Cerullo G Two-optical-cycle pulses in the mid-infrared from an optical parametric amplifier Opt Lett 2008332901ndash3

[207] Brida D Manzoni C Cirmi G Marangoni M Bonora S Villoresi P De Silvestri S Cerullo G Few-optical-cycle pulses tunable from the visible to the mid-infrared by optical parametric amplifiers J Opt 201012013001

[208] Kippenberg TJ Holzwarth R Diddams SA Microresonator-based optical frequency combs Science 2011332555ndash9

[209] Levy JS Gondarenko A Foster MA Turner-Foster AC Gaeta AL Lipson M CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects Nat Photonics 2009437ndash40

[210] DelrsquoHaye P Herr T Gavartin E Gorodetsky ML Holzwarth R Kippenberg TJ Octave spanningtunable frequency comb from a microresonator Phys Rev Lett 2011107063901

[211] Okawachi Y Saha K Levy JS Wen YH Lipson M Gaeta AL Octave-spanning frequency combgeneration in a silicon nitride chip Opt Lett 2011363398ndash400

[212] Matsko AB Savchenkov AA Liang W Ilchenko VS Seidel D Maleki L Mode-locked Kerr frequency combs Opt Lett 2011362845ndash7

[213] Herr T Brasch V Jost JD Wang CY Kondratiev NM Gorodetsky ML Kippenberg TJ Temporal solitons in optical microresonators httparxivorgabs12110733

[214] Saha K Okawachi Y Shim B Levy JS Salem R Johnson AR Foster MA Lamont MR Lipson M Gaeta AL Modelocking and femtosecond pulse generation in chip-based frequency combs Opt Express 2013211335ndash43

[215] Coen S Erkintalo M Universal scaling laws of Kerr frequency combs Opt Lett 2013381790ndash2

[216] Lugiato LA Lefever R Spatial dissipative structures in passive optical-systems Phys Rev Lett 1987582209ndash11

[217] Haelterman M Trillo S Wabnitz S Dissipative modulation instability in a nonlinear dispersive ring cavity Opt Commun 199291401ndash7

[218] Coen S Randle HG Sylvestre T Erkintalo M Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato-Lefever model Opt Lett 20133837ndash9

[219] Chembo YK Menyuk CR Spatiotemporal Lugiato-Lefever formalism for Kerr-comb generation in whispering-gallery-mode resonators Phys Rev A 201387053852

[220] Foltynowicz A Mas1owski P Ban T Adler F Cossel KC Briles TC Ye J Optical frequency comb spectroscopy Faraday Discussion 201115023ndash31

[221] Hartl I Li XD Chudoba C Ghanta RK Ko TH Fujimoto JG Ranka JK Windeler RS Ultrahigh-resolution optical coherence tomography using continuum generation in an air silica microstructure optical fiber Opt Lett 200126608ndash10

[222] Brabec T Krausz F Intense few-cycle laser fields Frontiers of nonlinear optics Rev Mod Phys 200072545ndash91

[223] Hu J Meyer J Richardson K Shah L Feature issue introduction mid-IR photonic materials Opt Mater Express 201331571ndash5

[224] Private communications with Dr Jacob Levy in Prof Lipsonrsquos group and Dr Johann Riemensberger in Prof Kippenbergrsquos group

[225] Zhang J Lin Q Piredda G Boyd RW Agrawal GP Fauchet PM Anisotropic nonlinear response of silicon in the near-infrared region Appl Phys Lett 200791071113

Page 19: Lin Zhang*, Anuradha M. Agarwal, Lionel C. Kimerling and ...

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp265

[85] Boyraz O Indukuri T Jalali B Self-phase-modulation induced spectral broadening in silicon waveguides Opt Express 200412829ndash34

[86] Rieger GW Virk KS Yong JF Nonlinear propagation of ultrafast 15 μm pulses in high-index-contrast silicon-on-insulator waveguides Appl Phys Lett 200484900ndash2

[87] Dulkeith E Vlasov YA Chen X Panoiu NC Osgood RM Jr Self-phase-modulation in submicron silicon-on-insulator photonic wires Opt Express 2006145524ndash34

[88] Hsieh I-W Chen X Dadap JI Panoiu NC Osgood RM Jr McNab SJ Vlasov YA Ultrafast-pulse self-phase modulation and third-order dispersion in Si photonic wire-waveguides Opt Express 20061412380ndash7

[89] Hsieh I-W Chen X Dadap JI Panoiu NC Osgood RM Jr McNab SJ Vlasov YA Cross phase modulation-induced spectral and temporal effects on co-propagating femtosecond pulses in silicon photonic wires Opt Express 2007151135ndash46

[90] Zhang J Lin Q Piredda G Boyd RW Agrawal GP Fauchet PM Optical solitons in a silicon waveguide Opt Express 2007157682ndash8

[91] Salem R Foster MA Turner AC Geraghty DF Lipson M Gaeta AL All-optical regeneration on a silicon chip Opt Express 2007157802ndash9

[92] Claps R Raghunathan V Dimitropoulos D Jalali B Anti-Sotkes Raman conversion in silicon waveguides Opt Express 2003112862ndash72

[93] Espinola RL Dadap JI Osgood RM Jr McNab SJ Vlasov YA C-band wavelength conversion in silicon photonic wire waveguides Opt Express 2005134341ndash9

[94] Fukuda H Yamada K Shoji T Takahashi M Tsuchizawa T Watanabe T Takahashi J Itabashi S Four-wave mixing in silicon wire waveguides Opt Express 2005134629ndash37

[95] Rong H Kuo Y Liu A Paniccia M Cohen O High efficiency wavelength conversion of 10 Gbs data in silicon waveguides Opt Express 2006141182ndash8

[96] Lin Q Zhang J Fauchet PM Agrawal GP Ultrabroadband parametric generation and wavelength conversion in silicon waveguides Opt Express 2006144786ndash99

[97] Foster MA Turner AC Sharping JE Schmidt BS Lipson M Gaeta AL Broad-band optical parametric gain on a silicon photonic chip Nature 2006441960ndash3

[98] Yamada K Fukuda H Tsuchizawa T Watanabe T Shoji T Itabashi S All-optical efficient wavelength conversion using silicon photonic wire waveguide IEEE Photon Technol Lett 2006181046ndash8

[99] Kuo Y Rong H Sih V Xu S Paniccia M Cohen O Demonstration of wavelength conversion at 40 Gbs data rate in silicon waveguides Opt Express 20061411721ndash6

[100] Foster MA Turner AC Salem R Lipson M Gaeta AL Broad-band continuous-wave parametric wavelength conversion in silicon nanowaveguides Opt Express 20071512949ndash58

[101] Dai Y Chen X Okawachi Y Turner-Foster AC Foster MA Lipson M Gaeta AL Xu C 1 μs tunable delay using parametric mixing and optical phase conjugation in Si waveguides Opt Express 2009177004ndash10

[102] De Leonardis F Passaro VMN Efficient wavelength conversion in optimized SOI waveguides via pulsed four wave mixing IEEE J Lightwave Technol 2011293523ndash35

[103] Yin L Lin Q Agrawal GP Soliton fission and supercontinuum generation in silicon waveguides Opt Lett 200732391ndash3

[104] Koonath P Solli DR Jalali B Continuum generation and carving on a silicon chip Appl Phys Lett 200791061111

[105] Hsieh I-W Chen X Liu X Dadap JI Panoiu NC C-Chou Y Xia F Green WM Vlasov YA Osgood RM Jr Supercontinuum generation in silicon photonic wires Opt Express 20071515242ndash8

[106] Kuyken B Liu X Osgood RM Jr Baets R Roelkens G Green WMJ Mid-infrared to telecom-band supercontinuum generation in highly nonlinear silicon-on-insulator wire waveguides Opt Express 20111920172ndash81

[107] DeVore PTS Solli DR Ropers C Koonath P Jalali B Stimulated supercontinuum generation extends broadening limits in silicon Appl Phys Lett 2012100101111

[108] Zhang L Lin Q Yue Y Yan Y Beausoleil RG Agarwal A Kimerling LC Michel J Wilner AE On-chip octave-spanning supercontinuum in nanostructured silicon waveguides using ultralow pulse energy IEEE J Sel Top Quant 2012181799ndash806

[109] Claps R Raghunathan V Dimitropoulos D Jalali B Influence of nonlinear absorption on Raman amplification in silicon waveguides Opt Express 2004122774ndash80

[110] Yin L Agrawal GP Impact of two-photon absorption on self-phase modulation in silicon waveguides Opt Lett 2007322031ndash3

[111] Ikeda K Saperstein RE Alic N Fainman Y Thermal and Kerr nonlinear properties of plasma-deposited silicon nitridesilicon dioxide waveguides Opt Express 20081612987ndash94

[112] Levy JS Gondarenko A Foster MA Turner-Foster AC Gaeta AL Lipson M CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects Nat Photonics 2010437ndash40

[113] Tan DTH Ikeda K Sun PC Fainman Y Group velocity dispersion and self phase modulation in silicon nitride waveguides Appl Phys Lett 201096061101

[114] Zhang L Yan Y Yue Y Lin Q Painter O Beausoleil RG Willner AE On-chip two-octave supercontinuum generation by enhancing self-steepening of optical pulses Opt Exp 20111911584ndash90

[115] Halir R Okawachi Y Levy JS Foster MA Lipson M Gaeta AL Ultrabroadband supercontinuum generation in a CMOS-compatible platform Opt Lett 2012371685

[116] Ye J Frequency comb spectroscopy from mid-infrared to extreme ultraviolet Conference on Lasers and Electro-Optics (CLEO) 2012 Tutorial CW1J4

[117] Popmintchev T Chen M-C Popmintchev D Arpin P Brown S Alisauskas S Andriukaitis G Balciunas T Mucke OD Pugzlys A Baltuska A Shim B Schrauth SE Gaeta A Hernandez-Garcia C Plaja L Becker A Jaron-Becker A Murnane MM Kapteyn HC Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers Science 20123361287ndash91

[118] Qin GS Yan X Kito C Liao M Chaudhari C Suzuki T Ohishi Y Ultrabroadband supercontinuum generation from ultraviolet to 628 microm in a fluoride fiber Appl Phys Lett 200995 161103ndash1ndash161103-3

[119] Soref RA Emelett SJ Buchwald WR Silicon waveguided components for the long-wave infrared region J Opt A 20068840ndash8

266emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

[120] Soref R Towards Silicon-based Longwave Integrated Optoelectronics (LIO) SPIE Proceedings 6898 (2008) paper 6898-5 SPIE Photonics West Silicon Photonics III Conference San Jose CA (21 Jan 2008)

[121] Mashanovich GZ Milosevic M Matavulj P Timotijevic B Stankovic S Yang PY Teo EJ Breese MBH Bettiol AA Reed GT Silicon photonic waveguides for different wavelength regions Semiconductor Sci Technol 200823064002

[122] Soref R Mid-infrared photonics in silicon and germanium Nat Photonics 20104495ndash7

[123] Green WMJ Liu X Osgood RM Vlasov YA Mid-infrared nonlinear optics in silicon photonic wire waveguides Photonics Society Summer Topical Meeting Series 201062ndash63

[124] Milosevic MM Nedeljkovic M Masaud T-B Jaberansary E Chong HMH Emerson NG Reed GT Mashanovich GZ Silicon waveguides and devices for the mid-infrared Appl Phys Lett 2012101121105

[125] Soref R Group IV photonics for the mid infrared SPIE Photonics West 2013 Proc of SPIE 20138629paper 862902

[126] Crowder JG Smith SD Vass A Keddie J Infrared methods for gas detection in Mid-Infrared Semiconductor Optoelec-tronics New York Springer-Verlag 2006

[127] George Socrates Infrared and Raman Characteristic Group Frequencies Tables and Charts 3rd Ed Chichester John Wiley amp Sons 2001

[128] Longshore R Raimondi P Lumpkin M Selection of detector peak wavelength for optimum infrared system performance Infrared Phys 197616639ndash47

[129] Findlay GA Cutten DR Comparison of performance of 3ndash5-and 8ndash12-microm infrared systems Appl Opt 1989285029ndash37

[130] Labadie L Wallner O Mid-infrared guided optics a perspective for astronomical instruments Opt Express 2009171947ndash62

[131] Pearl S Rotenberg N van Driel HM Three photon absorption in silicon for 2300ndash3300 nm Appl Phys Lett 200893131102

[132] Wang Z Liu H Huang N Sun Q Wen J Li X Influence of three-photon absorption on Mid-infrared cross-phase modulation in silicon-on-sapphire waveguides Opt Express 2013211840ndash8

[133] Hon NK Soref RA Jalali B The third-order nonlinear optical coefficients of Si Ge and Si1-xGex in the midwave and longwave infrared J Appl Phys 2011110011301

[134] Sheik-Bahae M Hutchings DC Hagan DJ Stryland EWV Dispersion of bound electric nonlinear refraction in solids IEEE J Quant Electron 1991271296ndash1309

[135] Jalali B Raghunathan V Shori R Fathpour S Prospects for silicon mid-IR Raman lasers IEEE J Sel Top Quantum Electron 2006121618ndash27

[136] Raghunathan V Borlaug D Rice RR Jalali B Demonstration of a mid-infrared silicon Raman amplifier Opt Express 20071514355ndash62

[137] Chavez Boggio JM Windmiller JR Knutzen M Jiang R Bres C Alic N Stossel B Rottwitt K Radic S 730-nm optical parametric conversion from near- to short-wave infrared band Opt Express 2008165435ndash43

[138] Lin Q Johnson TJ Perahia R Michael CP Painter OJ A proposal for highly tunable optical parametric oscillation in silicon micro-resonators Opt Express 20081610596ndash610

[139] Turner-Foster AC Foster MA Salem R Gaeta AL Lipson M Frequency conversion over two-thirds of an octave in silicon nanowaveguides Opt Express 2010181904ndash8

[140] Liu X Osgood RM Vlasov YA Green WMJ Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides Nat Photonics 20104557ndash60

[141] Zlatanovic S Park JS Moro S Boggio JMC Divliansky IB Alic N Mookherjea S Radic S Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source Nat Photonics 20104561ndash4

[142] Tien EK Huang YW Gao S Song Q Qian F Kalyoncu SK Boyraz O Discrete parametric band conversion in silicon for mid-infrared applications Opt Exp 20101821981ndash9

[143] Lau RKW Meacutenard M Okawachi Y Foster MA A C Turner-Foster Salem R Lipson M Gaeta AL Continuous-wave mid-infrared frequency conversion in silicon nanowaveguides Opt Lett 2011361263ndash5

[144] Roelkens G Green WMJ Kuyken B Liu X Hattasan N Gassenq A Cerutti L Rodriguez JB Osgood RM Tournie E Baets R III-Vsilicon photonics for short-wave infrared spectroscopy IEEE J Quant Electron 201248292ndash8

[145] Alloatti L Korn D Weimann C Koos C Freude W Leuthold J Second-order nonlinear silicon-organic hybrid waveguides Opt Express 20122020506ndash15

[146] Harris DC Durable 3ndash5 μm transmitting infrared window materials Infrared Phys Technol 199839185ndash201

[147] Carlie N Musgraves JD Zdyrko B Luzinov I Hu J Singh V Agarwal A Kimerling LC Canciamilla A Morichetti F Melloni A Richardson K Integrated chalcogenide waveguide resonators for mid-IR sensing leveraging material properties to meet fabrication challenges Opt Express 20101826728ndash43

[148] Eggleton BJ B Luther-Davies Richardson K Chalcogenide photonics Nat Photonics 20115141ndash8

[149] Madden SJ Vu KT High-Performance Integrated Optics with Tellurite Glasses Status and Prospects Int J Appl Glass Sci 20123289ndash98

[150] Bindra KS Bookey HT Kar AK Wherrett BS Liu X Jha A Nonlinear optical properties of chalcogenide glasses observation of multiphoton absorption App Phys Lett 2001791939ndash41

[151] Zakery A Ruan Y ARode V Samoc M Luther-Davies B Low-loss waveguides in ultrafast laser-deposited As2S3 chalcogenide films J Opt Soc Am B 200391844ndash52

[152] Lenz G Zimmermann J Katsufuji T MLines E Hwang HY Spalter S Slusher RE Cheong SW Sanghera JS Aggarwal ID Large Kerr effect in bulk Se-based chalcogenide glasses Opt Lett 200025254ndash6

[153] Sanghera JS Shaw LB Aggarwal ID Application of chalcogenide glass optical fibers CR Chimie 20025873ndash83

[154] Palik ED Handbook of optical constants of solids San Diego CA Academic 1998

[155] Philipp HR Optical properties of silicon nitride J Electrochem Soc 1973120295ndash300

[156] Malitson IH Interspecimen comparison of the refractive index of fused silica J Opt Soc Am 1965551205ndash8

[157] Barnes NP Piltch MS Temperature-dependent Sellmeier coefficients and nonlinear optics average power limit for germanium J Opt Soc Am 197969178ndash80

[158] Rodney WS Malitson IH King TA Refractive index of arsenic trisulfide J Opt Soc Am 195848633ndash636

[159] Ellipsometry measurement on the thin film samples by our group[160] Bristow AD Rotenberg N van Driel HM Two-photon

absorption and Kerr coefficients of silicon for 850ndash2200 nm Appl Phys Lett 200790191104

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp267

[161] Lin Q Zhang J Piredda G Boyd RW Fauchet PM Agrawal GP Dispersion of silicon nonlinearities in the near infrared region Appl Phys Lett 200791021111

[162] Mizrahi V DeLong KW Stegeman GI Saifi MA Andrejco MJ Two-photon absorption as a limitation to all-optical switching Opt Lett 1989141140ndash2

[163] Guider R NDaldosso APitanti EJordana Fedeli J-M Pavesi L NanoSi low loss horizontal slot waveguides coupled to high Q ring resonators Opt Express 20091720762ndash70 and its erratum

[164] Ferrera M Razzari L Duchesne D Morandotti R Yang Z Liscidini M Sipe JE Chu S Little BE Moss DJ Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures Nat Photonics 20082 737ndash40

[165] Smektala F Quemard C Leneindre L Lucas J Barthelemy A De Angelis C Chalcogenide glasses with large non-linear refractive indices J Non-Crystalline Solids 1998239139ndash42

[166] Boudebs G Sanchez F Troles J Smektala F Nonlinear optical properties of chalcogenide glasses- comparison between Mach-Zehnder interferometry and Z-scan techniques Opt Comm 2001199425ndash33

[167] Asobe M Suzuki K Kanamori T Kubodera K Nonlinear refractive index measurement in chalcogenide-glass fibers by self-phase modulation APL 1992601153ndash4

[168] Asobe M Kanamori T Kubodera K Ultrafast all-optical switching using highly nonlinear chalcogenide glass fiber IEEE Photon Technol Lett 19924362ndash5

[169] Asobe M Kanamori T Kubodera K Applications of highly nonlinear chalcogenide glass fibers in ultrafast all-optical switches IEEE J Quant Electron 1993292325ndash33

[170] Ruan Y Luther-Davies B Li W Rode A Kolev V Madden S Large phase shifts in As2S3 waveguides for all-optical processing devices Opt Lett 2005302605ndash7

[171] Laniel JM Hocirc N Valleacutee R Villeneuve A Nonlinear-refractive-index measurement in As2S3 channel waveguides by asymmetric self-phase modulation J Opt Soc Am B 200522437ndash45

[172] Cerqua-Richardson KA McKinley JM Lawrence B Joshi S Villeneuve A Comparison of nonlinear optical properties of sulfide glasses in bulk and thin film form Opt Mater 199810155ndash9

[173] Harbold JM Ilday FOuml Wise FW Sanghera JS Nguyen VQ Shaw LB Aggarwal ID Highly nonlinear As-S-Se glasses for all-optical switching Opt Lett 200227119ndash121

[174] Ruan YL Li WT Jarvis R Madsen N Rode A Luther-Davies B Fabrication and characterization of low loss rib chalcogenide waveguides made by dry etching Opt Express 2004125140ndash5

[175] Slusher RE Lenz G Hodelin J Sanghera J Shaw LB Aggarwal ID Large Raman gain and nonlinear phase shifts in high-purity As2Se3 chalcogenide fibers J Opt Soc Am B 2004211146ndash55

[176] Jacobsen R Andersen K Borel P Fage-Pedersen J Frandsen L Hansen O Kristensen M Lavrinenko A Moulin G Ou H Peucheret C Zsigri B Bjarklev A Strained silicon as a new electro-optic material Nature 2006441199ndash202

[177] Cazzanelli M Bianco F Borga E Pucker G Ghulinyan M Degoli E Luppi E Veacuteniard V Ossicini S Modotto D Wabnitz S Pierobon R Pavesi L Second-harmonic generation in

silicon waveguides strained by silicon nitride Nat Mater 201111148ndash54

[178] Avrutsky I Soref R Phase-matched sum frequency generation in strained silicon waveguides using their second-order nonlinear optical susceptibility Opt Express 20111921707ndash16

[179] Ghahramani E Moss DJ Sipe JE Second-harmonic generation in odd-period strained (Si)n(Ge)nSi superlattices and at SiGe interfaces Phys Rev Lett 1990642815ndash8

[180] Levy JS Foster MA Gaeta AL Lipson M Harmonic generation in silicon nitride ring resonators Opt Express 20111911415

[181] Zakery A Elliott SR Optical nonlinearities in chalcogenide glasses and their applications Springer Series in Optical Sciences 2007135

[182] Lee KK Lim DR Kimerling LC Shin J Cerrina F Fabrication of ultralow-loss SiSiO2 waveguides by roughness reduction Opt Lett 2001261888ndash90

[183] Cardenas J Poitras CB Robinson JT Preston K Chen L Lipson M Low loss etchless silicon photonic waveguides Opt Express 2009174752ndash7

[184] Biberman A Shaw MJ Timurdogan E Wright JB Watts MR Ultralow-loss silicon ring resonators Opt Lett 2012374236ndash8

[185] Walmsley IA Waxer L Dorrer C The role of dispersion in ultrafast optics Rev Sci Instrum 2001721ndash29

[186] Torres JP MHendrych Valencia A Angular dispersion an enabling tool in nonlinear and quantum optics Adv Opt Photon 20102319ndash69

[187] Yin LH Lin Q Agrawal GP Dispersion tailoring and soliton propagation in silicon waveguides Opt Lett 2006311295ndash7

[188] Dulkeith E Xia FN Schares L Green WMJ Vlasov YA Group index and group velocity dispersion in silicon-on-insulator photonic wires Opt Express 2006143853ndash63

[189] Turner AC Manolatou C Schmidt BS Lipson M Tailored anomalous group-velocity dispersion in silicon channel waveguides Opt Express 2006144357ndash62

[190] Dadap JI Panoiu NC Chen X I-Hsieh W Liu X Chou C-Y Dulkeith E McNab SJ Xia F Green WMJ Sekaric L Vlasov YA Osgood RM Jr Nonlinear-optical phase modification in dispersion-engineered Si photonic wires Opt Express 2008161280ndash99

[191] Milosevic MM Matavulj PS Yang PY Bagolini A Mashanovich GZ Rib waveguides for mid-infrared silicon photonics J Opt Soc Am B 2009261760ndash6

[192] Mashanovich GZ Milošević MM Nedeljkovic M Owens N Xiong B Teo EJ Hu Y Low loss silicon waveguides for the mid-infrared Opt Express 2011197112ndash9

[193] Reimer C Nedeljkovic M Stothard DJM Esnault MOS Reardon C OrsquoFaolain L Dunn M Mashanovich GZ Krauss TF Mid-infrared photonic crystal waveguides in silicon Opt Express 20122029361ndash8

[194] Baehr-Jones T Spott A Ilic R Spott A Penkov B Asher W Hochberg M Silicon-on-sapphire integrated waveguides for the midinfrared Opt Express 20101812127ndash35

[195] Li F Jackson S Grillet C Magi E Hudson D Madden SJ Moghe Y OrsquoBrien C Read A Duvall SG Atanackovic P Eggleton BJ Moss D Low propagation loss silicon-on-sapphire waveguides for the midinfrared Opt Express 20111915212ndash20

268emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

[196] Yue Y Zhang L Huang H Beausoleil RG Willner AE Silicon-on-nitride waveguide with ultralow dispersion over an octave-spanning mid-infared wavelength range IEEE Photonics J 20124126ndash32

[197] Khan S Chiles J Ma J Fathpour S Silicon-on-nitride waveguides for mid-and near-infrared integrated photonics Appl Phys Lett 2013102121104

[198] Cheng Z Chen X Wong CY Xu K Tsang HK Mid-infrared suspended membrane waveguide and ring resonator on silicon-on-insulator IEEE Photonics J 201241510ndash9

[199] Lin P-T Singh V Cai Y Kimerling LC Agarwal A Air-clad silicon pedestal structures for broadband mid-infrared microphotonics Opt Lett 2013381031ndash3

[200] Chang YC Paeder V Hvozdara L Hartmann JM Herzig HP Low-loss germanium strip waveguides on silicon for the mid-infrared Opt Lett 2012372883ndash5

[201] Zhang L Yue Y Y Xiao-Li R G Beausoleil Willner AE Highly dispersive slot waveguides Opt Express 2009177095ndash101

[202] Zhang L Yue Y Beausoleil RG Willner AE Analysis and engineering of chromatic dispersion in silicon waveguide bends and ring resonators Opt Express 2011198102ndash7

[203] Zhang L Mu J Singh V Agarwal A Kimerling LC Michel J Intra-cavity dispersion of microresonators and its engineering for octave-spanning Kerr frequency comb generation to be published

[204] Lin Q Zhang L Generalized nonlinear envelope equation with high-order dispersion of nonlinearity to be published

[205] Wang Y Yue R Han H Liao X Raman study of structural order of a-SiNxH and its change upon thermal annealing J Non-Crystalline Solids 2001291107ndash12

[206] Brida D Marangoni M Manzoni C De Silvestri S Cerullo G Two-optical-cycle pulses in the mid-infrared from an optical parametric amplifier Opt Lett 2008332901ndash3

[207] Brida D Manzoni C Cirmi G Marangoni M Bonora S Villoresi P De Silvestri S Cerullo G Few-optical-cycle pulses tunable from the visible to the mid-infrared by optical parametric amplifiers J Opt 201012013001

[208] Kippenberg TJ Holzwarth R Diddams SA Microresonator-based optical frequency combs Science 2011332555ndash9

[209] Levy JS Gondarenko A Foster MA Turner-Foster AC Gaeta AL Lipson M CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects Nat Photonics 2009437ndash40

[210] DelrsquoHaye P Herr T Gavartin E Gorodetsky ML Holzwarth R Kippenberg TJ Octave spanningtunable frequency comb from a microresonator Phys Rev Lett 2011107063901

[211] Okawachi Y Saha K Levy JS Wen YH Lipson M Gaeta AL Octave-spanning frequency combgeneration in a silicon nitride chip Opt Lett 2011363398ndash400

[212] Matsko AB Savchenkov AA Liang W Ilchenko VS Seidel D Maleki L Mode-locked Kerr frequency combs Opt Lett 2011362845ndash7

[213] Herr T Brasch V Jost JD Wang CY Kondratiev NM Gorodetsky ML Kippenberg TJ Temporal solitons in optical microresonators httparxivorgabs12110733

[214] Saha K Okawachi Y Shim B Levy JS Salem R Johnson AR Foster MA Lamont MR Lipson M Gaeta AL Modelocking and femtosecond pulse generation in chip-based frequency combs Opt Express 2013211335ndash43

[215] Coen S Erkintalo M Universal scaling laws of Kerr frequency combs Opt Lett 2013381790ndash2

[216] Lugiato LA Lefever R Spatial dissipative structures in passive optical-systems Phys Rev Lett 1987582209ndash11

[217] Haelterman M Trillo S Wabnitz S Dissipative modulation instability in a nonlinear dispersive ring cavity Opt Commun 199291401ndash7

[218] Coen S Randle HG Sylvestre T Erkintalo M Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato-Lefever model Opt Lett 20133837ndash9

[219] Chembo YK Menyuk CR Spatiotemporal Lugiato-Lefever formalism for Kerr-comb generation in whispering-gallery-mode resonators Phys Rev A 201387053852

[220] Foltynowicz A Mas1owski P Ban T Adler F Cossel KC Briles TC Ye J Optical frequency comb spectroscopy Faraday Discussion 201115023ndash31

[221] Hartl I Li XD Chudoba C Ghanta RK Ko TH Fujimoto JG Ranka JK Windeler RS Ultrahigh-resolution optical coherence tomography using continuum generation in an air silica microstructure optical fiber Opt Lett 200126608ndash10

[222] Brabec T Krausz F Intense few-cycle laser fields Frontiers of nonlinear optics Rev Mod Phys 200072545ndash91

[223] Hu J Meyer J Richardson K Shah L Feature issue introduction mid-IR photonic materials Opt Mater Express 201331571ndash5

[224] Private communications with Dr Jacob Levy in Prof Lipsonrsquos group and Dr Johann Riemensberger in Prof Kippenbergrsquos group

[225] Zhang J Lin Q Piredda G Boyd RW Agrawal GP Fauchet PM Anisotropic nonlinear response of silicon in the near-infrared region Appl Phys Lett 200791071113

Page 20: Lin Zhang*, Anuradha M. Agarwal, Lionel C. Kimerling and ...

266emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

[120] Soref R Towards Silicon-based Longwave Integrated Optoelectronics (LIO) SPIE Proceedings 6898 (2008) paper 6898-5 SPIE Photonics West Silicon Photonics III Conference San Jose CA (21 Jan 2008)

[121] Mashanovich GZ Milosevic M Matavulj P Timotijevic B Stankovic S Yang PY Teo EJ Breese MBH Bettiol AA Reed GT Silicon photonic waveguides for different wavelength regions Semiconductor Sci Technol 200823064002

[122] Soref R Mid-infrared photonics in silicon and germanium Nat Photonics 20104495ndash7

[123] Green WMJ Liu X Osgood RM Vlasov YA Mid-infrared nonlinear optics in silicon photonic wire waveguides Photonics Society Summer Topical Meeting Series 201062ndash63

[124] Milosevic MM Nedeljkovic M Masaud T-B Jaberansary E Chong HMH Emerson NG Reed GT Mashanovich GZ Silicon waveguides and devices for the mid-infrared Appl Phys Lett 2012101121105

[125] Soref R Group IV photonics for the mid infrared SPIE Photonics West 2013 Proc of SPIE 20138629paper 862902

[126] Crowder JG Smith SD Vass A Keddie J Infrared methods for gas detection in Mid-Infrared Semiconductor Optoelec-tronics New York Springer-Verlag 2006

[127] George Socrates Infrared and Raman Characteristic Group Frequencies Tables and Charts 3rd Ed Chichester John Wiley amp Sons 2001

[128] Longshore R Raimondi P Lumpkin M Selection of detector peak wavelength for optimum infrared system performance Infrared Phys 197616639ndash47

[129] Findlay GA Cutten DR Comparison of performance of 3ndash5-and 8ndash12-microm infrared systems Appl Opt 1989285029ndash37

[130] Labadie L Wallner O Mid-infrared guided optics a perspective for astronomical instruments Opt Express 2009171947ndash62

[131] Pearl S Rotenberg N van Driel HM Three photon absorption in silicon for 2300ndash3300 nm Appl Phys Lett 200893131102

[132] Wang Z Liu H Huang N Sun Q Wen J Li X Influence of three-photon absorption on Mid-infrared cross-phase modulation in silicon-on-sapphire waveguides Opt Express 2013211840ndash8

[133] Hon NK Soref RA Jalali B The third-order nonlinear optical coefficients of Si Ge and Si1-xGex in the midwave and longwave infrared J Appl Phys 2011110011301

[134] Sheik-Bahae M Hutchings DC Hagan DJ Stryland EWV Dispersion of bound electric nonlinear refraction in solids IEEE J Quant Electron 1991271296ndash1309

[135] Jalali B Raghunathan V Shori R Fathpour S Prospects for silicon mid-IR Raman lasers IEEE J Sel Top Quantum Electron 2006121618ndash27

[136] Raghunathan V Borlaug D Rice RR Jalali B Demonstration of a mid-infrared silicon Raman amplifier Opt Express 20071514355ndash62

[137] Chavez Boggio JM Windmiller JR Knutzen M Jiang R Bres C Alic N Stossel B Rottwitt K Radic S 730-nm optical parametric conversion from near- to short-wave infrared band Opt Express 2008165435ndash43

[138] Lin Q Johnson TJ Perahia R Michael CP Painter OJ A proposal for highly tunable optical parametric oscillation in silicon micro-resonators Opt Express 20081610596ndash610

[139] Turner-Foster AC Foster MA Salem R Gaeta AL Lipson M Frequency conversion over two-thirds of an octave in silicon nanowaveguides Opt Express 2010181904ndash8

[140] Liu X Osgood RM Vlasov YA Green WMJ Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides Nat Photonics 20104557ndash60

[141] Zlatanovic S Park JS Moro S Boggio JMC Divliansky IB Alic N Mookherjea S Radic S Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source Nat Photonics 20104561ndash4

[142] Tien EK Huang YW Gao S Song Q Qian F Kalyoncu SK Boyraz O Discrete parametric band conversion in silicon for mid-infrared applications Opt Exp 20101821981ndash9

[143] Lau RKW Meacutenard M Okawachi Y Foster MA A C Turner-Foster Salem R Lipson M Gaeta AL Continuous-wave mid-infrared frequency conversion in silicon nanowaveguides Opt Lett 2011361263ndash5

[144] Roelkens G Green WMJ Kuyken B Liu X Hattasan N Gassenq A Cerutti L Rodriguez JB Osgood RM Tournie E Baets R III-Vsilicon photonics for short-wave infrared spectroscopy IEEE J Quant Electron 201248292ndash8

[145] Alloatti L Korn D Weimann C Koos C Freude W Leuthold J Second-order nonlinear silicon-organic hybrid waveguides Opt Express 20122020506ndash15

[146] Harris DC Durable 3ndash5 μm transmitting infrared window materials Infrared Phys Technol 199839185ndash201

[147] Carlie N Musgraves JD Zdyrko B Luzinov I Hu J Singh V Agarwal A Kimerling LC Canciamilla A Morichetti F Melloni A Richardson K Integrated chalcogenide waveguide resonators for mid-IR sensing leveraging material properties to meet fabrication challenges Opt Express 20101826728ndash43

[148] Eggleton BJ B Luther-Davies Richardson K Chalcogenide photonics Nat Photonics 20115141ndash8

[149] Madden SJ Vu KT High-Performance Integrated Optics with Tellurite Glasses Status and Prospects Int J Appl Glass Sci 20123289ndash98

[150] Bindra KS Bookey HT Kar AK Wherrett BS Liu X Jha A Nonlinear optical properties of chalcogenide glasses observation of multiphoton absorption App Phys Lett 2001791939ndash41

[151] Zakery A Ruan Y ARode V Samoc M Luther-Davies B Low-loss waveguides in ultrafast laser-deposited As2S3 chalcogenide films J Opt Soc Am B 200391844ndash52

[152] Lenz G Zimmermann J Katsufuji T MLines E Hwang HY Spalter S Slusher RE Cheong SW Sanghera JS Aggarwal ID Large Kerr effect in bulk Se-based chalcogenide glasses Opt Lett 200025254ndash6

[153] Sanghera JS Shaw LB Aggarwal ID Application of chalcogenide glass optical fibers CR Chimie 20025873ndash83

[154] Palik ED Handbook of optical constants of solids San Diego CA Academic 1998

[155] Philipp HR Optical properties of silicon nitride J Electrochem Soc 1973120295ndash300

[156] Malitson IH Interspecimen comparison of the refractive index of fused silica J Opt Soc Am 1965551205ndash8

[157] Barnes NP Piltch MS Temperature-dependent Sellmeier coefficients and nonlinear optics average power limit for germanium J Opt Soc Am 197969178ndash80

[158] Rodney WS Malitson IH King TA Refractive index of arsenic trisulfide J Opt Soc Am 195848633ndash636

[159] Ellipsometry measurement on the thin film samples by our group[160] Bristow AD Rotenberg N van Driel HM Two-photon

absorption and Kerr coefficients of silicon for 850ndash2200 nm Appl Phys Lett 200790191104

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp267

[161] Lin Q Zhang J Piredda G Boyd RW Fauchet PM Agrawal GP Dispersion of silicon nonlinearities in the near infrared region Appl Phys Lett 200791021111

[162] Mizrahi V DeLong KW Stegeman GI Saifi MA Andrejco MJ Two-photon absorption as a limitation to all-optical switching Opt Lett 1989141140ndash2

[163] Guider R NDaldosso APitanti EJordana Fedeli J-M Pavesi L NanoSi low loss horizontal slot waveguides coupled to high Q ring resonators Opt Express 20091720762ndash70 and its erratum

[164] Ferrera M Razzari L Duchesne D Morandotti R Yang Z Liscidini M Sipe JE Chu S Little BE Moss DJ Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures Nat Photonics 20082 737ndash40

[165] Smektala F Quemard C Leneindre L Lucas J Barthelemy A De Angelis C Chalcogenide glasses with large non-linear refractive indices J Non-Crystalline Solids 1998239139ndash42

[166] Boudebs G Sanchez F Troles J Smektala F Nonlinear optical properties of chalcogenide glasses- comparison between Mach-Zehnder interferometry and Z-scan techniques Opt Comm 2001199425ndash33

[167] Asobe M Suzuki K Kanamori T Kubodera K Nonlinear refractive index measurement in chalcogenide-glass fibers by self-phase modulation APL 1992601153ndash4

[168] Asobe M Kanamori T Kubodera K Ultrafast all-optical switching using highly nonlinear chalcogenide glass fiber IEEE Photon Technol Lett 19924362ndash5

[169] Asobe M Kanamori T Kubodera K Applications of highly nonlinear chalcogenide glass fibers in ultrafast all-optical switches IEEE J Quant Electron 1993292325ndash33

[170] Ruan Y Luther-Davies B Li W Rode A Kolev V Madden S Large phase shifts in As2S3 waveguides for all-optical processing devices Opt Lett 2005302605ndash7

[171] Laniel JM Hocirc N Valleacutee R Villeneuve A Nonlinear-refractive-index measurement in As2S3 channel waveguides by asymmetric self-phase modulation J Opt Soc Am B 200522437ndash45

[172] Cerqua-Richardson KA McKinley JM Lawrence B Joshi S Villeneuve A Comparison of nonlinear optical properties of sulfide glasses in bulk and thin film form Opt Mater 199810155ndash9

[173] Harbold JM Ilday FOuml Wise FW Sanghera JS Nguyen VQ Shaw LB Aggarwal ID Highly nonlinear As-S-Se glasses for all-optical switching Opt Lett 200227119ndash121

[174] Ruan YL Li WT Jarvis R Madsen N Rode A Luther-Davies B Fabrication and characterization of low loss rib chalcogenide waveguides made by dry etching Opt Express 2004125140ndash5

[175] Slusher RE Lenz G Hodelin J Sanghera J Shaw LB Aggarwal ID Large Raman gain and nonlinear phase shifts in high-purity As2Se3 chalcogenide fibers J Opt Soc Am B 2004211146ndash55

[176] Jacobsen R Andersen K Borel P Fage-Pedersen J Frandsen L Hansen O Kristensen M Lavrinenko A Moulin G Ou H Peucheret C Zsigri B Bjarklev A Strained silicon as a new electro-optic material Nature 2006441199ndash202

[177] Cazzanelli M Bianco F Borga E Pucker G Ghulinyan M Degoli E Luppi E Veacuteniard V Ossicini S Modotto D Wabnitz S Pierobon R Pavesi L Second-harmonic generation in

silicon waveguides strained by silicon nitride Nat Mater 201111148ndash54

[178] Avrutsky I Soref R Phase-matched sum frequency generation in strained silicon waveguides using their second-order nonlinear optical susceptibility Opt Express 20111921707ndash16

[179] Ghahramani E Moss DJ Sipe JE Second-harmonic generation in odd-period strained (Si)n(Ge)nSi superlattices and at SiGe interfaces Phys Rev Lett 1990642815ndash8

[180] Levy JS Foster MA Gaeta AL Lipson M Harmonic generation in silicon nitride ring resonators Opt Express 20111911415

[181] Zakery A Elliott SR Optical nonlinearities in chalcogenide glasses and their applications Springer Series in Optical Sciences 2007135

[182] Lee KK Lim DR Kimerling LC Shin J Cerrina F Fabrication of ultralow-loss SiSiO2 waveguides by roughness reduction Opt Lett 2001261888ndash90

[183] Cardenas J Poitras CB Robinson JT Preston K Chen L Lipson M Low loss etchless silicon photonic waveguides Opt Express 2009174752ndash7

[184] Biberman A Shaw MJ Timurdogan E Wright JB Watts MR Ultralow-loss silicon ring resonators Opt Lett 2012374236ndash8

[185] Walmsley IA Waxer L Dorrer C The role of dispersion in ultrafast optics Rev Sci Instrum 2001721ndash29

[186] Torres JP MHendrych Valencia A Angular dispersion an enabling tool in nonlinear and quantum optics Adv Opt Photon 20102319ndash69

[187] Yin LH Lin Q Agrawal GP Dispersion tailoring and soliton propagation in silicon waveguides Opt Lett 2006311295ndash7

[188] Dulkeith E Xia FN Schares L Green WMJ Vlasov YA Group index and group velocity dispersion in silicon-on-insulator photonic wires Opt Express 2006143853ndash63

[189] Turner AC Manolatou C Schmidt BS Lipson M Tailored anomalous group-velocity dispersion in silicon channel waveguides Opt Express 2006144357ndash62

[190] Dadap JI Panoiu NC Chen X I-Hsieh W Liu X Chou C-Y Dulkeith E McNab SJ Xia F Green WMJ Sekaric L Vlasov YA Osgood RM Jr Nonlinear-optical phase modification in dispersion-engineered Si photonic wires Opt Express 2008161280ndash99

[191] Milosevic MM Matavulj PS Yang PY Bagolini A Mashanovich GZ Rib waveguides for mid-infrared silicon photonics J Opt Soc Am B 2009261760ndash6

[192] Mashanovich GZ Milošević MM Nedeljkovic M Owens N Xiong B Teo EJ Hu Y Low loss silicon waveguides for the mid-infrared Opt Express 2011197112ndash9

[193] Reimer C Nedeljkovic M Stothard DJM Esnault MOS Reardon C OrsquoFaolain L Dunn M Mashanovich GZ Krauss TF Mid-infrared photonic crystal waveguides in silicon Opt Express 20122029361ndash8

[194] Baehr-Jones T Spott A Ilic R Spott A Penkov B Asher W Hochberg M Silicon-on-sapphire integrated waveguides for the midinfrared Opt Express 20101812127ndash35

[195] Li F Jackson S Grillet C Magi E Hudson D Madden SJ Moghe Y OrsquoBrien C Read A Duvall SG Atanackovic P Eggleton BJ Moss D Low propagation loss silicon-on-sapphire waveguides for the midinfrared Opt Express 20111915212ndash20

268emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

[196] Yue Y Zhang L Huang H Beausoleil RG Willner AE Silicon-on-nitride waveguide with ultralow dispersion over an octave-spanning mid-infared wavelength range IEEE Photonics J 20124126ndash32

[197] Khan S Chiles J Ma J Fathpour S Silicon-on-nitride waveguides for mid-and near-infrared integrated photonics Appl Phys Lett 2013102121104

[198] Cheng Z Chen X Wong CY Xu K Tsang HK Mid-infrared suspended membrane waveguide and ring resonator on silicon-on-insulator IEEE Photonics J 201241510ndash9

[199] Lin P-T Singh V Cai Y Kimerling LC Agarwal A Air-clad silicon pedestal structures for broadband mid-infrared microphotonics Opt Lett 2013381031ndash3

[200] Chang YC Paeder V Hvozdara L Hartmann JM Herzig HP Low-loss germanium strip waveguides on silicon for the mid-infrared Opt Lett 2012372883ndash5

[201] Zhang L Yue Y Y Xiao-Li R G Beausoleil Willner AE Highly dispersive slot waveguides Opt Express 2009177095ndash101

[202] Zhang L Yue Y Beausoleil RG Willner AE Analysis and engineering of chromatic dispersion in silicon waveguide bends and ring resonators Opt Express 2011198102ndash7

[203] Zhang L Mu J Singh V Agarwal A Kimerling LC Michel J Intra-cavity dispersion of microresonators and its engineering for octave-spanning Kerr frequency comb generation to be published

[204] Lin Q Zhang L Generalized nonlinear envelope equation with high-order dispersion of nonlinearity to be published

[205] Wang Y Yue R Han H Liao X Raman study of structural order of a-SiNxH and its change upon thermal annealing J Non-Crystalline Solids 2001291107ndash12

[206] Brida D Marangoni M Manzoni C De Silvestri S Cerullo G Two-optical-cycle pulses in the mid-infrared from an optical parametric amplifier Opt Lett 2008332901ndash3

[207] Brida D Manzoni C Cirmi G Marangoni M Bonora S Villoresi P De Silvestri S Cerullo G Few-optical-cycle pulses tunable from the visible to the mid-infrared by optical parametric amplifiers J Opt 201012013001

[208] Kippenberg TJ Holzwarth R Diddams SA Microresonator-based optical frequency combs Science 2011332555ndash9

[209] Levy JS Gondarenko A Foster MA Turner-Foster AC Gaeta AL Lipson M CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects Nat Photonics 2009437ndash40

[210] DelrsquoHaye P Herr T Gavartin E Gorodetsky ML Holzwarth R Kippenberg TJ Octave spanningtunable frequency comb from a microresonator Phys Rev Lett 2011107063901

[211] Okawachi Y Saha K Levy JS Wen YH Lipson M Gaeta AL Octave-spanning frequency combgeneration in a silicon nitride chip Opt Lett 2011363398ndash400

[212] Matsko AB Savchenkov AA Liang W Ilchenko VS Seidel D Maleki L Mode-locked Kerr frequency combs Opt Lett 2011362845ndash7

[213] Herr T Brasch V Jost JD Wang CY Kondratiev NM Gorodetsky ML Kippenberg TJ Temporal solitons in optical microresonators httparxivorgabs12110733

[214] Saha K Okawachi Y Shim B Levy JS Salem R Johnson AR Foster MA Lamont MR Lipson M Gaeta AL Modelocking and femtosecond pulse generation in chip-based frequency combs Opt Express 2013211335ndash43

[215] Coen S Erkintalo M Universal scaling laws of Kerr frequency combs Opt Lett 2013381790ndash2

[216] Lugiato LA Lefever R Spatial dissipative structures in passive optical-systems Phys Rev Lett 1987582209ndash11

[217] Haelterman M Trillo S Wabnitz S Dissipative modulation instability in a nonlinear dispersive ring cavity Opt Commun 199291401ndash7

[218] Coen S Randle HG Sylvestre T Erkintalo M Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato-Lefever model Opt Lett 20133837ndash9

[219] Chembo YK Menyuk CR Spatiotemporal Lugiato-Lefever formalism for Kerr-comb generation in whispering-gallery-mode resonators Phys Rev A 201387053852

[220] Foltynowicz A Mas1owski P Ban T Adler F Cossel KC Briles TC Ye J Optical frequency comb spectroscopy Faraday Discussion 201115023ndash31

[221] Hartl I Li XD Chudoba C Ghanta RK Ko TH Fujimoto JG Ranka JK Windeler RS Ultrahigh-resolution optical coherence tomography using continuum generation in an air silica microstructure optical fiber Opt Lett 200126608ndash10

[222] Brabec T Krausz F Intense few-cycle laser fields Frontiers of nonlinear optics Rev Mod Phys 200072545ndash91

[223] Hu J Meyer J Richardson K Shah L Feature issue introduction mid-IR photonic materials Opt Mater Express 201331571ndash5

[224] Private communications with Dr Jacob Levy in Prof Lipsonrsquos group and Dr Johann Riemensberger in Prof Kippenbergrsquos group

[225] Zhang J Lin Q Piredda G Boyd RW Agrawal GP Fauchet PM Anisotropic nonlinear response of silicon in the near-infrared region Appl Phys Lett 200791071113

Page 21: Lin Zhang*, Anuradha M. Agarwal, Lionel C. Kimerling and ...

L Zhang et al Nonlinear Group IV photonicsemspthinspenspenspenspemsp267

[161] Lin Q Zhang J Piredda G Boyd RW Fauchet PM Agrawal GP Dispersion of silicon nonlinearities in the near infrared region Appl Phys Lett 200791021111

[162] Mizrahi V DeLong KW Stegeman GI Saifi MA Andrejco MJ Two-photon absorption as a limitation to all-optical switching Opt Lett 1989141140ndash2

[163] Guider R NDaldosso APitanti EJordana Fedeli J-M Pavesi L NanoSi low loss horizontal slot waveguides coupled to high Q ring resonators Opt Express 20091720762ndash70 and its erratum

[164] Ferrera M Razzari L Duchesne D Morandotti R Yang Z Liscidini M Sipe JE Chu S Little BE Moss DJ Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures Nat Photonics 20082 737ndash40

[165] Smektala F Quemard C Leneindre L Lucas J Barthelemy A De Angelis C Chalcogenide glasses with large non-linear refractive indices J Non-Crystalline Solids 1998239139ndash42

[166] Boudebs G Sanchez F Troles J Smektala F Nonlinear optical properties of chalcogenide glasses- comparison between Mach-Zehnder interferometry and Z-scan techniques Opt Comm 2001199425ndash33

[167] Asobe M Suzuki K Kanamori T Kubodera K Nonlinear refractive index measurement in chalcogenide-glass fibers by self-phase modulation APL 1992601153ndash4

[168] Asobe M Kanamori T Kubodera K Ultrafast all-optical switching using highly nonlinear chalcogenide glass fiber IEEE Photon Technol Lett 19924362ndash5

[169] Asobe M Kanamori T Kubodera K Applications of highly nonlinear chalcogenide glass fibers in ultrafast all-optical switches IEEE J Quant Electron 1993292325ndash33

[170] Ruan Y Luther-Davies B Li W Rode A Kolev V Madden S Large phase shifts in As2S3 waveguides for all-optical processing devices Opt Lett 2005302605ndash7

[171] Laniel JM Hocirc N Valleacutee R Villeneuve A Nonlinear-refractive-index measurement in As2S3 channel waveguides by asymmetric self-phase modulation J Opt Soc Am B 200522437ndash45

[172] Cerqua-Richardson KA McKinley JM Lawrence B Joshi S Villeneuve A Comparison of nonlinear optical properties of sulfide glasses in bulk and thin film form Opt Mater 199810155ndash9

[173] Harbold JM Ilday FOuml Wise FW Sanghera JS Nguyen VQ Shaw LB Aggarwal ID Highly nonlinear As-S-Se glasses for all-optical switching Opt Lett 200227119ndash121

[174] Ruan YL Li WT Jarvis R Madsen N Rode A Luther-Davies B Fabrication and characterization of low loss rib chalcogenide waveguides made by dry etching Opt Express 2004125140ndash5

[175] Slusher RE Lenz G Hodelin J Sanghera J Shaw LB Aggarwal ID Large Raman gain and nonlinear phase shifts in high-purity As2Se3 chalcogenide fibers J Opt Soc Am B 2004211146ndash55

[176] Jacobsen R Andersen K Borel P Fage-Pedersen J Frandsen L Hansen O Kristensen M Lavrinenko A Moulin G Ou H Peucheret C Zsigri B Bjarklev A Strained silicon as a new electro-optic material Nature 2006441199ndash202

[177] Cazzanelli M Bianco F Borga E Pucker G Ghulinyan M Degoli E Luppi E Veacuteniard V Ossicini S Modotto D Wabnitz S Pierobon R Pavesi L Second-harmonic generation in

silicon waveguides strained by silicon nitride Nat Mater 201111148ndash54

[178] Avrutsky I Soref R Phase-matched sum frequency generation in strained silicon waveguides using their second-order nonlinear optical susceptibility Opt Express 20111921707ndash16

[179] Ghahramani E Moss DJ Sipe JE Second-harmonic generation in odd-period strained (Si)n(Ge)nSi superlattices and at SiGe interfaces Phys Rev Lett 1990642815ndash8

[180] Levy JS Foster MA Gaeta AL Lipson M Harmonic generation in silicon nitride ring resonators Opt Express 20111911415

[181] Zakery A Elliott SR Optical nonlinearities in chalcogenide glasses and their applications Springer Series in Optical Sciences 2007135

[182] Lee KK Lim DR Kimerling LC Shin J Cerrina F Fabrication of ultralow-loss SiSiO2 waveguides by roughness reduction Opt Lett 2001261888ndash90

[183] Cardenas J Poitras CB Robinson JT Preston K Chen L Lipson M Low loss etchless silicon photonic waveguides Opt Express 2009174752ndash7

[184] Biberman A Shaw MJ Timurdogan E Wright JB Watts MR Ultralow-loss silicon ring resonators Opt Lett 2012374236ndash8

[185] Walmsley IA Waxer L Dorrer C The role of dispersion in ultrafast optics Rev Sci Instrum 2001721ndash29

[186] Torres JP MHendrych Valencia A Angular dispersion an enabling tool in nonlinear and quantum optics Adv Opt Photon 20102319ndash69

[187] Yin LH Lin Q Agrawal GP Dispersion tailoring and soliton propagation in silicon waveguides Opt Lett 2006311295ndash7

[188] Dulkeith E Xia FN Schares L Green WMJ Vlasov YA Group index and group velocity dispersion in silicon-on-insulator photonic wires Opt Express 2006143853ndash63

[189] Turner AC Manolatou C Schmidt BS Lipson M Tailored anomalous group-velocity dispersion in silicon channel waveguides Opt Express 2006144357ndash62

[190] Dadap JI Panoiu NC Chen X I-Hsieh W Liu X Chou C-Y Dulkeith E McNab SJ Xia F Green WMJ Sekaric L Vlasov YA Osgood RM Jr Nonlinear-optical phase modification in dispersion-engineered Si photonic wires Opt Express 2008161280ndash99

[191] Milosevic MM Matavulj PS Yang PY Bagolini A Mashanovich GZ Rib waveguides for mid-infrared silicon photonics J Opt Soc Am B 2009261760ndash6

[192] Mashanovich GZ Milošević MM Nedeljkovic M Owens N Xiong B Teo EJ Hu Y Low loss silicon waveguides for the mid-infrared Opt Express 2011197112ndash9

[193] Reimer C Nedeljkovic M Stothard DJM Esnault MOS Reardon C OrsquoFaolain L Dunn M Mashanovich GZ Krauss TF Mid-infrared photonic crystal waveguides in silicon Opt Express 20122029361ndash8

[194] Baehr-Jones T Spott A Ilic R Spott A Penkov B Asher W Hochberg M Silicon-on-sapphire integrated waveguides for the midinfrared Opt Express 20101812127ndash35

[195] Li F Jackson S Grillet C Magi E Hudson D Madden SJ Moghe Y OrsquoBrien C Read A Duvall SG Atanackovic P Eggleton BJ Moss D Low propagation loss silicon-on-sapphire waveguides for the midinfrared Opt Express 20111915212ndash20

268emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

[196] Yue Y Zhang L Huang H Beausoleil RG Willner AE Silicon-on-nitride waveguide with ultralow dispersion over an octave-spanning mid-infared wavelength range IEEE Photonics J 20124126ndash32

[197] Khan S Chiles J Ma J Fathpour S Silicon-on-nitride waveguides for mid-and near-infrared integrated photonics Appl Phys Lett 2013102121104

[198] Cheng Z Chen X Wong CY Xu K Tsang HK Mid-infrared suspended membrane waveguide and ring resonator on silicon-on-insulator IEEE Photonics J 201241510ndash9

[199] Lin P-T Singh V Cai Y Kimerling LC Agarwal A Air-clad silicon pedestal structures for broadband mid-infrared microphotonics Opt Lett 2013381031ndash3

[200] Chang YC Paeder V Hvozdara L Hartmann JM Herzig HP Low-loss germanium strip waveguides on silicon for the mid-infrared Opt Lett 2012372883ndash5

[201] Zhang L Yue Y Y Xiao-Li R G Beausoleil Willner AE Highly dispersive slot waveguides Opt Express 2009177095ndash101

[202] Zhang L Yue Y Beausoleil RG Willner AE Analysis and engineering of chromatic dispersion in silicon waveguide bends and ring resonators Opt Express 2011198102ndash7

[203] Zhang L Mu J Singh V Agarwal A Kimerling LC Michel J Intra-cavity dispersion of microresonators and its engineering for octave-spanning Kerr frequency comb generation to be published

[204] Lin Q Zhang L Generalized nonlinear envelope equation with high-order dispersion of nonlinearity to be published

[205] Wang Y Yue R Han H Liao X Raman study of structural order of a-SiNxH and its change upon thermal annealing J Non-Crystalline Solids 2001291107ndash12

[206] Brida D Marangoni M Manzoni C De Silvestri S Cerullo G Two-optical-cycle pulses in the mid-infrared from an optical parametric amplifier Opt Lett 2008332901ndash3

[207] Brida D Manzoni C Cirmi G Marangoni M Bonora S Villoresi P De Silvestri S Cerullo G Few-optical-cycle pulses tunable from the visible to the mid-infrared by optical parametric amplifiers J Opt 201012013001

[208] Kippenberg TJ Holzwarth R Diddams SA Microresonator-based optical frequency combs Science 2011332555ndash9

[209] Levy JS Gondarenko A Foster MA Turner-Foster AC Gaeta AL Lipson M CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects Nat Photonics 2009437ndash40

[210] DelrsquoHaye P Herr T Gavartin E Gorodetsky ML Holzwarth R Kippenberg TJ Octave spanningtunable frequency comb from a microresonator Phys Rev Lett 2011107063901

[211] Okawachi Y Saha K Levy JS Wen YH Lipson M Gaeta AL Octave-spanning frequency combgeneration in a silicon nitride chip Opt Lett 2011363398ndash400

[212] Matsko AB Savchenkov AA Liang W Ilchenko VS Seidel D Maleki L Mode-locked Kerr frequency combs Opt Lett 2011362845ndash7

[213] Herr T Brasch V Jost JD Wang CY Kondratiev NM Gorodetsky ML Kippenberg TJ Temporal solitons in optical microresonators httparxivorgabs12110733

[214] Saha K Okawachi Y Shim B Levy JS Salem R Johnson AR Foster MA Lamont MR Lipson M Gaeta AL Modelocking and femtosecond pulse generation in chip-based frequency combs Opt Express 2013211335ndash43

[215] Coen S Erkintalo M Universal scaling laws of Kerr frequency combs Opt Lett 2013381790ndash2

[216] Lugiato LA Lefever R Spatial dissipative structures in passive optical-systems Phys Rev Lett 1987582209ndash11

[217] Haelterman M Trillo S Wabnitz S Dissipative modulation instability in a nonlinear dispersive ring cavity Opt Commun 199291401ndash7

[218] Coen S Randle HG Sylvestre T Erkintalo M Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato-Lefever model Opt Lett 20133837ndash9

[219] Chembo YK Menyuk CR Spatiotemporal Lugiato-Lefever formalism for Kerr-comb generation in whispering-gallery-mode resonators Phys Rev A 201387053852

[220] Foltynowicz A Mas1owski P Ban T Adler F Cossel KC Briles TC Ye J Optical frequency comb spectroscopy Faraday Discussion 201115023ndash31

[221] Hartl I Li XD Chudoba C Ghanta RK Ko TH Fujimoto JG Ranka JK Windeler RS Ultrahigh-resolution optical coherence tomography using continuum generation in an air silica microstructure optical fiber Opt Lett 200126608ndash10

[222] Brabec T Krausz F Intense few-cycle laser fields Frontiers of nonlinear optics Rev Mod Phys 200072545ndash91

[223] Hu J Meyer J Richardson K Shah L Feature issue introduction mid-IR photonic materials Opt Mater Express 201331571ndash5

[224] Private communications with Dr Jacob Levy in Prof Lipsonrsquos group and Dr Johann Riemensberger in Prof Kippenbergrsquos group

[225] Zhang J Lin Q Piredda G Boyd RW Agrawal GP Fauchet PM Anisotropic nonlinear response of silicon in the near-infrared region Appl Phys Lett 200791071113

Page 22: Lin Zhang*, Anuradha M. Agarwal, Lionel C. Kimerling and ...

268emspenspenspenspthinspemspL Zhang et al Nonlinear Group IV photonics

[196] Yue Y Zhang L Huang H Beausoleil RG Willner AE Silicon-on-nitride waveguide with ultralow dispersion over an octave-spanning mid-infared wavelength range IEEE Photonics J 20124126ndash32

[197] Khan S Chiles J Ma J Fathpour S Silicon-on-nitride waveguides for mid-and near-infrared integrated photonics Appl Phys Lett 2013102121104

[198] Cheng Z Chen X Wong CY Xu K Tsang HK Mid-infrared suspended membrane waveguide and ring resonator on silicon-on-insulator IEEE Photonics J 201241510ndash9

[199] Lin P-T Singh V Cai Y Kimerling LC Agarwal A Air-clad silicon pedestal structures for broadband mid-infrared microphotonics Opt Lett 2013381031ndash3

[200] Chang YC Paeder V Hvozdara L Hartmann JM Herzig HP Low-loss germanium strip waveguides on silicon for the mid-infrared Opt Lett 2012372883ndash5

[201] Zhang L Yue Y Y Xiao-Li R G Beausoleil Willner AE Highly dispersive slot waveguides Opt Express 2009177095ndash101

[202] Zhang L Yue Y Beausoleil RG Willner AE Analysis and engineering of chromatic dispersion in silicon waveguide bends and ring resonators Opt Express 2011198102ndash7

[203] Zhang L Mu J Singh V Agarwal A Kimerling LC Michel J Intra-cavity dispersion of microresonators and its engineering for octave-spanning Kerr frequency comb generation to be published

[204] Lin Q Zhang L Generalized nonlinear envelope equation with high-order dispersion of nonlinearity to be published

[205] Wang Y Yue R Han H Liao X Raman study of structural order of a-SiNxH and its change upon thermal annealing J Non-Crystalline Solids 2001291107ndash12

[206] Brida D Marangoni M Manzoni C De Silvestri S Cerullo G Two-optical-cycle pulses in the mid-infrared from an optical parametric amplifier Opt Lett 2008332901ndash3

[207] Brida D Manzoni C Cirmi G Marangoni M Bonora S Villoresi P De Silvestri S Cerullo G Few-optical-cycle pulses tunable from the visible to the mid-infrared by optical parametric amplifiers J Opt 201012013001

[208] Kippenberg TJ Holzwarth R Diddams SA Microresonator-based optical frequency combs Science 2011332555ndash9

[209] Levy JS Gondarenko A Foster MA Turner-Foster AC Gaeta AL Lipson M CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects Nat Photonics 2009437ndash40

[210] DelrsquoHaye P Herr T Gavartin E Gorodetsky ML Holzwarth R Kippenberg TJ Octave spanningtunable frequency comb from a microresonator Phys Rev Lett 2011107063901

[211] Okawachi Y Saha K Levy JS Wen YH Lipson M Gaeta AL Octave-spanning frequency combgeneration in a silicon nitride chip Opt Lett 2011363398ndash400

[212] Matsko AB Savchenkov AA Liang W Ilchenko VS Seidel D Maleki L Mode-locked Kerr frequency combs Opt Lett 2011362845ndash7

[213] Herr T Brasch V Jost JD Wang CY Kondratiev NM Gorodetsky ML Kippenberg TJ Temporal solitons in optical microresonators httparxivorgabs12110733

[214] Saha K Okawachi Y Shim B Levy JS Salem R Johnson AR Foster MA Lamont MR Lipson M Gaeta AL Modelocking and femtosecond pulse generation in chip-based frequency combs Opt Express 2013211335ndash43

[215] Coen S Erkintalo M Universal scaling laws of Kerr frequency combs Opt Lett 2013381790ndash2

[216] Lugiato LA Lefever R Spatial dissipative structures in passive optical-systems Phys Rev Lett 1987582209ndash11

[217] Haelterman M Trillo S Wabnitz S Dissipative modulation instability in a nonlinear dispersive ring cavity Opt Commun 199291401ndash7

[218] Coen S Randle HG Sylvestre T Erkintalo M Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato-Lefever model Opt Lett 20133837ndash9

[219] Chembo YK Menyuk CR Spatiotemporal Lugiato-Lefever formalism for Kerr-comb generation in whispering-gallery-mode resonators Phys Rev A 201387053852

[220] Foltynowicz A Mas1owski P Ban T Adler F Cossel KC Briles TC Ye J Optical frequency comb spectroscopy Faraday Discussion 201115023ndash31

[221] Hartl I Li XD Chudoba C Ghanta RK Ko TH Fujimoto JG Ranka JK Windeler RS Ultrahigh-resolution optical coherence tomography using continuum generation in an air silica microstructure optical fiber Opt Lett 200126608ndash10

[222] Brabec T Krausz F Intense few-cycle laser fields Frontiers of nonlinear optics Rev Mod Phys 200072545ndash91

[223] Hu J Meyer J Richardson K Shah L Feature issue introduction mid-IR photonic materials Opt Mater Express 201331571ndash5

[224] Private communications with Dr Jacob Levy in Prof Lipsonrsquos group and Dr Johann Riemensberger in Prof Kippenbergrsquos group

[225] Zhang J Lin Q Piredda G Boyd RW Agrawal GP Fauchet PM Anisotropic nonlinear response of silicon in the near-infrared region Appl Phys Lett 200791071113