ON-CHIP GENERATION, CHARACTERIZATION AND BANDWIDTH

SCALING OF OPTICAL FREQUENCY COMBS

A Dissertation

Submitted to the Faculty

of

Purdue University

by

Yang Liu

In Partial Fulfillment of the

Requirements for the Degree

of

Doctor of Philosophy

December 2015

Purdue University

West Lafayette, Indiana

ii

ACKNOWLEDGMENTS

Firstly, I would like to express my sincere appreciation to my advisor Prof. An-

drew M. Weiner for his guidance, encouragement, and support throughout my grad-

uate study at Purdue. I would never get a chance to work in this exciting area of

silicon photonics and realize any of research achievements reported in this disser-

tation if without his guidance. He also set a decent role model for me to pursuit

throughout my life. My special thanks go to Prof. Minghao Qi. My research project

is a collaboration with his group, he always provided me with valuable support and

guidance. I also would like to thank Prof. Alexandra Boltasseva and Prof. Peter

Bermel for serving as my committee member and for their support during the course

of this research.

I am deeply thankful to my former and current colleagues in Ultrafast Optics and Op-

tical Fiber Communication Laboratory and Prof. Qi’s group. Dr. Daniel E. Leaird

helped me to start the lab work and gave me the best technical support. Dr. Yi

Xuan kept fabricating excellence devices. Thanks Dr. Xiaoxiao Xue, Andrew J. Met-

calf and Pei-Hsun Wang for their collaborations and generous discussions on various

topics. I also acknowledge fruitful discussions with and timely help from Dr. Victor

Torres- Company, Dr. Jian Wang, Dr. Rui Wu, Dr. Li Fan, Dr. Leo T. Varghese,

Dr. Yihan Li, Dr. Joseph Lukens, Amir Rashidinejad and Steve Chen.

Finally, I would be grateful to my family and my friends for their continuous under-

standing and support.

iii

TABLE OF CONTENTS

Page

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi

ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi

1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1 Optical frequency combs . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Optical waveguides . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3 Optical microresonators . . . . . . . . . . . . . . . . . . . . . . . . 5

1.4 On-chip Type I and Type II comb generation . . . . . . . . . . . . 7

2 GENERATION OF FREQUENCY COMBS WITH SUB-100 GHZ FSR INHIGH Q SILICON NITRIDE MICRORESONATORS . . . . . . . . . . . 11

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2 Design and fabrication of the microresonators . . . . . . . . . . . . 12

2.3 Characterization of ultra-high Q microresonators . . . . . . . . . . . 16

2.4 Coherent 25 GHz comb generation . . . . . . . . . . . . . . . . . . 28

2.5 Comb generation with external seeding . . . . . . . . . . . . . . . . 37

2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3 INVESTIGATION OF MODE COUPLING IN NORMAL-DISPERSIONSILICON NITRIDE MICRORESONATORS FOR KERR FREQUENCYCOMB GENERATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

3.2 Linear mode interaction and avoided crossings . . . . . . . . . . . . 49

3.3 Comb initialization through mode coupling . . . . . . . . . . . . . . 54

3.4 Comb broadening using highly nonlinear optical fiber (HNLF) . . . 67

3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

iv

Page

4 BANDWIDTH SCALING OF PHASE-MODULATED CW COMB THROUGHFOUR-WAVE MIXING ON SILICON NANO-WAVEGUIDE . . . . . . . 72

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

4.2 Experimental Setup and Results . . . . . . . . . . . . . . . . . . . . 74

4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

5 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

VITA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

v

LIST OF TABLES

Table Page

2.1 Summary of Q values obtained in transmission and cavity ring-down mea-surements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.1 Estimated coupling strength for 4 mode crossing areas shown in Fig. 3.3(a) 54

vi

LIST OF FIGURES

Figure Page

1.1 (a) Ideal frequency comb, (b) Representative output spectrum of a modelocked laser with a Gaussian envelope, (c) corresponding time domainrepresentation [6] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Light propagation in optical fiber [14]. . . . . . . . . . . . . . . . . . . 4

1.3 Scheme of micro-ring resonator [36]. . . . . . . . . . . . . . . . . . . . 6

1.4 Scheme of the type I (Natively mode spaced) comb generation. . . . . 7

1.5 Scheme of the NMS comb generation (a) Different stage of the MMS combgeneration (b) Amplitude noise spectrum of the comb [49] . . . . . . . 9

1.6 Time domain study for the Type I and Type II comb generation for theauto-correlation traces, red lines denote the bandwidth limited pulse calcu-lated by the spectra, blue lines denote the pulse generated after the phasecompensation using line-by-line pulse shaping and green lines denote thepulse without the phase compensation. [53] . . . . . . . . . . . . . . . 10

2.1 Cornells design of the micro-resonators with FSR of (a) 80 GHz, (b) 40GHz and (c) 20 GHz [56]. . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2 Purdue design finger shaped micro-resonators with FSR of 25 GHz (a)with through port only and (b) with both through port and drop port. 14

2.3 SEM micrographs of the slanted top view (a) and cross section (b) of thesilicon nitride waveguides. The SEM picture is taken by Dr. Yi Xuan. 15

2.4 Measurement scheme for frequency comb assisted diode laser spectroscopymethod. (BS: beam splitter, PD: photodiode, BP: bandpass filter) [62] 17

2.5 (a) Normalized transmission spectrum. (b) and (c)Measured (blue dots)and fitted (red dashed line) transmission spectrum for the resonance near1556.697 nm and 1553.8958 nm respectively. . . . . . . . . . . . . . . 18

2.6 Transmission for the resonance near 1556.68 nm showing a loaded Q of13.9 million and intrinsic Q of 17.0 million. . . . . . . . . . . . . . . . 18

2.7 (a) A section of transmission between 1554 nm to 1557 nm showing 3different TE mode families. (b) and (c) calculated intrinsic Q and loadedQ for resonances in this regime respectively. . . . . . . . . . . . . . . . 20

vii

Figure Page

2.8 Experiment setup for ring-down measurement. (AWG: Arbitrary wave-form generator, TL: Tunable laser, IM: intensity modulator, PD: Photo-diode, LNA: Low noise amplifier, RTS: Real-time scope) . . . . . . . . 21

2.9 (a). Reference optical signal when the pump is far from resonance. (b)Optical signal showing rising and falling edge when the pump is in reso-nance around 1553.697nm. (c) Log-plot of the falling edge data along withthe least-squares fit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.10 Ringdown measurement result at 1553.8958 nm (a) Optical signal showingrising and falling edge when the pump is in resonance. (b) Log-plot of thefalling edge data along with the least-squares fit. . . . . . . . . . . . . 24

2.11 Ringdown measurement result at 1556.65 nm(a) Optical signal when thepump is in resonance. (b) Zoom-in view of the falling edge. . . . . . . 25

2.12 Comb generation at (a) 5 mW (2.8 mW on chip) and (b) 40 mW (22.4mW on chip) pumping near 1553.696 nm respectively. . . . . . . . . . 26

2.13 Comb generation pumping with an on-chip laser without using externalfiber amplifiers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.14 Transmission spectrum for the resonance near 1554.535 nm taken at (a)through port and (b) drop port. The loaded Q and intrinsic Q is calculatedto be 8.25 million and 10.8 million respectively. . . . . . . . . . . . . . 29

2.15 Drop-port Ringdown measurement result at 1554.535 nm (a) Optical signalwhen the pump is in resonance. (b) Log-plot of the falling edge data. . 30

2.16 Comb generation at (a) 15 mW (8.4 mW on chip) and (b) 40 mW (22.4mW on chip) pumping near 1553.830 nm. . . . . . . . . . . . . . . . . 31

2.17 Comb generation of the micro-resonator with finger shape pumping at1.5W (a) Primary sidebands are first generated when tuning the pumpinto the resonance (b) Fill in sub-comb lines are generated by decreasingthe detuning (c) RF Intensity noise for comb of (a) red line, (b) Blue linecompared with the background intensity noise denoted as black line. . 33

2.18 Time domain study of the comb spectrum given in Fig. 2.17(b) (a) Spec-trum filtered and smoothed by a commercial pulse shaper (b) Generatedpulse (red line) compared with both theoretical bandwidth limited pulse(blue line) and the uncompensated pulse (black line) . . . . . . . . . . 34

2.19 Comb spectrum generated from a resonator in anomalous dispersion regimewith a pump power of 1.3 W at 1544.707 nm. . . . . . . . . . . . . . . 35

viii

Figure Page

2.20 (a) Intensity noise of the generated comb (b) Beat note using a high speedphotodiode and (c) Zoomed in the beat note centered at 24.482 GHz withRBW=3 kHz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

2.21 Experimental setup for coherent Kerr comb generation and line-by-linepulse shaping. (TL: Tunable laser, EDFA: Erbium doped fiber amplifier,BPF: optical band-pass filter, DCF: dispersion compensating fiber, PS:commercial pulse shaper, OSA: optical spectrum analyzer, AC: intensityauto-correlator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

2.22 (a) Comb spectrum before the intensity auto-correlator (c) Auto correla-tion trace of the compressed pulse (blue) compared with uncompensatedpulse (red) and theoretical bandwidth limited pulse. . . . . . . . . . . 38

2.23 (a) Layout of the silicon nitride resonator with spiral structure. (b) Trans-mission spectrum of the micro-resonator. . . . . . . . . . . . . . . . . 39

2.24 Experiment setup for the dual-pump comb generation system . . . . . 39

2.25 Cartoon for the process of dual-pump generation (a) Stiumlated FWM, (b)Single pump generated mult-FSR comb (c)Dual-pump comb generation. 41

2.26 Experimental result of dual-pump comb generation (a) Stiumlated FWM(b) Single pump generated mult-FSR comb (c)Dual-pump comb genera-tion (d) Intensity noise . . . . . . . . . . . . . . . . . . . . . . . . . . 42

2.27 External seeding at different separation (a)1 FSR (b)2 FSR and (c)3 FSR 43

2.28 Experiment setup for seeding with a coherence source . . . . . . . . . 44

2.29 Comb generation with a coherent seeding and its time domain study . 45

3.1 Numerical investigation of mode coupling effect when the resonances ofthe two modes get close and cross each other (a) no mode coupling (b)with mode coupling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

3.2 (a) Microscope image of the silicon nitride resonator with path length of5.92 mm. (b) Measured transmission spectrum of the resonator. Insetis the zoom-in transmission spectrum showing resonances from differenttransverse mode families. . . . . . . . . . . . . . . . . . . . . . . . . . 52

ix

Figure Page

3.3 (a) Measured FSR versus optical wavelength for two TE modes, plotted inred and blue and fitted with D ∼ 156ps/nm · km and D ∼ −160ps/nm ·km respectively. (b-d) Aligned resonances with fixed increment showingthe mode coupling with different coupling strength (b) Strong couplingcase centered at 1542 nm with clear avoided crossings (c) Weak couplingcase centered at 1552 nm (d) Zoomed-in view of the weak coupling case(e) Zoom-in view and fitted FSR spectrum in a mode crossing area (f)Calculated D and corresponding D2 value of mode 1 and mode 2 plottedin red and blue respectively. . . . . . . . . . . . . . . . . . . . . . . . 55

3.4 Comb generation at different pump wavelength with one of the 1st side-bands kept at an approximately constant location (a) around 1560 nm and(b) around 1550 nm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

3.5 (a) Microscope image of the silicon nitride resonator with path length of1.97 mm. (b) Aligned resonances centered at 1563 nm with fixed incre-ment showing the mode coupling. (c) Comb generation at different pumpwavelength; one of the 1st sidebands remains close to 1563 nm . . . . 59

3.6 (a) Measured FSR versus optical wavelength for two TE modes, plottedin red and blue showing mode interaction feature near 1545 nm for the 75GHz discussed above and (b) Corresponding comb generation at differentpump wavelength; one of the 1st sidebands remains close to 1545 nm (c)Measured FSR versus optical wavelength for two TE modes, plotted in redand blue showing mode interaction feature near 1561 nm for a resonatorwith FSR at about 37 GHz and (d) Corresponding comb generation atdifferent pump wavelength; one of the 1st sidebands remains close to 1561nm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

3.7 Generation of coherent mode-locked Type I comb due to the mode coupling(a) Generated comb spectrum at the drop port (b) 15 lines are selected,amplified and filtered for time-domain characterization. (c) Autocorrela-tion of time domain pulse compared with that of theoretical bandwidth-limited pulse, showing good coherence and mode locking behavior. (d)Intensity noise compared with the measurement system noise floor . . 62

3.8 (a) Simulated comb generation pumping at different resonances in normaldispersion microresonator with mode coupling (b) and (c) Simulated modecoupling initialized Type I comb spectrum and its intracavity intensityrespectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

3.9 Observation of Pinned 1st sidebands for the resonator with passively modelocked Type I comb as discussed in Ref. [52] . . . . . . . . . . . . . . . 65

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Figure Page

3.10 Generation of coherent mode-locked Type I comb due to the mode coupling(a) Generated comb spectrum at the drop port (b) 15 lines are selected,amplified and filtered for time-domain characterization. (c) Autocorrela-tion of time domain pulse compared with that of theoretical bandwidth-limited pulse, showing good coherence and mode locking behavior. (d)Intensity noise compared with the measurement system noise floor . . 68

3.11 Experimental setup for our comb generation and bandwidth scaling scheme.CW-continuous wave laser, EDFA High power amplifier, DCF dispersioncompensating fiber, HNLF Highly nonlinear optical fiber, SMF singlemode fiber, OSA optical spectrum analyzer, AC auto-correlator . . . . 69

3.12 (a) Original comb spectrum generated from the resonator. (b) Comb spec-trum after bandwidth scaling using HLNF (c) Measured auto-correlationtrace for the scaled comb before (red) and after (blue) the compressioncompared with the theoretical bandwidth limited pulse (black). . . . . 69

4.1 (a) Experimental setup. CW: continuous wave laser, IM: Intensity modu-lator, PM: Phase modulator, EDFA: High power erbium-doped fiber am-plifier, OSA: optical spectrum analyzer (b) Bandwidth scaling of the CWcomb. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

4.2 (a) Spectrum for the FWM with CW inputs, (b) FWM conversion effi-ciency spectrum pumping at 1550 nm . . . . . . . . . . . . . . . . . . 77

4.3 (a) Spectrum for the FWM with CW inputs, (b) FWM conversion effi-ciency spectrum pumping at 1550 nm . . . . . . . . . . . . . . . . . . 78

4.4 Wavelength tuning of FWM generated frequency combs. (a) Input spec-trum of the PM-IM comb. Output spectra of comb with different wave-length separation between 2 CW lasers. The wavelength separation of thetwo inputs are 5 nm, 10 nm and 20 nm, for (b)-(d) respectively. . . . . 80

4.5 RF frequency tuning of FWM generated frequency combs. Output spectraof comb with RF frequencies of (a) 12.5 GHz, (b)15 GHz and (c)17.5 . 81

xi

ABSTRACT

Liu, Yang PhD, Purdue University, December 2015. On-Chip Generation, Charac-terization and Bandwidth Scaling of Optical Frequency Combs . Major Professor:Andrew M. Weiner.

Recently, on-chip comb generation based on high quality factor microresonators

has been intensively studied due to its simplicity, small size and low cost fabrication.

Frequency combs with free spectral ranges (FSRs) of a few tens of GHz are of spe-

cific interest for communication applications. However for silicon nitride resonators

in this FSR regime a huge pump power is required which far exceeds the maximum

available power from current on-chip laser sources. Meanwhile, most research em-

ploys microresonators with anomalous dispersion, for which modulation instability

is believed to play a key role in initiation of the comb. Comb generation in normal

dispersion microresonators has also been reported but is less well understood.

We demonstrate Silicon nitride microresonators with intrinsic Qs up to 17 million at

an FSR of 24.7 GHz. These Q values are the highest recorded for Silicon nitride res-

onators used for comb generation. The frequency comb onset power can be as low as

2.8 mW, within reach of on-chip semiconductor lasers. Furthermore, we report a de-

tailed investigation of few-moded, normal dispersion silicon nitride microresonators,

showing that mode coupling can strongly modify the local dispersion, even changing

its sign. We demonstrate a link between mode coupling and initiation of comb gener-

ation by showing experimentally pinning of one of the initial comb sidebands near a

mode crossing frequency. Associated with this route to comb formation, we observe

direct generation of coherent, bandwidth-limited pulses at repetition rates down to

75 GHz, without the need to first pass through a chaotic state. Finally we investigate

the four-wave mixing (FWM) process in silicon nano-waveguides by demonstrating

xii

an on-chip scheme to scale the bandwidth of the electrooptic (EO) frequency comb

lines. With a input of 55 lines from EO frequency comb, it can generate a flat-topped

frequency comb with over 100 lines in a 5-dB bandwidth.

1

1. INTRODUCTION

Our research targets the on-chip generation and characterization of the frequency

comb lines. Frequency combs have long been demonstrated to be suitable for a variety

of applications including optical communications [1], radio frequency (RF) photonics

[2] and optical arbitrary waveform generation (OAWG) [3]. Recently, research related

specifically to the on-chip generation of frequency combs has received a great deal of

attention. Their appeal lies in the small form factor, reduced complexity (compared

to traditional comb generation), and the possibility of being photonically integrated.

Before going deep into our work, we will discuss some basic concept including optical

frequency combs, on-chip optical waveguides and resonators.

1.1 Optical frequency combs

An optical frequency comb [4,5] is a name given to a pulsed laser source emitting

a periodic waveform with a stabilized repetition rate. In the frequency domain, such

a source is comprised of a discrete set of frequencies spaced by a constant period.

This looks like a comb, hence the name. Traditionally, mode locked lasers which emit

a periodic train of short pulses have been the primary means of generation optical

frequency combs. Desirable properties in a frequency comb include stable frequency

positions of the individual comb lines as well as precisely predictable dispersion. By

employing suitable locking mechanisms, the frequency positions of the comb lines can

be stabilized, however exact determination of individual frequencies is more challeng-

ing. The difficulty arises because the absolute optical frequencies constituting the

comb are not exact multiples of the repetition rate owing to a mismatch between the

phase and group velocities in the laser cavity. The individual comb lines are given by

Eq.(1.1) [4]

2

Fig. 1.1. (a) Ideal frequency comb, (b) Representative output spec-trum of a mode locked laser with a Gaussian envelope, (c) correspond-ing time domain representation [6]

fm = mfrep + ε (1.1)

Where frep is the repetition rate of the laser and ε is known as the carrier envelope

offset. Fig. 1.1 schematically shows that the value of ε is not easy to obtain which

makes exact determination of the frequencies difficult. Fig. 1.1(a) shows an ideal

frequency comb with an infinite bandwidth. Fig. 1.1(b) shows a schematic of a

realistic spectrum from a mode locked laser with a Gaussian envelope comprised of

comb lines which are offset from multiples of the repetition rate by the carrier envelope

offset frequency. Fig. 1.1(c) shows the envelope of time domain trace corresponding

to the comb.

3

In the last few decades, driven by metrological applications, there has been signif-

icant developments in frequency combs resulting in the ability measure and lock the

carrier envelope offset. Such combs are called self-referenced frequency combs and

they have stabilized frequency lines with known frequency positions [4, 5].

However, knowledge of the exact frequency locations is not a requirement for all

applications. Whether the exact frequency locations are known or not, the periodi-

cally spaced comb lines can still produce short bandwidth limited pulses in the time

domain, which can be used in many applications. In some of these applications it

is beneficial to manipulate the pulses into user defined shapes or waveforms. This

can be achieved with the well-established technique of femtosecond pulse shaping [7].

The true strength of using frequency combs together with pulse shapers come when

spectral lines constituting the comb can be controlled individually [3]. In the time

domain line-by-line control corresponds to 100% duty factor shaped waveforms with

arbitrary user defined features.

Before we go into the next section, there is an important point that needs to

be discussed. An optical frequency comb can refer to any source with a stabilized

repetition rate and stable carrier frequencies. This can be at very small repetition

rates (i.e. kHz) all the way to THz. However, for many applications, for e.g. in

optical communications, the interesting regime will be in repetition rates of tens of

GHz corresponding to the data rates used. Also, in order to be able to address

individual spectral lines using current pulse shapers, it is necessary to have relatively

wider spacing (again of the order of GHz). So when we refer to OAWG, we are usually

talking about relatively high repetition rate frequency combs. However, mode locked

lasers don’t scale well into these repetition rates while maintaining frequency stability.

For this reason, there has been significant development in alternate frequency comb

sources allows for high repetition rates [8–11]. In these methods, comb generation

using on-chip microresonators has attracted a lot of attention [10,12,13]. In our work,

we are focusing on the on-chip comb sources with repetition rate of the order of tens

of GHz and with good coherence.

4

Fig. 1.2. Light propagation in optical fiber [14].

1.2 Optical waveguides

Waveguides used at optical frequencies are typically made from dielectrics. A

dielectric material with high permittivity, and thus high index of refraction, is sur-

rounded by a material with lower permittivity. The most common optical waveguide

in use is optical fiber. Guiding light in this manner can be simply understood using

the linear propagation approximation depicted in Fig. 1.2 where the optical field is

confined in the high refractive index area through total internal reflection.

On-chip optical waveguides, which guide light in a similar manner, have attracted

increased attention in recent years for applications in high speed data communication

between micro-chips [15–20]. The essential advantages of silicon photonics compared

to the conventional fiber optical systems are simplicity, small size, and very low power

consumption.

Another important application of on-chip optical waveguides is for use in nonlinear

optics. Normally, the on-chip waveguides have extremely small cross-section and good

field concentration in the core area allowing for high energy density. This high energy

density enhances the nonlinear interaction between the optical field and the material.

Also, materials that are used for the fabrication of the on-chip optical waveguides

can be chosen to have large nonlinear coefficient compared to that of SiO2, which is

typically used for most optical fiber, allowing for a greater nonlinear interaction. Us-

ing these on-chip waveguides many nonlinear processes have demonstrated, including

5

self- [21] and cross- [22] phase modulation, second harmonic generation (SHG) [23],

parametric amplification [24], Raman amplification [25] and four wave mixing [26].

One thing to note for the nonlinear applications is dispersion management. The

phase matching condition is of key importance for optical nonlinear phenomenon [24].

In optical waveguides, not only materials themselves will introduce dispersion, but due

to their extremely small size structural dispersion will also be present. To better meet

the phase condition, several methods have been used to engineer the disperion. One

method is to vary the cross section [27] or alternatively by selecting a different shape,

like was done with the ridge waveguides in [28]. Another method, which has been

demonstrated in lithium niobate waveguides, involves using either periodically [29]

or aperiodically poled [30] waveguides to meet the phase matching condition for the

SHG for certain bandwidth.

1.3 Optical microresonators

Optical resonators are optical structures that can trap light by exploiting either

total internal reflection at the air/dielectric interfaces, or through distributed Bragg

reflection from periodical structures such as multilayered structures or arrays of holes.

The term microresonators is given to optical resonators at µm dimensions. These

resonators have compact size (small modal volume, V ), high mode quality factor, Q

(defined as the ratio of the energy stored to the energy dissipated in the microres-

onator), and large free spectral range (FSR, the spacing between neighboring high-Q

resonances) [31]. These characteristics enable microresonators to have a wide range

of applications in the fields of nonlinear optics, optical communications and chip-level

quantum optics [32].

From the viewpoint of communications, optical waveguides discussed in the pre-

vious section along with optical resonators are used together to construct photonic

devices, modules, circuits and chips. Examples include a continuous-wave Raman

laser [33], optical switches [34] and optical isolator [35].

6

Fig. 1.3. Scheme of micro-ring resonator [36].

An important structure for microresonators is the micro-ring configuration. By

definition, an optical micro-ring resonator is a set of waveguides, in which at least one

is a closed loop, which are formed to couple light from the input and to the output.

As shown in Fig. 1.3, when light of the resonant wavelength is passed through the

loop from input waveguide, it builds up in intensity over multiple round-trips due to

constructive interference and is coupled to the output bus waveguide which serves as

a detector waveguide [36]. In the application where very high Q is needed, we need

to match the coupling strength with the round trip loss in the resonator. The case

when these are exactly matched is called critical coupling. Following the definition we

term the weaker coupling as under coupling and stronger coupling as over coupling.

By manipulating the coupling strength, we can tune the the percentage of the power

that gets into resonance while leaving the intrinsic Q unchanged.

There are a variety of applications that take advantage of micro-ring configura-

tions. Two such examples are light emitting diode (LED) [37] and low-power con-

suming high-speed modulations which utilize carrier injection [38] or depletion [39].

Compared with the modulators in a Mach-Zehnder interference configuration [40,41],

7

Fig. 1.4. Scheme of the type I (Natively mode spaced) comb generation.

micro-ring based modulators can have a much smaller driving voltage but with a nar-

rower operational bandwidth. Other signal processing units have also been demon-

strated in small footprint, such as, filters [42], multiplexers [43], polarization con-

verter [44], and optical isolator [45,46].

1.4 On-chip Type I and Type II comb generation

A very important application for the microresonators that was discussed above

is the on-chip comb generation. When a continuous-wave (CW) laser is input into

a microresonator at a cavity resonance frequency, intracavity power builds up and

enables additional cavity modes to oscillate via cascaded four-wave mixing (FWM)

in the resonator [10,12,47,48].

It is generally believed that there are two different comb generation process: the

first we call Type I [13], which is also referred to as Natively Mode-Spaced (NMS) [49]

comb generation. In this case, as shown in Fig. 1.4, the first parametric sidebands

are generated adjacent to the pump and then spread throughout the spectrum. The

comb lines in this process usually have good coherence.

The other process is termed Type II [13] or Multi-Mode Spaced (MMS) [49] comb

generation. In this case, the first parametric sidebands are generated at a spacing

which is more than 1 FSR away from the pump (Fig. 1.5(a) stage 1). Usually if only

these initial sidebands are presented, the comb lines exhibit good coherence and can

8

be understood as a NMS case with higher FSR. At later stages (stage2 to 3) of comb

evolution (achieved by reducing detuning or increasing the input power), secondary

lines are generated around the primary lines via FWM processes, resulting in natively

mode-spaced lines. In stage 2, the secondary lines have not yet merged and RF noise

is not observed. However, when the lines begin to merge as shown in stage 3, they

may have a small frequency mismatch. Although the secondary lines around each

primary lines have the same spacing (a single FSR), the original lines that they are

formed around are not necessarily integer numbers of FSRs away from the pump.

The position of these original lines can be affected by both dispersion and nonlinear

self- or cross-phase modulation. Therefore, when the secondary lines merge, they may

have a small offset which causes amplitude noise. The amplitude noise first shows

as single peaks. With higher power, they can eventually develop into broad RF beat

note.

A good way to examine the coherence of the comb lines is to investigate the

time domain pulses with a line-by-line pulse shaper. if the comb lines are of good

coherence, by compensating for the phase using the pulse shaper, one can get a

bandwidth limited pulse. However, if the comb lines are not coherent, a perfectly

compressed pulse cannot be generated. Automatic phase locking behavior has been

observed in some cases recently [50–52], however, in my experience, it is not the usual

case. A time domain study of the two types of comb generation is given in Ref. [53].

From Fig. 1.6, we can see that, for Type I comb, the bandwidth limited pulse can be

generated after line-by-line pulse shaping which means good coherence. For a Type II

comb, without the secondary lines, the pulse can also be compressed to a bandwidth

limited pulse. However, when with secondary fill-in lines, intensity noise appears,

in the form of single peaks and the perfect compressed pulse cannot be achieved,

inferring that the lines are less coherent.

9

Fig. 1.5. Scheme of the NMS comb generation (a) Different stageof the MMS comb generation (b) Amplitude noise spectrum of thecomb [49]

10

Fig. 1.6. Time domain study for the Type I and Type II comb gener-ation for the auto-correlation traces, red lines denote the bandwidthlimited pulse calculated by the spectra, blue lines denote the pulsegenerated after the phase compensation using line-by-line pulse shap-ing and green lines denote the pulse without the phase compensa-tion. [53]

11

2. GENERATION OF FREQUENCY COMBS WITH

SUB-100 GHZ FSR IN HIGH Q SILICON NITRIDE

MICRORESONATORS

2.1 Introduction

As discussed in the introduction, on-chip optical comb generation using high qual-

ity factor (Q) resonators has been intensively investigated recently. These cavities can

be very small and can generate the comb lines with large FSR (eg., 600 GHz in [13]

leading to a train of pulses with extremely high repetition rate. However lower repeti-

tion rate frequency combs with a FSR of a few tens of GHz, are of greater interest for

communication applications. These low GHz class combs have repetition rates that

coincide with communication data rates, and thus provide a direct link between op-

tical and electrical signals enabling various applications in RF photonics. There have

been a number of attempts to generate frequency combs at this repetition rate level:

a FSR with 36 GHz was demonstrated in fused-quartz [54], 35 GHz in MgF2 [49] and

22.9 GHz in silica disk resonators [55]. Another material that has attracted atten-

tion is silicon nitride due to its complementary metal-oxide-semiconductor (CMOS)

compatible fabrication techniques allowing for easy monolithic integration. Genera-

tion of comb lines in silicon nitride with 25 GHz FSR or less has been demonstrated

recently [56–58].

From an integration perspective, a primary challenge for those low repetition rate

silicon nitride microresonators has been to reduce the required pump power for comb

generation. The pump power for these reports are all over 2W, which far exceeds the

maximum available power from current on-chip laser sources whose output power is

usually below a few tens of mW. Since the pump power decreases quadratically with

12

increasing quality factor (Q) [59], there has been a greater focus on optimization of

device fabrication, in order to increase the Q of the resonators [60,61].

Loss contributions which limit the intrinsic Q in silicon nitride resonators include

material absorption, surface roughness, bending loss, and stitching errors during the

lithography process. In addition, fabricating thick silicon nitride waveguides has

proved difficult due to high tensile stress within silicon nitride, which makes the films

susceptible to cracking during processing. Nevertheless, recent progress in silicon

nitride fabrication techniques has led to reports of microresonator with intrinsic Q

values of 20 million on 400 nm thick silicon nitride [61] and 7 million on 910 nm

thick silicon nitride [60]. However, no frequency comb generation has previously been

reported with such high-Q rings. In this thesis, we demonstrate an intrinsic Q of 17

million in a 600 nm thick silicon nitride microresonator resonator with comb initiation

power as low as 2.8 mW.

In the following sections, I will discuss the design and fabrication process of the

silicon nitride resonators with low repetition rates in Sec. 2.2, I will talk about the

Q characterization process for resonators with over 10 million and demonstrate an

intrinsic Q of over 17 million with comb initiation power as low as 2.8 mW at 25

GHz in Sec. 2.3, I will discuss some 25 GHz coherent comb generation processes from

our silicon nitride microresonators in Sec. 2.4, I will introduce dual-pump seeding as

a possible method to generate more comb lines in a multi-FSR sideband generation

system in Sec. 2.5, I will summarize this part in Sec. 2.6.

2.2 Design and fabrication of the microresonators

Most silicon nitride micro-resonators that are used for the comb generation have

a circular shape as this is the simplest design. When we move to lower repetition

rates, for example, 25 GHz, the length of the resonator increases to as long as 6 mm

which corresponds to nearly 1 mm in radius for a circular design. However, most

e-beams used to pattern the resonator have a smaller writing field. This means that

13

Fig. 2.1. Cornells design of the micro-resonators with FSR of (a) 80GHz, (b) 40 GHz and (c) 20 GHz [56].

the resonator cannot be finished in one writing process because the stage which holds

the chip need to be move mechanically for the e-beam to cover the full area. This

mechanical movement causes stitching errors which will bring additional loss to the

resonator and will greatly reduce the quality factor. Thus spiral geometry is employed

in ref. [56]. Another advantage of the spiral design is for different sizes of resonator,

the coupling between the resonator and the waveguide can kept the same which will

makes it easier to get the critical coupling [56].

In this report, we developed a new design which we called the finger scheme as

shown in Fig. 2.2. It is more compact than the circular design to have the resonator

fits in an e-beam writing field to avoid the stitching error. It is also very convinient

to add a drop port as shown in Fig. 2.2(b). According to the recent report [52],

smoother comb lines spectra can be observed at the drop port and passively mode-

locked pulses with low background can be generated without the need to filter out or

suppress the strong pump line.

The fabrication of the resonators was done by Dr. Yi Xuan in the Birck Nan-

otechnology Center at Purdue University. For the resonators shown in Fig. 2.2, the

fabrication process can be generally described as follows: 600 nm thick stoichiometric

LPCVD Silicon nitride film was grown in three installments of 166-200 nm each on

patterned 3.5µm thick thermal oxide islands on a Si wafer at 800◦C using dichlorosi-

14

Fig. 2.2. Purdue design finger shaped micro-resonators with FSR of25 GHz (a) with through port only and (b) with both through portand drop port.

15

Fig. 2.3. SEM micrographs of the slanted top view (a) and crosssection (b) of the silicon nitride waveguides. The SEM picture istaken by Dr. Yi Xuan.

lane and ammonia as precursors. A negative EBL resist, hydrogen- silsesquioxane

(HSQ), was spun on Silicon nitride and patterned with a 100 KV EBL system. The

HSQ pattern was transferred to Silicon nitride by CF4-based plasma etching chem-

istry. Fig. 2.3(a) is a tilted-view SEM micrograph showing the etched Silicon nitride

microring with a smooth sidewall. Fig. 2.3(b) is a typical SEM cross-sectional image

of a Silicon nitride waveguide with 2 µm×600 nm cross-section showing a 84◦ vertical

etching profile. Inverse tapers were introduced at both ends of the bus waveguides to

reduce the fiber-to-chip coupling loss. Then, a 3 µm low-temperature oxide (LTO)

was deposited on top of the device acting as upper-cladding. To minimize the me-

chanical vibration of the optical fibers during measurement with high input powers

necessary for frequency comb generation, U-shaped grooves were dry-etched into the

Si substrate to accommodate the lensed fibers and to allow them to be placed close

to the waveguide edges. Finally, the chip was annealed at 1200 ◦C for 3 hours to

remove the residue N-H bonds in the SiN film and densify the LTO upper-cladding

to further promote the Q factor.

16

2.3 Characterization of ultra-high Q microresonators

We first characterize the Q of the microresonators. The most straight forward

method is to use a tunable laser to directly scan the transmission of the resonators

and calculate the quality factor accordingly. However, the linewidth of the resonator

with a Q over 10 million is 20 MHz while the resolution of our tunable laser is 0.1

pm (∼ 12.5MHz) which is far not enough. To address this limitation, we utilize two

independent methods to accurately determine the Q of the silicon nitride resonators.

The first method is to use frequency comb assisted diode laser spectroscopy introduced

in [62] to accurately measure the transmission for Q value calculation. The setup is

given in Fig. 2.4. In this method, a fiber laser frequency comb is used to beat with

a tunable laser to generate a running beat note. The beat note is detected by a

photodiode (PD2) and pass through 2 bandpass filters. The output signals of the

bandpass filters are detected by an oscilloscope to generate the calibration frequency

marks. Another part of the tunable laser signal will be sent to the resonator for

spectroscopy [62]. This measurement was done with Dr. Xiaoxiao Xue.

We first measured the resonator shown in Fig. 2.2(a). The height of the resonator

is 600 nm and width is 3 µm, the width of the bus waveguide is 1 µm and the gap

between the resonator and the bus waveguide is 200 nm. The normalized transmis-

sion of TE mode can be seen in Fig. 2.5(a) and a zoomed-in view of two selected

resonances at 1553.697 nm and 1553.8958 nm are shown and fitted in Fig. 2.5(b)

and (c) respectively. Using the method we developed in ref [63], we measured the

coupling condition of each resonances and all the TE resonances are under coupled so

we can calculate the intrinsic Q (Qi) accordingly. The quality factors are calculated

to be Ql = 6.93(Qi = 11.9) million at 1553.697 nm and Ql = 8.34(Qi = 14.5) million

at 1553.8958 nm. Another example for resonance near 1556.69 nm is given in Fig2.6.

This resonance have a smaller extinction ratio but a loaded Q of 13.9 million and

intrinsic Q of 17.0 million.

17

Fig. 2.4. Measurement scheme for frequency comb assisted diode laserspectroscopy method. (BS: beam splitter, PD: photodiode, BP: band-pass filter) [62]

18

Fig. 2.5. (a) Normalized transmission spectrum. (b) and (c)Measured(blue dots) and fitted (red dashed line) transmission spectrum for theresonance near 1556.697 nm and 1553.8958 nm respectively.

Fig. 2.6. Transmission for the resonance near 1556.68 nm showing aloaded Q of 13.9 million and intrinsic Q of 17.0 million.

19

We take a more detailed analysis for the TE resonances of this resonator by looking

at a section of the transmission spectrum between 1554 nm and 1557 nm which are

shown in Fig. 2.7(a). There are 3 modes within every ∼ 0.2 nm corresponding to an

FSR of ∼ 25 GHz. Different modes possess slightly different FSRs, extinction ratios

and quality factors. We calculated both loaded and intrinsic Q of the resonances in

this regime in Fig. 2.7(b) and (c). Over 10 resonances have the intrinsic Q over 10

million showing that the high Q is not an isolated case, but for a number of resonances

of this mode family.

To confirm the high Q values obtained above, we performed cavity ring-down

measurements [64] to directly measure the photon lifetimes. This measurement was

done with Andrew J. Metcalf. The basic idea of this measurement is that when we

use a CW in resonance input which is turned of at time toff , the output optical power

P (t) after t > toff can be exressed as:

P (t) ∼ e−(t−toff )

τ (t > toff ) (2.1)

where τ is the decay time constant with Q = τω in which ω is the resonance frequency.

So we can extract the Q value from the exponential decay of the falling edge. The

experimental setup is given in Fig. 2.8. In order to quickly turn off the pump we

utilized a high extinction LiNbO3 intensity modulator (IM) driven by an electronic

Arbitrary Waveform Generator (AWG) programed to generate a 1 MHz 50% duty

cycle square wave from the CW pump. The average power at the input of ring was

-7 dBm. The optical signal at the output of the resonator is detected with a 12 GHz

photodetector. The electrical signal is then and amplified with a low noise amplifier

(LNA) before being detected on fast real-time scope (20 Gs/s). Fig. 2.9(a) serves

as a reference and shows the optical gating signal when the pump is far detuned

from resonance. When tuned into resonance around 1553.697 nm we observe two

peaks, plotted in Fig. 2.9(b), which temporally coincide with the rising and falling

edge of the input optical signal. At the instant the pump is gated on we observe the

first peak whose amplitude is equivalent to the incident wave. As the field in the

ring begins to charge up the measured waveform drops to zero due to interference

20

Fig. 2.7. (a) A section of transmission between 1554 nm to 1557 nmshowing 3 different TE mode families. (b) and (c) calculated intrinsicQ and loaded Q for resonances in this regime respectively.

21

Fig. 2.8. Experiment setup for ring-down measurement. (AWG: Ar-bitrary waveform generator, TL: Tunable laser, IM: intensity mod-ulator, PD: Photodiode, LNA: Low noise amplifier, RTS: Real-timescope)

22

Resonance wavelengthTransmission Cavity ring-down

Loaded Intrinsic Loaded Intrinsic

1553.697 nm 6.93× 106 1.19× 107 8.06× 106 1.38× 107

1553.896 nm 8.33× 106 1.45× 107 9.34× 106 1.63× 107

Table 2.1.

Summary of Q values obtained in transmission and cavity ring-downmeasurements.

between the incident and radiated fields. When the pump is gated off the incident

field is now zero and we just are left with the decaying radiated field from the cavity.

Selecting this falling edge and performing a least-squares fit, we calculate a time

constant τ of 6.64 ns and 7.70 ns for the 1553.697 nm and 1553.8958 nm resonances,

respectively. In order to help visualize the time constant we provide a log-plot of

the falling edge data along with the least-squares fit in Fig. 2.9(c). The loaded Ql

can be directly calculated from the fall time. The intrinsic Q is estimated using

the Qi/Ql ratio calculated from the transmission spectrum. The ringdown result at

1553.8958 nm is given in Fig. 2.10. It is worth noting that from Fig. 2.7, through

fitting the transmission spectrum we can get relatively high Qs between 1556 nm

and 1557 nm but we choose the resonances at 1553.697 nm and 1553.8958 nm for

ringdown measurement. The reason is that these two resonances are both close to

critical coupling regime which have relatively large extinction ratios. This makes it

much easier to do the data analysis. We performed a ringdown measurement at the

resonance near 1556.65nm which has a smaller extinction ratio and the result is given

in Fig. 2.11. A zoom-in view of the falling edge is given in Fig. 2.11(b). We didn’t

see a clear exponential decaying as both the resonator field decaying and the laser

turning off will contribute to the falling edge which makes the situation much more

complicated in this case.

23

Fig. 2.9. (a). Reference optical signal when the pump is far fromresonance. (b) Optical signal showing rising and falling edge whenthe pump is in resonance around 1553.697nm. (c) Log-plot of thefalling edge data along with the least-squares fit.

24

Fig. 2.10. Ringdown measurement result at 1553.8958 nm (a) Opticalsignal showing rising and falling edge when the pump is in resonance.(b) Log-plot of the falling edge data along with the least-squares fit.

25

Fig. 2.11. Ringdown measurement result at 1556.65 nm(a) Opticalsignal when the pump is in resonance. (b) Zoom-in view of the fallingedge.

26

Fig. 2.12. Comb generation at (a) 5 mW (2.8 mW on chip) and (b)40 mW (22.4 mW on chip) pumping near 1553.696 nm respectively.

A summary of the Q values from both the transmission and cavity ring-down

measurements are shown in Table 2.1, showing a close comparison between both

measurements.

With an ultra-high intrinsic Q of 17 million, the power requirements for frequency

combs can be significantly reduced as the threshold power scales down with Q2 for

Kerr comb generation. As a result, we observed the onset of a frequency comb at

an input power of ∼ 5 mW when pumping a single CW input to the silicon nitride

microresonator. Taking into account the 2.5 dB coupling loss per facet, the onset

power should be less than 2.8 mW on chip. The generated optical spectrum when

pumping the resonance near 1553.696 nm at 2.8 mW is shown in Fig. 2.12(a) and

with higher input power of ∼ 40 mW a relatively broadband comb can be observed

as shown in Fig. 2.12(b). The threshold power is in the range of the output power

of our on-chip laser and Fig. 2.13 showed the comb generation spectrum using the

on-chip laser without any external fiber amplifiers.

For resonator shown in Fig. 2.2(b), the height and width of the resonator, the

width of the bus waveguide are the same as they are for the resonator in Fig. 2.2(a),

27

1530 1540 1550 1560 1570 1580−70

−60

−50

−40

−30

−20

−10

Wavelength (nm)

Pow

er (

dBm

)

Fig. 2.13. Comb generation pumping with an on-chip laser withoutusing external fiber amplifiers.

28

the gap between resonator and bus waveguide is 400 nm and the most significant

difference is that it has a drop-port structure with a drop gap of 700 nm. The

Normalized transmission at through and drop port for resonance around 1554.535 nm

are shown in Fig. 2.14(a) and (b) respectively. The calculated Ql is 8.25 million and

Qi is 10.8 million for resonance at 1554.535 nm. It should be more straighforward to

do the ringdown measurement at the drop-port as we can directly get the intracavity

field at drop-port while at the through port the output is the combination of the

intracavity field and the remaining input light. However in this case the coupling

between the resonator and the drop port is so weak, the in resonance output power of

the drop-port is about 30 dB less than the input power which makes the photodiode

output signal very weak and noisy. One drop-port ringdown measurement result for

this resonator at the resonance near 1554.535 nm is given in Fig. 2.15. We can see

that the falling edge, although shows exponential decay, but is very noisy. We tried

to fit the data, the fitted Qs for this resonance are in the range of 6 to 9 million,

which shows a very large variance. We tried to use an EDFA after the drop-port,

although we get more power to the photodiode, but still see a large variance of the

estimated Q values. But we believe that the transmission sweeping and fitting method

is sufficiently accurate to estimate the Q value for this resonator. With this resonator,

the threshold of comb generation is 15 mW (∼ 8.4 mW on chip), the comb generation

results pumping near 1553.830 nm at threshold power and a higher power (∼ 40 mW )

are given in Fig. 2.16(a) and (b) respectively.

2.4 Coherent 25 GHz comb generation

The combs generated from the ultra-high Q resonators discussed above have very

low pump power; however, these combs are incoherent with intensity noise which

means that the comb lines cannot be compressed to a bandwidth limited pulse using

line-by-line pulse shaping. In this section, I will show two examples of coherent comb

generation at 25 GHz repetition rate. For the first example, the resonator is again

29

Fig. 2.14. Transmission spectrum for the resonance near 1554.535 nmtaken at (a) through port and (b) drop port. The loaded Q and in-trinsic Q is calculated to be 8.25 million and 10.8 million respectively.

30

Fig. 2.15. Drop-port Ringdown measurement result at 1554.535 nm(a) Optical signal when the pump is in resonance. (b) Log-plot of thefalling edge data.

31

Fig. 2.16. Comb generation at (a) 15 mW (8.4 mW on chip) and (b)40 mW (22.4 mW on chip) pumping near 1553.830 nm.

32

in normal dispersion regime, the threshold power of the comb generation is 0.6 W.

When pumping near 1550.4 nm, The primary sideband has the separation of 2-FSR.

In this test, we fix the pump power to 1.5W, but change the detuning in order to

study the comb behavior. When the pump begins to tune into the resonance, while

still at a relatively large detuning, only primary sidebands are generated, as shown

in Fig. 2.17(a). By decreasing the detuning, sub-comb lines are filled in with 1-FSR

separation, as shown in Fig. 2.17(b). Interestingly, when we look at the intensity

noise which is shown in Fig. 2.17(c), no obvious intensity noise is introduced because

of the fill in lines and we observe only a very small difference between the background

noise and the comb noise. We believe this noise is from the EDFA, not from the comb

itself and thus still believe the comb lines should be coherent.

To further investigate the coherence of the generated comb lines, we use a com-

mercial pulse shaper to select 9 lines from the spectrum. To get a better pulse, we

adjust the power of the comb lines to make the spectrum smoother (Fig. 2.18(a)),

and then compensate for the phase. The auto-correlation trace given by the red line

in Fig. 2.18(b) shows that it is very similar to the theoretical bandwidth limited pulse

as plotted by the blue line which was calculated using the measured spectrum and

assuming a flat phase. The uncompensated pulse is given in the black line. We can

see that by compensating the phase, an almost perfectly compressed pulse is gener-

ated which means that the generated comb lines with 25 GHz repetition rate have

good coherence.

In our second example, the height of the silicon nitride resonator is 800 nm and

the width is 2um, which means that the resonator is in anomalous dispersion regime.

This resonator doesn’t have a drop port and the through gap is 300 nm. The comb

spectrum when the pump power is 1.3 W at 1544.707 nm is shown in Fig. 2.19.

The intensity noise of the comb is given in Fig. 2.20(a) showing low noise and good

coherence. We also use a high speed photodiode to directly look at the beat note

of the generated comb. As shown in Fig. 2.20(b), a single clear beat note centered

at around 24.48 GHz is observed within 0 to 45 GHz range. We zoomed in the

33

Fig. 2.17. Comb generation of the micro-resonator with finger shapepumping at 1.5W (a) Primary sidebands are first generated whentuning the pump into the resonance (b) Fill in sub-comb lines aregenerated by decreasing the detuning (c) RF Intensity noise for combof (a) red line, (b) Blue line compared with the background intensitynoise denoted as black line.

34

Fig. 2.18. Time domain study of the comb spectrum given in Fig.2.17(b) (a) Spectrum filtered and smoothed by a commercial pulseshaper (b) Generated pulse (red line) compared with both theoreticalbandwidth limited pulse (blue line) and the uncompensated pulse(black line)

35

Fig. 2.19. Comb spectrum generated from a resonator in anomalousdispersion regime with a pump power of 1.3 W at 1544.707 nm.

beat note in Fig. 2.20(c) with a center frequency at 24.482 GHz using the resolution

bandwidth (RBW) of 3 kHz, a clean and narrow beat note is observed which confirms

the coherence of the generated comb.

We used the setup shown in Fig. 2.21 to further confirm the coherence of the

comb lines and to study their time domain profile. A section of the comb lines are

filtered out using a band-pass filter (BPF), amplified using an EDFA and shaped by

a commercial line-by-line pulse shaper (PS) before being sent to the intensity auto-

correlator (AC) to measure the time domain profile. The dispersion compensating

fiber before the PS is used to compensate for the dispersion of the fiber link from the

resonator to the AC. The filtered and amplified spectrum is shown in Fig. 2.22(a)

and the compressed auto-correlation trace is compared with the uncompressed trace

and the theoretical bandwidth limited pulse in Fig. 2.22(b). We can see that without

shaping, the time domain profile of the comb lines is pulse like but no bandwidth

limited. It can be compressed to an almost bandwidth limited pulse using line-by-

36

Fig. 2.20. (a) Intensity noise of the generated comb (b) Beat note us-ing a high speed photodiode and (c) Zoomed in the beat note centeredat 24.482 GHz with RBW=3 kHz

37

Fig. 2.21. Experimental setup for coherent Kerr comb generation andline-by-line pulse shaping. (TL: Tunable laser, EDFA: Erbium dopedfiber amplifier, BPF: optical band-pass filter, DCF: dispersion com-pensating fiber, PS: commercial pulse shaper, OSA: optical spectrumanalyzer, AC: intensity auto-correlator.

line pulse shaper which again showing good coherence of the comb lines. It is also

worth noting that most of the broadband coherent combs need to go through a chaotic

and noisy state before reach the coherent state [50,65]; however, this comb is coherent

immediately upon generation.

2.5 Comb generation with external seeding

To generate comb with more lines and get a better control of the comb, we intro-

duce additional inputs besides the pump to the comb generation system. External

seeding of this type has already been applied to influence comb generation in silica

disk whispering gallery mode resonators [66]. Here we demonstrate that by introduc-

ing a second input to a silicon nitride micro-resonator (a resonator which normally

generates a multiple FSR comb with a single CW pump), a substantial number of

new lines can be generated without increasing the intensity noise. In addition, we

demonstrate the ability to control of the separation of the sidebands. The silicon ni-

tride resonator we used here has a 2µm×515 nm waveguide cross-sections. According

to our simulation, the silicon nitride waveguide with this dimension shows a normal

dispersion. The total path length of the resonator is 1.9 mm which corresponds to a

77 GHz FSR. As shown in Fig. 2.23(a), the resonator has a spiral structure. The gap

between the resonator and the coupling waveguide is 700 nm. The transmission spec-

38

Fig. 2.22. (a) Comb spectrum before the intensity auto-correlator (c)Auto correlation trace of the compressed pulse (blue) compared withuncompensated pulse (red) and theoretical bandwidth limited pulse.

39

Fig. 2.23. (a) Layout of the silicon nitride resonator with spiral struc-ture. (b) Transmission spectrum of the micro-resonator.

Fig. 2.24. Experiment setup for the dual-pump comb generation system

trum of TE modes is given in Fig. 2.23(b). The inset shows the resonance we used

to generate the comb, and the loaded quality factor calculated from the transmission

spectrum of this resonance is 1.19× 106.

The experimental seeding setup is shown in Fig. 2.24. Two CW lasers are com-

bined and amplified with an EDFA and input into the resonator. After the resonator,

similar to the single pump setup, optical spectrum and intensity noise is measured.

The process of the comb generation with this dual-pump scheme as shown in Fig.

40

2.25 can be expressed as follows. When input with small power below the comb gen-

eration threshold, stimulated FWM of the two inputs will be observed as shown in

Fig. 2.25(a), while with single input, multi-FSR comb can be generated. Using a

single input which is above the threshold, a multi-FSR comb can be generated as in

Fig. 2.25(b). However, if the dual-input has at least one of them above the comb

generation threshold, the process can be regarded as a combination of the two pro-

cesses. As shown in Fig. 2.25(c), not only FWM around the two inputs is observed

but also the sub-comb lines around the previous generated multi-FSR comb can also

be observed.

The experimental results are given in Fig. 2.26. The threshold for the comb

generation is 200 mW. When we have two CW inputs both at the 100 mW level, as

shown in Fig. 2.26(a), stimulated FWM is observed. In comparison, if we have one

CW input at 250 mW which is above the threshold, it will give a multi-FSR comb

generation as shown in Fig. 2.26(b). If we have two inputs at 250 mW each, we can

see that not only FWM lines are generated around the inputs, but also around each

of the initial primary sidebands from the comb generation process. The results are

given in Fig. 2.26(c), a number of new lines which have similar shape as the FWM

lines near the pump were generated. The intensity noise is given in Fig. 2.26(d),

from the figure, we can see that no obvious intensity noise is introduced because of

the generation of the new lines.

We also try to change the position of the seeding. The wavelength of the pump is

kept fixed while the separation between the pump and the seeding is changed from

1 FSR to 3 FSR. The experimental result is given in Fig. 2.27. We found that by

changing the separation, the new lines generated from the seeding have the same

separation as our initial multiple-line pump source. This experiment confirms that

the new lines are generated from the seeding, it also demonstrates that by introducing

the seeding, we can achieve the control of the sub-lines.

Finally, we tried to study the coherence of the comb lines generated from the

seeding. The experimental setup is given in Fig. 2.28. This time we need a coherent

41

Fig. 2.25. Cartoon for the process of dual-pump generation (a) Stium-lated FWM, (b) Single pump generated mult-FSR comb (c)Dual-pump comb generation.

42

Fig. 2.26. Experimental result of dual-pump comb generation (a)Stiumlated FWM (b) Single pump generated mult-FSR comb (c)Dual-pump comb generation (d) Intensity noise

43

Fig. 2.27. External seeding at different separation (a)1 FSR (b)2 FSRand (c)3 FSR

44

Fig. 2.28. Experiment setup for seeding with a coherence source

source. We used our home build Electrooptic (EO) comb which is similar to Ref. [67]

but with only one phase and one intensity modulator. The comb source was built up

by Andrew J. Metcalf. As it is difficult to achieve the modulation at 75 GHz repetition

rate, we use the RF source at 15 GHz to generate the comb at this repetition rate

and use a commercial pulse shaper to select 2 lines at 75 GHz seperation. These

two lines are amplified using an EDFA and input into the micro-resonator. After the

comb lines are generated, a band pass filter (BPF) is used to filter out a portion of

lines and another pulse shaper is used to correct the phase and the lines before being

amplified and sent to an auto-correlator.

The results are given in Fig. 2.29. The comb spectrum with and without the

seeding are given in Fig. 2.29(a) and Fig. 2.29(d) respectively. The selected lines

(shown after amplification) before the auto-correlator are given in Fig. 2.29(b). The

RF spectrum is shown in Fig. 2.29(c) and no intensity noise is observed. The auto-

correlation trace is given in Fig. 2.29(e) in which the compensated pulse is compared

45

Fig. 2.29. Comb generation with a coherent seeding and its time domain study

with both the uncompensated one and the bandwidth limited pulse which was calcu-

lated using the spectrum given in Fig. 2.29(b). We found that the compressed pulse

is quite similar to the theoretical bandwidth limited pulse which means that the lines

selected exhibit good coherence.

2.6 Summary

In this section, we demonstrate 25 GHz ultra-high Q microresonators for low

power comb generation. The Q value can be as high as 17-million and the threshold

power of frequency combs generation can be as low as 2.8 mW onset. We have

also first demonstrate 25GHz coherent combs with limited number of lines and then a

broadband comb which generated directly coherent without the need of going through

a chaotic and noisy state. Finally we demonstrate that by introducing a second

46

input, either CW or coherent EO comb, comb generation via stimulated FWM can

be observed. At the same time new lines around the original multiple-FSR-spaced

comb lines can be generated without increasing the intensity noise.

47

3. INVESTIGATION OF MODE COUPLING IN

NORMAL-DISPERSION SILICON NITRIDE

MICRORESONATORS FOR KERR FREQUENCY COMB

GENERATION

3.1 Introduction

As discussed previously, modulational instability (MI) of the CW pump mode is

commonly cited as an important mechanism for comb generation [48, 68, 69]. Ac-

cording both to experiment and to theoretical analysis, comb generation prefer-

ably occurs in resonators with anomalous dispersion. However, comb generation

in resonators characterized with normal dispersion has also been observed experi-

mentally [13, 52, 53, 63, 70–73]. Several models have been proposed to describe this

phenomenon. Although MI gain is missing in fibers or waveguides with normal disper-

sion, when it comes to resonators, the detuning provides an extra degree of freedom

which enables MI to take place in the normal dispersion regime, hence providing

a route to comb generation [48, 69, 74]. However, this mechanism requires either a

precise relationship between detuning and pump power, making it difficult to realize

practically, or hard excitation, a nonadiabatic process under which pump photons

must be initially present in the resonator [68].

Mode coupling has also been suggested as a mechanism enabling comb generation

in resonators with normal dispersion [75]. When resonances corresponding to differ-

ent families of transverse modes approach each other in frequency, they may interact

due to imperfections in the resonator. The theory of mode coupling in resonators has

been well-established [76], and frequency shifts and avoided crossings have been ob-

served [77–82]. In the anomalous dispersion regime, mode coupling has been reported

to affect the bandwidth scaling of frequency combs [83] and the process of soliton for-

48

mation [84]. However, in these cases anomalous dispersion is still considered to be

the determining factor for comb generation; mode coupling is considered to be detri-

mental, inhibiting the formation of solitons and limiting comb bandwidth. In the

normal dispersion regime, measurements have been performed with CaF2 whispering

gallery mode resonators [75]. The experiments demonstrate strong local frequency

shifts that are attributed to mode interactions and show a correlation between the

presence of such local frequency shifts and the ability to generate combs in these

normal dispersion resonators. Significant changes in comb spectra have been ob-

served when pumping different longitudinal modes spaced by only a few free spectral

ranges (FSR), both in normal dispersion silicon nitride microring resonators [13] and

in the whispering gallery mode resonators of [75]; in the latter case, such effects were

specifically attributed to mode interactions.

In this section, we perform comb-assisted precision spectroscopy measurements

[62] of few-moded silicon nitride microresonators in the normal dispersion regime

over frequency ranges spanning dozens of FSRs. As a result we are able to clearly

map out mode interactions and obtain plots of resonant frequencies exhibiting strong

avoided crossings closely analogous to those that occur for quantum mechanical energy

surfaces [85–87]. The frequency shifts affecting a series of resonances from both

mode families can lead to a strong change in local dispersion, even changing its

sign. We provide clear experimental evidence that this mode coupling plays a major

role in the comb generation process for our normal dispersion resonators by showing

experimentally, for the first time to our knowledge, that the location of one of the

two initial sidebands at the onset of comb generation is pinned at a mode crossing

frequency, even as the pump wavelength is changed substantially.

These effects allow us to realize a Type I comb [13], also termed a natively mode-

spaced (NMS) comb [49] in a resonator with FSR slightly under 75 GHz. In such

a comb the initial sidebands are generated via a soft excitation mechanism and are

spaced one FSR from the pump; the comb exhibits low noise and high coherence

immediately upon generation [13,49,52,53,72]. We also find that the Type-I comb as

49

generated here corresponds directly to a train of bandwidth-limited pulses. This is in

sharp contrast to Type II combs [13] (also termed multiple mode-spaced (MMS) combs

[49]) for which the initial sidebands are separated from the pump by several FSR,

after which additional, more closely sidebands are generated (usually with increasing

intracavity power) to arrive at single FSR spacing. Such Type II combs exhibit poor

coherence and high noise [13, 49, 53, 54]. Mode-locking transitions in which Type

II combs switch into a coherent, low noise state have been observed experimentally

and studied theoretically [49–51,63,65,68,73,74,84,88–96]. However, these methods

require careful and sometimes complex tuning of the pump frequency or power [84];

the mode-locking transition is often difficult to achieve and until very recently has

not been observed in normal dispersion microresonators. Our recent demonstration of

dark pulse formation in resonators with normal dispersion is linked to a mode-locking

transition [63], but the waveforms generated are quite distinct from the bandwidth-

limited pulses reported here.

3.2 Linear mode interaction and avoided crossings

In this part, the simulation code is developed by Dr. Xiaoxiao Xue and comb

assisted spectroscopy measurement is collaborated with Steve Chen and Dr. Xiaoxiao

Xue. The field in the microresonators can be expressed using the following mode

coupling equations:

dE1

dt=

(− 1

τo1− 1

τe1− jδ1

)E1 + jκ12E2 +

√2

τe1E0 (3.1a)

dE2

dt=

(− 1

τo2− 1

τe2− jδ2

)E2 + jκ21E1 +

√2

τe2E0 (3.1b)

Here E1 and E2 are the intracavity fields for mode 1 and 2 respectively, 1/τo1 and

1/τo2 are decay rates due to the intrinsic loss for both modes while 1/τe1 and 1/τe2

are coupling rates between the resonator and the bus waveguides. δ1 = ω − ω1 and

δ2 = ω−ω2 are the frequency detunings where ω1 and ω2 are the resonant frequencies.

50

κ12 = |κ21|∗ = κ are mode coupling coefficients. We can simulate mode interaction

effects using the mode coupling equations.

Two modes are assumed working close to 1550 nm in the resonator with τo1 =

2.79 × 10−9s , τe1 = 4.00 × 10−9s and τo2 = 5.78 × 10−10s, τe1 = 3.38 × 10−9s,

respectively. This corresponds to two modes working in the under-coupling regime:

mode 1 with loaded Q of 106, intrinsic Q of 1.70× 106 and extinction ratio of 15 dB;

mode 2 with loaded Q of 3 × 105, intrinsic Q of 3.51 × 105 and extinction ratio of

3 dB, respectively. We solve eq.3.1 and plot the resulting transmission spectra for

different separations (over the range -5 GHz to 5 GHz) between the resonances of the

two modes. Without mode coupling (κ = 0, Fig. 3.1(a)), the resonances approach

and cross each other at a constant rate. However, with mode coupling turned on

(κ = j · 8.25 × 109s−1 compared with 1/τo1 = 3.58 × 108s−1, Fig. 3.1(b)), the dips

in transmission are shifted in frequency, resulting in an avoided crossing. The mode

interactions also lead to significant changes in the extinction ratios and linewidths of

the resonant features. Similar effects are observed in our experiments, as we relate

below.

Our experiments utilize silicon nitride resonators fabricated to have 2µm×550nm

waveguide cross-section. According to simulation for two transverse electric (TE)

modes, TE1 and TE2, these waveguides are clearly in the normal dispersion regime

with D ∼ −156 ps/nm · km and D ∼ −160 ps/nm · km respectively [52]. We

first study a resonator with a total path length of 5.92 mm which corresponds to a

FSR slightly under 25 GHz. Similar to [56], to avoid the stitching error we intro-

duce a finger-shaped structure for the resonator so that it can fit in a single field of

our electron beam lithography tool. Fig. 3.2(a) shows a microscope image of the

microresonator. The light is coupled both in and out through lensed fibers which

are positioned in U-grooves to improve stability when working at high power [52].

Fiber-to-fiber coupling loss is ∼ 5 dB. The measured transmission spectrum, showing

resonances throughout the lightwave C band, is given in Fig. 3.2(b). If we zoom

in the transmission spectrum as shown in the inset, resonances of 2 transverse mode

51

Fig. 3.1. Numerical investigation of mode coupling effect when theresonances of the two modes get close and cross each other (a) nomode coupling (b) with mode coupling.

52

Fig. 3.2. (a) Microscope image of the silicon nitride resonator withpath length of 5.92 mm. (b) Measured transmission spectrum of theresonator. Inset is the zoom-in transmission spectrum showing reso-nances from different transverse mode families.

families with different depth can be observed. The loaded Q factors at the frequencies

shown are ca. 1×106 (intrinsic Q ∼ 1.7×106) and 0.3×106 (intrinsic Q ∼ 0.35×106)

for modes 1 and 2, respectively.

We use the frequency-comb-assisted spectroscopy method of [62] to accurately

determine the resonance positions and compute the changes in FSR with wavelength

to estimate the dispersion for TE modes. The measured FSRs are given in Fig.

3.3(a). The FSRs for the two modes are around 24.8 GHz and 24.4 GHz, respec-

tively. Both modes are fitted with our simulated dispersion showing good accordance

which confirms that the resonator is in the normal dispersion regime for TE modes

with D2/2π ≈ 474 kHz, where D2/2π denotes the difference in FSR for adjacent

resonances which can be expressed as:

D2

2π= λ2 · neff · FSR2 ·D (3.2)

However, at several wavelengths for which the resonances associated with the two

transverse modes are closely spaced (1532 nm, 1542 nm and 1562 nm), the FSRs of the

53

two modes change significantly, such that their FSRs become more similar. In these

cases we clearly observe that the mode coupling results in a major modification to

the local dispersion, even changing the sign of dispersion in some wavelength regions.

To take a closer look at this phenomenon, in Fig. 3.3(b) we plot the transmission

spectrum in the vicinity of the mode crossing regime near 1542 nm. To visualize

the data in a form analogous to the simulations of Fig. 3.1, we vertically align

different pieces of the transmission spectrum separated by a constant 24.82 GHz

increment (the nominal FSR of the higher Q mode around 1542 nm). Since the

average dispersion contributes a change in FSR below 15 MHz in the range plotted

without mode coupling, one of the modes should appear as very nearly a vertical line,

while the other should appear as a tilted line due to the difference in FSRs. However

in Fig. 3.3(b), we observe that the curves bend as they approach each other, resulting

in an avoided crossing, similar to the simulation results of Fig. 3.1(b). Changes in

the extinction ratio of the resonances are also clearly evident in the mode interaction

region. These data provide detailed and compelling evidence of strong mode coupling

effects on the linear spectrum.

A different case for the mode crossing is observed around 1552 nm. Here there is

no obvious change in FSR around the wavelength where the resonances of these modes

get close. The aligned resonance pairs are shown in Fig. 3.3(c). The picture resembles

the case shown in Fig. 3.1(a), where no mode coupling is assumed. However, if we

zoom-in on the data, we can again see slight shifts in the positions of the resonances

when they are close enough. In this case mode coupling effects are present but weak.

We have estimated the mode coupling strength according to the shift of resonance

positions for each of the four mode crossings; the results are given in Table 3.1. The

coupling strength ranges from 1.50×1010 at 1562 nm to 1.65×109 at 1552 nm. We can

also calculate the local dispersion of the two modes in the crossing region by fitting the

FSR spectra and calculating their derivatives. The results for the strongest coupling

case at 1562 nm are given in Figs.3.3 (e) and (f). We can see that for mode 1, the D

value changes from around −156ps/nm · km to over 5000ps/nm · km. Not only does

54

Wavelength(nm) 1532 1542 1552 1562

Coupling strength |κ| (s−1) 6.50× 109 8.52× 109 1.65× 109 1.50× 1010

Table 3.1.Estimated coupling strength for 4 mode crossing areas shown in Fig. 3.3(a)

the magnitude increase by more than a decade, but also the sign changes from normal

to anomalous. For mode 2, the magnitude of D changes by a similar amount. The

D2 value, however, remains below 20 MHz, which is less than the resonance linewidth

(ca. 200 MHz). Hence, according to the analysis of [49], the dispersion is still not

large enough to enforce Type I comb generation.

3.3 Comb initialization through mode coupling

In comb generation experiments, we pumped the micro-resonator with a single CW

input at 1.75W (this is the value prior to the chip, without accounting for coupling

loss) tuned to different resonances of the high-Q mode family and recorded the comb

spectra. The results are given in Fig. 3.4. In Fig. 3.4(a) we pump at 28 different

resonances between 1554 and 1560 nm. The frequency spacing of the comb varies from

33 FSR for pumping at 1554 nm to 7 FSR for pumping at 1559.4 nm. We observe

that the nearest long wavelength sideband remains anchored at approximately 1560.5

nm, very close to the ∼ 1562 nm mode interaction feature. With the pump shifted

by a total of 694 GHz (27 FSRs), we find that the long wavelength sideband varies by

no more than ±25 GHz(±1 FSR). Meanwhile the short wavelength sideband varies

at twice the rate of the pump tuning, for a total frequency variation of ∼ 1.3 THz.

Similar behavior is observed when we pump between 1546 nm to 1549.5 nm. As shown

in Fig. 3.4(b), one of the sidebands is anchored near 1550.5 nm, close to the weaker

1552 nm mode interaction feature. In this case comb generation is missing for some

pump wavelengths, which may be the result of the weak coupling strength. Pinning

of one of the sidebands at 1532 nm and at 1542 nm has also been observed, but for

55

Fig. 3.3. (a) Measured FSR versus optical wavelength for two TEmodes, plotted in red and blue and fitted with D ∼ 156ps/nm · kmand D ∼ −160ps/nm · km respectively. (b-d) Aligned resonanceswith fixed increment showing the mode coupling with different cou-pling strength (b) Strong coupling case centered at 1542 nm withclear avoided crossings (c) Weak coupling case centered at 1552 nm(d) Zoomed-in view of the weak coupling case (e) Zoom-in view andfitted FSR spectrum in a mode crossing area (f) Calculated D andcorresponding D2 value of mode 1 and mode 2 plotted in red andblue respectively.

56

a smaller number of pump wavelengths. The different mode interaction features may

compete with each other in initializing the combs. Pinning around the 1562 nm mode

interaction region, which has the strongest coupling strength, occurs for the largest

number of pump wavelengths. The observed pinning of one of the initial sidebands

very close to a mode interaction feature clearly suggests that mode coupling is a major

factor in comb generation in this normal dispersion microresonator.

According to the anomalous dispersion analysis of Ref. [49], increasingly large

dispersion is needed to generate NMS (Type I) combs as the resonator FSR decreases.

Physically the increased dispersion brings the MI gain peak closer to the pump. In

order to reduce the gain peak to single FSR frequency offset, it was shown that the D2

parameter should be made close to the resonance width (200 MHz for silicon nitride

resonators with Q ∼ 106). For example, for a resonator with FSR ∼ 100 GHz, the

dispersion required for the generation of a Type I comb would beD ≈ 4.2×103ps/nm·

km. Furthermore, according to Eq.3.2, the dispersion required grows quadratically as

the resonator size is further increased (required D grows as inverse square of the FSR).

Such dispersions are generally too large to achieve practically; perhaps as a result, no

observation of Type I comb generation in sub-100 GHz silicon nitride resonators has

been reported. However, mode coupling can dramatically change the local dispersion,

both increasing its magnitude and changing its sign. Generation of Type I combs from

large whispering gallery mode (WGM) resonators has previously been reported and

attributed to mode coupling [74, 75]. In our experiments we have observed Type I

comb generation in SiN for a resonator with a FSR slightly below 75 GHz. We have

not yet obtained a NMS comb from resonators with even smaller FSR. However, as

shown in Fig. 3.4(b), a comb with 2-FSR separation is observed when the 25 GHz

FSR resonator is pumped at 1550.41 nm. This means that the 1st sideband is less

than 50 GHz from the pump, which is still very difficult to achieve without mode

coupling effects.

The fabricated ∼ 75 GHz FSR resonator is shown in Fig. 3.5(a). Unlike the 25-

GHz resonator discussed earlier, it has a drop-port design which has been observed

57

Fig. 3.4. Comb generation at different pump wavelength with oneof the 1st sidebands kept at an approximately constant location (a)around 1560 nm and (b) around 1550 nm

58

to reduce the power difference between the pump and adjacent comb lines, yielding a

smoother comb spectrum without the usual strong pump background [52]. Using the

frequency-comb-assisted spectroscopy method, two mode families with FSRs around

74.7 GHz and 72 GHz are observed. The two families of resonances approach each

other around 1563 nm. Different sections of the transmission spectrum are aligned in a

similar fashion as for Fig. 3.3 An avoided crossing evidencing mode coupling is clearly

observed. The comb results are shown in Fig. 3.5(c) for pumping between 1554.71

nm and 1566.59 nm. Again one of the 1st sidebands is pinned near the mode crossing

wavelength. Although the first sideband has a 13-FSR separation when pumping at

1555 nm, a Type I comb can be generated for pumping at 1562.62 nm, 1563.22 nm,

1563.81 and 1564.43 nm (as shown in the circled area). We note that in this case,

pinning of the 1st sideband is observed for pumping at either the blue side or the

red side of the mode crossing area. . Very close to the mode interaction region, the

estimated D2 can be increased to over 200 MHz, which is on the order of resonance

linewidth. This satisfies the dispersion requirement for Type I comb generation as

predicted in Ref. [49]. Two additional examples, one for this 75GHz resonator with a

mode coupling feature at a different wavelength and one for another resonator with

a FSR of about 37 GHz are shown in Fig3.6.

As an example, pumping at 1562.62 nm with 1.6W input, more than 20 comb

lines with 1 FSR separation are generated. The spectrum observed at the drop port

is shown in Fig. 3.7(a). Fifteen of the lines are selected by a bandpass filter and

amplified in an EDFA; the resulting spectrum is shown in Fig. 3.7(b). The amplified

and filtered comb is directed to an intensity autocorrelator based on second harmonic

generation in a noncollinear geometry. A length of dispersion compensating fiber

(DCF) is used to achieve dispersion compensation of the entire fiber link (including

the EDFA) connecting the SiN chip to the autocorrelator. The length of DCF was

adjusted by injecting a short pulse laser from a passively mode-locked fiber laser into

the front end of the fiber link and minimizing its autocorrelation width. The auto-

correlation trace measured for the comb is plotted in Fig. 3.7(c). Also plotted is

59

Fig. 3.5. (a) Microscope image of the silicon nitride resonator withpath length of 1.97 mm. (b) Aligned resonances centered at 1563 nmwith fixed increment showing the mode coupling. (c) Comb generationat different pump wavelength; one of the 1st sidebands remains closeto 1563 nm

60

Fig. 3.6. (a) Measured FSR versus optical wavelength for two TEmodes, plotted in red and blue showing mode interaction feature near1545 nm for the 75 GHz discussed above and (b) Corresponding combgeneration at different pump wavelength; one of the 1st sidebandsremains close to 1545 nm (c) Measured FSR versus optical wavelengthfor two TE modes, plotted in red and blue showing mode interactionfeature near 1561 nm for a resonator with FSR at about 37 GHz and(d) Corresponding comb generation at different pump wavelength; oneof the 1st sidebands remains close to 1561 nm

61

the autocorrelation of the ideal bandwidth-limited pulse, calculated from the spec-

trum of Fig. 3.7(b) with the assumption of flat phase. Clearly the generated pulses,

with estimated duration of 2.7 ps FWHM, are very close to bandwidth-limited. We

have also used a photodetector and spectrum analyzer to look at the low frequency

intensity noise of the comb (measurement bandwidth: ∼ 500MHz). The intensity

noise is below the background level of our measurement setup. Similar low noise,

bandwidth-limited pulse generation is observed for the Type I combs generated via

pumping at other resonances of this same resonator. These data demonstrate that

the Type I combs reported here are generated directly in a mode-locked state featur-

ing low noise, high coherence, and bandwidth-limited temporal profile, though with

a limited number of comb lines.

To better understand the comb generation behavior as influenced by mode cou-

pling, we performed simulations for our 75 GHz microresonator using the Lugiato-

Lefever (L-L) equation(3.3) [50, 63,97]:

tR∂E(t, τ)

∂t=

[−α− iδ0 − iL

β22

+ iγL |E(t, τ)|2]E(t, τ) +

√θEin (3.3)

where E(t, τ) is the intracavity field; t and τ are slow and fast time respectively;

tR is cavity roundtrip time; α = (αi + θ)/2 is the roundtrip amplitude loss where

αi is the roundtrip intensity loss due to absorption and scattering in the cavity and

θ is intensity loss from the coupling between the resonator and the bus waveguide;

δ0 = (ω0−ωp)tR is the phase detuning where ωp is the pump frequency and ω0 is the

resonant frequency closest to ωp; L is the roundtrip length, β2 = d2βdω|ω=ω0 ; γ is the

nonlinear coefficient and Ein is the pump field.

As suggested by Ref. [75], we introduced phase shift terms to model the effect of

mode interaction. Here we introduced phase shifts to the four resonances (numbered

-1 to 2 with reference to Fig. 3.8) which experience the largest frequency shifts due

to the mode coupling. The phase shifts are selected by normalizing the measured

resonance frequency shifts by the FSR value; 2π shift per roundtrip in phase cor-

responds to a 1 FSR change of resonance frequency. As shown in Fig. 3.8(a), the

resonator is pumped at different resonances; one of the sidebands stays pinned at the

62

Fig. 3.7. Generation of coherent mode-locked Type I comb due tothe mode coupling (a) Generated comb spectrum at the drop port (b)15 lines are selected, amplified and filtered for time-domain charac-terization. (c) Autocorrelation of time domain pulse compared withthat of theoretical bandwidth-limited pulse, showing good coherenceand mode locking behavior. (d) Intensity noise compared with themeasurement system noise floor

63

resonance with the largest phase shift (denoted frequency 0 in Fig. 3.8(a)). A type

I comb is observed for pumping at an adjacent resonance; the resulting spectrum

is shown in Fig. 3.8(b). We note that the resonance frequency shifts are measured

under cold cavity conditions with very low input optical power. In comb generation

experiments the optical powers are much higher; thermal and other nonlinear effects

shift the positions of the resonances (usually leading to a blue shift). Furthermore,

the different modes are expected to shift at somewhat different rates. This effect,

which would modify the frequency offsets of the interacting modes compared to our

low power transmission measurements, is not considered in our simulation. This may

explain why in the simulation the pinned sideband is fixed at one specific resonance,

while in experiment the sideband is pinned more loosely (moves by about ±1FSR in

Fig. 3.5(c)).

Our group has previously reported direct Type I generation, with behavior similar

to that shown in Fig. 3.7, from a smaller, normal dispersion SiN microresonator with

∼ 230 GHz FSR [52]. Although we speculated that mode interactions may have

played a role in allowing comb generation, as pointed out theoretically in [75], we were

unable to present data to support this speculation. Based on the insight developed

in the current paper, we decided to reexamine our data from the device of [52]. Fig.

3.9 shows the comb spectra obtained for pump powers just above threshold, plotted

in the same fashion as Figs.3.4 and 3.5(c). This format clearly shows pinning of one

of the initial sidebands, revealing what we now understand to be a signature of comb

initiation through mode coupling.

The pathway to coherent pulse generation reported here is clearly distinct from

that observed in [54, 63, 73, 84], which attain broader comb bandwidths but need to

navigate through a chaotic state before arriving at a transition to mode-locking. A

theoretical explanation for the observed direct generation of approximately bandwidth-

limited pulses is still not fully available. The intracavity field corresponding to the

Type I comb in the simulation results of Fig. 3.8(b) does correspond to single pulses

in each time period (Fig. 3.8(c)). However, the pulses from simulation are not fully

64

Fig. 3.8. (a) Simulated comb generation pumping at different reso-nances in normal dispersion microresonator with mode coupling (b)and (c) Simulated mode coupling initialized Type I comb spectrumand its intracavity intensity respectively.

65

Fig. 3.9. Observation of Pinned 1st sidebands for the resonator withpassively mode locked Type I comb as discussed in Ref. [52]

66

bandwidth-limited; the comb field is phase modulated and temporally broadened (the

corresponding autocorrelation trace has a FWHM of 4.53 ps compared to 3.6 ps of

the bandwidth-limited pulse). This discrepancy suggests some factors may be missing

in the model. One possibility is that instead of adding a phase shift to a single reso-

nance, phase shifts should be assigned to a group of resonances distributed around the

mode interaction region. Another, more radical idea is that a heretofore unidentified

nonlinear amplitude modulation mechanism may be present, as suggested briefly in

Ref. [49, 52]. Mode interactions may contribute to such a mechanism, since a super-

position of transverse modes leads to a longitudinally modulated spatial profile which

may either increase or decrease overlap with waveguide imperfections. Nonlinearity

could shift such spatial profiles, under appropriate circumstances reducing loss, anal-

ogous to decreased loss through nonlinear lensing in Kerr lens mode-locked lasers.

Another possibility suggested in Ref. [73] is that wavelength dependent Q introduces

a spectral filtering effect which contributes to shaping the time domain field. How-

ever, in our resonators a similar variation of the Q factor is not observed (although

some variations in Q do appear to be induced around the mode coupling region).

Finally, we note that previous studies have associated mode coupling with asym-

metric comb spectra [71, 75]. However, mode interaction spectra such as those in

Figs.3.4 and 3.5 were neither reported nor registered with the generated combs. In

our experiments asymmetric spectra were observed for both resonators studied; Fig.

3.10 shows four examples with the mode interaction region identified through the

pinned 1st sideband. For the resonator with ∼ 25 GHz FSR, the separations be-

tween the pump and the 1st sideband are 15 FSR and 2 FSR in Figs.3.10(a) and

3.10(b), respectively; for the ∼ 75 GHz FSR resonator, the pump position is changed

from the short wavelength side of the coupling region (Fig. 3.10(c)) to the long

wavelength side (Fig. 3.10(d)). In each case the 1st sideband pinned close to the

mode crossing has higher power than the 1st sideband on the other side of the pump.

However, fewer comb lines are generated on the side of the pump corresponding to

the pinned sideband. We may understand this behavior by noting that flattened dis-

67

persion is favorable for broadband comb generation [89, 98, 99]. In our experiments

mode coupling modifies the local dispersion, allowing MI gain for initiation of comb

generation but at the same time giving rise to significant higher order dispersion that

limits growth of the comb bandwidth on the mode interaction side. Since approxi-

mately bandwidth-limited pulses are generated directly, it may be possible to obtain

wider bandwidths through amplification and spectral broadening in nonlinear fiber,

without the need for intermediate pulse shaping.

3.4 Comb broadening using highly nonlinear optical fiber (HNLF)

This part is collaborated with Andrew J Metcalf. As discussed in the previous

section, the Type I comb generated through mode interaction showing good coherence

and bandwidth limited time profile which makes it possible to use HNLF to get it

broadened.

Fig. 3.11 shows the experimental setup. We take the comb output at the drop

port instead of the through port in order to get rid of the remaining pump and achieve

a smoother spectrum. This allows us to directly use our comb without attenuating

the pump as what was required for the previous reports [100,101]. Our Type I comb

spectrum comprised of a modest 15 comb lines when pumping at 1.6W is shown

in Fig. 3.12(a). This Type I comb is generated directly as a short pulse featuring

low noise, high coherence, and bandwidth-limited temporal profile [102]. To broaden

the comb bandwidth, the comb is amplified using a high power EDFA and input it

into 150 meters of HNLF with a dispersion parameter D ∼ −2ps/nm · km. The

dispersion compensating fiber (DCF) before the EDFA is used to compensate the

added dispersion between the chip and the HNLF so the bandwidth limited pulse

generated from the chip is preserved. After the broadening, part of the power is

measured using an optical spectrum analyzer (OSA); the rest will go through a length

of SMF to compensate for the dispersion of the HNLF. The time domain profile of

the comb is measured using an auto-correlator (AC).

68

Fig. 3.10. Generation of coherent mode-locked Type I comb due tothe mode coupling (a) Generated comb spectrum at the drop port (b)15 lines are selected, amplified and filtered for time-domain charac-terization. (c) Autocorrelation of time domain pulse compared withthat of theoretical bandwidth-limited pulse, showing good coherenceand mode locking behavior. (d) Intensity noise compared with themeasurement system noise floor

69

Fig. 3.11. Experimental setup for our comb generation and bandwidthscaling scheme. CW-continuous wave laser, EDFA High power am-plifier, DCF dispersion compensating fiber, HNLF Highly nonlinearoptical fiber, SMF single mode fiber, OSA optical spectrum analyzer,AC auto-correlator

Fig. 3.12. (a) Original comb spectrum generated from the resonator.(b) Comb spectrum after bandwidth scaling using HLNF (c) Mea-sured auto-correlation trace for the scaled comb before (red) and af-ter (blue) the compression compared with the theoretical bandwidthlimited pulse (black).

70

The broadened comb spectrum when the input power to HNLF is set at 3.23W is

given in Fig. 3.12(b). It has more than 70 lines (> 5THz) with 20 lines (∼ 1.5THz)

with-in 5 dB bandwidth which both are more than 4 times of the original comb

generated from the microresonator. We note here that at lower input power, the comb

also gets broadened but with less bandwidth. We get about 45 lines at 1W, however,

the higher the power, the larger the bandwidth and the smoother the comb spectrum.

The measured auto-correlation trace (blue) compared with the original pulse (black)

from the resonator and the theoretical bandwidth limited pulse calculated from the

broadened comb spectrum assuming the flat phase (red) is given in Fig. 3.12(c).

Compared to the original pulse from the resonator, the duration of the pulse after the

broadening (∼ 580fs) is less than one fourth of the original pulse (∼ 2.74ps). The

measured trace fits well with the bandwidth limited pulse computed assuming flat

spectral phase (which implies the spectral phase of the broadened comb is primarily

quadratic, for which compensation via dispersive fiber is sufficient). Thus we have

demonstrated a simple scheme using HNLF to broaden the bandwidth of a type I Kerr

frequency comb generated from a normal dispersion silicon nitride microresonator.

The bandwidth of the broadened comb (> 5THz) is over 4 times of the original Kerr

frequency comb with quadratic phase which can be compressed almost to a bandwidth

limited pulse via simple dispersive fiber propagation.

3.5 Summary

In this section, we have demonstrated what we believe to be conclusive evidence

of the impact of mode coupling on initiation of comb generation in normal dispersion

silicon nitride microresonators. We have also demonstrated mode- coupling-assisted

Type I comb generation resulting in direct generation of bandwidth-limited pulses,

without the need to navigate through a chaotic state. This comb can be broadened

using HNLF to over 4 times (> 5THz) of its original bandwidth and the broadened

71

line can be directly compressed to a bandwidth limited pulse using only single mode

fiber without line-by-line shaping.

72

4. BANDWIDTH SCALING OF PHASE-MODULATED

CW COMB THROUGH FOUR-WAVE MIXING ON

SILICON NANO-WAVEGUIDE

4.1 Introduction

Strong sinusoidal phase modulation of a continuous-wave (CW) laser can create

multiple sidebands to form a frequency comb [9, 103]. This technique enables the

creation of high-repetition-rate combs with stable optical frequencies while allowing

for independent tuning of the repetition rate and optical center frequency. These

attributes, combined with the simplicity of the technique, make it an ideal candidate

for applications in optical communications [104], radio-frequency (RF) photonics [105]

and optical arbitrary waveform generation (OAWG) [3]. By phase modulation (PM)

alone, the spectral lines suffer from significant line-to-line amplitude variations, i.e.

poor spectral flatness. The spectral flatness of the comb can be improved considerably

by adding an intensity modulator (IM) in series with the PM [106, 107]. In this

scheme, the IM acts to carve out a flat-topped pulse train from the CW source,

whereas the phase modulator introduces quadratic phase on each pulse (thus acting

as a time-lens [108]). When correctly aligned, the carved pulse will coincide with

the cusp of the phase modulation at the point where the chirp imposed is almost

linear, yielding a flatter spectral profile. This process can be interpreted in terms

of time-to-frequency mapping [109]: if the chirping is sufficiently large, the envelope

of the optical spectrum will become a scaled replica of the intensity pulse [110]. In

many applications, increasing the bandwidth of the combs is also desirable. However,

the bandwidth of the combs generated in this IM-PM scheme is limited due to the

bandwidth and RF power-handling capability of the PM. Of course, by placing several

phase modulators in tandem, larger bandwidths can be achieved (see, e.g. [67, 111]).

73

Another method is by first compressing the comb to a short pulse and then using

nonlinear propagation in dispersion decreasing or highly nonlinear fiber (HNLF) to

broaden the spectrum [11,112,113].

Our group has also demonstrated a method that achieved simultaneous band-

width enhancement and improved flatness by exploiting four-wave mixing (FWM) in

a highly nonlinear fiber (HNLF) [114]. In this method, two optical frequency combs

centered at different frequencies,ω1 and ω2 (with ω2 > ω1) are mixed in a HNLF.

Initially, each comb has narrow bandwidth and poor flatness. However, after trav-

eling through a cascade of FWM processes, new frequency combs can be generated

exhibiting enhanced spectral width and flatness. For example, when properly phase-

matched, the complex envelope of the Nth-order higher-frequency sideband centered

at (N + 1)ω2 −Nω1 will be proportional to

[e2(t)]N+1 [e∗1(t)]

N (4.1)

where e1(t) and e2(t) denote the complex field envelopes of the seed combs centered

at ω1 and ω2, respectively. The frequency converted signal will display an equivalent

modulation index increased by a factor of 2N+1, provided the phase conjugation in

e1(t) is properly managed [114].

Recently, several groups have investigated nonlinear processes in silicon waveg-

uides, such as parametric amplification [24], Raman amplification [25], and FWM [26],

which provide very high nonlinearity in a chip-based geometry. These devices have

proven to be practical in optical signal processing applications which require broad-

band wavelength conversion [28,115,116]. In this report, we utilize on-chip FWM to

introduce a more compact and flexible scheme for spectral broadening of a frequency

comb. This technique, based on principles similar to [114], allowed us to achieve

> 100 lines at 10-GHz spacing within a 5-dB bandwidth.

74

4.2 Experimental Setup and Results

The fabrication of the waveguide is done by Dr. Li Fan, Dr. Leo T. Varghese

and Dr. Yi Xuan. This experiment is collaborated with Andrew J. Metcalf, Dr.

Victor Torres-Company and Dr. Rui Wu. Fig.4.1 shows the experimental setup.

This setup differs from the setup of ref. [114] in three aspects. First, the 100 m

of HNLF is replaced by a silicon nano-waveguide, which is only 1 cm in length.

Second, the dispersion of the silicon chip can be tailored by engineering the waveguide

cross-section geometry, which in turn increases the conversion bandwidth [28, 115].

Finally, the signal centered at ω1 will not be modulated but instead combined with

the 2nd CW directly. In this case, the initial fields are given by e1(t) ∼ 1 and

e2(t) ∼ a(t)exp[jφ(t)], where a(t) is the amplitude introduced by the IM and φ(t)

is the phase introduced by the PM stage. Two inputs are mixed to produce a new

first order FWM component at 2ω2−ω1 given by e22(t)e∗1(t) = a(t)2exp[2jφ(t)] . This

indicates the new combs bandwidth is roughly doubled with respect to the signal

centered around ω2. Compared to ref. [114], this setup is more compact and flexible,

although it comes at the expense of a reduction in the achievable bandwidth scaling.

The reason behind these differences is that in [114], the signal centered at ω1 first

goes through an IM and is then combined with the second CW input centered at ω2,

after which both signals enter the PM followed by a dispersive element. The role

of the dispersive element was to delay the modulated signal by half an RF period.

For this, the length L of the dispersive element must satisfy D · L · ∆λ = Trep/2,

where D is the dispersion parameter of the dispersive element, ∆λ is the wavelength

difference between the 2 CW inputs and Trep is the period of the RF modulation. This

delay effectively performs a phase shift to the field envelope term e∗1(t) in Eq.4.1 to

ensure that the phase modulations of the two fields add together in the FWM process.

Although this approach will effectively enhance the bandwidth by a factor of three

for first order mixing terms (50% higher than achieved with our current scheme), the

75

Fig. 4.1. (a) Experimental setup. CW: continuous wave laser, IM: In-tensity modulator, PM: Phase modulator, EDFA: High power erbium-doped fiber amplifier, OSA: optical spectrum analyzer (b) Bandwidthscaling of the CW comb.

dispersion (denoted as DL) must be changed in accord with the changes in ∆λ or

Trep. Therefore, wavelength or repetition rate tunability is compromised.

Our silicon waveguide was patterned with electron-beam lithography on a silicon-

on-insulator wafer. We designed the cross-section geometry so that it has a zero-

group-velocity dispersion (GVD) wavelength within the C-band for quasi-TM polar-

ization. The geometry is 800 nm in width by 250 nm in thickness. The two ends of

the waveguide are inversely tapered to 100 nm allowing light to be coupled in and out

through a fiber taper. The end of the waveguide is followed by a U-groove to stabilize

the fiber for high-power applications. The above setup provides a fiber-to-fiber loss

of -8 dB which includes the coupling and propagation losses. The propagation loss

for our silicon waveguide is estimated to be about 3.5 dB/cm [117]. Finally, the non-

linear parameter is calculated to be in the order of 10−1[rad/(W · cm)], three orders

of magnitude higher than the HNLF in [114].

76

We first test our waveguide with CW input for both pump and probe; the mea-

sured FWM spectrum at the nano-waveguides output is given in Fig.4.2(a), which

shows a -19 dB conversion efficiency (defined as the idler to probe power ratio at the

chips output) when the pump power is 200 mW. At this power level, the waveguides

sometimes get damaged after several hours of operation. We also measured the con-

version efficiency spectrum of this waveguide. The result for pumping at 1550 nm is

given in Fig.4.2(b). We can achieve a relatively broad and flat conversion efficiency

(> 100nm,< 5dB variation) when pumping at 1550 nm. Since the FWM conversion

bandwidth is inversely proportional to the square root of the product of the inter-

action length and the GVD [118], this means that the zero dispersion point of the

waveguide is very close to 1550 nm. The measurement limit in these experiments is

given by the tuning range of the probe laser (1460-1580 nm). In our context, this

means that the two frequency combs can be placed significantly further apart and

generate broader combs operating at high repetition rates. It is worth noting that

simultaneous broadband and flat conversion efficiency can be achieved for any pump-

ing wavelength within the EDFA gain bandwidth, allowing our input frequency to be

chosen anywhere within this range.

We demonstrate our technique using a high-power frequency-tunable electro-optic

comb source, which is comprised of 3 phase modulators and 1 intensity modulator.

The performance details of this light source can be found in [67]. Our FWM results

are shown in Fig.4.3. The input frequency comb is centered at 1545 nm with 10

GHz repetition rate and is comprised of about 55 lines at 5-dB bandwidth, as shown

in Fig.4.3(a). The input unmodulated CW is centered at 1560 nm. As expected,

the FWM generated near 1530 nm has more than 100 lines in a 5 dB bandwidth.

The small asymmetry and dips visible in the FWM term are likely caused by the

conversion efficiency variations as indicated in Fig. 1(b). This could be optimized by

a more careful engineering of waveguide dispersion.

We now illustrate the wavelength-tuning capabilities of the broadened FWM

combs. Here, the seed is instead synthesized using a simpler comb generator con-

77

Fig. 4.2. (a) Spectrum for the FWM with CW inputs, (b) FWMconversion efficiency spectrum pumping at 1550 nm

78

Fig. 4.3. (a) Spectrum for the FWM with CW inputs, (b) FWMconversion efficiency spectrum pumping at 1550 nm

79

sisting of a single IM and single PM with 10 GHz repetition rate (spectrum shown in

Fig. 4(a)). The wavelength separation between the CW and seed comb is continuously

varied keeping their wavelengths centered near 1550 nm (((λ1 + λ2))/2 ≈ 1550nm).

Fig. 4(b)-(d) illustrates the first generated FWM sideband when the spacing between

the input CW waveform and seed comb is set to 5 nm, 10 nm and 20 nm, respectively.

The bandwidth of the comb generated through FWM is again roughly twice that of

the seed comb and remains approximately constant as it is tuned.

Finally we demonstrate the ability of RF frequency tuning. Unfortunately, the

waveguide that has its zero-group-velocity dispersion wavelength close to 1550 nm

got damaged before we did the repetition rate tuning experiment. Using another

waveguide, which has less conversion bandwidth and efficiency, we demonstrated the

tuning of RF frequency from 12.5 GHz to 17.5 GHz. The scaled comb is given in Fig.

4.5(the original comb has around 15 lines generated from 1PM and 1 IM comb source,

the input optical power is 250 mW) which shows good flatness for scaled combs in all

three cases.

In the quest towards a fully integrated system, we note the recent advances in

hybrid silicon-organic electro-optic comb generators [119] and erbium waveguide am-

plifiers [120] developed in a silicon-on-insulator platform.

4.3 Summary

In summary, we have demonstrated a simple on-chip scheme to scale the band-

width of a phase and intensity modulated CW comb. Compared with the previous

nonlinear optical fiber scheme [114], it has comparable bandwidth (> 1THz) and

good flatness (> 100 lines within 5-dB bandwidth), but the scheme is much more

flexible and compact (nonlinear media is only 1cm compared to 100 meter HNLF,

and also without 300 meter SMF), and shows low operating power.

80

Fig. 4.4. Wavelength tuning of FWM generated frequency combs. (a)Input spectrum of the PM-IM comb. Output spectra of comb withdifferent wavelength separation between 2 CW lasers. The wavelengthseparation of the two inputs are 5 nm, 10 nm and 20 nm, for (b)-(d)respectively.

81

Fig. 4.5. RF frequency tuning of FWM generated frequency combs.Output spectra of comb with RF frequencies of (a) 12.5 GHz, (b)15GHz and (c)17.5

82

5. SUMMARY

We have presented a comprehensive study, which includes both theoretical analysis

and experimental demonstrations, on the generation and characterization of on-chip

frequency combs. The main accomplishments of this thesis can be summarized as

follows:

In Chapter 2, we demonstrated 25 GHz microresonators with Q values up to 17 mil-

lion and provided verification using two independent methods. The comb generation

threshold power for these high-Q resonators was shown to be as low as 2.8 mW at the

comb onset. We reported direct generation of a broadband coherent comb at 25 GHz

FSR without the need to navigate through a chaotic state in anomalous dispersion

regime. In addition, we demonstrated that by introducing a second pump laser to the

multiple-FSR-spaced comb generation system, new lines around the original comb

line could be generated without increasing the intensity noise.

In Chapter 3, we investigated mode coupling in silicon nitride microresonators. We are

able to clearly map out mode interactions and obtain evidence of resonant frequencies

exhibiting strong avoided crossings. Further, we experimentally demonstrated that

the location of one of the two initial sidebands present at the onset of comb generation

is pinned at a mode crossing frequency. We believe this to be conclusive evidence that

mode coupling on initiation of comb generation in normal dispersion silicon nitride

microresonators. We demonstrate mode- coupling-assisted Type I comb generation

resulting in direct generation of bandwidth-limited pulses. This comb can be broad-

ened using HNLF greater than 4 times (> 5THz) the original comb bandwidth. We

were then able to directly compress the broadened comb to form bandwidth limited

pulses using only single mode fiber without line-by-line shaping.

In Chapter 4, we demonstrated bandwidth scaling of an optoelectronic test comb,

using FWM in a 1-cm silicon nano-waveguide. The broadened combs had over 1THz

83

bandwidth and exhibited good spectral flatness (> 100 lines with 5-dB bandwidth).

Our on-chip method produced similar scaling to a previous scheme using HNLF [114],

but with advantages in operating power, flexibility, and compactness.

Next, we discuss some possible future improvements and/or directions to extend the

work presented in this dissertation:

Although we were able to demonstrate combs in our high Q resonators, the only co-

herent broadband comb we achieved required a high pump power of 1.3 Watts; this

falls short of our goal to achieve low threshold power and broadband coherent combs

simultaneously. One possible explanation as to why we did not observe a coherent

transition in the high-Q resonator, suggested in [84], is that the mode crossing and

coupling may prevent soliton formation. The width of the high Q resonators in this

case are 3 µm, which support 3 TE modes, resulting in a large number of mode

crossing and coupling points throughout the spectrum. However, if we were to nar-

row the width of the resonator to the single mode regime (≤ 1 µm), the Q will be

greatly reduced. One possible solution is to introduce a mode filter by tapering down

a small portion of the microresonator to locally support a single mode while allowing

multimode operation in the rest of the ring. This method may allow us to keep the

high Q feature while still making the resonator single mode.

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84

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VITA

93

VITA

Yang Liu was born in China in 1985. He received his BS and MS degree in Electrical

Engineering both from Shanghai Jiao Tong University, Shanghai, China in 2007 and

2010 respectively. Since 2010, he has been pursuing his Ph.D. degree at Purdue Uni-

versity, West Lafayette, IN.

He has been a research assistant in the Ultrafast Optics and Optical Fiber Commu-

nications Laboratory since he joined Purdue University and his main focus is silicon

photonics. During the course of his graduate study, Yang has authored/co-authored

over 10 publications in peer reviewed journals and international conferences.