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Li P, Li Q, Tang W, Wang W, Zhang W, Little BE, Chu ST, Shore KA, Qin Y, Wang Y. Scalable parallel ultrafast optical random bit generation based on a single chaotic microcomb. LIGHT, SCIENCE & APPLICATIONS 2024; 13:66. [PMID: 38438369 PMCID: PMC10912654 DOI: 10.1038/s41377-024-01411-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/14/2023] [Revised: 02/05/2024] [Accepted: 02/17/2024] [Indexed: 03/06/2024]
Abstract
Random bit generators are critical for information security, cryptography, stochastic modeling, and simulations. Speed and scalability are key challenges faced by current physical random bit generation. Herein, we propose a massively parallel scheme for ultrafast random bit generation towards rates of order 100 terabit per second based on a single micro-ring resonator. A modulation-instability-driven chaotic comb in a micro-ring resonator enables the simultaneous generation of hundreds of independent and unbiased random bit streams. A proof-of-concept experiment demonstrates that using our method, random bit streams beyond 2 terabit per second can be successfully generated with only 7 comb lines. This bit rate can be easily enhanced by further increasing the number of comb lines used. Our approach provides a chip-scale solution to random bit generation for secure communication and high-performance computation, and offers superhigh speed and large scalability.
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Affiliation(s)
- Pu Li
- Institute of Advanced Photonics Technology, School of Information Engineering, Guangdong University of Technology, Guangzhou, 51006, China
- Key Laboratory of Photonic Technology for Integrated Sensing and Communication, Ministry of Education of China, Guangdong University of Technology, Guangzhou, 51006, China
- Guangdong Provincial Key Laboratory of Information Photonics Technology, Guangdong University of Technology, Guangzhou, 51006, China
| | - Qizhi Li
- Key Laboratory of Advanced Transducers and Intelligent Control System, Ministry of Education, Taiyuan University of Technology, Taiyuan, 030024, China
| | - Wenye Tang
- Key Laboratory of Advanced Transducers and Intelligent Control System, Ministry of Education, Taiyuan University of Technology, Taiyuan, 030024, China
| | - Weiqiang Wang
- State Key Laboratory of Transient Optics and Photonics, Xi'an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi'an, 710119, China
| | - Wenfu Zhang
- State Key Laboratory of Transient Optics and Photonics, Xi'an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi'an, 710119, China
| | - Brent E Little
- State Key Laboratory of Transient Optics and Photonics, Xi'an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi'an, 710119, China
| | - Sai Tek Chu
- Department of Physics and Materials Science, City University of Hong Kong, Hong Kong, China
| | - K Alan Shore
- School of Electronic Engineering, Bangor University, Bangor, Wales, LL57 1UT, UK
| | - Yuwen Qin
- Institute of Advanced Photonics Technology, School of Information Engineering, Guangdong University of Technology, Guangzhou, 51006, China
- Key Laboratory of Photonic Technology for Integrated Sensing and Communication, Ministry of Education of China, Guangdong University of Technology, Guangzhou, 51006, China
- Guangdong Provincial Key Laboratory of Information Photonics Technology, Guangdong University of Technology, Guangzhou, 51006, China
| | - Yuncai Wang
- Institute of Advanced Photonics Technology, School of Information Engineering, Guangdong University of Technology, Guangzhou, 51006, China.
- Key Laboratory of Photonic Technology for Integrated Sensing and Communication, Ministry of Education of China, Guangdong University of Technology, Guangzhou, 51006, China.
- Guangdong Provincial Key Laboratory of Information Photonics Technology, Guangdong University of Technology, Guangzhou, 51006, China.
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2
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Zhou H, Geng Y, Cui W, Huang SW, Zhou Q, Qiu K, Wei Wong C. Soliton bursts and deterministic dissipative Kerr soliton generation in auxiliary-assisted microcavities. LIGHT, SCIENCE & APPLICATIONS 2019; 8:50. [PMID: 31149335 PMCID: PMC6538660 DOI: 10.1038/s41377-019-0161-y] [Citation(s) in RCA: 54] [Impact Index Per Article: 10.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/24/2018] [Revised: 05/10/2019] [Accepted: 05/14/2019] [Indexed: 05/14/2023]
Abstract
Dissipative Kerr solitons in resonant frequency combs offer a promising route for ultrafast mode-locking, precision spectroscopy and time-frequency standards. The dynamics for the dissipative soliton generation, however, are intrinsically intertwined with thermal nonlinearities, limiting the soliton generation parameter map and statistical success probabilities of the solitary state. Here, via use of an auxiliary laser heating approach to suppress thermal dragging dynamics in dissipative soliton comb formation, we demonstrate stable Kerr soliton singlet formation and soliton bursts. First, we access a new soliton existence range with an inverse-sloped Kerr soliton evolution-diminishing soliton energy with increasing pump detuning. Second, we achieve deterministic transitions from Turing-like comb patterns directly into the dissipative Kerr soliton singlet pulse bypassing the chaotic states. This is achieved by avoiding subcomb overlaps at lower pump power, with near-identical singlet soliton comb generation over twenty instances. Third, with the red-detuned pump entrance route enabled, we uncover unique spontaneous soliton bursts in the direct formation of low-noise optical frequency combs from continuum background noise. The burst dynamics are due to the rapid entry and mutual attraction of the pump laser into the cavity mode, aided by the auxiliary laser and matching well with our numerical simulations. Enabled by the auxiliary-assisted frequency comb dynamics, we demonstrate an application of automatic soliton comb recovery and long-term stabilization against strong external perturbations. Our findings hold potential to expand the parameter space for ultrafast nonlinear dynamics and precision optical frequency comb stabilization.
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Affiliation(s)
- Heng Zhou
- Key Lab of Optical Fiber Sensing and Communication Networks, University of Electronic Science and Technology of China, 611731 Chengdu, China
| | - Yong Geng
- Key Lab of Optical Fiber Sensing and Communication Networks, University of Electronic Science and Technology of China, 611731 Chengdu, China
| | - Wenwen Cui
- Key Lab of Optical Fiber Sensing and Communication Networks, University of Electronic Science and Technology of China, 611731 Chengdu, China
| | - Shu-Wei Huang
- Fang Lu Mesoscopic Optics and Quantum Electronics Laboratory, University of California, Los Angeles, CA 90095 USA
- Department of Electrical, Computer, and Energy Engineering, University of Colorado, Boulder, CO 80309 USA
| | - Qiang Zhou
- Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, 611731 Chengdu, China
| | - Kun Qiu
- Key Lab of Optical Fiber Sensing and Communication Networks, University of Electronic Science and Technology of China, 611731 Chengdu, China
| | - Chee Wei Wong
- Fang Lu Mesoscopic Optics and Quantum Electronics Laboratory, University of California, Los Angeles, CA 90095 USA
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3
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Liu M, Wang L, Sun Q, Li S, Ge Z, Lu Z, Zeng C, Wang G, Zhang W, Hu X, Zhao W. Influences of high-order dispersion on temporal and spectral properties of microcavity solitons. OPTICS EXPRESS 2018; 26:16477-16487. [PMID: 30119478 DOI: 10.1364/oe.26.016477] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/12/2018] [Accepted: 06/07/2018] [Indexed: 06/08/2023]
Abstract
We theoretically and numerically investigate the effects of high-order dispersion (HOD) on microcavity solitons, both in time and frequency domain with an extended normalized Lugiato-Lefever equation (LLE). The observed temporal drift of bright and dark solitons is shown to originate from high-odd-order dispersion, while the sign determines the direction of soliton movement and the amplitude decides the drift speed. HOD can also be introduced to stabilize the breathing bright and dark cavity solitons. In spectral domain, the nonlinear symmetry breaking is mainly introduced by third-order dispersion, whereas both third- and fourth-order dispersion can introduce dispersive wave accompanied by soliton tail oscillation. This work could give insight for exploring detailed intracavity pulse dynamics and spectral characteristics of Kerr combs influenced by HOD, as well as provide a viable route to delicate control of Kerr comb generation through tailoring the dispersion parameters.
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4
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Matsko AB, Maleki L. Bose-Hubbard hopping due to resonant Rayleigh scattering. OPTICS LETTERS 2017; 42:4764-4767. [PMID: 29140364 DOI: 10.1364/ol.42.004764] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/21/2017] [Accepted: 10/17/2017] [Indexed: 06/07/2023]
Abstract
We show theoretically that dynamic behavior of light confined in the modes of a nonlinear optical ring cavity characterized by resonant Rayleigh scattering can be described using the Bose-Hubbard model. Nonlinear interaction between clockwise and counterclockwise optical modes results in instability and intermode hopping occurring at a rate defined by the frequency separation of the Rayleigh doublet harmonics. Hopping may lead to an instability and breathing behavior of a Kerr frequency comb observed in the cavity.
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5
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Liao P, Bao C, Kordts A, Karpov M, Pfeiffer MHP, Zhang L, Cao Y, Almaiman A, Mohajerin-Ariaei A, Tur M, Fejer MM, Kippenberg TJ, Willner AE. Pump-linewidth-tolerant wavelength multicasting using soliton Kerr frequency combs. OPTICS LETTERS 2017; 42:3177-3180. [PMID: 28809901 DOI: 10.1364/ol.42.003177] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/29/2017] [Accepted: 07/12/2017] [Indexed: 06/07/2023]
Abstract
We experimentally demonstrate pump-linewidth-tolerant wavelength multicasting using microresonator-based soliton Kerr frequency combs. When Kerr comb lines serve as coherent pumps in a periodically poled lithium niobate waveguide, the linewidth of the multicast signal almost remains that of the original signal at different linewidths of Kerr combs, ranging from 100 kHz to 1 MHz. However, in conventional multicasting where free-running (FR) pumps are used, the linewidth of the converted signal significantly increases. Furthermore, the error vector magnitude (EVM) performance demonstrates eight-fold error-free multicasting of 10 Gbaud 16-quadrature amplitude modulation signals, even when the linewidths of the Kerr combs are as broad as 1 MHz (no Kalman filtering algorithm in the receiver). In contrast, the EVM performance of the signal copy is degraded with an FR laser as a dummy pump.
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6
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Bao C, Xuan Y, Jaramillo-Villegas JA, Leaird DE, Qi M, Weiner AM. Direct soliton generation in microresonators. OPTICS LETTERS 2017; 42:2519-2522. [PMID: 28957274 DOI: 10.1364/ol.42.002519] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2017] [Accepted: 05/26/2017] [Indexed: 06/07/2023]
Abstract
We investigate, numerically and experimentally, the effect of thermo-optical (TO) chaos on soliton generation dynamics in microresonators. Numerical simulations that include the thermal dynamics show that the generated solitons can either survive or annihilate when the pump laser is scanned from blue to red and then stop at a fixed wavelength; the outcome is stochastic and is strongly related to the number of solitons generated. The random fluctuations of the cavity resonance occurring under TO chaos are also found to trigger delayed spontaneous soliton generation after the laser scan ends, which could enable soliton excitation with slow laser tuning speed. Stochastic soliton annihilation/survival, as well as delayed spontaneous soliton generation, is observed experimentally in a silicon-nitride microresonator.
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7
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Xue X, Leo F, Xuan Y, Jaramillo-Villegas JA, Wang PH, Leaird DE, Erkintalo M, Qi M, Weiner AM. Second-harmonic-assisted four-wave mixing in chip-based microresonator frequency comb generation. LIGHT, SCIENCE & APPLICATIONS 2017; 6:e16253. [PMID: 30167244 PMCID: PMC6062166 DOI: 10.1038/lsa.2016.253] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/11/2016] [Revised: 11/01/2016] [Accepted: 11/11/2016] [Indexed: 05/31/2023]
Abstract
Simultaneous Kerr comb formation and second-harmonic generation with on-chip microresonators can greatly facilitate comb self-referencing for optical clocks and frequency metrology. Moreover, the presence of both second- and third-order nonlinearities results in complex cavity dynamics that is of high scientific interest but is still far from being well-understood. Here, we demonstrate that the interaction between the fundamental and the second-harmonic waves can provide an entirely new way of phase matching for four-wave mixing in optical microresonators, enabling the generation of optical frequency combs in the normal dispersion regime under conditions where comb creation is ordinarily prohibited. We derive new coupled time-domain mean-field equations and obtain simulation results showing good qualitative agreement with our experimental observations. Our findings provide a novel way of overcoming the dispersion limit for simultaneous Kerr comb formation and second-harmonic generation, which might prove to be especially important in the near-visible to visible range where several atomic transitions commonly used for the stabilization of optical clocks are located and where the large normal material dispersion is likely to dominate.
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Affiliation(s)
- Xiaoxiao Xue
- Department of Electronic Engineering, Tsinghua University, Beijing 100084, China
- School of Electrical and Computer Engineering, Purdue University, 465 Northwestern Avenue, West Lafayette, IN 47907-2035, USA
| | - François Leo
- The Dodd-Walls Centre for Photonic and Quantum Technologies, Department of Physics, The University of Auckland, Auckland 1142, New Zealand
- OPERA-photonics, Université libre de Bruxelles (U.L.B.), 50 Avenue F. D. Roosevelt, CP 194/5, B-1050 Bruxelles, Belgium
| | - Yi Xuan
- School of Electrical and Computer Engineering, Purdue University, 465 Northwestern Avenue, West Lafayette, IN 47907-2035, USA
- Birck Nanotechnology Center, Purdue University, 1205 West State Street, West Lafayette, IN 47907, USA
| | - Jose A Jaramillo-Villegas
- School of Electrical and Computer Engineering, Purdue University, 465 Northwestern Avenue, West Lafayette, IN 47907-2035, USA
- Facultad de Ingenierías, Universidad Tecnológica de Pereira, Pereira RIS 660003, Colombia
| | - Pei-Hsun Wang
- School of Electrical and Computer Engineering, Purdue University, 465 Northwestern Avenue, West Lafayette, IN 47907-2035, USA
| | - Daniel E Leaird
- School of Electrical and Computer Engineering, Purdue University, 465 Northwestern Avenue, West Lafayette, IN 47907-2035, USA
| | - Miro Erkintalo
- The Dodd-Walls Centre for Photonic and Quantum Technologies, Department of Physics, The University of Auckland, Auckland 1142, New Zealand
| | - Minghao Qi
- School of Electrical and Computer Engineering, Purdue University, 465 Northwestern Avenue, West Lafayette, IN 47907-2035, USA
- Birck Nanotechnology Center, Purdue University, 1205 West State Street, West Lafayette, IN 47907, USA
| | - Andrew M Weiner
- School of Electrical and Computer Engineering, Purdue University, 465 Northwestern Avenue, West Lafayette, IN 47907-2035, USA
- Birck Nanotechnology Center, Purdue University, 1205 West State Street, West Lafayette, IN 47907, USA
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Liao P, Bao C, Kordts A, Karpov M, Pfeiffer MHP, Zhang L, Mohajerin-Ariaei A, Cao Y, Almaiman A, Ziyadi M, Wilkinson SR, Tur M, Kippenberg TJ, Willner AE. Dependence of a microresonator Kerr frequency comb on the pump linewidth. OPTICS LETTERS 2017; 42:779-782. [PMID: 28198861 DOI: 10.1364/ol.42.000779] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We experimentally investigate the dependence of Kerr comb generation, comb linewidth, and coherent system performance on the pump linewidth in a microresonator. We find that the generation of the primary comb can have a larger tolerance to the pump linewidth compared with that of the low-phase-noise comb. In addition, the linewidths of the generated combs are almost linearly dependent on the pump linewidth in the primary and low-phase-noise states. Furthermore, the optical signal-to-noise ratio penalty between the pump and generated Kerr combs in a coherent communication system is less than 0.2 dB in both the primary and low-phase-noise states, showing that Kerr frequency combs in these two states can have similar coherent system performance to the pump.
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9
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Bao C, Liao P, Kordts A, Zhang L, Karpov M, Pfeiffer MHP, Cao Y, Yan Y, Almaiman A, Xie G, Mohajerin-Ariaei A, Li L, Ziyadi M, Wilkinson SR, Tur M, Kippenberg TJ, Willner AE. Dual-pump generation of high-coherence primary Kerr combs with multiple sub-lines. OPTICS LETTERS 2017; 42:595-598. [PMID: 28146536 DOI: 10.1364/ol.42.000595] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We experimentally generate high-coherence primary Kerr combs with multiple sub-lines by using dual pumps and demonstrate the application of a primary comb state in multichannel communications. We find that more than 10 primary comb lines can be generated within the spectrum of modulation instability gain in our microring resonator. The generation is also verified by numerical simulations and the measured linewidth confirms the high coherence of the generated primary comb lines. We also demonstrate the high-coherence characteristics in a coherent communication experiment, in which each comb line is encoded with 20 Gbaud quadrature phase-shift-keyed signals.
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10
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Bao C, Liao P, Kordts A, Karpov M, Pfeiffer MHP, Zhang L, Yan Y, Xie G, Cao Y, Almaiman A, Ziyadi M, Li L, Zhao Z, Mohajerin-Ariaei A, Wilkinson SR, Tur M, Fejer MM, Kippenberg TJ, Willner AE. Demonstration of optical multicasting using Kerr frequency comb lines. OPTICS LETTERS 2016; 41:3876-3879. [PMID: 27519112 DOI: 10.1364/ol.41.003876] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We experimentally demonstrate optical multicasting using Kerr frequency combs generated from a Si3N4 microresonator. We obtain Kerr combs in two states with different noise properties by varying the pump wavelength in the resonator and investigate the effect of Kerr combs on multicasting. Seven-fold multicasting of 20 Gbaud quadrature phase-shift-keyed signals and four-fold multicasting of 16-quadrature amplitude modulation signals have been achieved when low-phase-noise combs are input into a periodically poled lithium niobate waveguide. In addition, we find that the wavelength conversion efficiency in the PPLN waveguide for chaotic combs with high noise is similar to that for low-noise combs, while the signal quality of the multicast copy is significantly degraded.
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11
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Renninger WH, Rakich PT. Closed-form solutions and scaling laws for Kerr frequency combs. Sci Rep 2016; 6:24742. [PMID: 27108810 PMCID: PMC4842990 DOI: 10.1038/srep24742] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2015] [Accepted: 04/05/2016] [Indexed: 11/16/2022] Open
Abstract
A single closed-form analytical solution of the driven nonlinear Schrödinger equation is developed, reproducing a large class of the behaviors in Kerr-comb systems, including bright-solitons, dark-solitons, and a large class of periodic wavetrains. From this analytical framework, a Kerr-comb area theorem and a pump-detuning relation are developed, providing new insights into soliton- and wavetrain-based combs along with concrete design guidelines for both. This new area theorem reveals significant deviation from the conventional soliton area theorem, which is crucial to understanding cavity solitons in certain limits. Moreover, these closed-form solutions represent the first step towards an analytical framework for wavetrain formation, and reveal new parameter regimes for enhanced Kerr-comb performance.
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Affiliation(s)
- William H Renninger
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA
| | - Peter T Rakich
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA
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12
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Liang W, Eliyahu D, Ilchenko VS, Savchenkov AA, Matsko AB, Seidel D, Maleki L. High spectral purity Kerr frequency comb radio frequency photonic oscillator. Nat Commun 2015; 6:7957. [PMID: 26260955 PMCID: PMC4918344 DOI: 10.1038/ncomms8957] [Citation(s) in RCA: 125] [Impact Index Per Article: 13.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/05/2014] [Accepted: 07/01/2015] [Indexed: 12/02/2022] Open
Abstract
Femtosecond laser-based generation of radio frequency signals has produced astonishing improvements in achievable spectral purity, one of the basic features characterizing the performance of an radio frequency oscillator. Kerr frequency combs hold promise for transforming these lab-scale oscillators to chip-scale level. In this work we demonstrate a miniature 10 GHz radio frequency photonic oscillator characterized with phase noise better than -60 dBc Hz(-1) at 10 Hz, -90 dBc Hz(-1) at 100 Hz and -170 dBc Hz(-1) at 10 MHz. The frequency stability of this device, as represented by Allan deviation measurements, is at the level of 10(-10) at 1-100 s integration time-orders of magnitude better than existing radio frequency photonic devices of similar size, weight and power consumption.
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Affiliation(s)
- W. Liang
- OEwaves Inc., 465 North Halstead Street, Suite 140, Pasadena, California 91107, USA
| | - D. Eliyahu
- OEwaves Inc., 465 North Halstead Street, Suite 140, Pasadena, California 91107, USA
| | - V. S. Ilchenko
- OEwaves Inc., 465 North Halstead Street, Suite 140, Pasadena, California 91107, USA
| | - A. A. Savchenkov
- OEwaves Inc., 465 North Halstead Street, Suite 140, Pasadena, California 91107, USA
| | - A. B. Matsko
- OEwaves Inc., 465 North Halstead Street, Suite 140, Pasadena, California 91107, USA
| | - D. Seidel
- OEwaves Inc., 465 North Halstead Street, Suite 140, Pasadena, California 91107, USA
| | - L. Maleki
- OEwaves Inc., 465 North Halstead Street, Suite 140, Pasadena, California 91107, USA
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13
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Huang SW, Zhou H, Yang J, McMillan JF, Matsko A, Yu M, Kwong DL, Maleki L, Wong CW. Mode-locked ultrashort pulse generation from on-chip normal dispersion microresonators. PHYSICAL REVIEW LETTERS 2015; 114:053901. [PMID: 25699441 DOI: 10.1103/physrevlett.114.053901] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/14/2014] [Indexed: 05/27/2023]
Abstract
We describe generation of stable mode-locked pulse trains from on-chip normal dispersion microresonators. The excitation of hyperparametric oscillation is facilitated by the local dispersion disruptions induced by mode interactions. The system is then driven from hyperparametric oscillation to the mode-locked state with over 200 nm spectral width by controlled pump power and detuning. With the continuous-wave-driven nonlinearity, the pulses sit on a pedestal, akin to a cavity soliton. We identify the importance of pump detuning and wavelength-dependent quality factors in stabilizing and shaping the pulse structure, to achieve a single pulse inside the cavity. We examine the mode-locking dynamics by numerically solving the master equation and provide analytic solutions under appropriate approximations.
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Affiliation(s)
- S-W Huang
- Mesoscopic Optics and Quantum Electronics, University of California, Los Angeles, California 90095, USA and Optical Nanostructures Laboratory, Center for Integrated Science and Engineering, Solid-State Science and Engineering, and Mechanical Engineering, Columbia University, New York, New York 10027, USA
| | - H Zhou
- Optical Nanostructures Laboratory, Center for Integrated Science and Engineering, Solid-State Science and Engineering, and Mechanical Engineering, Columbia University, New York, New York 10027, USA
| | - J Yang
- Mesoscopic Optics and Quantum Electronics, University of California, Los Angeles, California 90095, USA and Optical Nanostructures Laboratory, Center for Integrated Science and Engineering, Solid-State Science and Engineering, and Mechanical Engineering, Columbia University, New York, New York 10027, USA
| | - J F McMillan
- Optical Nanostructures Laboratory, Center for Integrated Science and Engineering, Solid-State Science and Engineering, and Mechanical Engineering, Columbia University, New York, New York 10027, USA
| | - A Matsko
- OEwaves Inc., Pasadena, California 91107, USA
| | - M Yu
- Institute of Microelectronics, Singapore 117685, Singapore
| | - D-L Kwong
- Institute of Microelectronics, Singapore 117685, Singapore
| | - L Maleki
- OEwaves Inc., Pasadena, California 91107, USA
| | - C W Wong
- Mesoscopic Optics and Quantum Electronics, University of California, Los Angeles, California 90095, USA and Optical Nanostructures Laboratory, Center for Integrated Science and Engineering, Solid-State Science and Engineering, and Mechanical Engineering, Columbia University, New York, New York 10027, USA
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14
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Shugayev R, Bermel P. Time-domain simulations of nonlinear interaction in microring resonators using finite-difference and coupled mode techniques. OPTICS EXPRESS 2014; 22:19204-19218. [PMID: 25321006 DOI: 10.1364/oe.22.019204] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Nonlinear interactions within compact, on-chip microring resonant cavities is a topic of increasing interest in current silicon photonics research. Frequency combs, one of the emerging nonlinear applications in microring optics, offers great potential from both scientific and practical perspectives. However, the mechanisms of comb formation appear to differ from traditional frequency combs formed by pulsed femtosecond lasers, and thus require detailed elucidation through theory and simulation. Here we propose a technique to mimic the accuracy of finite-difference time domain (FDTD) full wave nonlinear optical simulations with only a small fraction of the computational resources. Our new hybrid approach combines a single linear FDTD simulation of the key interaction parameters, then directly inserts them into a coupled-mode theory simulation. Comparison of the hybrid approach and full FDTD shows a good match both in frequency domain and in time domain. Thus, it retains the advantage of FDTD in terms of direct connection with experimental designs, while finishing much faster and sidestepping stability issues associated with direct simulation of nonlinear phenomena. The hybrid technique produces several key results explored in this paper, including: demonstrating that comb formation can occur with both anomalous and normal dispersion; suggesting a new mechanism for incoherent (Type II) frequency comb formation; and illustrating a method for creating soliton-like pulses in on-chip microresonators.
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15
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Rogov AS, Narimanov EE. Frequency comb formation and transition to chaos in microresonators with near-zero dispersion. OPTICS LETTERS 2014; 39:4305-4308. [PMID: 25078163 DOI: 10.1364/ol.39.004305] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We investigate the frequency comb formation in microresonators with near-zero dispersion, study the route from integrability to chaos in the corresponding nonlinear system, and demonstrate the key role of nonlinear dynamics of such a system for frequency comb generation and stability.
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16
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Wang S, Guo H, Bai X, Zeng X. Broadband Kerr frequency combs and intracavity soliton dynamics influenced by high-order cavity dispersion. OPTICS LETTERS 2014; 39:2880-2883. [PMID: 24978227 DOI: 10.1364/ol.39.002880] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We numerically investigate the influence of high-order dispersion (HOD) on temporal and spectral characteristics of microresonator-based optical frequency combs. Theoretical analysis based on the moment method associated with numerical simulations are utilized to study the comb evolution dynamics, showing that temporal shifts of steady-state intracavity solitons are induced by high-odd-order dispersion rather than high-even-order dispersion. The role of HOD on comb spectral envelopes is also elucidated through analyzing the intracavity dispersive wave generations. We further demonstrate that the spectral envelope of a broadband optical frequency comb can be engineered by using a cavity dispersion profile with multiple zero dispersion wavelengths.
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17
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Parra-Rivas P, Gomila D, Leo F, Coen S, Gelens L. Third-order chromatic dispersion stabilizes Kerr frequency combs. OPTICS LETTERS 2014; 39:2971-2974. [PMID: 24978250 DOI: 10.1364/ol.39.002971] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Using numerical simulations of an extended Lugiato-Lefever equation we analyze the stability and nonlinear dynamics of Kerr frequency combs generated in microresonators and fiber resonators, taking into account third-order dispersion effects. We show that cavity solitons underlying Kerr frequency combs, normally sensitive to oscillatory and chaotic instabilities, are stabilized in a wide range of parameter space by third-order dispersion. Moreover, we demonstrate how the snaking structure organizing compound states of multiple cavity solitons is qualitatively changed by third-order dispersion, promoting an increased stability of Kerr combs underlined by a single cavity soliton.
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Abrams DM, Slawik A, Srinivasan K. Nonlinear oscillations and bifurcations in silicon photonic microresonators. PHYSICAL REVIEW LETTERS 2014; 112:123901. [PMID: 24724649 DOI: 10.1103/physrevlett.112.123901] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/23/2013] [Indexed: 06/03/2023]
Abstract
Silicon microdisks are optical resonators that can exhibit surprising nonlinear behavior. We present a new analysis of the dynamics of these resonators elucidating the mathematical origin of spontaneous oscillations and deriving predictions for observed phenomena such as a frequency comb spectrum with MHz-scale repetition rate. We test predictions through laboratory experiment and numerical simulation.
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Affiliation(s)
- Daniel M Abrams
- Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, Illinois 60208, USA and Northwestern Institute on Complex Systems, Northwestern University, Evanston, Illinois 60208, USA and Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA
| | - Alex Slawik
- Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, Illinois 60208, USA
| | - Kartik Srinivasan
- Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
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19
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Liang W, Eliyahu D, Matsko AB, Ilchenko VS, Seidel D, Maleki L. Spectrally pure RF photonic source based on a resonant optical hyper-parametric oscillator. ACTA ACUST UNITED AC 2014. [DOI: 10.1117/12.2044826] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
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20
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Coillet A, Chembo YK. Routes to spatiotemporal chaos in Kerr optical frequency combs. CHAOS (WOODBURY, N.Y.) 2014; 24:013113. [PMID: 24697375 DOI: 10.1063/1.4863298] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We investigate the various routes to spatiotemporal chaos in Kerr optical frequency combs, obtained through pumping an ultra-high Q-factor whispering-gallery mode resonator with a continuous-wave laser. The Lugiato-Lefever model is used to build bifurcation diagrams with regards to the parameters that are externally controllable, namely, the frequency and the power of the pumping laser. We show that the spatiotemporal chaos emerging from Turing patterns and solitons display distinctive dynamical features. Experimental spectra of chaotic Kerr combs are also presented for both cases, in excellent agreement with theoretical spectra.
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Affiliation(s)
- Aurélien Coillet
- Optics Department, FEMTO-ST Institute [CNRS UMR6174], 16 Route de Gray, 25030 Besançon cedex, France
| | - Yanne K Chembo
- Optics Department, FEMTO-ST Institute [CNRS UMR6174], 16 Route de Gray, 25030 Besançon cedex, France
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21
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Torres-Company V, Castelló-Lurbe D, Silvestre E. Comparative analysis of spectral coherence in microresonator frequency combs. OPTICS EXPRESS 2014; 22:4678-4691. [PMID: 24663786 DOI: 10.1364/oe.22.004678] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Microresonator combs exploit parametric oscillation and nonlinear mixing in an ultrahigh-Q cavity. This new comb generator offers unique potential for chip integration and access to high repetition rates. However, time-domain studies reveal an intricate spectral coherence behavior in this type of platform. In particular, coherent, partially coherent or incoherent combs have been observed using the same microresonator under different pumping conditions. In this work, we provide a numerical analysis of the coherence dynamics that supports the above experimental findings and verify particular design rules to achieve spectrally coherent microresonator combs. A particular emphasis is placed in understanding the differences between so-called Type I and Type II combs.
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22
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Del'Haye P, Beha K, Papp SB, Diddams SA. Self-injection locking and phase-locked states in microresonator-based optical frequency combs. PHYSICAL REVIEW LETTERS 2014; 112:043905. [PMID: 24580454 DOI: 10.1103/physrevlett.112.043905] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/12/2013] [Indexed: 06/03/2023]
Abstract
Microresonator-based optical frequency combs have been a topic of extensive research during the last few years. Several theoretical models for the comb generation have been proposed; however, they do not comprehensively address experimental results that show a variety of independent comb generation mechanisms. Here, we present frequency-domain experiments that illuminate the transition of microcombs into phase-locked states, which show characteristics of injection locking between ensembles of comb modes. In addition, we demonstrate the existence of equidistant optical frequency combs that are phase stable but have nondeterministic phase relationships between individual comb modes.
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Affiliation(s)
- Pascal Del'Haye
- National Institute of Standards and Technology (NIST), Boulder, Colorado 80305, USA
| | - Katja Beha
- National Institute of Standards and Technology (NIST), Boulder, Colorado 80305, USA
| | - Scott B Papp
- National Institute of Standards and Technology (NIST), Boulder, Colorado 80305, USA
| | - Scott A Diddams
- National Institute of Standards and Technology (NIST), Boulder, Colorado 80305, USA
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23
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Erkintalo M, Coen S. Coherence properties of Kerr frequency combs. OPTICS LETTERS 2014; 39:283-6. [PMID: 24562127 DOI: 10.1364/ol.39.000283] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
We use numerical simulations based on an extended Lugiato-Lefever equation (LLE) to investigate the stability properties of Kerr frequency combs generated in microresonators. In particular, we show that an ensemble average calculated over sequences of output fields separated by a fixed number of resonator roundtrips allows the coherence of Kerr combs to be quantified in terms of the complex degree of first-order coherence. We identify different regimes of comb coherence, linked to the solutions of the LLE. Our approach provides a practical and unambiguous way of assessing the stability of Kerr combs that is directly connected to an accessible experimental quantity.
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24
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Matsko AB, Maleki L. On timing jitter of mode locked Kerr frequency combs. OPTICS EXPRESS 2013; 21:28862-28876. [PMID: 24514400 DOI: 10.1364/oe.21.028862] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We study fundamental timing jitter in repetition rate of a mode locked Kerr frequency comb generated in an externally pumped nonlinear ring resonator. We show that the increase in the integrated power of the comb harmonics, and the corresponding decrease of the duration of the associated pulse, results in the increase of low frequency noise, and a decrease in high frequency noise.
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25
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Grudinin IS, Baumgartel L, Yu N. Impact of cavity spectrum on span in microresonator frequency combs. OPTICS EXPRESS 2013; 21:26929-26935. [PMID: 24216915 DOI: 10.1364/oe.21.026929] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
We experimentally study the factors that limit the span in frequency combs derived from the crystalline whispering gallery mode resonators. We observe that cavity dispersion is the key property that governs the parameters of the combs resulting from cascaded four wave mixing process. Two different regimes of comb generation are observed depending on the precise cavity dispersion behavior at the pump wavelength. In addition, the comb generation efficiency is found to be affected by the crossing of modes of different families. The influence of Raman lasing and its dependence on temperature is discussed.
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26
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Ulvila V, Phillips CR, Halonen L, Vainio M. Frequency comb generation by a continuous-wave-pumped optical parametric oscillator based on cascading quadratic nonlinearities. OPTICS LETTERS 2013; 38:4281-4284. [PMID: 24177073 DOI: 10.1364/ol.38.004281] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
We report optical frequency comb generation by a continuous-wave pumped optical parametric oscillator (OPO) without any active modulation. The OPO is configured as singly resonant with an additional nonlinear crystal (periodically poled MgO:LiNbO3) placed inside the OPO for phase mismatched second harmonic generation (SHG) of the resonating signal beam. The phase mismatched SHG causes cascading χ(2) nonlinearities, which can substantially increase the effective χ(3) nonlinearity in MgO:LiNbO3, leading to spectral broadening of the OPO signal beam via self-phase modulation. The OPO generates a stable 4 THz wide (-30 dB) frequency comb centered at 1.56 μm.
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27
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Lamont MRE, Okawachi Y, Gaeta AL. Route to stabilized ultrabroadband microresonator-based frequency combs. OPTICS LETTERS 2013; 38:3478-81. [PMID: 24104792 DOI: 10.1364/ol.38.003478] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/15/2023]
Abstract
We perform the first theoretical modeling of the full spectral-temporal dynamics of octave-spanning parametric microresonator comb generation through use of the Lugiato-Lefever model extended to include higher-order dispersion and self-steepening. We show that three distinct stages are necessary to achieve single-pulse modelocking and discuss the dispersion characteristics required for ultrabroadband, stabilized comb generation. Our simulations agree well with previous experimental demonstrations and predict many of the observed features, including multipulse generation, dispersive wave generation, modelocking, and comb stabilization.
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28
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Coen S, Erkintalo M. Universal scaling laws of Kerr frequency combs. OPTICS LETTERS 2013; 38:1790-1792. [PMID: 23722745 DOI: 10.1364/ol.38.001790] [Citation(s) in RCA: 79] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
Using the known solutions of the Lugiato-Lefever equation, we derive universal trends of Kerr frequency combs. In particular, normalized properties of temporal cavity soliton solutions lead us to a simple analytic estimate of the maximum attainable bandwidth for given pump resonator parameters. The result is validated via comparison with past experiments encompassing a diverse range of resonator configurations and parameters.
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Affiliation(s)
- Stéphane Coen
- Physics Department, The University of Auckland, Private Bag 92019, Auckland 1142, New Zealand.
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