PURDUE UNIVERSITY GRADUATE SCHOOL Thesis/Dissertation Acceptance

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1 Graduate School ETD Form 9 (Revised 12/07) PURDUE UNIVERSITY GRADUATE SCHOOL Thesis/Dissertation Acceptance This is to certify that the thesis/dissertation prepared By Fahmida Ferdous Entitled On Chip Frequency Comb: Characterization and Optical Arbitrary Waveform Generation For the degree of Doctor of Philosophy Is approved by the final examining committee: ANDREW M. WEINER MINGHAO QI Chair MUHAMMAD A. ALAM VLADIMIR M. SHALAEV To the best of my knowledge and as understood by the student in the Research Integrity and Copyright Disclaimer (Graduate School Form 20), this thesis/dissertation adheres to the provisions of Purdue University s Policy on Integrity in Research and the use of copyrighted material. ANDREW M. WEINER Approved by Major Professor(s): Approved by: M. R. Melloch Head of the Graduate Program Date

2 Graduate School Form 20 (Revised 9/10) PURDUE UNIVERSITY GRADUATE SCHOOL Research Integrity and Copyright Disclaimer Title of Thesis/Dissertation: On Chip Frequency Comb: Characterization and Optical Arbitrary Waveform Generation For the degree of Doctor Choose of your Philosophy degree I certify that in the preparation of this thesis, I have observed the provisions of Purdue University Executive Memorandum No. C-22, September 6, 1991, Policy on Integrity in Research.* Further, I certify that this work is free of plagiarism and all materials appearing in this thesis/dissertation have been properly quoted and attributed. I certify that all copyrighted material incorporated into this thesis/dissertation is in compliance with the United States copyright law and that I have received written permission from the copyright owners for my use of their work, which is beyond the scope of the law. I agree to indemnify and save harmless Purdue University from any and all claims that may be asserted or that may arise from any copyright violation. Fahmida Ferdous Printed Name and Signature of Candidate Date (month/day/year) *Located at

3 ON CHIP FREQUENCY COMB: CHARACTERIZATION AND OPTICAL ARBITRARY WAVEFORM GENERATION A Dissertation Submitted to the Faculty of Purdue University by Fahmida Ferdous In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy December 2012 Purdue University West Lafayette, Indiana

4 ii In memory of Hosne Ara my mother and my best friend and Ferdous Alam my beloved husband

5 iii ACKNOWLEDGMENTS First, I want to thank my advisor Prof A. M. Weiner for his continuous advice, suggestions and support throughout this amazing journey of knowledge. It was a great exciting and pleasant opportunity to be a member of his group, to learn from him and to do research on very interesting topics. I specially thank Dr. D. E. Leaird who made the complex experimental procedure easy and always there when I needed any technical support. I would like to thank my Ph.D. committee members and colleagues for valuable discussions. I would like to thank Dee Dee Dexter for invaluable help on official matters. I would also thank our collaborators Dr. H. Miao, Dr. K. Srinivasan and Dr. V. Aksyuk at NIST, Gaithersburg, MD for the silicon nitride ring fabrication and valuable technical discussion and guideline. I express my deep gratitude to my parents, my brothers and sister who always supported and encouraged me throughout my life and study. They always were on my side in my good and bad times. Although, nothing I could write would be enough to express my appreciations to my family, I can not resist writing a few words to show my deep appreciation to my husband Dr. Ferdous Alam who gave me suggestions and encouragements from time to time and always supported me mentally; and my baby boy Raed Alam whose heavenly smiles always make my world wonderful. I appreciate all my good purdue friends who made purdue life nice and warm which help me to stay focused in my research. I really appreciate the dinner invitations and crone maize outing with Prof Weiner and Brenda Weiner s family which always refresh me to start my research with full energy and enthusiasm.

6 iv TABLE OF CONTENTS LIST OF TABLES Page LIST OF FIGURES vii ABSTRACT xiii 1 INTRODUCTION Optical frequency comb Optical arbitary waveform generation Optical waveguide optical resonator Organization of the thesis DUAL COMB ELECTRIC FIELD CROSS-CORRELATION TECHNIQUE Introduction Conventional EFXC and Dual Comb EFXC Experimental set up and Data processing Results Future work SPECTRAL LINE-BY-LINE PULSE SHAPING OF AN ON-CHIP MI- CRORESONATOR FREQUENCY COMB Introduction Four wave mixing and comb generation On chip frequency comb characterization Si 3 N 4 ring and Experiment setup Results Device fabrication Experimental procedure vi

7 v Page 3.8 Simulation Conclusion TIME DOMAIN COHERENCE STUDY OF SILICON NITRIDE MICRORES- ONATOR FREQUENCY COMBS Introduction Si 3 N 4 ring and experimental setup Results Visibility curves Conclusion FUTURE WORK Intoduction Future work SHG Frequency-resolved optical gating Comb improvement and dispersion measurement RF beating experiment Pulse generation from Kerr combs On-chip pulsed light source LIST OF REFERENCES VITA

8 vi LIST OF TABLES Table Page 3.1 Summary of groups working on Comb generation

9 vii Figure LIST OF FIGURES Page 1.1 Schematic diagram (a) Ideal frequency comb, (b) Representative output spectrum of a mode locked laser with a Gaussian envelope, (c) corresponding time domain representation [3] Schematic diagram of pulse shaping (a) Group of lines regime, (b) Lineby-line regime [6] OAWG with frame to frame update [7] Pulse shaper [3] Light propagation in fiber [9] Schematic of experimental setup. Here f CEO is 100 MHz; f sig is GHz; f ref is f sig + f rep ; f rep is 220 KHz. CW: continuous-wave laser; PM: phase modulator; IM: intensity modulator; Amp: optical amplifier; PD: photo detector; AO: acousto-optic frequency shifter (a) EFXC data for bandwidth-limited signal showing multiple periods,(b) EFXC data for bandwidth-limited signal zoomed-in to show the fringe period, (c) EFXC data for π phase step signal, and (d) EFXC data for cubic phase signal (Color online) Retrieved (a) amplitude and phase for (b) approximately bandwidth-limited signal, (c) quadratic phase, (d) cubic phase, (e) π phase step signals obtained via pulse shaper, and (f) after propagation through 20 km optical fiber. In (b) 9 sets of data are overlaid. Circles (c-f): retrieved phase; lines: applied phase through pulse shaper (c-e) and quadratic fit (f) Optical frequency comb generation in a micro resonator. (a) shows the resonator and the output comb spectrum. The individual comb modes are spaced by FSR of the cavity. (b) shows the principle of the comb generation process. Degenerate and nondegenerate FWM allow conversion of a CW laser into an optical frequency comb [37] The role of dispersion in comb generation. Due to the dispersion in the cavity, FSR varies with the optical frequency, so that the cavity resonances are not spaced equally in frequency. The generated optical frequency comb (lines), in contrast, is perfectly equidistant [55]

10 viii Figure Page 3.3 (a) Microscope image of a 40 µm radius microring with the coupling region. (b) Image of a fiber pigtail. (c) Transmission spectrum of the microring resonator. (d) Zoomed in spectrum of an optical mode with a 1.2 pm linewidth Scheme of the experimental setup for line-by-line pulse shaping of a frequency comb from a silicon nitride microring. CW: continuous-wave; EDFA: erbium doped fiber amplifier; FPC: fiber polarization controller; µring: silicon nitride microring; OSA: optical spectrum analyzer Spectra of generated optical frequency combs. For each spectrum the CW pump wavelength, estimated power coupled to the access waveguide, and ring radius will be succinctly indicated (a) nm, 0.45 W, 40 µm; (b) nm, 66 mw, 100 µm; (c) nm, 1.4 W, 200 µm; (d) nm, 1.4 W, 200 µm; (e) nm, 1.4 W, 100 µm; and (f) nm, 1.4 W, 100 µm Spectra of generated optical frequency combs. CW pump wavelengths are indicated in the figures. All the spectrums are taken from the same 200µm radius ring with 500 nm gap between ring and waveguide. The CW power and other experimental parameters remains same (1.1 W) (a) Spectrum of the generated comb (Fig. 3.5(a)) after the pulse shaper, along with the phase applied to the LCM pixels of the pulse shaper for optimum SHG. (b) Autocorrelation traces. Here the red line is the compressed pulse, the dark blue line is the uncompressed pulse, and the black line is calculated by taking the spectrum shown in Fig. 3.7(a) and assuming flat spectral phase. The contrast ratio of the autocorrelation measured after phase compensation is 7:1. (c) The odd pulse: applied the same phase as Fig.3.7 (a), but with an additional π phase added for pixels 1-64 (wavelengths longer than 1550 nm). Red line: experimental autocorrelation; black line: autocorrelation calculated using the spectrum of Fig. 3.7(a), with a π step centered at 1550 nm in the spectral phase. (d) Normalized intensity autocorrelation traces for compressed pulses, measured at 0, 14, and 62 minutes after spectral phase characterization, respectively... 32

11 ix Figure Page 3.8 (a) and (b) Spectra of the generated combs (corresponding to Fig. 3.5(c) and 3.5(b), respectively) after the pulse shaper, along with the phase applied to the LCM pixels for optimum SHG signals. (c) and (d) Autocorrelation traces corresponding to (a) and (b). Red lines are the compressed pulses after phase correction, dark blue lines are the uncompressed pulses, and black lines are calculated by taking the spectra shown in (a) and (b) and assuming flat spectral phase. The contrast ratios of the autocorrelations measured after phase compensation are 14:1 and 12:1, respectively. Here Light gray traces show the range of simulated autocorrelation traces Schematic diagram of frequency instability due to uncorrelated line-to-line random phase. Here red arrow shows the effect of δf n. δf n is the small fixed shifts (assumed to be random and uncorrelated) of the individual frequencies from their ideal, evenly spaced positions Theoretical traces for nonlinear SHG autocorrelation measurements [18, 61]. The contrast ratio is 2:1 for continuous noise and 2:1:0 for a finite duration noise burst. A single coherent pulse decays smoothly to zero background level. The pulse duration can be estimate from the full width half maximum (FWHM) τ of the correlation trace G 2 (τ) (a), (b) and (c) Spectra of the generated comb (corresponding to Fig. 3.5(d), 3.5(e) and 3.5(f), respectively) after the pulse shaper, along with phase applied to the LCM pixels for optimum SHG signals. (d), (e) and (f) Autocorrelation traces corresponding to (a), (b) and (c). Red lines are the compressed pulse after phase correction, dark blue lines are the uncompressed pulse, and black lines are the calculated trace by taking the spectrum shown in (a), (b) and (c) and assuming flat spectral phase. Here Light gray traces show the range of simulated autocorrelation traces (a) Spectrum of the generated comb (Fig. 3.5(f)) after the pulse shaper, along with the phase applied to the LCM pixels of the pulse shaper for optimum SHG. (b) Autocorrelation traces. Here the red line is the compressed pulse, the dark blue line is the uncompressed pulse, and the black line is calculated by taking the spectrum shown in Fig. 3.12(a) and assuming flat spectral phase. (c) The odd pulse: applied the same phase as Fig. 3.12(a), but with an additional π phase added for wavelengths longer than 1554 nm. Red line: experimental autocorrelation; black line: autocorrelation calculated using the spectrum of Fig. 3.12(a), with a π step centered at 1555 nm in the spectral phase. Figs. 3.11(c)(f) are repeated as Figs (a)(b)

12 x Figure Page 3.13 (a)si 3 N 4 microring. (b)v groove (left rectangular shape) is connected to inverse tapered waveguide. (c)sem of the wave guide (d) SEM of the V groove Simulated intensity autocorrelation traces in which uncorrelated random spectral phases are uniformly distributed in the range 0 to φ, for various values of φ. The experimental autocorrelation trace from Fig. 3.11(f) is also plotted (black line) Selected simulated intensity profiles with uncorrelated random spectral phases that are uniformly distributed in the range 0 to φ = 0.8π. These plots are normalized to the peak intensity calculated for the case of 0 phase fluctuations Possible routes to comb formation. The optical frequency axis is portrayed in free spectral range (FSR) units. Arrows are drawn in an attempt to represent the approximate order in which new comb lines are generated; no attempt is made to indicate all the couplings involved in the four wave mixing process. (a) Case where initial comb lines are spaced by one FSR from the pump line, with subsequent comb lines, generated through cascaded four wave mixing, spreading out from the center. (b) Case where initial comb lines are spaced from the pump line by N FSRs, where N>1 is an integer. Here N=3 is assumed. (c) When the pump laser is tuned closer into resonance, additional lines are observed to fill in, resulting in spectral lines spaced by nominally 1 FSR a) Spectrum of the generated 3 FSR spacing comb after the pulse shaper. (b) Autocorrelation traces corresponding to (a). (c) Spectrum of the generated 1 FSR spacing comb after the pulse shaper. Here we tune the CW laser 53 pm towards the red side than that of (a). (d) Autocorrelation traces corresponding to (c) Spectra and autocorrelation traces for 3 subfamilies of comb lines with 3 FSR spacing selected from the spectrum shown in Fig. 4.2(c). Blue and red traces are experimental traces before and after phase compensation respectively. Black traces are calculated by taking the OSA spectrums and assuming flat spectral phase Spectra and autocorrelation traces for 2 subfamilies of comb lines with 2 FSR spacing selected from the spectrum shown in Fig. 4.2(c). Blue and red traces are experimental traces before and after phase compensation respectively. Black traces are calculated by taking the OSA spectrums and assuming flat spectral phase

13 xi Figure Page 4.5 Autocorrelation traces for 3 line experiments for different φ for lines { 3, 0, 3}, for which high coherence is observed. Here colored lines are the experimental traces and black lines are the simulated traces Autocorrelation traces for 3 line experiments for different φ for lines { 2, 1, 4}, for which low coherence is observed. Here colored lines are the experimental traces and black lines are the simulated traces Autocorrelation traces for 3 line experiments for different φ for lines { 7, 4, 1}, for which low coherence is observed. Here colored lines are the experimental traces and black lines are the simulated traces Visibility traces of (a) three subfamilies of 3 FSRs, (b) two subfamilies of 2 FSRs, and (c) two subfamilies of 1 FSR. Here in the visibility curves, red, green and black lines are the experimental data; blue lines are ideal theoretical curves calculated assuming full coherence based on the power spectra corresponding to the respective red line visibility curves. Numbers in curly braces indicate the 3 lines that are used in the experiments. Error bars (shown for representative curves) and shaded areas represent the mean ± one standard deviation Proposed model for type II comb formation. (a) First: generation of a cascade of sidebands spaced by N FSRs (Nδω) from the pump. Here N=6 is illustrated. (b)-(c) The 2nd event is an independent four-wave mixing process, which creates new sidebands spaced by a different amount,±nδω (n=1,2 or 3...for different lines), from each of the lines in the previous step. Due to dispersion, it is very unlikely that the new frequency spacings will be exact submultiples of the original N FSR spacing; i.e.,δω δω Polarization insensitive ultra low-power SHG FROG setup [65] The model used for simulation. Here h,b and w are the height, base of the Si 3 N 4 and cladding layer(sio 2 ) dimension respectively Simulation results of the present device. Here h,b and θ are the height, base and angle from the vertical direction of the Si 3 N 4 respectively Schematic diagram of the experimental setup for dispersion calculation. Here OPO: optical parametric osillator; DUT: device under test Simulation results with various dimensions to find optimum device dimension for next generation device. Here h,b and θ are the height, base and angle from the vertical direction of the Si 3 N 4 respectively (a) Schematic diagram for RF beating experiment. (b) expected results: One line will be beat with tunable laser and multiple lines will be seen in RF spectrum analyzer

14 xii Figure Page 5.7 High coherent temporal case: (a) Spectrum of the generated comb after the pulse shaper with applied phases. (b) Autocorrelation traces. Here red line is the experimental AC trace when we apply red dot phases of Fig 5.7(a). Black line is the calculated AC considering spectrum shown in Fig 5.7(a) and assuming spectrum flat spectral phases. Blue line is the experimental AC trace without pulse compression. Green line is the experimental AC trace when we apply green dot phases of Fig 5.7(a) Partial coherent temporal case: (a) Spectrum of the generated comb after the pulse shaper with applied phases. (b) Autocorrelation traces. Here red line is the experimental AC trace when we apply red dot phases of Fig 5.8(a). Black line is the calculated AC considering spectrum shown in Fig 5.8(a) and assuming spectrum flat spectral phases. Blue line is the experimental AC trace without pulse compression. Green line is the experimental AC trace when we apply green dot phases of Fig 5.8(a) Schematic diagram for on-chip pulsed light source

15 xiii ABSTRACT Fahmida Ferdous Ph.D., Purdue University, December On Chip Frequency Comb: Characterization and Optical Arbitrary Waveform Generation. Major Professor: Andrew M. Weiner. Recently, on-chip comb generation methods based on nonlinear optical modulation in ultrahigh quality factor monolithic micro-resonators have been demonstrated. In these methods, two pump photons are transformed into sideband photons in a four wave mixing process mediated by the Kerr nonlinearity. The essential advantages of these methods are simplicity, small size, very high repetition rates and sometimes CMOS compatibility. We investigate line-by-line pulse shaping of such combs generated in silicon nitride ring resonators. We demonstrate a simple example of optical arbitrary waveform generation (OAWG) from Kerr comb. We observe two distinct paths to comb formation which exhibit strikingly different time domain behaviors. For combs formed as a cascade of sidebands spaced by a single free spectral range (FSR) that spread from the pump, we are able to compress to nearly bandwidthlimited pulses. This indicates high coherence across the spectra and provides new data on the high passive stability of the spectral phase. For combs where the initial sidebands are spaced by multiple FSRs which then fill in to give combs with single FSR spacing, the time domain data reveal partially coherent behavior. We also investigate the behaviors of a few sub-families of the partially coherent combs selected by a pulse shaper. We observe different coherence properties for different groups of comb lines. Furthermore we will discuss an ultrafast characterization techniques called dual comb electric field cross correlation. This linear technique will provide both low optical power and broader bandwidth capability for full time domain characterization of OAWG from Kerr comb.

16 1 1. INTRODUCTION Our research is focused on different aspects of optical arbitrary waveform (OAWG) such as generation, characterization and applications. OAWG is a very powerful tool for high precision spectroscopy, broad band gas sensing, optical clock, attosecond physics and also in RF photonics and in silicon photonics. Before going to deep in our work, we will discuss some basic things such as optical comb, OAWG, waveguide and resonator. 1.1 Optical frequency comb Optical frequency comb consists of periodic discrete spectral lines with fixed frequency positions [1, 2]. Frequency comb can be generated in mode locked lasers with stabilized repetition rates and center frequencies. Attributes that are desirable in a frequency comb include having stable frequency positions of individual comb lines and knowing the exact frequency position of the individual comb lines. By suitable locking mechanisms, the frequency positions of the comb lines can be stabilized, however exact determination of individual frequencies is hard. This happens because the absolute optical frequencies constituting the comb will not be exact multiples of the repetition rate owing to difference between the phase and group velocities in the laser cavity. The individual comb lines are given by the equation [2] f m = mf rep + ε (1.1) where f rep is the repetition rate of the laser and ε is known as the carrier envelope offset, whose value is not easy to obtain and because of which, exact determination

17 2 Fig Schematic diagram (a) Ideal frequency comb, (b) Representative output spectrum of a mode locked laser with a Gaussian envelope, (c) corresponding time domain representation [3]. of frequencies becomes difficult. Fig 1.1 schematically shows this. 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 where the comb lines are offset from multiples of the repetition rate by the carrier envelope offset frequency ε. Fig 1.1(c) shows the envelope of time domain trace corresponding to the comb. In the last decade, driven by metrological applications, there were significant developments in frequency combs and methods to measure and lock the carrier envelope offset was proposed. Such combs are called self referenced frequency combs and they have stabilized frequency lines with known frequency positions [1, 2]. The repetition rate can be very small (i.e. GHz) to THz. However, for practical applications, for e.g. in optical communications, the interesting regime will be in repetition

18 3 rates of 10s of GHz corresponding to the data rates used. Also, in order to be able to address individual spectral lines in a pulse shaper, 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. Due to this reason, there has been significant development of alternate frequency comb sources with high repetition rates [4, 5]. In fact all the frequency comb sources which we use in our work are novel sources and not mode locked lasers. 1.2 Optical arbitary waveform generation Utilizing such combs together with the well established techniques of femtosecond pulse shaping, individual spectral lines can be controlled independently allowing very high complexity waveform generation. This is known as optical arbitrary waveform generation (OAWG) and promises to have significant impact in optical science and technology. By shaping the amplitude and phase of individual lines of a frequency comb, 100% duty factor waveforms can be generated via OAWG. Figure 1.2 schematically shows the difference between conventional pulse shaping (group of lines regime) and OAWG (line-by-line regime). In the group of lines case, in time domain shaped pulses are isolated in time, where as in the line-by-line regime they occupy the entire time window leading to 100 % duty factor waveforms. Another interesting extension of this regime is the case when the pulse shaping operation is modified at the repetition rate of the comb. In this case, the waveform updates on a frame to frame basis allowing for potentially infinite record length, very high complexity waveforms. This is schematically shown in fig 1.3. Let us now briefly describe the operating principle of femtosecond pulse shaping by which the waveforms are generated [8]. In a Fourier pulse shaping apparatus, the spectrum of an incident pulse is spread spa-

19 4 Fig Schematic diagram of pulse shaping (a) Group of lines regime, (b) Line-by-line regime [6]. Fig OAWG with frame to frame update [7].

20 5 Fig Pulse shaper [3]. tially using a spectral disperser (a diffraction grating) and focused onto a spatial light modulator (SLM), which transfers spatial phase and amplitude information onto the complex optical spectrum. This Fourier synthesis procedure results, after the optical frequencies are recombined, in programmable user-defined waveforms. An important requirement of the OAWG setup is the ability to spectrally resolve individual comb lines. This can be achieved in conventional grating based pulse shapers using bigger beams and finer groove spacings on the gratings. Fig 1.4 shows the schematic of a grating based high resolution pulse shaper aligned in a reflective configuration used to address comb lines individually.

21 6 Fig Light propagation in fiber [9]. 1.3 Optical waveguide Silicon photonics is attracting more interest in recent years since it provides a possible solution for chip-scale high speed data communication, for example, between two Central Processing Units. Traditional copper transmission line suffers from delay limitation in high speed data transmission, while optical signal does not have this problem. The essential advantages of silicon photonics are simplicity, small size, very low power consumption and CMOS compatibility. Lets first discussed briefly about the basic building block: waveguides. Waveguides used at optical frequencies are typically dielectric waveguides, a dielectric material with high permittivity, and thus high index of refraction, is surrounded by a material with lower permittivity. The simple way to understand the guides of optical waves is by total internal reflection. The most common optical waveguide is optical fiber. People can simply understand the optical fiber in linear propagation approximation as in Fig. 1.5: The optical field is confined in the high refractive index area. Since the boundary condition is com-

22 7 plicated now (dielectric waveguide), there is evanescent field decaying exponentially outside the waveguide boundary. Normally, the waveguide has extremely small intersection. The size is so small that automatically kills off the high modes. The benefit of single mode propagation is to avoid mode dispersion. Every single mode will have different propagation constant (except degenerate modes). So the optical power in individual mode travels through the waveguide with different velocity. This is called mode dispersion. It will broaden the data packet in time domain hence increase the bit error rate in high speed data transmission. Single mode waveguide will naturally eliminate the mode dispersion. In most cases we need to couple the optical power from outside fiber into the waveguide. For single mode optical fiber, the mode profile is around 10 µm in diameter. In silicon waveguide the mode profile is generally similar as the waveguide geometry (< 1µm). To match the modes, one strategy is to use a taper part on chip to match the mode between fiber and waveguide, or inverse taper or grating-assisted coupling. In our lab we normally used the first two which require accurate alignment between the fiber and waveguide. 1.4 optical resonator With the state-of-art fabrication of silicon waveguide, both passive and active devices are demonstrated on silicon chip with excellent performances. Optical cavities are one of the most popular devices under research. Optical cavities are a major component of lasers, surrounding the gain medium and providing feedback of the laser light. They are also used in optical parametric oscillators and some interferometers. The functions as filter, modulator, switcher, spectral shaper, sensor and as comb sources have been investigated profoundly. The typical micro ring resonator is a compact optical cavity which shows periodical response in spectrum domain. It can be side coupled by one or two straight waveguide to form a pole-type filter.the cavity

23 8 contains a dielectric round waveguide or a round disk, where the optical beam can bounce back and forth at the ring or disk boundary. It is called whispering gallery mode (WGM). WGMs occur at particular resonant wavelengths of light confined to a cylindrical or spherical volume with an index of refraction greater than that surrounding it. At these wavelengths, the light undergoes total internal reflection at the volume surface and becomes trapped within the volume for timescales of the order of nanoseconds. Micro ring resonator is a round planar waveguide where the light is going along the waveguide. No reflection happens. Several schemes can be used to feed the power into the resonator. The most common way is using coupling between the micro resonator and waveguide. As introduced in last part the mode propagated in waveguide has the evanescent field outside the edge. Putting two waveguide very close would let the power to transfer between two waveguide. In the application where very high Q is needed, we need to match the coupling strength with the round trip loss in the resonator. This case is called critical coupling. Following the definition we call the weaker coupling as under coupling and stronger coupling as over coupling. By manipulating the coupling strength, we can in some sense tuning the loaded Q value of resonator with the intrinsic Q value unchanged. 1.5 Organization of the thesis The dissertation is organized into the following chapters. In chapter 2 we will discuss a characterization technique for optical arbitrary waveforms based on two frequency combs. We will present one characterization techniques which may be used in future for characterization of on chip comb. In chapter 3, a novel method which is recently developed for the generation of the on chip comb will be discussed. Lineby-line pulse shaping of Kerr combs generated in silicon nitride ring resonators is discussed. A simple example of optical arbitrary waveform generation (OAWG) from

24 9 Kerr comb is demonstrated. Two distinct paths to comb formation which exhibit strikingly different time domain behaviors is observed. In chapter 4, the behaviors of a few sub-families of the partially coherent combs selected by a pulse shaper is investigated. Different coherence properties for different groups of comb lines is observed. In chapter 5, some future directions are discussed.

25 10 2. DUAL COMB ELECTRIC FIELD CROSS-CORRELATION TECHNIQUE 2.1 Introduction The use of a pulse shaper [8] to manipulate optical frequency combs [11, 12] on a line by line basis, termed optical arbitrary waveform generation [13 15], leads to new challenges in ultrafast waveform characterization. Waveforms generated through lineby-line pulse shaping exhibit several unique attributes. Such waveforms may exhibit 100% duty cycle, with shaped waveforms spanning the full time domain repetition period of the frequency comb, and with spectral amplitude and phase changing abruptly from line to line. Although methods for full characterization of ultrashort pulse fields, such as frequency-resolved optical gating (FROG) and spectral phase interferometry for direct electrical field reconstruction (SPIDER), are well developed [16 18], such methods are typically applied to measurement of low duty cycle pulses that are isolated in time, with spectra that are smoothly varying, and with relatively low timebandwidth product. Hence new characterization approaches are desired for shaped waveforms generated from frequency combs. A few techniques for OAWG characterization have recently been reported [6, 15, 19, 20]. Some of these techniques require a series of measurements performed sequentially which limits measurement speed [6,15], while others require nonlinear optics and/or an array detector [15, 19, 20]. Here we demonstrate a novel electric field cross-correlation (EFXC) technique in which a precharacterized reference comb is used to measure an unknown signal field from a second optical comb. Although related to standard EFXC techniques, our experiment is con- 0 This work is published in [10]

26 11 structed in a way uniquely suited to characterization of shaped waveforms from comb sources. Our technique requires only a linear point detector and is simple to construct. It provides both high measurement sensitivity and fast (tens of microseconds) data acquisition. Our work is closely related to recent coherent multi-heterodyne spectroscopy experiments in which a pair of stabilized combs is exploited for rapid measurement of absorption and phase spectra of gas phase samples [21]. Our work is also related to Linear Optical Sampling [22] which has recently been implemented with dual self-referenced and stabilized, 100 MHz repetition rate comb sources to achieve 15 bit sampling resolution [23]. An important difference is that our setup uses simple comb sources based on modulation of a CW laser [4, 24, 25] rather than octave-spanning self-referenced combs. Our simple combs operate at a relatively high repetition rate (10 GHz), which is advantageous both for applications in telecommunications and for arbitrary optical waveform generation, and our measurements are applied to shaped waveform characterization rather than spectroscopy. 2.2 Conventional EFXC and Dual Comb EFXC EFXC measures the interference between a signal field (a s ) and reference field (a r ) in the time domain as a function of the relative delay (τ). Traditionally, the delay is swept using a mechanical translation stage [26]. The resulting time-average power is recorded using a slow photo-detector as a function of delay and is written as follows [18]: < P out (τ) >= 1 2 (U s + U r + {a s a r(t τ) exp jω 0 τ + C.C.}dt). (2.1) Here U s and U r are the pulse energies and ω o is the carrier frequency. The unknown signal pulse can be fully recovered from a known, well characterized reference pulse. Note that in the traditional scheme, the phase delay and group delay vary at exactly

27 12 Fig Schematic of experimental setup. Here f CEO is 100 MHz; f sig is GHz; f ref is f sig + f rep ; f rep is 220 KHz. CW: continuous-wave laser; PM: phase modulator; IM: intensity modulator; Amp: optical amplifier; PD: photo detector; AO: acousto-optic frequency shifter. the same rate, as expressed in Eq.2.1. In our scheme the EFXC is recorded without any moving parts. We use two frequency combs with different repetition rates: the difference in the repetition rates ( f rep ) causes the signal and reference pulse envelopes to walk through each other in time T =1/ f rep. By controlling f rep, we can control the group delay sweep. The phase delay sweep is controlled by adjusting the offset f CEO between the optical center frequencies of the combs (analogous to adjusting the carrier-envelope offset frequency [12]). 2.3 Experimental set up and Data processing Our experimental setup is given in Fig A CW laser at 1542 nm is split into reference and signal arms, each of which is provisioned with a phase and intensity modulator arranged in series to produce up to 30 comb lines at 10 GHz line spacing [4]. In each arm the generated comb is compressed into approximately

28 13 bandwidth-limited pulses by using the pulse shaper to phase compensate individual frequency components [4]. After phase correction the intensity autocorrelation is in excellent agreement with that simulated assuming flat spectral phase. This provides evidence that our reference pulse is at least close to transform-limited. An acoustooptic modulator (AO) is used to provide a f CEO =100 MHz frequency shift to the signal comb, which sets the EFXC fringe period to 10 ns in time. The comb repetition rates are offset by f rep =220 khz, so the group delay sweeps though the 100 ps comb period in 4.5 µs. Figure 2.2(a) shows several periods of the EFXC trace captured using a digital oscilloscope, from which we can easily see the 4.5 µs periodicity. Figure 2.2(b) shows a zoom-in view in which we can see the 10 ns fringe period and the 1 ns sampling time. An important point to note is that a full waveform period corresponds to 450 fringes, much less than the 20,000 fringes that would be required for a conventional EFXC trace. Our ability to sweep phase and group delay independently significantly reduces the number of fringes which must be recorded, hence easing data acquisition requirements. Figure 2.2(a) is EFXC data for an approximately band- limited signal pulse. Here the lack of complete symmetry is attributed to slight differences both in the power spectra and in the compensated spectral phase profile of the two combs. An interesting point is that the EFXC from Fig. 2.2(a) exhibits larger wings than that of the intensity autocorrelation (not shown). Because EFXC depends on field rather than intensity, it is a more sensitive tool to display low amplitude wings. Figures 2.2(c) and 2.2(d) show EFXC traces (plotted over 110 ps of equivalent time, slightly more than one waveform period) obtained when the signal arm line-by-line pulse shaper is programmed to impart respectively an abrupt π phase step and a cubic phase profile onto the spectrum (the specified phase profiles are superimposed onto the phase settings used for compression). Application of a π phase step onto half of the spectrum splits the original pulse into an asymmetric pulse

29 Fig (a) EFXC data for bandwidth-limited signal showing multiple periods,(b) EFXC data for bandwidth-limited signal zoomed-in to show the fringe period, (c) EFXC data for π phase step signal, and (d) EFXC data for cubic phase signal. 14

30 15 doublet, sometimes termed an odd pulse [27]. The resulting doublet is clearly visible from the EFXC. Cubic spectral phase results in more complicated waveform reshaping with strong oscillatory features. The resulting signal fills the entire waveform period, a clear hallmark of line-by-line pulse shaping. Spectral information may be retrieved by Fourier analysis of the EFXC data. For conventional EFXC the Fourier transform of Eq.2.1 gives [18] F {< P out (τ) >} = {A s(ω ω 0 )A r(ω ω 0 ) + A s(ω ω 0 )A r (ω ω 0 )} (2.2) where noninterferometric terms are omitted. In our implementation the first and second term in Eq. 2.2 appear around f CEO =100 MHz and -100 MHz, respectively. For our analysis we select the features centered around 100 MHz and set the rest of the Fourier transform to zero. Data consist of a series of discrete lines spaced by f rep =220 khz. After we rescale the frequency axis to map the line spacing to the 10 GHz period of our combs, we obtain the spectral amplitude shown in Fig. 2.3(a). Here we have divided our result by the spectral amplitude profile of the reference, obtained from an optical spectrum analyzer (OSA). The profile in Fig. 2.3(a) is in qualitative agreement with an independent measurement using an OSA (not shown). The discrete line nature of the retrieved spectrum provides proof that phase coherence is preserved in our EFXC measurements. The average linewidth in Fig. 2.3(a) is 900 MHz, which corresponds closely to our expectation based on data acquisition over a 50 µs interval (corresponds to 11 waveform periods). Increased linewidths are observed when data are recorded over shorter record lengths, in inverse proportion to the number of waveform periods..

31 Fig (Color online) Retrieved (a) amplitude and phase for (b) approximately bandwidth-limited signal, (c) quadratic phase, (d) cubic phase, (e) π phase step signals obtained via pulse shaper, and (f) after propagation through 20 km optical fiber. In (b) 9 sets of data are overlaid. Circles (c-f): retrieved phase; lines: applied phase through pulse shaper (c-e) and quadratic fit (f). 16

32 Results We now focus on spectral phase measurements. Figure 2.3(b) shows spectral phase information obtained for an approximately bandwidth-limited signal pulse, with constant and linear spectral phase suppressed. Nine independent data sets are overlaid. The average standard deviation of the results at any one frequency is 0.02π. In contrast, the mean phases show a variation across frequency with 0.1π standard deviation. The latter variation represents errors in the compensated phases of reference and signal fields (more precisely, the difference in the spectral phase errors). Fig 2.3 (c-f) shows examples of retrieved phase for shaped signal fields. Here the mean frequency-dependent phases from Fig. 2.3(b) are subtracted in order to isolate the effect of pulse shaping. Figures 2.3(c-e) shows results obtained when the pulse shaper is programmed (a) for quadratic spectral phase, (b) for cubic spectral phase, EFXC from Fig. 2.2(d), and (c) for a π phase step, EFXC from Fig. 2.2(c). In the figures circles represent retrieved phase values at the peaks of comb lines, and lines represent phase functions programmed onto the pulse shaper. Standard deviations between retrieved and programmed phases are 0.05 π, 0.1 π, and 0.04 π for Figs. 2.2(c-e), respectively. These results reflect well both on measurement accuracy and pulse shaping fidelity. Fig 2.3(f) shows spectral phase retrieved after the signal field is transmitted through 20 km of standard single-mode fiber. For this measurement f rep was increased to 850 khz. The standard deviation between the retrieved phase and a quadratic fit (solid line) is 0.1 π. The dispersion coefficient is calculated as 16.5 ps/(nm-km), consistent with the known dispersion of the standard single mode fiber. This result demonstrates the ability to perform EFXC over significant length of fiber, with accuracy comparable to that obtained in experiments without long fibers and on a time scale fast enough that fiber fluctuations do not significantly degrade the interferometric measurement process.

33 Future work This linear technique will provide both low optical power and broader bandwidth capability for full time domain characterization of OAWG from Kerr comb.

34 19 3. SPECTRAL LINE-BY-LINE PULSE SHAPING OF AN ON-CHIP MICRORESONATOR FREQUENCY COMB 3.1 Introduction Optical frequency combs consisting of periodic discrete spectral lines with fixed frequency positions are powerful tools for high precision frequency metrology, spectroscopy, broadband gas sensing, and other applications [1, 21, 29 33]. Frequency combs generated in mode locked lasers can be self-referenced to have both stabilized optical frequencies and repetition rates (with repetition rates below 1 GHz in most cases) [12]. An alternative approach based on strong electro-optic phase modulation of a continuous wave (CW) laser provides higher repetition rates, up to a few tens of GHz, but without stabilization of the optical frequency [5, 24, 34, 35]. Recently, a novel method for optical frequency comb generation, known as Kerr comb generation, by nonlinear wave mixing in a microresonator has been reported [36 45]. The essential advantages of Kerr comb generation are simplicity, small size, and very high repetition rate and compatibility with low-cost, batch fabrication processes of the microresonators. 3.2 Four wave mixing and comb generation Frequency comb generation in a variety of micro systems including microtoroids [37, 40, 42], microspheres [46], microrings [28, 38, 39, 43, 44, 47], spiral [48], disk [49], oblate spheriod [50] and millimeter-scale crystalline resonators [41,47,50 53] has been 0 This work is published in [28]

35 20 demonstrated. Materials used in these systems include silica [37, 39, 40, 42, 46, 49], silicon nitride [28, 43, 44, 46 48], fused quartz [52], calcium fluoride [41, 51], and magnesium fluoride [47, 50, 53]. Their free-spectral range (FSR) may vary from a few gigahertz to a few terahertz, depending on the resonator s radius. Provided that the material is low loss and the resonator has smooth surfaces, the light can be trapped for few microseconds by total internal reflection. Their quality factor Q can be exceptionally high as shown in table 3.1. The Q is defined [54]: Q = Q l = λ 0 λ 3dB (3.1) Q i = 2 Q l /[1 ± R 0 (λ 0 )] (3.2) where λ 0, λ 3dB, + and - are resonance wavelength, 3 db down bandwidth from resonance, for under coupling and for over coupling. R 0 (λ 0 ) is normalized transmission power at λ 0 ( when spectrum in linear scale: maximum power is normalized to 1 ).

36 21 Table 3.1 Summary of groups working on Comb generation Group Shape Material n n2(cm 2 /W ) Q FSR Intertion Loss (db) NIST-Purdue micro ring Silicon nitride GHz 3 (lenced fiber) Cornell [48] spiral resonator Silicon nitride GHz Cornell [38] micro ring Silicon nitride GHz-1.17 THz 7 Razzari [39] micro ring Silica GHz-6 THz 9 MPQ [37] micro toroid Silica > 10 8 / GHz/86 GHz Caltech [49] disk resonator Silica GHz JPL [41] micro toroid Calcium fluoride(caf2) GHz 3 (prism couple) OEwaves [50] oblate spheriod magnesium fluoride(mgf2) GHz MPQ [53] crystalline magnesium fluoride(mgf2) > GHz NIST-CO [52] crystalline fused quartz GHz

37 22 In these resonators, the small confinement volume, high photon density, and long photon storage time (proportional to the quality factor Q) induce a very strong lightmatter interaction. Their high optical finesse and small mode volume has led to a significant reduction in the threshold of nonlinear optical processes. This leads to generate a highly efficient FWM, where two pump photons are transformed into two sideband photons through the Kerr nonlinearity. Provided that the pump is powerful enough, an optical-frequency comb, sometimes referred to as a Kerr comb, is generated through a cascaded FWM, resulting from interactions involving any four photons fulfilling energy and angular momentum conservation requirements. Figure 3.1 can help to understand the mechanism. This mechanism is first proposed. But recently a new approach is suggested which will be discussed in later. Here high Q micro resonator (toroid) is pumped with intense CW source (> 10mW, 1550nm) [37]. The high n 2 of the silica initiates the FWM process and results in the creation of signal and idler photons from two pump photons: ν pump +ν pump = ν I +ν s as shown in Fig 3.1. The conservation of energy ensures that the generated photon pairs are symmetric in frequency with respect to the pump. This mechanism is resonantly enhanced by the cavity if idler, signal and pump frequencies all coincide with optical modes of the micro resonator. It is important to note that this process can be cascaded via nondegenerate FWM among pump and first-order sideband, to produce higher order sidebands (ν pump + ν I = ν II + ν s ) as Fig This cascaded mechanism ensures that the frequency difference of pump and first-order sidebands pump ν pump ν I = ν s ν II is exactly transferred to all higher-order inter-sideband spacings. Thus, provided that the cavity exhibits a sufficiently equidistant mode spacing, successive FWM to higher orders intrinsically leads to the generation of sidebands with equal spacing, that is, an optical frequency comb. But due to the dispersion in the cavity, FSR varies with the optical frequency, so that the cavity resonances are not spaced

38 Fig Optical frequency comb generation in a micro resonator. (a) shows the resonator and the output comb spectrum. The individual comb modes are spaced by FSR of the cavity. (b) shows the principle of the comb generation process. Degenerate and nondegenerate FWM allow conversion of a CW laser into an optical frequency comb [37]. 23

39 24 Fig The role of dispersion in comb generation. Due to the dispersion in the cavity, FSR varies with the optical frequency, so that the cavity resonances are not spaced equally in frequency. The generated optical frequency comb (lines), in contrast, is perfectly equidistant [55]. equally in frequency. The generated optical frequency comb (lines), in contrast, is perfectly equidistant as shown in Fig Therefore the generated sidebands walk off from the cavity resonances with increasing sideband order, reducing the cavity enhancement of the FWM. As a consequence, uncompensated cavity dispersion can eventually limit the comb bandwidth. 3.3 On chip frequency comb characterization Most investigations of Kerr combs have emphasized their spectral properties, including optical and RF frequency stability. A few experiments have reported time domain autocorrelation data [52, 55]. Here we expand the time domain understanding of these devices by manipulating their temporal behavior through programmable optical pulse shaping [8]. The large mode spacing of Kerr combs facilitates pulse

40 25 shaping at the individual line level, also termed optical arbitrary waveform generation (OAWG) [6, 13, 56 58], a technology which offers significant opportunities for impact both in technology (e.g., telecommunications, lidar) and ultrafast optical science (e.g., coherent control and spectroscopy). We demonstrate line-by-line pulse shaping of microresonators based frequency combs. An important feature of our approach is that transform-limited pulses may in principle be realized for any spectral phase signature arising from a coherent comb generation process. Furthermore, the ability to achieve successful pulse compression provides new information on the passive stability of the frequency dependent phase of coherent Kerr combs. Our time-domain experiments also reveal differences in coherence properties associated with different pathways to comb formation. 3.4 Si 3 N 4 ring and Experiment setup Fig. 3.3(a) shows a microscope image of a 40 µm radius silicon nitride microring resonator with coupling waveguide (described in the Device fabrication section). For robust and low-loss coupling of light into and out of the devices, a process for fiber pigtailing the chip is developed at NIST by Dr. Houxun Miao, as shown in Fig. 3.3(b). The fiber pigtailing used for this device eliminates the time consuming task of free space coupling and significantly enhances transportability. Other devices studied employ a similar V-groove scheme to facilitate coupling alignment, but without permanent fiber attachment. Spectroscopy of the resonator s optical modes is performed with a swept wavelength tunable diode laser with time-averaged linewidth of less than 5 MHz. Figure 3.3(c) shows the transmission spectrum of two orders of transverse magnetic (TM) modes (with different free spectral range (FSR) and coupling depth), which have their electric field vectors predominantly normal to the plane of the resonator. Fig. 3.3(d) shows a zoomed in spectrum for a mode at nm with a

41 26 Fig (a) Microscope image of a 40 µm radius microring with the coupling region. (b) Image of a fiber pigtail. (c) Transmission spectrum of the microring resonator. (d) Zoomed in spectrum of an optical mode with a 1.2 pm linewidth. line width of 1.2 pm, corresponding to a loaded optical quality factor (Q) of The average FSR of the series of high Q modes is measured to be 4.8 nm. The loaded Qs of the microresonators used in this chapter are typically to Fig. 3.4 shows the experimental setup. CW light is launched into the microresonator, with a polarization controller used to align the input polarization with the TM mode. The generated frequency comb is launched to a line-by-line pulse shaper for spectral phase measurement and correction, which are accomplished simultaneously by optimizing the second harmonic generation (SHG) signal [4, 20], as described in Experimental procedure. The pulse shaper is also used to attenuate the pump line, which in our experiments is typically 10 to 23 db stronger than the adjacent comb lines, and is sometimes programmed to attenuate some of the neighboring lines as well. This results in a spectrum with line-to-line power variations reduced (but not completely eliminated), which improves time domain pulse quality. In Ref. [20], the

42 27 Fig Scheme of the experimental setup for line-by-line pulse shaping of a frequency comb from a silicon nitride microring. CW: continuous-wave; EDFA: erbium doped fiber amplifier; FPC: fiber polarization controller; µring: silicon nitride microring; OSA: optical spectrum analyzer. phase measurement by this SHG optimization method is compared with another independent method based on spectral shearing interferometry. The difference between the two measurements was comparable to the π/12 step size of the SHG optimization method. This provides an estimate of both the precision and the accuracy of our phase measurement method. In addition to autocorrelation measurements which provide information on the temporal intensity, comb spectra are measured both directly after the microresonator and after the pulse shaper and subsequent Erbium doped fiber amplifier (EDFA). 3.5 Results We have investigated comb generation with subsequent line-by-line shaping in a number of devices and have observed two distinct paths to comb formation which

43 28 exhibit strikingly different time domain behaviors. Comb spectra measured directly after generation are shown in Fig. 3.5, with estimated optical powers coupled to the access waveguides given in the figure caption. In some cases the comb is observed to form as a cascade of sidebands spaced by approximately one FSR that spread from the pump (Figs. 3.5(a), 3.5(b) and 3.5(c) with comb spacings of 600 GHz, 230 GHz, 115 GHz, respectively). In such cases, which we will refer to as Type I comb formation, high quality pulse compression is achieved, signifying good coherence properties. In other cases (Figs. 3.5(d) and 3.5(f)), the initial sidebands are spaced by multiple FSRs from the pump. With changes in pump power or wavelength, additional lines spread out from each of these initial sidebands, eventually merging to form a spectrum composed of lines separated by approximately one FSR. For example, Fig. 3.5(d) shows a comb comprising nearly 300 lines spaced by 115 GHz; the initial sidebands, which remain evident as strong peaks, are spaced by approximately 27 FSRs. Figure 3.6 shows another example of Type II comb formation. This route to comb formation, which we will call Type II, has been discussed by several authors [39,41,59,60]. With our devices, Type II formation results in a larger number of lines, but compressibility is degraded in a way that provides clear evidence of partial coherence. Different regimes of comb generation with distinct coherence properties have also recently been reported for combs generated from silica microresonators [52]. In addition, comb linewidth variations with different pumping conditions have also been reported [42]. Figure 3.7 shows a first set of pulse shaping results from a 40 µm radius microresonator (Fig. 3.3(a)) which generates the Type I comb shown in Fig. 3.5(a), comprising twenty-six comb lines with a repetition rate of 600 GHz. The average output power for an estimated 0.45 W coupled into the input waveguide is measured to be 0.10 W. We select 9 comb lines (limited by the bandwidth of the pulse shaper and the bandwidth of the EDFA before the autocorrelator) to perform the line-by-

44 Fig Spectra of generated optical frequency combs. For each spectrum the CW pump wavelength, estimated power coupled to the access waveguide, and ring radius will be succinctly indicated (a) nm, 0.45 W, 40 µm; (b) nm, 66 mw, 100 µm; (c) nm, 1.4 W, 200 µm; (d) nm, 1.4 W, 200 µm; (e) nm, 1.4 W, 100 µm; and (f) nm, 1.4 W, 100 µm. 29

45 Fig Spectra of generated optical frequency combs. CW pump wavelengths are indicated in the figures. All the spectrums are taken from the same 200µm radius ring with 500 nm gap between ring and waveguide. The CW power and other experimental parameters remains same (1.1 W). 30

46 31 line pulse shaping experiments. The spectrum after the pulse shaper and the spectral phase profile which is found to maximize the SHG signal are shown in Fig. 3.7(a). Fig. 3.7(b) shows the measured autocorrelation traces before and after spectral phase correction. The signal appears nearly unmodulated in time without phase correction, while a clear pulse-like signature is present after correction. Such pulse compression clearly demonstrates successful line-by-line pulse shaping. The intensity profile of the compressed pulse, calculated based on the spectrum (Fig. 3.7(a)) assuming a flat spectral phase, has a full width at half maximum (FWHM) of 312 fs. The corresponding intensity autocorrelation trace is calculated (as shown in Fig. 3.7(b)) and is in good agreement with the experimental trace. The finite signal level remaining between the autocorrelation peaks arises due to the finite number of lines and the uneven profile of the spectrum. The widths of experimental and computed autocorrelation traces are 460 fs and 427 fs, respectively, which differ by 7%. From this we take the uncertainty in our 312 fs pulse duration estimation as 7%. As a preliminary example of arbitrary waveform generation, we program the pulse shaper to apply a π-step function to the spectrum of the compressed pulse; Fig. 3.7(c) shows the result. The π step occurs at the pixel number 64 (corresponds to 1550 nm in wavelength). Application of a π phase step onto half of the spectrum is known to split an original pulse into an electric field waveform that is antisymmetric in time, sometimes termed an odd pulse [27]. The resulting autocorrelation triplet is clearly visible as shown in Fig. 3.7(c) and in good agreement with the autocorrelation that is computed based on the spectrum in Fig. 3.7(a) and a spectral phase that is flat except for a π-step centered at 1550 nm. This result constitutes a clear example of line-by-line pulse shaping for simultaneous compression and waveform shaping. Similar high quality pulse compression results have been achieved with other devices exhibiting Type I comb formation. Figure 3.8 shows data for larger silicon nitride ring resonators (200

47 Fig (a) Spectrum of the generated comb (Fig. 3.5(a)) after the pulse shaper, along with the phase applied to the LCM pixels of the pulse shaper for optimum SHG. (b) Autocorrelation traces. Here the red line is the compressed pulse, the dark blue line is the uncompressed pulse, and the black line is calculated by taking the spectrum shown in Fig. 3.7(a) and assuming flat spectral phase. The contrast ratio of the autocorrelation measured after phase compensation is 7:1. (c) The odd pulse: applied the same phase as Fig.3.7 (a), but with an additional π phase added for pixels 1-64 (wavelengths longer than 1550 nm). Red line: experimental autocorrelation; black line: autocorrelation calculated using the spectrum of Fig. 3.7(a), with a π step centered at 1550 nm in the spectral phase. (d) Normalized intensity autocorrelation traces for compressed pulses, measured at 0, 14, and 62 minutes after spectral phase characterization, respectively. 32

48 33 µm and 100 µm radii) which generate combs spaced by 115 GHz (Fig. 3(c)) and 230 GHz (Fig. 3(b)), respectively. These devices have fiber to fiber coupling loss as low as 3 db when lensed fibers are used. The comb spectrum obtained for pumping the 200 µm radius device at 1547 nm exhibits 12 spectral lines, covering 10 nm bandwidth. The comb spectrum obtained for pumping the 100 µm radius device at 1549 nm exhibits 25 spectral lines, covering 45 nm bandwidth (20 spectral lines are left after the shaper). The autocorrelation data again show that although originally the signals are at most weakly modulated in time, phase correction results in obvious compression into pulse-like waveforms, yielding autocorrelation FWHMs of 1.78 ps and 976 fs for 200 µm and 100 µm rings, respectively. In both cases the shape and on-off contrasts of the autocorrelation are in fairly close agreement with the results simulated using the measured spectra and assuming flat spectral phase. Time domain experiments access information about coherence that is not available from frequency domain data such as the comb spectra. For example, the ability to achieve pulse compression and phase shaping results as shown in Figs. 3.7 and 3.8 provides clear evidence of coherence across the comb spectrum. Note that intensity autocorrelation measurements are insensitive both to overall optical phase and to optical phase that varies linearly with frequency. Small changes in pulse repetition rate that would arise from small changes in comb spacing would also be difficult to observe from autocorrelation data (provided that the comb spacing remains uniform across the spectrum). However, autocorrelations do provide information on changes in pulse duration associated with spectral phase variations quadratic or higher in frequency. The close agreement in the shape and on-off contrast of experimental autocorrelation traces, compared with those calculated on the basis of the measured comb spectra (with flat spectral phase), provides evidence that the obtained pulses are not only close to bandwidth-limited, but also that they have high coherence. We also observe the autocorrelations over an

49 Fig (a) and (b) Spectra of the generated combs (corresponding to Fig. 3.5(c) and 3.5(b), respectively) after the pulse shaper, along with the phase applied to the LCM pixels for optimum SHG signals. (c) and (d) Autocorrelation traces corresponding to (a) and (b). Red lines are the compressed pulses after phase correction, dark blue lines are the uncompressed pulses, and black lines are calculated by taking the spectra shown in (a) and (b) and assuming flat spectral phase. The contrast ratios of the autocorrelations measured after phase compensation are 14:1 and 12:1, respectively. Here Light gray traces show the range of simulated autocorrelation traces. 34

50 35 extended period. Fig. 3.7(d) shows autocorrelation traces measured at different times within a 62 minute interval, with the same spectral phase profile applied by the pulse shaper for all measurements. Clearly the compression results remain similar over the one hour time period indicated in the figure, which means that the relative average phases of the comb lines must remain approximately fixed; slow drifts in relative average spectral phase must conservatively remain substantially below π. Assume now that the field consists of lines at frequencies f o + nf rep + δf n, where f o is the carrierenvelop offset frequency, f rep is the repetition rate and the δf n refer to small fixed shifts (assumed to be random and uncorrelated) of the individual frequencies from their ideal, evenly spaced positions shown in Fig Such frequency shifts would give rise to phase errors for the different spectral lines that grow in time according to δφ n = 2πδf n t. Since the δf n, and hence the linear drifts of the δφ n, are taken as uncorrelated, the characteristic size of the phase errors should (conservatively) satisfy δφ n < 0.7π in order to avoid significant waveform changes. With 3600 s observation time, we may then estimate that the assumed δf n are conservatively of the order 10 4 Hz or below. Our estimation is consistent with measurements performed for combs from silica microtoroids, by beating with a self-referenced comb from a modelocked laser, which indicated uniformity in the comb spacing at least at the 10 3 Hz level [37]. In contrast to the data presented so far for Type I combs, for which the time domain data indicate good coherence, we now discuss our observations for Type II combs, in which the initial sidebands are spaced by multiple FSRs from the pump. First we discuss the compression experiments for a Type II comb obtained from a 200 µm radius ring pumped at 1549 nm, with the directly generated spectrum of Fig. 3.5(d). We performed pulse compression experiments on a group of 24 comb lines centered at 1558 nm. The spectrum after smoothing and phase correction is shown in Fig. 3.11(a), and the autocorrelation data are shown in Fig. 3.11(d).

51 Fig Schematic diagram of frequency instability due to uncorrelated line-to-line random phase. Here red arrow shows the effect of δf n. δf n is the small fixed shifts (assumed to be random and uncorrelated) of the individual frequencies from their ideal, evenly spaced positions. 36

52 37 Fig Theoretical traces for nonlinear SHG autocorrelation measurements [18, 61]. The contrast ratio is 2:1 for continuous noise and 2:1:0 for a finite duration noise burst. A single coherent pulse decays smoothly to zero background level. The pulse duration can be estimate from the full width half maximum (FWHM) τ of the correlation trace G 2 (τ). Once again phase compensation results in substantial compression compared to the original waveform which shows only weak modulation. However, a new feature is that the on-off contrast of the experimental autocorrelation is significantly worse than the simulated trace which assumes phases that are frequency independent and constant in time. The significantly degraded autocorrelation contrast is a hallmark of partial coherence, which can occur when the spectral phase function varies in a nontrivial way during the measurement time. It is known that the autocorrelation of continuous intensity noise consists of a single peak centered at zero delay on top of a constant positive background [18,61]. For a Gaussian random field with phases completely randomized, the ratio of the peak value to the background is 2:1 as shown in Fig The width of the autocorrelation peak gives the time scale for the intensity fluctuations and does not imply the existence of a meaningful pulse duration. Furthermore, the shape of the autocorrelation will not be affected by spectral phase shaping. On the other hand, a coherent train of periodic pulses shows a series of peaks at delays

53 38 corresponding to the pulse separation and exhibits high autocorrelation contrast as shown in Fig The autocorrelation trace does provide information on the pulse duration and may definitely be changed by spectral phase shaping. In our experiments with Type II combs, the autocorrelation shows contrast better than 2:1, but significantly less than would be expected with perfect phase compensation. The portion of the autocorrelation above the background remains responsive to spectral phase shaping and allows compression to bandwidth-limited peaks which repeat at the inverse of the comb spacing. This behavior corresponds to fluctuations of the spectral phase on a time scale fast compared to the measurement time and with amplitude that is significant but less than 2π, or in other words, partial coherence. In this regime the signal consists of a deterministic average waveform superimposed with fluctuating noise-like waveforms with the same repetition period. As explained in the Simulation section, a rough estimate of the amplitude of the spectral phase fluctuations may be obtained from the autocorrelation contrast. From the data in Fig. 3.14, we estimate uncorrelated variations of the spectral phase over an approximate range of ±0.4π. We have observed similar autocorrelation data characteristic of partial coherence in a number of experiments with Type II combs, with minima of the experimental autocorrelation traces lying above the simulated ones assuming full coherence by 17-28% relative to the peak. The uncertainty in simulated traces is estimated by repeating the simulations for spectra recorded sequentially during the autocorrelation measurement. The simulated traces with largest positive and negative variation in contrast are shown as light gray lines in Fig. 3.11(d); this variation is significantly less than that observed experimentally. In contrast, experimental autocorrelations for Type I combs exhibit minima at most 5% above simulated traces. This difference is sufficiently small that it may arise from a combination of effects such as uncertainty or variation in power spectra used for simulations, imperfect compensation of average

54 39 spectral phase, and in some cases contributions from amplified spontaneous emission (ASE). Although we cannot rule out some level of fast phase fluctuations, our Type I combs clearly exhibit significantly lower phase fluctuations and higher coherence than Type II combs. Fig. 3.11(e)-(f) shows another interesting example obtained with 100 µm radius rings (for directly generated spectra, see Figs. 3.5(e)-(f)). Here we pump a mode at nm, which most readily generates stable comb spectra at 460 GHz spacing (twice the FSR). The spectrum after shaping and amplification comprises eight lines as shown in Fig. 3.11(b), and the experimental and simulated autocorrelation traces exhibit comparable contrast in Fig. 3.11(e). Thus, the coherence of this comb appears to be high, similar to Type I combs. However, if the pump wavelength is tuned sufficiently while maintaining lock [62] to the same resonance, the spectrum broadens and intermediate comb lines fill in, resulting in a Type II comb with 230 GHz spacing. Directly generated and post-shaper spectra and the autocorrelation traces are shown in Figs. 3.5(f), 3.11(c) and 3.11(f) for pumping at nm, a large shift compared to the low power linewidth. Although the shapes of the compressed and simulated autocorrelation traces are similar, with a FWHM of 432 fs, the experimental background level is significantly increased, again indicating reduced coherence for Type II combs. Figure 3.12 (c) also shows that odd pulse can be found from TypeII combs also. Here we can easily see the triplet peaks but there are mismatch between background. These examples demonstrate important coherence differences in combs generated from the same resonance in the same device under different pumping conditions. 3.6 Device fabrication We have collaboration for device fabrication with NIST (National Institute of Standard and Testing). Devices are fabricated by Dr. Houxun Miao at NIST. NIST

55 40 Fig (a), (b) and (c) Spectra of the generated comb (corresponding to Fig. 3.5(d), 3.5(e) and 3.5(f), respectively) after the pulse shaper, along with phase applied to the LCM pixels for optimum SHG signals. (d), (e) and (f) Autocorrelation traces corresponding to (a), (b) and (c). Red lines are the compressed pulse after phase correction, dark blue lines are the uncompressed pulse, and black lines are the calculated trace by taking the spectrum shown in (a), (b) and (c) and assuming flat spectral phase. Here Light gray traces show the range of simulated autocorrelation traces.

56 41 Fig (a) Spectrum of the generated comb (Fig. 3.5(f)) after the pulse shaper, along with the phase applied to the LCM pixels of the pulse shaper for optimum SHG. (b) Autocorrelation traces. Here the red line is the compressed pulse, the dark blue line is the uncompressed pulse, and the black line is calculated by taking the spectrum shown in Fig. 3.12(a) and assuming flat spectral phase. (c) The odd pulse: applied the same phase as Fig. 3.12(a), but with an additional π phase added for wavelengths longer than 1554 nm. Red line: experimental autocorrelation; black line: autocorrelation calculated using the spectrum of Fig. 3.12(a), with a π step centered at 1555 nm in the spectral phase. Figs. 3.11(c)(f) are repeated as Figs (a)(b).

57 Fig (a)si 3 N 4 microring. (b)v groove (left rectangular shape) is connected to inverse tapered waveguide. (c)sem of the wave guide (d) SEM of the V groove. 42

58 43 researchers start with a (100) silicon wafer. A 3 µm thick silicon dioxide layer was grown in a thermal oxidation furnace. Then, a silicon nitride layer was deposited using low-pressure chemical vapor deposition (LPCVD). The nitride layer was patterned with electron-beam lithography and etched through using a reactive ion etch (RIE) of CHF 3 /O 2 to form microring resonators and waveguides coupling light into and out of the resonators. The waveguides were linearly tapered down to a width of 100 nm at their end for low loss coupling to/from optical fibers [63]. Another 3 µm oxide layer was deposited using a low temperature oxide (LTO) furnace for the top cladding. The wafer was annealed for 3 h at C in an ambient N 2 environment. A photolithography and liftoff process was used to define a metal mask for V-grooves that provide self-aligned regions where the on-chip waveguide inverse tapers are accessible by optical fibers placed in the V-grooves. After mask definition, the V-grooves were formed by RIE of the unprotected oxide and nitride layers and KOH etching of the silicon. Figure 3.13 shows the images and SEM of the device. The height of the ring resonators is 430 nm and 550 nm for devices corresponding to Figure 3.5, and Figure 3.5(b) to 3.5(f), respectively. The widths of the rings and of the accessing waveguides are 2 µm and 1 µm throughout the paper. The radii indicated within the paper are those at the outermost edge of the devices. The gap between the ring and the waveguide is 700 nm in Fig 3(a), 500 nm in Fig 3.5(b), and 800 nm in Fig 3.5(c)-(f); the difference in ring-waveguide gap will modify the device coupling. 3.7 Experimental procedure Microresonators are pumped with CW powers estimated between 66 mw to 1.4 W coupled into the input guide, in all cases well above the threshold for comb formation. Line-by-line pulse shaping is implemented using a fiber-coupled Fourier-transform

59 44 pulse shaper that incorporates a pixel liquid crystal modulator (LCM) array to independently control both the intensity and phase of each spectral line. The output waveform from the pulse shaper is fed to an intensity autocorrelation setup through an EDFA. The path from the output of the microring chip to the autocorrelator comprises 18 m of standard single mode fiber (SMF). The thickness of the BBO crystal used for SHG is 0.6 mm, corresponding to an estimated 1-dB phase matching bandwidth of 200 nm, well beyond the bandwidth of the combs investigated here. Briefly, the phase is corrected by adjusting the phase of one comb line at a time to maximize the SHG signal from the autocorrelation measurement at zero delay. To optimize the SHG signal, the phase of the new frequency component is varied from 0 to 2π in steps of π/12. Once the SHG is optimized, the pulses are compressed close to the bandwidth limit, and the opposite of the phase applied on the pulse shaper gives an estimate of the original spectral phase after the comb has propagated to the autocorrelator. 3.8 Simulation Here, we briefly discuss the effect of variations of the phase of each of the comb lines on the intensity autocorrelation. Simulations are performed by taking the spectrum measured with an optical spectrum analyzer (OSA), assuming that the spectral phase is flat, and then applying an uncorrelated random phase variation to each of the comb lines. The intensity autocorrelation is then calculated. This is repeated for different realizations of the phase variations, while keeping the same phase variation statistics. Then the results are averaged to obtain the autocorrelation trace in the presence

60 45 of time varying spectral phases that are averaged in the experimental measurement procedure. The temporal intensity I i (t) for the i th realization is given by: I i (t) = n pn exp φ ni exp jn ωt 2 (3.3) where p n is the power of the n th comb line, as obtained from the spectrum, ω is the comb spacing in angular frequency unit, and φ ni represents the random phase applied to the n th comb line in the i th realization. The φ ni are uniformly distributed in the range 0 to φ and are mutually uncorrelated. The intensity autocorrelation for the i th realization, G 2i, is given by: G 2i (τ) = I i (t)i i (t τ)dt (3.4) The G 2i are not normalized since different realizations of intensity waveforms with different peak to average power ratios will contribute differently to the autocorrelation signals. The simulated autocorrelation is obtained by averaging N realizations as, G 2 (τ) = N i=1 G 2i(τ) N i=1 G 2i(0) (3.5) We show simulations based on the comb spectrum shown in Fig 3.11(c). The are assumed to be uniformly distributed between 0 and a maximum phase variation φ. Simulations are performed for φ = 0, 0.2π, 0.4π, 0.6π, 0.8π, and π. For each value of φ, we average N=2000 realizations of the unnormalized autocorrelations. Fig shows the averaged autocorrelation traces. The backgrounds of the autocorrelation traces clearly increase with increased φ. However, the shape of the autocorrelation is not very sensitive to φ. The background level for φ = 0.8π matches that of the experimental autocorrelation trace of Fig. 3.11(f). Although this gives a rough estimate of the amplitude of the phase fluctuations for the experiments of Figs. 3.11(c) and 3.11(f), we note that this estimate is not necessarily precise since the form of the phase fluctuation statistics is not known. For these simulations we postulated phase

61 46 Fig Simulated intensity autocorrelation traces in which uncorrelated random spectral phases are uniformly distributed in the range 0 to φ, for various values of φ. The experimental autocorrelation trace from Fig. 3.11(f) is also plotted (black line). fluctuations that are uniformly distributed and uncorrelated, with the same statistics for all the lines, but there is no reason to believe this particular assumption holds in the experiments. To provide some further insights, in Fig. 3.15, we show four examples of the intensity profiles obtained with φ = 0.8π. These traces are normalized to the peak intensity of the zero phase fluctuation trace. The four intensity profiles are selected for: (a) peak intensity below average, (b) highest peak intensity, (c) lowest peak intensity, and (d) approximately average peak intensity, relative to the 2000 realizations for φ = 0.8π. Although the intensity remains periodic in time and in all cases some degree of intensity peaking is maintained, we clearly see that the instantaneous intensity waveform is strongly affected by uncorrelated phase fluctuations. Since the integrated intensity remains constant, those intensity realizations with lower peak intensity are accompanied by higher energy between peaks, which contributes to the increased background level of the autocorrelation traces.

62 Fig Selected simulated intensity profiles with uncorrelated random spectral phases that are uniformly distributed in the range 0 to φ = 0.8π. These plots are normalized to the peak intensity calculated for the case of 0 phase fluctuations. 47

63 Conclusion In summary, we have demonstrated line-by-line pulse shaping on frequency combs generated from silicon nitride microring resonators. Combs formed via distinct routes (Types I and II in the text) represent different time domain behaviors corresponding to coherent and partially coherent properties. For Type I combs, nearly bandwidthlimited optical pulses were achieved after spectral phase correction, and a simple example of arbitrary waveform generation was presented. For type II combs, compressed pulse trains were accompanied by significant autocorrelation background, signifying larger spectral phase fluctuations. The ability to controllably compress and reshape combs generated through nonlinear wave mixing in microresonators provides new evidence of phase coherence (or partial coherence) across the spectrum. Furthermore, in future investigations the ability to extract the phase of individual lines may furnish clues into the physics of the comb generation process

64 49 4. TIME DOMAIN COHERENCE STUDY OF SILICON NITRIDE MICRORESONATOR FREQUENCY COMBS 4.1 Introduction The different types of comb formation are studied theoretically and experimentally [47, 50 52]. However, the physics behind the comb generation is not yet fully understood. In previous chapter, we studied the time domain properties of microresonator combs and revealed two different paths of comb formation that lead to strikingly different time-domain behaviors [28]. Combs formed as a cascade of sidebands spaced by a single free spectral range (FSR) that spread from the pump (which were called Type I combs) exhibit high coherence. However, combs where the initial sidebands are spaced by multiple FSRs that then fill in to give combs with single FSR (which were called Type II combs) show partial coherence. As reported in this work and also [28] autocorrelation data for combs exhibiting multi-fsr spacing show good compressibility and high coherence. By slightly tuning the pump frequency, we cause the missing lines to fill in to give a comb at single-fsr spacing - a Type II comb. Now however the comb shows degraded compressibility and reduced coherence. Apparently motivated by our findings in [28], the Kippenberg group has recently published a paper in which they use RF beating measurements to characterize Type II combs. Their data provide evidence that individual comb lines may exhibit spectral substructure too fine to be resolved in normal OSA measurements, again consistent with the simple picture of Type II comb formation. Here we study the properties of Type II combs, by investigating the time domain behaviors of a few subfamilies of 0 This work is published in [64]

65 50 frequency lines selected by a pulse shaper. We observe different coherence properties for different groups of comb lines. Our recent time domain experiments result in the new observation, not seen in the previous studies, that some sub families combs exhibit markedly high coherence while whole family shows reduced coherence. Figure 4.1 provides a schematic view of routes to comb generation. Figure 4.1(a) depicts the Type I comb generation process, in which initial comb lines are generated at ± 1FSR from the pump. Subsequent lines generated via cascaded four wave mixing spread out from the center. Energy conservation ensures that the new lines are exactly evenly spaced from the pump. Hence, this process is expected to result in a high degree of coherence. Here and throughout this thesis, we use the term FSR to refer to the average FSR for the series of high Q modes studied in the vicinity of the pump frequency. It should be understood that the frequency difference between adjacent modes, or FSR, varies slightly with frequency due to group velocity dispersion. Figure 4.1(b) shows the case where comb lines are initially generated at ±N FSRs from the pump, where N is an integer greater than one (N=3 for the example shown). Such behavior has been reported frequently in the literature. This process is again expected to produce equal frequency spacings, which should result in high coherence. Our data published in [28] demonstrate that both the process of Fig. 4.1(a) and the process of Fig. 4.1(b) admit high quality pulse compression, providing evidence of stable spectral phase and good coherence. By varying the pump laser, e.g., tuning it further into resonance, additional spectral lines may be observed to fill in between those of Fig. 4.1(b), resulting in a Type II comb with nominally single FSR spacing. In the case illustrated in Fig. 4.1(c), each of the lines from Fig. 4.1(b) has spawned additional lines at ±1 FSR through an independent four-wave mixing process. Although the lines within any one of the triplets resulting from this last process are expected to be equally spaced, there is nothing to guarantee that such spacings are exact submultiples

66 51 of the original multiple-fsr comb spacing. In fact, due to group velocity dispersion, it is very unlikely that all the new lines will be spaced precisely evenly in frequency. As a result of such an imperfect frequency-division process, the relative phases between certain groups of generated lines will vary with time. The time domain waveform, which arises from the interference of the generated optical frequency components, will therefore vary on a time scale set by the non uniformity of the frequency spacings. In this sense we may say that the coherence is compromised. One consequence of a process such as that illustrated in Fig. 4.1(c) would be that different groups of lines may exhibit different degrees of coherence. For example, the initial comb lines spaced by multiple FSRs, e.g., at frequencies { 6, 3, 0, 3, 6 } (relative to the pump in FSR units) in Fig. 4.1(b), are coupled and should therefore have equal frequency spacing and high mutual coherence. Likewise, individual triplets of lines, shown in Fig. 4.1(c), e.g., { 1, 0, 1}, which are spawned from a single line in the previous step, are coupled and may also exhibit relatively high mutual coherence. In our experiments we test this hypothesis by using a pulse shaper to select such groups of lines out of a Type II comb. Time domain experiments confirm good compressibility and coherence. In additional experiments a pulse shaper is used to select other groups of lines for which direct coupling is not expected at the early stage of comb formation depicted in Fig In such cases we observe that compressibility and coherence are degraded. With further evolution beyond that sketched, the various frequency triplets of Fig. 4.1(c) may each spawn additional lines through cascaded four-wave mixing, which will then approximately overlap. However, because of the imperfect frequency division, the overlap between newly generated lines will not be exact. RF beating measurements have recently been used to characterize the evolution of such Type II combs [47]. The beating data provide evidence that individual comb lines may exhibit spectral substructure too fine to be resolved in normal optical

67 52 Fig Possible routes to comb formation. The optical frequency axis is portrayed in free spectral range (FSR) units. Arrows are drawn in an attempt to represent the approximate order in which new comb lines are generated; no attempt is made to indicate all the couplings involved in the four wave mixing process. (a) Case where initial comb lines are spaced by one FSR from the pump line, with subsequent comb lines, generated through cascaded four wave mixing, spreading out from the center. (b) Case where initial comb lines are spaced from the pump line by N FSRs, where N>1 is an integer. Here N=3 is assumed. (c) When the pump laser is tuned closer into resonance, additional lines are observed to fill in, resulting in spectral lines spaced by nominally 1 FSR.

68 53 spectrum analyzer measurements, consistent with the picture suggested here. Such spectral substructure leads to increased noise if the now roughly, but not exactly, overlapping frequency components fail to lock together. Increased RF noise in the Type II regime was also reported in [52](L 2 regime in their notation). In [52] further tuning of the pump into the resonance led to a new regime (L 3 in their notation) characterized by substantial narrowing of the RF spectrum, with improved noise performance. Reduction of the RF noise with further tuning into resonance was also reported in [43, 47, 48]. The experiments presented in here focus on the Type II regime and result in the new observation, not seen in previous studies, that some subgroups of comb lines retain mutual coherence markedly higher than that of the overall partially coherent Type II comb. Such coherence behavior contains structure that bears on the early stages of the comb generation process. 4.2 Si 3 N 4 ring and experimental setup We use a silicon nitride ring resonator with 100 µm outer radius, 2 µm width and 550 nm thickness for the frequency comb generation. Light is coupled into/out of the resonator via an on-chip waveguide with 1 µm width and 800 nm ring-waveguide gap. The two ends of the waveguide are inversely tapered to 100 nm for low loss waveguide-fiber coupling (1.5 db per facet with lensed fiber). Our experiments use a silicon nitride ring resonator with 100 µm outer radius, 2 µm waveguide width and 550 nm waveguide thickness for the frequency comb generation. The loaded Q of the resonator is and the normalized transmission at resonance is 20%. The average FSR for the series of high Q modes is measured to be 1.85 nm ( 231 GHz at 1550 nm center wavelength). Strong CW pumping light (estimated to be 27.6 dbm into the accessing waveguide) is launched into an optical mode at around nm. The generated frequency

69 54 comb is sent to a line-by-line pulse shaper, which both assists in spectral phase characterization and enables pulse compression as shown in Fig. 3.4 [28]. By slowly tuning the wavelength of the pump light from the blue to the red side, we first observed an optical frequency comb with spectral lines spaced by 3 FSRs; then the spectral lines in between fill in to form a comb with one FSR spacing. Figure 4.2 shows the spectrum of the 3 FSR spacing comb after equalization by the pulse shaper. Figure 4.2b shows the autocorrelation traces before (blue) and after (red) phase correction together with the calculated autocorrelation trace (black) for the spectrum shown in Fig 4.2a assuming flat spectral phase. The measured autocorrelation trace after phase correction is in good agreement with the calculation, indicating high coherence of the comb. Fig 4.2c and 4.2d show the spectrum and the autocorrelation traces of the corresponding 1 FSR comb (after slowly tuning the laser wavelength to the red side). The significant difference of the measured autocorrelation trace from the calculation indicates partial coherence for this Type II comb. 4.3 Results To better understand the partial coherence properties of a Type II comb, we use a pulse shaper to first filter out 3 subfamilies of comb lines from the spectrum shown in Fig. 4.2c, with 3 FSR comb spacing each, while keeping the initial phase profile the same as in the previous phase correction experiment shown in Fig. 4.2d. These selected spectra and corresponding autocorrelation traces are shown in Fig 4.3. Fig. 4.3(a) shows the spectrum resulting when every third comb line is selected, including the pump. This leaves lines { 6, 3, 0, 3, 6 }, which is the same set of comb lines present in the original multiple FSR spectrum of Fig. 4.2(a). The autocorrelation data are similar to those of Fig. 4.2(b). Without phase compensation the autocorrelation is modulated only weakly; phase compensation results in strong compression. As before,

70 55 Fig a) Spectrum of the generated 3 FSR spacing comb after the pulse shaper. (b) Autocorrelation traces corresponding to (a). (c) Spectrum of the generated 1 FSR spacing comb after the pulse shaper. Here we tune the CW laser 53 pm towards the red side than that of (a). (d) Autocorrelation traces corresponding to (c).

71 56 Fig Spectra and autocorrelation traces for 3 subfamilies of comb lines with 3 FSR spacing selected from the spectrum shown in Fig. 4.2(c). Blue and red traces are experimental traces before and after phase compensation respectively. Black traces are calculated by taking the OSA spectrums and assuming flat spectral phase. an autocorrelation is also calculated for comparison by taking the measured spectrum and assuming flat spectral phase. The very close agreement between experimental and calculated autocorrelations, including on-off contrast, shows that high coherence is maintained for this subfamily of lines. Figures 4.3(c) and 4(d) show the results when a group consisting of every third line is selected, but this time shifted from the pump. In particular, the pulse shaper is programmed to pass lines { 5, 2, 1, 4 } (frequencies relative to the pump in FSR units). These lines are not directly coupled in the early stages of comb formation outlined in Figs. 1(b)-(c). Figures 4.3(e) and (f) show the results of another family with lines { 4, 1, 2, 5 }. Now there is significant difference

72 57 between experimental and calculated (again assuming flat phase) autocorrelations. For the data shown in Figs. 4.3(e-f), the spectrum is relatively smooth. Therefore the autocorrelation calculated for full coherence and flat phase has high on-off contrast. In this case the loss of contrast in the experiment is seen very prominently. Phase compensation provides only weak compression, with the experimental autocorrelation minimum falling only to 20 % of the peak in Fig. 4.3(f). Clearly, the coherence is badly degraded. For the data of Figs. 4.3(c-d), the spectrum is uneven. As a result the calculated autocorrelation for the case of full coherence already has high background and low on-off contrast. Although additional loss of contrast is evident in the experiment, indicating reduced coherence, the appearance is less dramatic. The loss of mutual coherence for this set of lines will be supported with further data in Fig. 4.6 below. Similar results are obtained in another experiment in which the pulse shaper is programmed to pass every second line. Data obtained for the set of lines including the pump{ 6, 4, 2, 0, 2, 4 } are shown in Figs. 4.4 (a) and (b); similar data are shown in Figs. 4.4(c) and (d) are obtained for the complementary set of alternating comb lines. Again poor autocorrelation contrast is observed, as expected since a majority of the selected lines are not directly coupled in the early stages of the presented model of comb formation. 4.4 Visibility curves We further probe the coherence within the comb in experiments in which sets comprising only three spectral lines are selected. For two spectral lines of fixed relative power, the intensity autocorrelation is independent of the relative phase. Therefore, three is the minimum number of lines which show sensitivity to spectral phase and its variations. Following a procedure similar to that reported in [52], the pulse shaper is used to vary the relative phase φ of the longest wavelength line, with the phases

73 58 Fig Spectra and autocorrelation traces for 2 subfamilies of comb lines with 2 FSR spacing selected from the spectrum shown in Fig. 4.2(c). Blue and red traces are experimental traces before and after phase compensation respectively. Black traces are calculated by taking the OSA spectrums and assuming flat spectral phase.

74 59 Fig Autocorrelation traces for 3 line experiments for different φ for lines { 3, 0, 3}, for which high coherence is observed. Here colored lines are the experimental traces and black lines are the simulated traces. of the other two lines arbitrarily set to zero. Figure 4.5 shows the evolution of the autocorrelation traces with φ when the pulse shaper selects lines { 3, 0, 3}. These are a subset of the lines selected for the data of Figs. 4.3 (a) and (b) for which high coherence was observed. The traces vary substantially as the relative phase is changed, evolving from a single strong peak for φ = 0 spaced by the autocorrelation period T to a pair of weak peaks spaced by T/2 for φ = π. Here the autocorrelation period T 1.43 ps is the inverse of the 700 GHz frequency separation between selected comb lines. When φ is increased to 2π, the autocorrelation recovers to the same form as φ = 0. The experimental traces (colored lines) are in close agreement with those calculated (black lines) based on the measured spectrum and the programmed phases. The close correspondence between

75 60 Fig Autocorrelation traces for 3 line experiments for different φ for lines { 2, 1, 4}, for which low coherence is observed. Here colored lines are the experimental traces and black lines are the simulated traces. the traces shows that the phase fluctuations are small and the coherence among the selected lines is high. Quite different results are obtained for the triplet of lines { 2, 1, 4}, which is selected from the set of lines of Fig. 4.3(c) which showed degraded coherence. As shown in Fig. 4.6, the autocorrelation traces show only minor changes as φ is varied. This lack of dependence on the relative phase demonstrates that the coherence among this triplet of lines, which are not directly coupled in the early stages of our model of comb formation, is very weak. Similar results Fig. 4.7 showing loss of coherence are observed when three lines are selected from the spectrum of Fig. 4.3(e).

76 Fig Autocorrelation traces for 3 line experiments for different φ for lines { 7, 4, 1}, for which low coherence is observed. Here colored lines are the experimental traces and black lines are the simulated traces. 61

77 62 Another way to view the results of such experiments is through the visibility curves V ( φ), as in [52]: V ( φ) = p(τ p) p(τ p + T/2) p(τ p ) + p(τ p + T/2) (4.1) where p(τ p ) is the intensity autocorrelation peak, τ p is the delay at which the peak occurs. p(τ p + T/2) is the value of the intensity autocorrelation half way between the peaks. Note that because the autocorrelation is periodic for data sets such as those of Figs. 4.5 and 4.6, we have three equivalent measurement points representing the autocorrelation peaks [p(τ p ) and p(τ p ± T )] and two equivalent measurement points [p(τ p ± T/2)] representing the autocorrelation value midway between the peaks. In order to extract values for V from the data, for each autocorrelation trace we average the equivalent points representing p(τ p ) and p(τ p ± T/2), respectively, then plug into the equation given above. We estimate the statistical uncertainty by evaluating V using the various pairs of individual (not averaged) measurement points representing the autocorrelation at and midway between its peaks. Another means to assess the uncertainty is to compare the obtained values for V (0) and V (2π), since the visibility should be unchanged with 2π phase shift. For six of the seven visibility curves reported below, the values for V (0) and V (2π) agree to within the estimated uncertainty. Experimental visibility curves are compared with ideal theoretical curves which are computed based on the measured optical power spectrum and assuming full coherence. Multiple traces of the optical spectra are recorded simultaneously with each autocorrelation measurement; this permits estimation of statistical uncertainty in the scale of the theoretical curves due to small variations in the measured spectra. Uncertainties quoted below represent one standard deviation. Figure 4.8(a) shows visibility curves for triplets of lines separated by three FSRs. The visibility of the { 3, 0, 3} triplet (red line), which includes the pump, exhibits strong dependence on φ, with minimum visibility equal to 8% ± 1% of the max-

78 63 Fig Visibility traces of (a) three subfamilies of 3 FSRs, (b) two subfamilies of 2 FSRs, and (c) two subfamilies of 1 FSR. Here in the visibility curves, red, green and black lines are the experimental data; blue lines are ideal theoretical curves calculated assuming full coherence based on the power spectra corresponding to the respective red line visibility curves. Numbers in curly braces indicate the 3 lines that are used in the experiments. Error bars (shown for representative curves) and shaded areas represent the mean ± one standard deviation.

79 64 imum visibility. The data are close to the ideal theoretical curve (blue line). In contrast, the visibility curves for triplets shifted away from the pump, { 2, 1, 4} and { 7, 4, 1}, show only weak dependence on φ, with minimum visibility equal to 66% ± 6% and 77% ± 7% of the maximum visibility, respectively. For comparison, the ratio of minimum to maximum visibility that would be expected ideally (with full coherence) are 9% ± 0.4% and 24% ± 1%, respectively. (The difference in ideal visibility ratios is explained by differences in the relative intensities of the selected lines.) The strong reduction in visibility clearly signifies degraded coherence. Figure 4.8(b) shows visibility curves for triplets { 4, 2, 0} and { 3, 1, 1}, each of which is spaced nominally by 2 FSRs. Again only weak variation in visibility, hence low coherence, is observed. These data consistently show low coherence for line triplets which lack direct coupling in the early stages of our model of comb formation. Figure 4.8(c) shows visibility curves for triplets spaced nominally by a single FSR. For the { 1, 0, 1} triplet, the visibility curve (red) exhibits large variation with φ, with minimum visibility equal to 13% ± 13% of the maximum visibility. This provides evidence that relatively good coherence remains, consistent with the coupling within this triplet of lines suggested by our model, Fig. 4.1(c). As a counter example, we next selected the triplet { 2, 1, 0}, comprising the pump and two lines to one side of the pump. Since the -2 line would not have direct coupling to the -1 and 0 lines in the second step of our hypothesized comb generation model, degraded coherence is predicted. This is confirmed by the corresponding (black) visibility curve in Fig. 4.8(c), for which the variation is significantly reduced with minimum visibility equal to 58% ± 5% of the maximum visibility. Our data give qualitative support to the simple model suggested by Fig. 4.1(c), namely, groups of lines that are directly coupled should have high coherence, while groups of lines that are not directly coupled should lack coherence. However, at a

80 65 quantitative level, the correspondence is not complete. For example, the peak visibility data for the { 1, 0, 1} triplet in Fig. 4.8(c) is somewhat lower than the theoretical trace, which suggests the coherence may be less than 100 %. Similarly, although variation of the visibility for the { 2, 1, 0} triplet in Fig. 4.8(c) is clearly suppressed compared to the { 1, 0, 1} case, the suppression is incomplete: some variation remains. This suggests that although the coherence is reduced, it does not reach zero. An explanation for these observations may involve further cascaded four-wave mixing beyond the early stage of comb formation portrayed in Fig. 4.1(c), which will cause the individual subcombs to spread until they overlap, as discussed in [47] for both crystalline magnesium fluoride and planar silicon nitride microresonators. Figure 4.9 shows a sketch illustrating this process, in this case with the initial lines separated by 6 FSRs. The important point is that in the final stage illustrated, any region of the comb spectrum consists of distinct overlapped subcombs (distinct in the sense that either the offset frequencies, the line spacings, or both are different). Because the pulse shaper does not resolve the distinct subcombs, the overall coherence of selected comb lines depends on the simultaneous contributions of different subcombs. Simulations that model the generated frequencies as coherent within individual subcombs but incoherent across distinct subcombs are able to approximately reproduce our observations in the visibility data, provided that the number of lines in the subcombs and their relative intensities are appropriately adjusted. As a final point, we comment on the relationship between our experiments and those presented in [47]. Our measurements provide information mainly on which sets of lines stay in phase with each other and which do not. They do not directly tell us whether phase variations (when significant) arise because different subsets of lines have different offset frequencies, because different subsets of lines have different repetition frequencies, or because of other unspecified reasons. In this sense we

81 66 Fig Proposed model for type II comb formation. (a) First: generation of a cascade of sidebands spaced by N FSRs (Nδω) from the pump. Here N=6 is illustrated. (b)-(c) The 2nd event is an independent four-wave mixing process, which creates new sidebands spaced by a different amount,±nδω (n=1,2 or 3...for different lines), from each of the lines in the previous step. Due to dispersion, it is very unlikely that the new frequency spacings will be exact submultiples of the original N FSR spacing; i.e.,δω δω.

82 67 get different information than [47], which beats the comb generated by the microresonator with a self-referenced comb from a mode-locked laser to precisely measure the individual optical frequencies. On the other hand, our measurements directly probe optical coherence, which the measurements in [47] do not access. 4.5 Conclusion In conclusion, we have used an optical pulse shaper to probe the coherence of a frequency comb generated via cascaded four-wave mixing in a silicon nitride microresonator. Our measurements reveal a striking variation in the degree of mutual coherence exhibited for different groups of lines selected out of the full comb. The structure observed in the mutual coherence provides evidence consistent with a simple model of partially coherent comb formation.

83 68 5. FUTURE WORK 5.1 Intoduction In this chapter, several experiments which are very interesting and will give us more insight about comb formations are discussed. We discussed current limitation and also ways to solve the limitations. 5.2 Future work SHG Frequency-resolved optical gating In Kerr combs, some of the lines have very low power. We need to find an measurement technique which can detect phases from very low power. The technique discussed in chapter 2 can be used. As an second measurement technique, we are planning to use SHG frequency-resolved optical gating (FROG). By using aperiodically poled lithium niobate (A-PPLN) waveguides as the nonlinear medium, our group demonstrated ultra low-power multishot SHG FROG in the telecommunication band with a measurement sensitivity of mw 2, an 8 orders of magnitude improvement over SHG FROG using bulk crystals and 5 orders of magnitude better than previously reported for any FROG measurement modality [65]. Here we will use a fiber-pigtailed A-PPLN waveguide with 50 nm phase-matching curve centered at 1542 nm at room temperature. This will cover the combs spectrum after the pulse shaper and EDFA. Figure 5.1 shows the scheme of the polarization insensitive FROG setup [65]. The polarization of the signal pulse from comb is scrambled with a wide band fiber pigtailed polarization scrambler (General Photonics Corporation, PCD-

84 69 Fig Polarization insensitive ultra low-power SHG FROG setup [65]. 104), with more than 100 nm operating range centered at 1550 nm, and 700 KHz scrambling frequency. The scrambled pulses are then launched into a Michelson interferometer to produce pulse pairs with various delays. One of the interferometer arms is dithered over a few optical cycles at a rate of 160 Hz to wash out the interference fringes. The pulse pairs are coupled into the A-PPLN waveguide with a fiber-pigtailed collimator to produce SHG signals. The SHG spectrum for each delay is recorded by a spectrometer and an intensified CCD camera which yields the raw FROG data. To get a background-free FROG trace, a spectrum taken at a large delay is subtracted from the raw data. The spectrum of the pulses is recorded separately by an OSA for frequency marginal correction. We use commercial software (Femtosoft FROG) to completely retrieve the intensity and phase information of the pulses.

85 Comb improvement and dispersion measurement We have the micro resonator from NIST which has 10 times higher quality factor than that of Cornell micro resonator as seen in table 3.1. But we have narrower bandwidth than that of them. The reason may be due to the dispersion of the waveguide as discussed in section 4.2. We have done some simulation with the device dimensions for waveguide dispersion. The simulation is done in MPB [66]. The schematic model of device is shown in Fig 5.2. We have used fixed n equal to 1.42 and 2.05 for SiO 2 and Si 3 N 4 respectively unless otherwise stated. Here the cladding region is SiO 2 around 3µm. We have seen that the dispersion is quite high for the device as shown in Fig 5.3. Here we have varied n also as we guess n to be 2.05 but it may varies on fabrication process. As n is depend on fabrication process, we need to calculate dispersion experimentally. Also in the simulation, we assumed the material dispersion to be zero. But that may be not true. To verify both of these we are planning to do dispersion experiment. For dispersion calculation, we ( also one colleague Jian Wang from Prof. Qi) will use optical parametric oscillator (OPO) which has wavelength coverage from 1.1 to 2.6 µm. It has 150 mw power. We will use Fourier-transform spectral interferometry (FTSI) [67]. Schematic diagram of the experimental setup is shown in Fig 5.4. A 130 femtosecond laser pulse train from a tunable OPO is split such that one part is sent to the waveguide and the other travels through a reference arm. The polarization is optimized to excite the low-loss TE-like mode of the waveguide. Output of the waveguide is combined with the reference arm in a coupler. When the output pulses are measured with an OSA one observes a wavelength-dependent modulation of the optical spectrum, or a spectral interferogram. The frequency of the modulation of the spectral interferogram is proportional to the time delay between the two pulses. By extracting the variation of the time delay as a function of the center wavelength of the pulses, one obtains the group index of refraction of the entire

86 Fig The model used for simulation. Here h,b and w are the height, base of the Si 3 N 4 and cladding layer(sio 2 ) dimension respectively. 71

87 Fig Simulation results of the present device. Here h,b and θ are the height, base and angle from the vertical direction of the Si 3 N 4 respectively. 72

88 73 Fig Schematic diagram of the experimental setup for dispersion calculation. Here OPO: optical parametric osillator; DUT: device under test. system. In order to find the group index solely of the waveguides, the measurements are repeated with the waveguide removed from the system. For now, we also try to calculate optimum device performance by simulation. From, Fig 5.5, we see that if we have device with θ=2.5 or 3 and b=1.5 or 2µm, then h= nm will be good choice as in that region dispersion will be zero. Our 2nd generation devices have these dimensions. 5.3 RF beating experiment Clearly there is much more left to be investigated about TypeII comb formation. Different lines may act differently. We believe such investigations will enhance our understanding of comb formation, hopefully providing insight that will aid efforts to enforce coherence. Frequency domain studies will include measurement of RF spectra obtained by beating comb lines with reference lasers, including a commercial, selfreferenced, mode-locked fiber laser comb that we have recently ordered. Schematic diagram of this experiment is shown in Fig. 5.6(a). Different sideband orders generated from adjacent comb lines can overlap, again leading to RF beat signals as shown in Fig 5.6(b) diagnostic of comb uniformity and noise.

89 Fig Simulation results with various dimensions to find optimum device dimension for next generation device. Here h,b and θ are the height, base and angle from the vertical direction of the Si 3 N 4 respectively. 74

90 Fig (a) Schematic diagram for RF beating experiment. (b) expected results: One line will be beat with tunable laser and multiple lines will be seen in RF spectrum analyzer. 75

91 Pulse generation from Kerr combs Recently we have observed that with sufficient care, at least partially reproducible spectral phase profiles may be observed in successive lab sessions with the pump laser turned off in between as shown in Figs 5.7 and 5.8. Fig. 5.7 shows the spectrum after equalization by the pulse shaper, the applied spectral phase, and the corresponding autocorrelation (AC) traces. Here we first get comb with 3 FSRs spacing with high coherent temporal behavior. In Fig 5.7(b) red line is the AC trace when we apply red dot phases of Fig 5.7(a). Black line is the calculated AC considering spectrum shown in Fig 5.7(a) and assuming spectrum flat spectral phases. Blue line is the AC trace without pulse compression. Green line is the experimental AC trace when we apply green dot phases of Fig 5.7(a). Here we did the phase compensation 24 hrs ago with green dot phases. Then we turn off the laser. On next day, we turn on laser and with almost same conditions of the previous day, we generate the comb. Then redo the pulse compression experiment and get red line curve. Then applying the previous day phase file we also get pulse compression. Both of them matches well with calculated AC traces and also shows clear pulse compression. Fig 5.8 shows the spectrum for the same devices. After tuning a CW wavelength we get 1 FSR spacing comb from 3 FSRs comb like Fig 5.7 with partial coherent temporal behavior. We normally called this as Type II comb. Here the color sequences as those of Fig 5.7. The red and green traces matches well with each other but show difference with the calculated trace. Further researches are needed to know whether pulses produced within the microresonators themselves. Also why two different phase profile have almost same pulse shape as shown in Figs 5.7 and 5.8.

92 77 Fig High coherent temporal case: (a) Spectrum of the generated comb after the pulse shaper with applied phases. (b) Autocorrelation traces. Here red line is the experimental AC trace when we apply red dot phases of Fig 5.7(a). Black line is the calculated AC considering spectrum shown in Fig 5.7(a) and assuming spectrum flat spectral phases. Blue line is the experimental AC trace without pulse compression. Green line is the experimental AC trace when we apply green dot phases of Fig 5.7(a).

93 Fig Partial coherent temporal case: (a) Spectrum of the generated comb after the pulse shaper with applied phases. (b) Autocorrelation traces. Here red line is the experimental AC trace when we apply red dot phases of Fig 5.8(a). Black line is the calculated AC considering spectrum shown in Fig 5.8(a) and assuming spectrum flat spectral phases. Blue line is the experimental AC trace without pulse compression. Green line is the experimental AC trace when we apply green dot phases of Fig 5.8(a). 78

94 On-chip pulsed light source In my current research, I used free space pulse shaper. But if we can make onchip OAWG, we also can have pulse shaper on chip. So combing Kerr comb chips and pulse shaper chip will be a breakthrough. An integrated 8-channel optical spectral shaper is demonstrated by cascading eight silicon microring add-drop filters on a silicon-on-insulator platform [68, 69]. Each microring is side coupled to a Mach- Zehnder arm, which is embedded in the through port waveguide. Compact metal heaters are fabricated on top of the microrings and the Mach-Zehnder arms for thermal control purpose. Thermal tuning changes the resonance wavelength and power spectrum extinction ratio of each microring add-drop filter. It consequently controls the spectral shaper in a programmable fashion. RF waveforms are demonstrated with fundamental frequencies from 10 GHz to 60 GHz. Various types of RF signals, including single frequency waveform, phase shift RF burst, apodized single frequency waveform and chirped burst, have been generated through this chip. Their demonstration may be a starting point for the miniaturization of ultra broad bandwidth microwave photonics and for system-level application of silicon photonics. In the setup introduced above, single mode fiber spool as the stretcher source is required to provide dispersion. This part is hard to be deployed on chip. An advanced design for RFAWG using tunable delay line is investigated [69]. Here an optical pulse is separated into eight pulses by cascaded add-drop microring resonators. Each pulse is delayed by an all-pass microring train. Then eight pulses are recombined together to form the arbitrary waveform. The on-chip pulse pulsed light source will be as Fig 5.9:

95 Fig Schematic diagram for on-chip pulsed light source. 80