AIP Advances 6, 065316 (2016); https://doi.org/10.1063/1.4954399 6, 065316

© 2016 Author(s).

All-optical diode structure based onasymmetrical coupling by a micro-cavityand FP cavity at two sides of photoniccrystal waveguideCite as: AIP Advances 6, 065316 (2016); https://doi.org/10.1063/1.4954399Submitted: 06 March 2016 . Accepted: 08 June 2016 . Published Online: 16 June 2016

Bin Liu, Yun-Feng Liu, Chen Jia, and Xing-Dao He

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Paper published as part of the special topic on Chemical Physics, Energy, Fluids and Plasmas, Materials Science

and Mathematical Physics

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AIP ADVANCES 6, 065316 (2016)

All-optical diode structure based on asymmetrical couplingby a micro-cavity and FP cavity at two sides of photoniccrystal waveguide

Bin Liu,1,a Yun-Feng Liu,1 Chen Jia,2 and Xing-Dao He11Jiangxi Engineering Laboratory for Optoelectronics Testing Technology, NanchangHangKong University, Nanchang 330063, China2Nanchang Institute of Science and Technology, Nanchang 3301608, China

(Received 6 March 2016; accepted 8 June 2016; published online 16 June 2016)

A high efficiency all-optical diode based on photonic crystal (PC) waveguidehas been proposed and numerically investigated by finite-difference time-domain(FDTD) method. The structure is asymmetrically coupled by a micro-cavity con-taining nonlinear Kerr medium and a FP cavity at sides of PC waveguide. Because ofinterference between two cavities, Fano peak and FP peak can both appear in trans-mission spectra and unidirectional transmission can be achieved. The working wave-length can set between two peaks and near to the Fano peak. For forward launch withsuitable light intensity, nonlinear Kerr effect of micro-cavity can been excited. It willresult in red shift of Fano peak and achieving forward transmission. But for backwardlaunch, a stronger incidence light is needed to the excite Kerr effect due to the designof asymmetric structure. This design has many advantages, including high maximumtransmittance, high transmittance contrast ratio, low power threshold, short responsetime, and ease of integration. C 2016 Author(s). All article content, except whereotherwise noted, is licensed under a Creative Commons Attribution (CC BY) license(http://creativecommons.org/licenses/by/4.0/). [http://dx.doi.org/10.1063/1.4954399]

I. INTRODUCTION

Photonic crystal is a new type of optical artificial material.1,2 In the recent two decades, studieson PCs have become a hottopic due to the ability to control the propagation of electromagneticwaves, because of its photonic band structure and localized photonic states. A great deal of researchis focused on finding new physical properties of photonic crystals, designing new PC device andfabricating PC structure.3–11

In 1994, Michael Scalora firstly reports an all-optical diode using one-dimensional nonlinearphotonic crystals with a spatial graduation in the linear refractive index.12,13 All-optical diodes asa kind of new photonic device, have great potential applications in integrated optical circuits andoptical interconnection systems, because of function of forward transmission and backward cut-off,just like electron diodes in circuit. in recent years, various types of all-optical diode structure havebeen reported, such as left-handed periodic structures,14 tunable surface plasmon polaritons in asilver grating coated with a nonlinear organic material,15 asymmetric nonlinear absorption mate-rial layers,16 periodically poled lithium niobate waveguides,17 light tunneling heterostructures withone-dimensional PCs and lossy metallic film,18 Electro-tunable optical diode based on liquid-crystalphotonic crystal heterojunctions,19,20 and so on.

As a widespread physical phenomena, Fano resonance attracted the interest of a large numberof researchers to study the physical characteristics and potential applications.21–23 One of the hotspots is PC bistability switching.24,25 The resonance peak is transmission peak or reflection peakdepending on the interference between micro-cavity and waveguide or waveguide reflector. Themicro-cavity in PC has an ultra-high quality factor Q = ω0/∆ω. ∆ω is full width half maximum,

aElectronic mail: liubin_d@126.com

2158-3226/2016/6(6)/065316/7 6, 065316-1 ©Author(s) 2016.

065316-2 Liu et al. AIP Advances 6, 065316 (2016)

and ω0 is center frequency. For a single-mode cavity, whatever it is transmission or reflection typeFano resonance cavity, the optical intensity which is coupled into cavity is proportional to Q factorIcav = I0

Qπ

.26 Icav is the optical intensity in cavity, and I0 is the input optical intensity. If the cavitymedium is the third order nonlinear Kerr material, it means that the nonlinear effect can be enhancedQπ

. The high quality PC micro-cavity has a good effect for enhancing nonlinear effect. So all-opticaldiode based on nonlinear photonic crystal micro-cavities became a research hotspot.27–29 Yi Yuet al, have been experimentally demonstrated the all-optical diode in a nonlinear photonic-crystalmicro-cavity with broken symmetry.30 In the structure, A partially transmitting element is intro-duced in PC waveguide above the nanocavity by designing a blockade hole, and the symmetryof the structure is broken by displacing the partially transmitting element by one lattice constanttowards one port.

In the paper, we study a self-inducing type all-optical diode based on asymmetrical two-dimensional nonlinear photonic crystal micro-cavitiy, of which unidirectional transmission is accom-plished by the input signal without involving any external pumps. It is designed as an asymmetricalstructure composed by a nonlinear micro-cavity and a FP cavity at two sides of PC waveguide. Theimportant characteristics including maximum transmittance, forward and backward transmittancy,power threshold, and response time are analyzed by using nonlinear FDTD technique in detail.

II. THE MODEL

First, a transmission-type Fano resonant micro-cavity with ultra-high quality factor in anair-bridge slab PC consisting of square lattice is designed in Fig. 1(a). The lattice constant ofphotonic crystal is set as a. An elliptical point defect is set in the first layer below a line defect PCwaveguide. The radius of dielectric cylinder is r=0.3a. In addition, one dielectric cylinder above themicro-cavity as reflector layer (R) is adding to block the line defect PC waveguide. The refractive

FIG. 1. (a) and (b) schematic diagram and transmission spectra of micro-cavity.

065316-3 Liu et al. AIP Advances 6, 065316 (2016)

indexs of air and GaAs are n0=1 and n=3.46. The major and minor axes of elliptical point defect setas 0.534a and 0.3a, respectively. The transmission spectra of Fano micro-cavity is calculated in theFig. 1(b). We can see that the Fano peak is very steep, especially for the left side. The Q factor iscalculated about 4500. So only a very small change of refractive index of point defect can achievethe moving of resonance peak.

If Kerr nonlinear effect is introduced into the medium and the working wavelength is set inthe reflection band nearby Fano peak, Fano peak will gets red-shifted. In this process, the state ofresonant reflection will convert to resonant transmission in a certain light intensity. A switch processfrom off to on is achieved. But, for input light from strong to weaken process, the state of resonanttransmission convert to resonant reflection in another light intensity. This is a switch process fromon to off. The two light intensities corresponding to mutation of transmittance is different. It canbe designed as optical bistability switch devices. Transmission spectra of the Fano resonance cavitycan be effectively adjusted by changing the structure parameters and refractive index of ellipticalpoint defect, which is very advantageous to design new functional devices. To obtain a completepicture of the photonic properties of both the individual components and their combined implemen-tation, both time-domain and frequency-domain computational methods were employed. Since thecomputational methods used in this analysis rely on Maxwell’s equations, which are scale invariant,all geometric parameters in the simulations were scaled to the PC lattice constant (denoted a).

An all-optical diode requires two conditions: one is the asymmetrical structure, and the otheris nonlinear. We design a FP cavity in the second layer above PC waveguide [shown in Fig. 2(a)].In addition, an asymmetrical structure is formed by setting the reflector layer R below the left endof FP cavity. The transmission spectra is calculated in Fig. 3(b). There is a transmission peak atnormalized frequency 0.44458 nearby Fano peak. This design ensure effective interference betweenFP cavity and Fano cavity.

FIG. 2. (a) and (b) schematic diagram and transmission spectra of FP cavity.

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FIG. 3. (a) Schematic diagram of the all-optical diode structure based on PC waveguide. (b) Transmission spectra of thestructure coupled by Fano cavity and FP cavity without nonlinear effect.

III. SIMULATION RESULTS AND ANALYSIS

The structure of all-optical diode is shown in Fig. 3(a), which include the asymmetricallycoupling by the Fano micro-cavity and FP cavity at two sides of PC waveguide. First, we calculatethe transmission spectra without nonlinear effect in Fig. 3(b). We can observe two transmissionpeaks: the narrow one is Fano peak of micro-cavity, and the other wide one is FP peak. We select thenormalized frequency 0.44603 as working wavelength, which is in the reflection band between Fanopeak and FP peak, and close to Fano peak. The distribution of optical field in the micro-cavity is fargreater than other areas, so the nonlinear effect can be ignored except point defect.

Now, we study the transmission characteristics by inducing nonlinear Kerr effect. The Kerrcoefficient of GaAs is set as n2 = 1.5∗10−5µm2/w. For forward launch with working wavelength λ0,the input light is reflected by reflector R. But the micro-cavity is close to reflector R, so evanescentwave inevitably couple into micro-cavity to produce Kerr effect. Furthermore this nonlinear effectincreases with growth of optical intensity. For backward launch, the input light is also reflected byreflector R. But because of the design of asymmetric structure, the evanescent wave will enter FPcavity firstly. So evanescent wave entered micro-cavity is less than forward launch. Under the sameinput intensity, the change of refractive index of micro-cavity with forward launch is more thanbackward launch. Using above effect, we can design an efficient optical diode.

Figure 4(a) shows the distribution of optical field with forward launch at input power densityP=0.4mw/µm. With this input intensity, Kerr effect of the Fano micro-cavity is produced effec-tively. So Fano peak will red shift to λ0. Then, we observe that the light transmit through thewaveguide instead of reflect back. But for backward launch, the same power density P=0.4mw/µmis not strong enough to produce Kerr effect. So the input light cutoff with backward launch[shown in Fig. 4(b)]. The function of forward transmission, backward cut-off have been achieved atP=0.4mw/µm.

065316-5 Liu et al. AIP Advances 6, 065316 (2016)

FIG. 4. Electric field distributions with nonlinear Kerr effect at λ0=0.44603 and P=0.4mw/µm. (a) forward launch; (b)backward launch.

Nest, we study the relationship between forward and backward transmittances with power den-sity of light at λ0. Seen in Fig. 5, solid line and dashed line indicate transmittances of forward andbackward launch with power density, respectively. The transmittance of forward launch suddenlychange from low to high at P=0.35mw/µm. For backward launch, the power density of transmit-tance mutation is 0.52mw/µm. So at 0.35mw/um ≤ P < 0.52mw/um, the function of unidirectionaltransmission as all-optical diode can be achieved. The threshold intensity which indicates the lowestintensity for unidirectional transmission only needs approximate 0.35mw/um. In the structure, the

FIG. 5. Relationship between transmission with forward and backward input power density at λ0=0.44603.

065316-6 Liu et al. AIP Advances 6, 065316 (2016)

FIG. 6. Change of transmittances and electric-field distributions over time at P=0.4mw/µm and λ0=0.44603. (a) and (b)change of transmittances for forward launch and backward launch. (c) and (d) the corresponding electric-field evolution forforward launch and backward launch at T>50ps. (Multimedia view) [URL: http://dx.doi.org/10.1063/1.4954399.1] [URL:http://dx.doi.org/10.1063/1.4954399.2]

maximum transmittance which indicates light efficiency in the case of forward transmission canreach about 80%, and transmittance contrast ratio

�T+λ − T−λ

�/�T+λ + T−λ

�reach about 0.8.

Final, we analyze the response time of device. At P=0.4mw/µm, the dynamic changes oftransmittances over time are shown in Fig. 6(a) and 6(b) corresponding to forward launch andbackward launch, respectively. For forward launch in Fig. 6(a), the transmittance increases withgrowth of time and become stable forward transmission after T=50ps. The corresponding videoof electric-field distribution at T>50ps has been shown in Fig. 6(c) (Multimedia view). For back-ward launch, the input light is always cut-off [shown in Fig. 6(b)], and the corresponding videoof electric-field distribution at T>50ps has been shown in Fig. 6(d) (Multimedia view). The resultdemonstrates that the response time approximates to picosecond level.

IV. CONCLUSION

We present a high efficiency all-optical diode based on PC waveguide. The structure is asym-metrical coupling by a side-coupled Fano micro-cavity and FP cavity. The transmission charac-teristics are numerically investigated by using nonlinear FDTD method. Because of the asym-metric design, backward launch need stronger incidence light to excite Kerr effect of micro-cavitythan forward launch, so the function of unidirectional transmission can be achieved. Comparingwith previous literatures, the new structure presented here has high transmission in positive direc-tion (about 80%), high transmittance contrast ratio (about 0.8), low power threshold (less than1mw/µm), and excellent response time (picosecond level). In addition, the working waveband ofdevice can be flexibly adjusted by changing the lattice constant a. We believe that the asymmetricstructure has great potential for use in nonlinear optical applications and easily being integrated onoptical chip.

ACKNOWLEDGMENTS

This work was supported by the National Natural Science Foundation of China (Grant No.61205119).

065316-7 Liu et al. AIP Advances 6, 065316 (2016)

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