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Yi X, Yang QF, Zhang X, Yang KY, Li X, Vahala K. Single-mode dispersive waves and soliton microcomb dynamics. Nat Commun 2017; 8:14869. [PMID: 28332495 PMCID: PMC5376647 DOI: 10.1038/ncomms14869] [Citation(s) in RCA: 46] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/24/2016] [Accepted: 02/06/2017] [Indexed: 11/15/2022] Open
Abstract
Dissipative Kerr solitons are self-sustaining optical wavepackets in resonators. They use the Kerr nonlinearity to both compensate dispersion and offset optical loss. Besides providing insights into nonlinear resonator physics, they can be applied in frequency metrology, precision clocks, and spectroscopy. Like other optical solitons, the dissipative Kerr soliton can radiate power as a dispersive wave through a process that is the optical analogue of Cherenkov radiation. Dispersive waves typically consist of an ensemble of optical modes. Here, a limiting case is studied in which the dispersive wave is concentrated into a single cavity mode. In this limit, its interaction with the soliton induces hysteresis behaviour in the soliton's spectral and temporal properties. Also, an operating point of enhanced repetition-rate stability occurs through balance of dispersive-wave recoil and Raman-induced soliton-self-frequency shift. The single-mode dispersive wave can therefore provide quiet states of soliton comb operation useful in many applications.
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Affiliation(s)
- Xu Yi
- T.J. Watson Laboratory of Applied Physics, California Institute of Technology, Pasadena, California 91125, USA
| | - Qi-Fan Yang
- T.J. Watson Laboratory of Applied Physics, California Institute of Technology, Pasadena, California 91125, USA
| | - Xueyue Zhang
- T.J. Watson Laboratory of Applied Physics, California Institute of Technology, Pasadena, California 91125, USA
- Department of Microelectronics and Nanoelectronics, Tsinghua University, Beijing 100084, China
| | - Ki Youl Yang
- T.J. Watson Laboratory of Applied Physics, California Institute of Technology, Pasadena, California 91125, USA
| | - Xinbai Li
- T.J. Watson Laboratory of Applied Physics, California Institute of Technology, Pasadena, California 91125, USA
- State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Electronics Engineering and Computer Science, Peking University, Beijing 100871, China
| | - Kerry Vahala
- T.J. Watson Laboratory of Applied Physics, California Institute of Technology, Pasadena, California 91125, USA
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Li Q, Briles TC, Westly DA, Drake TE, Stone JR, Ilic BR, Diddams SA, Papp SB, Srinivasan K. Stably accessing octave-spanning microresonator frequency combs in the soliton regime. OPTICA 2017; 4:193-203. [PMID: 28603754 PMCID: PMC5460676 DOI: 10.1364/optica.4.000193] [Citation(s) in RCA: 86] [Impact Index Per Article: 12.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/19/2023]
Abstract
Microresonator frequency combs can be an enabling technology for optical frequency synthesis and timekeeping in low size, weight, and power architectures. Such systems require comb operation in low-noise, phase-coherent states such as solitons, with broad spectral bandwidths (e.g., octave-spanning) for self-referencing to detect the carrier-envelope offset frequency. However, accessing such states is complicated by thermo-optic dispersion. For example, in the Si3N4 platform, precisely dispersion-engineered structures can support broadband operation, but microsecond thermal time constants often require fast pump power or frequency control to stabilize the solitons. In contrast, here we consider how broadband soliton states can be accessed with simple pump laser frequency tuning, at a rate much slower than the thermal dynamics. We demonstrate octave-spanning soliton frequency combs in Si3N4 microresonators, including the generation of a multi-soliton state with a pump power near 40 mW and a single-soliton state with a pump power near 120 mW. We also develop a simplified two-step analysis to explain how these states are accessed without fast control of the pump laser, and outline the required thermal properties for such operation. Our model agrees with experimental results as well as numerical simulations based on a Lugiato-Lefever equation that incorporates thermo-optic dispersion. Moreover, it also explains an experimental observation that a member of an adjacent mode family on the red-detuned side of the pump mode can mitigate the thermal requirements for accessing soliton states.
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Affiliation(s)
- Qing Li
- Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
- Maryland NanoCenter, University of Maryland, College Park, Maryland 20742, USA
| | - Travis C. Briles
- Time and Frequency Division, National Institute of Standards and Technology, Boulder, Colorado 80305, USA
| | - Daron A. Westly
- Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - Tara E. Drake
- Time and Frequency Division, National Institute of Standards and Technology, Boulder, Colorado 80305, USA
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Jordan R. Stone
- Time and Frequency Division, National Institute of Standards and Technology, Boulder, Colorado 80305, USA
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - B. Robert Ilic
- Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - Scott A. Diddams
- Time and Frequency Division, National Institute of Standards and Technology, Boulder, Colorado 80305, USA
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Scott B. Papp
- Time and Frequency Division, National Institute of Standards and Technology, Boulder, Colorado 80305, USA
| | - Kartik Srinivasan
- Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
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53
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Arafin S, Simsek A, Kim SK, Dwivedi S, Liang W, Eliyahu D, Klamkin J, Matsko A, Johansson L, Maleki L, Rodwell M, Coldren L. Towards chip-scale optical frequency synthesis based on optical heterodyne phase-locked loop. OPTICS EXPRESS 2017; 25:681-695. [PMID: 28157957 DOI: 10.1364/oe.25.000681] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
An integrated heterodyne optical phase-locked loop was designed and demonstrated with an indium phosphide based photonic integrated circuit and commercial off-the-shelf electronic components. As an input reference, a stable microresonator-based optical frequency comb with a 50-dB span of 25 nm (~3 THz) around 1550 nm, having a spacing of ~26 GHz, was used. A widely-tunable on-chip sampled-grating distributed-Bragg-reflector laser is offset locked across multiple comb lines. An arbitrary frequency synthesis between the comb lines is demonstrated by tuning the RF offset source, and better than 100Hz tuning resolution with ± 5 Hz accuracy is obtained. Frequency switching of the on-chip laser to a point more than two dozen comb lines away (~5.6 nm) and simultaneous locking to the corresponding nearest comb line is also achieved in a time ~200 ns. A low residual phase noise of the optical phase-locking system is successfully achieved, as experimentally verified by the value of -80 dBc/Hz at an offset of as low as 200 Hz.
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54
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Jang JK, Okawachi Y, Yu M, Luke K, Ji X, Lipson M, Gaeta AL. Dynamics of mode-coupling-induced microresonator frequency combs in normal dispersion. OPTICS EXPRESS 2016; 24:28794-28803. [PMID: 27958523 DOI: 10.1364/oe.24.028794] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We experimentally and theoretically investigate the dynamics of microresonator-based frequency comb generation assisted by mode coupling in the normal group-velocity dispersion (GVD) regime. We show that mode coupling can initiate intracavity modulation instability (MI) by directly perturbing the pump-resonance mode. We also observe the formation of a low-noise comb as the pump frequency is tuned further into resonance from the MI point. We determine the phase-matching conditions that accurately predict all the essential features of the MI and comb spectra, and extend the existing analogy between mode coupling and high-order dispersion to the normal GVD regime. We discuss the applicability of our analysis to the possibility of broadband comb generation in the normal GVD regime.
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55
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Lobanov VE, Lihachev GV, Pavlov NG, Cherenkov AV, Kippenberg TJ, Gorodetsky ML. Harmonization of chaos into a soliton in Kerr frequency combs. OPTICS EXPRESS 2016; 24:27382-27394. [PMID: 27906310 DOI: 10.1364/oe.24.027382] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Dissipative Kerr solitons have paved the way to broadband and fully coherent optical frequency combs in microresonators. Here, we demonstrate numerically that slow frequency tuning of the pump laser in conjunction with phase or amplitude modulation corresponding to the free spectral range of the microresonator, provides reliable convergence of an initially excited chaotic comb state to a single dissipative Kerr soliton (DKS) state. The efficiency of this approach depends on both frequency tuning speed and modulation depth. The relevance of the proposed method is confirmed experimentally in a MgF2 microresonator.
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56
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Webb KE, Erkintalo M, Coen S, Murdoch SG. Experimental observation of coherent cavity soliton frequency combs in silica microspheres. OPTICS LETTERS 2016; 41:4613-4616. [PMID: 28005849 DOI: 10.1364/ol.41.004613] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
We report on the experimental observation of coherent cavity soliton frequency combs in silica microspheres. Specifically, we demonstrate that careful alignment of the microsphere relative to the coupling fiber taper allows for the suppression of higher-order spatial modes, reducing mode interactions and enabling soliton formation. Our measurements show that the temporal cavity solitons have sub-100-fs durations, exhibit considerable Raman self-frequency shift, and generally come in groups of three or four, occasionally with equidistant spacing in the time domain. RF amplitude noise measurements and spectral interferometry confirm the high coherence of the observed soliton frequency combs, and numerical simulations show good agreement with experiments.
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57
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Bao C, Jaramillo-Villegas JA, Xuan Y, Leaird DE, Qi M, Weiner AM. Observation of Fermi-Pasta-Ulam Recurrence Induced by Breather Solitons in an Optical Microresonator. PHYSICAL REVIEW LETTERS 2016; 117:163901. [PMID: 27792392 DOI: 10.1103/physrevlett.117.163901] [Citation(s) in RCA: 41] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/21/2016] [Indexed: 05/27/2023]
Abstract
We present, experimentally and numerically, the observation of Fermi-Pasta-Ulam recurrence induced by breather solitons in a high-Q SiN microresonator. Breather solitons can be excited by increasing the pump power at a relatively small pump phase detuning in microresonators. Out of phase power evolution is observed for groups of comb lines around the center of the spectrum compared to groups of lines in the spectral wings. The evolution of the power spectrum is not symmetric with respect to the spectrum center. Numerical simulations based on the generalized Lugiato-Lefever equation are in good agreement with the experimental results and unveil the role of stimulated Raman scattering in the symmetry breaking of the power spectrum evolution. Our results show that optical microresonators can be exploited as a powerful platform for the exploration of soliton dynamics.
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Affiliation(s)
- Chengying Bao
- School of Electrical and Computer Engineering, Purdue University, 465 Northwestern Avenue, West Lafayette, Indiana 47907-2035, USA
| | - Jose A Jaramillo-Villegas
- School of Electrical and Computer Engineering, Purdue University, 465 Northwestern Avenue, West Lafayette, Indiana 47907-2035, USA
- Facultad de Ingenierías, Universidad Tecnológica de Pereira, Pereira, Risaralda 66003, Colombia
| | - Yi Xuan
- School of Electrical and Computer Engineering, Purdue University, 465 Northwestern Avenue, West Lafayette, Indiana 47907-2035, USA
- Birck Nanotechnology Center, Purdue University, 1205 West State Street, West Lafayette, Indiana 47907, USA
| | - Daniel E Leaird
- School of Electrical and Computer Engineering, Purdue University, 465 Northwestern Avenue, West Lafayette, Indiana 47907-2035, USA
| | - Minghao Qi
- School of Electrical and Computer Engineering, Purdue University, 465 Northwestern Avenue, West Lafayette, Indiana 47907-2035, USA
- Birck Nanotechnology Center, Purdue University, 1205 West State Street, West Lafayette, Indiana 47907, USA
| | - Andrew M Weiner
- School of Electrical and Computer Engineering, Purdue University, 465 Northwestern Avenue, West Lafayette, Indiana 47907-2035, USA
- Birck Nanotechnology Center, Purdue University, 1205 West State Street, West Lafayette, Indiana 47907, USA
- Purdue Quantum Center, Purdue University, 1205 West State Street, West Lafayette, Indiana 47907, USA
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58
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Yi X, Yang QF, Yang KY, Vahala K. Theory and measurement of the soliton self-frequency shift and efficiency in optical microcavities. OPTICS LETTERS 2016; 41:3419-3422. [PMID: 27472583 DOI: 10.1364/ol.41.003419] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Dissipative Kerr cavity solitons experience a so-called self-frequency shift (SFS) as a result of Raman interactions. The frequency shift has been observed in several microcavity systems. The Raman process has also been shown numerically to influence the soliton pumping efficiency. Here, a perturbed Lagrangian approach is used to derive simple analytical expressions for the SFS and the soliton efficiency. The predicted dependences of these quantities on soliton pulse width are compared with measurements in a high-Q silica microcavity. The Raman time constant in silica is also inferred. Analytical expressions for the Raman SFS and soliton efficiency greatly simplify the prediction of soliton behavior over a wide range of microcavity platforms.
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59
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Matsko AB, Liang W, Savchenkov AA, Eliyahu D, Maleki L. Optical Cherenkov radiation in overmoded microresonators. OPTICS LETTERS 2016; 41:2907-2910. [PMID: 27367062 DOI: 10.1364/ol.41.002907] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We show that an optical analog of Cherenkov radiation (dispersive wave) is observable in a nonlinear microring resonator generating Kerr frequency comb and containing linearly interacting families of equidistant modes. The radiation results from disruptions in the frequency dependent group velocity dispersion of the pumped cavity modes and is emitted into different mode families of the resonator. This effect reveals itself as a dispersive shaped structure in the spectral envelope of the frequency comb. We found that the dips in the comb spectrum correspond to peaks of the emission of the power in the other mode families of the resonator. The spectrum of the combs that includes both mode families does not have any dips, but peaks and resembles the Cherenkov radiation spectra frequently observed in Kerr comb systems. This Letter shows that a correct description of the Kerr comb in presence of mode anti-crossings should take into account not only the pumped mode family with modified dispersion parameter, but also the modes of the interacting families.
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60
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Liu J, Brasch V, Pfeiffer MHP, Kordts A, Kamel AN, Guo H, Geiselmann M, Kippenberg TJ. Frequency-comb-assisted broadband precision spectroscopy with cascaded diode lasers. OPTICS LETTERS 2016; 41:3134-3137. [PMID: 27367120 DOI: 10.1364/ol.41.003134] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Frequency-comb-assisted diode laser spectroscopy, employing both the accuracy of an optical frequency comb and the broad wavelength tuning range of a tunable diode laser, has been widely used in many applications. In this Letter, we present a novel method using cascaded frequency agile diode lasers, which allows us to extend the measurement bandwidth to 37.4 THz (1355-1630 nm) at megahertz resolution with scanning speeds above 1 THz/s. It is demonstrated as a useful tool to characterize a broadband spectrum for molecular spectroscopy, and in particular it enables us to characterize the dispersion of integrated microresonators up to the 4th-order.
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61
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Smooth and flat phase-locked Kerr frequency comb generation by higher order mode suppression. Sci Rep 2016; 6:26255. [PMID: 27181420 PMCID: PMC4867630 DOI: 10.1038/srep26255] [Citation(s) in RCA: 36] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2016] [Accepted: 04/28/2016] [Indexed: 11/08/2022] Open
Abstract
High-Q microresonator is perceived as a promising platform for optical frequency comb generation, via dissipative soliton formation. In order to achieve a higher quality factor and obtain the necessary anomalous dispersion, multi-mode waveguides were previously implemented in Si3N4 microresonators. However, coupling between different transverse mode families in multi-mode waveguides results in periodic disruption of dispersion and quality factor, and consequently causes perturbation to dissipative soliton formation and amplitude modulation to the corresponding spectrum. Careful choice of pump wavelength to avoid the mode crossing region is thus critical in conventional Si3N4 microresonators. Here, we report a novel design of Si3N4 microresonator in which single-mode operation, high quality factor, and anomalous dispersion are attained simultaneously. The novel microresonator is consisted of uniform single-mode waveguides in the semi-circle region, to eliminate bending induced mode coupling, and adiabatically tapered waveguides in the straight region, to avoid excitation of higher order modes. The intrinsic quality factor of the microresonator reaches 1.36 × 106 while the group velocity dispersion remains to be anomalous at −50 fs2/mm. With this novel microresonator, we demonstrate that broadband phase-locked Kerr frequency combs with flat and smooth spectra can be generated by pumping at any resonances in the optical C-band.
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62
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Yi X, Yang QF, Youl Yang K, Vahala K. Active capture and stabilization of temporal solitons in microresonators. OPTICS LETTERS 2016; 41:2037-40. [PMID: 27128068 DOI: 10.1364/ol.41.002037] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
Soliton mode locking and femtosecond pulse generation have recently been demonstrated in high-Q optical microcavities and provide a new way to miniaturize frequency comb systems, as well as create integrated comb systems on a chip. However, triggering the mode-locking process is complicated by a well-known thermal hysteresis that can destabilize the solitons. Moreover, on a longer time scale, thermal drifting of the cavity resonant frequency relative to the pumping frequency causes loss of mode locking. In this Letter, an active feedback method is used both to capture specific soliton states and to stabilize the states indefinitely. The capture and stabilization method provides a reliable way to overcome thermal effects during soliton formation and to excite a desired number of circulating cavity solitons. It is also used to demonstrate a low pumping power of 22 mW for generation of microwave-repetition-rate solitons on a chip.
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63
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Karpov M, Guo H, Kordts A, Brasch V, Pfeiffer MHP, Zervas M, Geiselmann M, Kippenberg TJ. Raman Self-Frequency Shift of Dissipative Kerr Solitons in an Optical Microresonator. PHYSICAL REVIEW LETTERS 2016; 116:103902. [PMID: 27015482 DOI: 10.1103/physrevlett.116.103902] [Citation(s) in RCA: 70] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/02/2015] [Indexed: 05/27/2023]
Abstract
The formation of temporal dissipative Kerr solitons in microresonators driven by a continuous-wave laser enables the generation of coherent, broadband, and spectrally smooth optical frequency combs as well as femtosecond pulse sources with compact form factors. Here we report the observation of a Raman-induced soliton self-frequency shift for a microresonator dissipative Kerr soliton also referred to as the frequency-locked Raman soliton. In amorphous silicon nitride microresonator-based single soliton states the Raman effect manifests itself by a spectrum that is sech^{2} in shape and whose center is spectrally redshifted from the continuous wave pump laser. The shift is theoretically described by the first-order shock term of the material's Raman response, and we infer a Raman shock time of ∼20 fs for amorphous silicon nitride. Moreover, we observe that the Raman-induced frequency shift can lead to a cancellation or overcompensation of the soliton recoil caused by the formation of a coherent dispersive wave. The observations are in agreement with numerical simulations based on the Lugiato-Lefever equation with a Raman shock term. Our results contribute to the understanding of Kerr frequency combs in the soliton regime, enable one to substantially improve the accuracy of modeling, and are relevant to the understanding of the fundamental timing jitter of microresonator solitons.
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Affiliation(s)
- Maxim Karpov
- École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Hairun Guo
- École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Arne Kordts
- École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Victor Brasch
- École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Martin H P Pfeiffer
- École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Michail Zervas
- École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Michael Geiselmann
- École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Tobias J Kippenberg
- École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
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64
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Kordts A, Pfeiffer MHP, Guo H, Brasch V, Kippenberg TJ. Higher order mode suppression in high-Q anomalous dispersion SiN microresonators for temporal dissipative Kerr soliton formation. OPTICS LETTERS 2016; 41:452-455. [PMID: 26907395 DOI: 10.1364/ol.41.000452] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
High-Q silicon nitride (SiN) microresonators enable optical Kerr frequency comb generation on a photonic chip and have recently been shown to support fully coherent combs based on temporal dissipative Kerr soliton formation. For bright soliton formation, it is necessary to operate SiN waveguides in the multimode regime in order to produce waveguide induced anomalous group velocity dispersion. However, this regime can lead to local disturbances of the dispersion due to avoided crossings caused by coupling between different mode families and, therefore, prevent the soliton formation. Here, we demonstrate that a single-mode "filtering" section inside high-Q resonators enables efficiently suppression of avoided crossings, while preserving high quality factors (Q∼10(6)). We verify the approach by demonstrating single soliton formation in SiN resonators with a filtering section.
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65
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Akhmediev N, Devine N. APPLIED OPTICS. How Cherenkov radiative losses can improve optical frequency combs. Science 2016; 351:340-1. [PMID: 26798000 DOI: 10.1126/science.aad8694] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Affiliation(s)
- N Akhmediev
- Optical Sciences Group, Research School of Physics and Engineering, Australian National University, Canberra, ACT 2600, Australia.
| | - N Devine
- Optical Sciences Group, Research School of Physics and Engineering, Australian National University, Canberra, ACT 2600, Australia
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66
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Webb KE, Jang JK, Anthony J, Coen S, Erkintalo M, Murdoch SG. Measurement of microresonator frequency comb coherence by spectral interferometry. OPTICS LETTERS 2016; 41:277-280. [PMID: 26766693 DOI: 10.1364/ol.41.000277] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We experimentally investigate the spectral coherence of microresonator optical frequency combs. Specifically, we use a spectral interference method, typically used in the context of supercontinuum generation, to explore the variation of the magnitude of the complex degree of first-order coherence across the full comb bandwidth. We measure the coherence of two different frequency combs and observe wholly different coherence characteristics. In particular, we find that the observed dynamical regimes are similar to the stable and unstable modulation instability regimes reported in previous theoretical studies. Results from numerical simulations are found to be in good agreement with experimental observations. In addition to demonstrating a new technique to assess comb stability, our results provide strong experimental support for previous theoretical analyses.
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67
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Brasch V, Geiselmann M, Herr T, Lihachev G, Pfeiffer MHP, Gorodetsky ML, Kippenberg TJ. Photonic chip-based optical frequency comb using soliton Cherenkov radiation. Science 2015; 351:357-60. [PMID: 26721682 DOI: 10.1126/science.aad4811] [Citation(s) in RCA: 201] [Impact Index Per Article: 22.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/18/2015] [Accepted: 12/03/2015] [Indexed: 11/02/2022]
Abstract
Optical solitons are propagating pulses of light that retain their shape because nonlinearity and dispersion balance each other. In the presence of higher-order dispersion, optical solitons can emit dispersive waves via the process of soliton Cherenkov radiation. This process underlies supercontinuum generation and is of critical importance in frequency metrology. Using a continuous wave-pumped, dispersion-engineered, integrated silicon nitride microresonator, we generated continuously circulating temporal dissipative Kerr solitons. The presence of higher-order dispersion led to the emission of red-shifted soliton Cherenkov radiation. The output corresponds to a fully coherent optical frequency comb that spans two-thirds of an octave and whose phase we were able to stabilize to the sub-Hertz level. By preserving coherence over a broad spectral bandwidth, our device offers the opportunity to develop compact on-chip frequency combs for frequency metrology or spectroscopy.
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Affiliation(s)
- V Brasch
- École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - M Geiselmann
- École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - T Herr
- École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - G Lihachev
- Russian Quantum Center, Skolkovo 143025, Russia. Faculty of Physics, M. V. Lomonosov Moscow State University, Moscow 119991, Russia
| | - M H P Pfeiffer
- École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - M L Gorodetsky
- Russian Quantum Center, Skolkovo 143025, Russia. Faculty of Physics, M. V. Lomonosov Moscow State University, Moscow 119991, Russia
| | - T J Kippenberg
- École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland.
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68
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Weng W, Luiten AN. Mode-interactions and polarization conversion in a crystalline microresonator. OPTICS LETTERS 2015; 40:5431-5434. [PMID: 26625018 DOI: 10.1364/ol.40.005431] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We observe couplings between orthogonally polarized modes in a birefringent whispering-gallery-mode resonator. The modes show strong interactions leading to polarization conversion and avoid mode crossings. We show that a phenomenological model, based on the coupled-mode theory, is in good agreement with the experiments. The device provides an excellent laboratory to perform controllable and tunable mode interactions.
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69
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Fülöp A, Krückel CJ, Castelló-Lurbe D, Silvestre E, Torres-Company V. Triply resonant coherent four-wave mixing in silicon nitride microresonators. OPTICS LETTERS 2015; 40:4006-4009. [PMID: 26368698 DOI: 10.1364/ol.40.004006] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Generation of multiple tones using four-wave mixing (FWM) has been exploited for many applications, ranging from wavelength conversion to frequency comb generation. FWM is a coherent process, meaning that its dynamics strongly depend on the relative phase among the waves involved. The coherent nature of FWM has been exploited for phase-sensitive processing in different waveguide structures, but it has never been studied in integrated microresonators. Waveguides arranged in a resonant way allow for an effective increase in the wavelength conversion efficiency (at the expense of a reduction in the operational bandwidth). In this Letter, we show that phase shaping of a three-wave pump provides an extra degree of freedom for controlling the FWM dynamics in microresonators. We present experimental results in single-mode, normal-dispersion high-Q silicon nitride resonators, and numerical calculations of systems operating in the anomalous dispersion regime. Our results indicate that the wavelength conversion efficiency and modulation instability gain in microcavities pumped by multiple waves can be significantly modified with the aid of simple lossless coherent control techniques.
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70
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Huang SW, Yang J, Lim J, Zhou H, Yu M, Kwong DL, Wong CW. A low-phase-noise 18 GHz Kerr frequency microcomb phase-locked over 65 THz. Sci Rep 2015; 5:13355. [PMID: 26311406 PMCID: PMC4550847 DOI: 10.1038/srep13355] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2015] [Accepted: 07/23/2015] [Indexed: 11/27/2022] Open
Abstract
Laser frequency combs are coherent light sources that simultaneously provide pristine frequency spacings for precision metrology and the fundamental basis for ultrafast and attosecond sciences. Recently, nonlinear parametric conversion in high-Q microresonators has been suggested as an alternative platform for optical frequency combs, though almost all in 100 GHz frequencies or more. Here we report a low-phase-noise on-chip Kerr frequency comb with mode spacing compatible with high-speed silicon optoelectronics. The waveguide cross-section of the silicon nitride spiral resonator is designed to possess small and flattened group velocity dispersion, so that the Kerr frequency comb contains a record-high number of 3,600 phase-locked comb lines. We study the single-sideband phase noise as well as the long-term frequency stability and report the lowest phase noise floor achieved to date with -130 dBc/Hz at 1 MHz offset for the 18 GHz Kerr comb oscillator, along with feedback stabilization to achieve frequency Allan deviations of 7 × 10(-11) in 1 s. The reported system is a promising compact platform for achieving self-referenced Kerr frequency combs and also for high-capacity coherent communication architectures.
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Affiliation(s)
- S.-W. Huang
- Mesoscopic Optics and Quantum Electronics Laboratory, University of California, Los Angeles, CA, USA
- Optical Nanostructures Laboratory, Center for Integrated Science and Engineering, Solid-State Science and Engineering, and Mechanical Engineering, Columbia University, New York, NY, USA
| | - J. Yang
- Mesoscopic Optics and Quantum Electronics Laboratory, University of California, Los Angeles, CA, USA
- Optical Nanostructures Laboratory, Center for Integrated Science and Engineering, Solid-State Science and Engineering, and Mechanical Engineering, Columbia University, New York, NY, USA
| | - J. Lim
- Mesoscopic Optics and Quantum Electronics Laboratory, University of California, Los Angeles, CA, USA
| | - H. Zhou
- University of Electronic Science and Technology of China, Chengdu, Sichuan, China
| | - M. Yu
- Institute of Microelectronics, Singapore, Singapore
| | - D.-L. Kwong
- Institute of Microelectronics, Singapore, Singapore
| | - C. W. Wong
- Mesoscopic Optics and Quantum Electronics Laboratory, University of California, Los Angeles, CA, USA
- Optical Nanostructures Laboratory, Center for Integrated Science and Engineering, Solid-State Science and Engineering, and Mechanical Engineering, Columbia University, New York, NY, USA
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71
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Miller SA, Okawachi Y, Ramelow S, Luke K, Dutt A, Farsi A, Gaeta AL, Lipson M. Tunable frequency combs based on dual microring resonators. OPTICS EXPRESS 2015; 23:21527-21540. [PMID: 26367998 DOI: 10.1364/oe.23.021527] [Citation(s) in RCA: 33] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
In order to achieve efficient parametric frequency comb generation in microresonators, external control of coupling between the cavity and the bus waveguide is necessary. However, for passive monolithically integrated structures, the coupling gap is fixed and cannot be externally controlled, making tuning the coupling inherently challenging. We design a dual-cavity coupled microresonator structure in which tuning one ring resonance frequency induces a change in the overall cavity coupling condition. We demonstrate wide extinction tunability with high efficiency by engineering the ring coupling conditions. Additionally, we note a distinct dispersion tunability resulting from coupling two cavities of slightly different path lengths, and present a new method of modal dispersion engineering. Our fabricated devices consist of two coupled high quality factor silicon nitride microresonators, where the extinction ratio of the resonances can be controlled using integrated microheaters. Using this extinction tunability, we optimize comb generation efficiency as well as provide tunability for avoiding higher-order mode-crossings, known for degrading comb generation. The device is able to provide a 110-fold improvement in the comb generation efficiency. Finally, we demonstrate open eye diagrams using low-noise phase-locked comb lines as a wavelength-division multiplexing channel.
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72
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Lobanov VE, Lihachev G, Kippenberg TJ, Gorodetsky ML. Frequency combs and platicons in optical microresonators with normal GVD. OPTICS EXPRESS 2015; 23:7713-7721. [PMID: 25837109 DOI: 10.1364/oe.23.007713] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We predict the existence of a novel type of the flat-top dissipative solitonic pulses, "platicons", in microresonators with normal group velocity dispersion (GVD). We propose methods to generate these platicons from cw pump. Their duration may be altered significantly by tuning the pump frequency. The transformation of a discrete energy spectrum of dark solitons of the Lugiato-Lefever equation into a quasicontinuous spectrum of platicons is demonstrated. Generation of similar structures is also possible with bi-harmonic, phase/amplitude modulated pump or via laser injection locking.
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73
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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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