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.

© 2016 Optical Society of America

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  1. P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
    [Crossref]
  2. A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, “Tunable optical frequency comb with a crystalline whispering gallery mode resonator,” Phys. Rev. Lett. 101, 093902 (2008).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  4. J. Li, H. Lee, T. Chen, and K. J. Vahala, “Low-pump-power, low-phase-noise, and microwave to millimeter-wave repetition rate operation in microcombs,” Phys. Rev. Lett. 109, 233901 (2012).
    [Crossref]
  5. X. Xue and A. M. Weiner, “Microwave photonics connected with microresonator frequency combs,” Front. Optoelectron. 9, 238–248 (2016).
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  6. T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photonics 6, 480–487 (2012).
    [Crossref]
  7. I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Four-wave-mixing parametric oscillations in dispersion-compensated high-Q silica microspheres,” Phys. Rev. A 76, 043837 (2007).
    [Crossref]
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  21. X. Yi, Q.-F. Yang, K. Y. Yang, M.-G. Suh, and K. Vahala, “Soliton frequency comb at microwave rates in a high-Q silica microresonator,” Optica 2, 1078–1085 (2015).
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    [Crossref]
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    [Crossref] [PubMed]
  25. C. Bao, L. Zhang, A. Matsko, Y. Yan, Z. Zhao, G. Xie, A. M. Agarwal, L. C. Kimerling, J. Michel, L. Maleki, and A. E. Willner, “Nonlinear conversion efficiency in Kerr frequency comb generation,” Opt. Lett. 39, 6126–6129 (2014).
    [Crossref] [PubMed]
  26. P. Del’Haye, K. Beha, S. B. Papp, and S. A. Diddams, “Self-injection locking and phase-locked states in microresonator-based optical frequency combs,” Phys. Rev. Lett. 112, 043905 (2014).
    [Crossref]
  27. T. Hansson and S. Wabnitz, “Dynamics of microresonator frequency comb generation: models and stability,” Nanophotonics 5, 231–243 (2016).
    [Crossref]
  28. C. Milián, A. V. Gorbach, M. Taki, A. V. Yulin, and D. V. Skryabin, “Solitons and frequency combs in silica microring resonators: Interplay of the raman and higher-order dispersion effects,” Phys. Rev. A 92, 033851 (2015).
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  29. M.-G. Suh, Q.-F. Yang, K. Y. Yang, X. Yi, and K. Vahala, “Microresonator soliton dual-comb spectroscopy,” arXiv:1607.08222 (2016).
  30. J. A. Jaramillo-Villegas, X. X. Xue, P. H. Wang, D. E. Leaird, and A. M. Weiner, “Deterministic single soliton generation and compression in microring resonators avoiding the chaotic region,” Opt. Express 23, 9618–9626 (2015).
    [Crossref] [PubMed]
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  34. T. Kobatake, T. Kato, H. Itobe, Y. Nakagawa, and T. Tanabe, “Thermal effects on Kerr comb generation in a CaF2 whispering gallery mode microcavity,” IEEE Photonics J. 8, 4501109 (2016).
    [Crossref]
  35. H. Guo, M. Karpov, E. Lucas, A. Kordts, M. H. P. Pfeiffer, V. Brasch, G. Lihachev, V. E. Lobanov, M. L. Gorodetsky, and T. J. Kippenberg, “Universal dynamics and deterministic switching of dissipative Kerr solitons in optical microresonators,” Nat. Phys., advance online publication (2016).
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  36. C. Joshi, J. K. Jang, K. Luke, X. Ji, S. A. Miller, A. Klenner, Y. Okawachi, M. Lipson, and A. L. Gaeta, “Thermally controlled comb generation and soliton modelocking in microresonators,” Opt. Lett. 41, 2565–2568 (2016).
    [Crossref] [PubMed]
  37. M. Yu, Y. Okawachi, A. G. Griffith, M. Lipson, and A. L. Gaeta, “Mode-locked mid-infrared frequency combs in a silicon microresonator,” Optica 3, 854–860 (2016).
    [Crossref]
  38. J. K. Jang, M. Erkintalo, S. Coen, and S. G. Murdoch, “Temporal tweezing of light through the trapping and manipulation of temporal cavity solitons,” Nat. Commun. 6, 7370 (2015).
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  39. J. K. Jang, M. Erkintalo, S. G. Murdoch, and S. Coen, “Writing and erasing of temporal cavity solitons by direct phase modulation of the cavity driving field,” Opt. Lett. 40, 4755–4758 (2015).
    [Crossref] [PubMed]
  40. H. Taheri, A. A. Eftekhar, K. Wiesenfeld, and A. Adibi, “Soliton formation in whispering-gallery-mode resonators via input phase modulation,” IEEE Photonics J. 7, 9 (2015).
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  42. C. Bao, J. Jaramillo-Villegas, Y. Xuan, D. E. Leaird, M. Qi, and A. M. Weiner, “Observation of Fermi-Pasta-Ulam recurrence in an on-chip optical microresonator,” arXiv:1606.06788 (2016).
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
  47. J. K. Jang, M. Erkintalo, K. Luo, G.-L. Oppo, S. Coen, and S. G. Murdoch, “Controlled merging and annihilation of localised dissipative structures in an ac-driven damped nonlinear schrödinger system,” New J. Phys. 18, 033034 (2016).
    [Crossref]
  48. D. Turaev, A. G. Vladimirov, and S. Zelik, “Long-range interaction and synchronization of oscillating dissipative solitons,” Phys. Rev. Lett. 108, 263906 (2012).
    [Crossref] [PubMed]
  49. G. P. Lin, R. Martinenghi, S. Diallo, K. Saleh, A. Coillet, and Y. K. Chembo, “Spectro-temporal dynamics of Kerr combs with parametric seeding,” Appl. Opt. 54, 2407–2412 (2015).
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2016 (8)

X. Xue and A. M. Weiner, “Microwave photonics connected with microresonator frequency combs,” Front. Optoelectron. 9, 238–248 (2016).
[Crossref]

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip based optical frequency comb using soliton Cherenkov radiation,” Science 351, 357–360 (2016).
[Crossref] [PubMed]

A. A. Savchenkov, A. B. Matsko, and L. Maleki, “On frequency combs in monolithic resonators,” Nanophotonics 5, 363 (2016).
[Crossref]

T. Hansson and S. Wabnitz, “Dynamics of microresonator frequency comb generation: models and stability,” Nanophotonics 5, 231–243 (2016).
[Crossref]

T. Kobatake, T. Kato, H. Itobe, Y. Nakagawa, and T. Tanabe, “Thermal effects on Kerr comb generation in a CaF2 whispering gallery mode microcavity,” IEEE Photonics J. 8, 4501109 (2016).
[Crossref]

J. K. Jang, M. Erkintalo, K. Luo, G.-L. Oppo, S. Coen, and S. G. Murdoch, “Controlled merging and annihilation of localised dissipative structures in an ac-driven damped nonlinear schrödinger system,” New J. Phys. 18, 033034 (2016).
[Crossref]

C. Joshi, J. K. Jang, K. Luke, X. Ji, S. A. Miller, A. Klenner, Y. Okawachi, M. Lipson, and A. L. Gaeta, “Thermally controlled comb generation and soliton modelocking in microresonators,” Opt. Lett. 41, 2565–2568 (2016).
[Crossref] [PubMed]

M. Yu, Y. Okawachi, A. G. Griffith, M. Lipson, and A. L. Gaeta, “Mode-locked mid-infrared frequency combs in a silicon microresonator,” Optica 3, 854–860 (2016).
[Crossref]

2015 (10)

G. P. Lin, R. Martinenghi, S. Diallo, K. Saleh, A. Coillet, and Y. K. Chembo, “Spectro-temporal dynamics of Kerr combs with parametric seeding,” Appl. Opt. 54, 2407–2412 (2015).
[Crossref] [PubMed]

J. A. Jaramillo-Villegas, X. X. Xue, P. H. Wang, D. E. Leaird, and A. M. Weiner, “Deterministic single soliton generation and compression in microring resonators avoiding the chaotic region,” Opt. Express 23, 9618–9626 (2015).
[Crossref] [PubMed]

K. Luo, J. K. Jang, S. Coen, S. G. Murdoch, and M. Erkintalo, “Spontaneous creation and annihilation of temporal cavity solitons in a coherently driven passive fiber resonator,” Opt. Lett. 40, 3735–3738 (2015).
[Crossref] [PubMed]

J. K. Jang, M. Erkintalo, S. G. Murdoch, and S. Coen, “Writing and erasing of temporal cavity solitons by direct phase modulation of the cavity driving field,” Opt. Lett. 40, 4755–4758 (2015).
[Crossref] [PubMed]

X. Yi, Q.-F. Yang, K. Y. Yang, M.-G. Suh, and K. Vahala, “Soliton frequency comb at microwave rates in a high-Q silica microresonator,” Optica 2, 1078–1085 (2015).
[Crossref]

J. K. Jang, M. Erkintalo, S. Coen, and S. G. Murdoch, “Temporal tweezing of light through the trapping and manipulation of temporal cavity solitons,” Nat. Commun. 6, 7370 (2015).
[Crossref] [PubMed]

H. Taheri, A. A. Eftekhar, K. Wiesenfeld, and A. Adibi, “Soliton formation in whispering-gallery-mode resonators via input phase modulation,” IEEE Photonics J. 7, 9 (2015).
[Crossref]

V. E. Lobanov, G. Lihachev, and M. L. Gorodetsky, “Generation of platicons and frequency combs in optical microresonators with normal GVD by modulated pump,” EPL 112, 54008 (2015).
[Crossref]

C. Milián, A. V. Gorbach, M. Taki, A. V. Yulin, and D. V. Skryabin, “Solitons and frequency combs in silica microring resonators: Interplay of the raman and higher-order dispersion effects,” Phys. Rev. A 92, 033851 (2015).
[Crossref]

A. G. Griffith, R. K. W. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. J. Yu, C. T. Phare, C. B. Poitras, A. L. Gaeta, and M. Lipson, “Silicon-chip mid-infrared frequency comb generation,” Nat. Commun. 6, 5 (2015).
[Crossref]

2014 (8)

B. J. M. Hausmann, I. Bulu, V. Venkataraman, P. Deotare, and M. Loncar, “Diamond nonlinear photonics,” Nat. Photonics 8, 369–374 (2014).
[Crossref]

V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, “Generation of Kerr frequency combs in a sapphire whispering gallery mode microresonator,” Opt. Eng. 53, 122607 (2014).
[Crossref]

T. Herr, V. Brasch, J. D. Jost, I. Mirgorodskiy, G. Lihachev, M. L. Gorodetsky, and T. J. Kippenberg, “Mode spectrum and temporal soliton formation in optical microresonators,” Phys. Rev. Lett. 113, 123901 (2014).
[Crossref] [PubMed]

C. Godey, I. V. Balakireva, A. Coillet, and Y. K. Chembo, “Stability analysis of the spatiotemporal Lugiato-Lefever model for Kerr optical frequency combs in the anomalous and normal dispersion regimes,” Phys. Rev. A 89, 063814 (2014).
[Crossref]

P. Del’Haye, K. Beha, S. B. Papp, and S. A. Diddams, “Self-injection locking and phase-locked states in microresonator-based optical frequency combs,” Phys. Rev. Lett. 112, 043905 (2014).
[Crossref]

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2014).
[Crossref]

T. Hansson, D. Modotto, and S. Wabnitz, “On the numerical simulation of Kerr frequency combs using coupled mode equations,” Opt. Commun. 312, 134–136 (2014).
[Crossref]

C. Bao, L. Zhang, A. Matsko, Y. Yan, Z. Zhao, G. Xie, A. M. Agarwal, L. C. Kimerling, J. Michel, L. Maleki, and A. E. Willner, “Nonlinear conversion efficiency in Kerr frequency comb generation,” Opt. Lett. 39, 6126–6129 (2014).
[Crossref] [PubMed]

2013 (3)

H. Jung, C. Xiong, K. Y. Fong, X. Zhang, and H. X. Tang, “Optical frequency comb generation from aluminum nitride microring resonator,” Opt. Lett. 38, 2810–2813 (2013).
[Crossref] [PubMed]

S. B. Papp, P. Del’Haye, and S. A. Diddams, “Mechanical control of a microrod-resonator optical frequency comb,” Phys. Rev. X 3, 031003 (2013).

C. Y. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. W. Hänsch, N. Picquè, and T. J. Kippenberg, “Mid-infrared optical frequency combs at 2.5 um based on crystalline microresonators,” Nat. Commun. 4, 1345 (2013).
[Crossref]

2012 (5)

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photonics 6, 480–487 (2012).
[Crossref]

J. Li, H. Lee, T. Chen, and K. J. Vahala, “Low-pump-power, low-phase-noise, and microwave to millimeter-wave repetition rate operation in microcombs,” Phys. Rev. Lett. 109, 233901 (2012).
[Crossref]

I. S. Grudinin, L. Baumgartel, and N. Yu, “Frequency comb from a microresonator with engineered spectrum,” Opt. Express 20, 6604–6609 (2012).
[Crossref] [PubMed]

A. B. Matsko, A. A. Savchenkov, and L. Maleki, “On excitation of breather solitons in an optical microresonator,” Opt. Lett. 37, 4856–4858 (2012).
[Crossref] [PubMed]

D. Turaev, A. G. Vladimirov, and S. Zelik, “Long-range interaction and synchronization of oscillating dissipative solitons,” Phys. Rev. Lett. 108, 263906 (2012).
[Crossref] [PubMed]

2011 (1)

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332, 555–559 (2011).
[Crossref] [PubMed]

2010 (3)

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics 4, 41–45 (2010).
[Crossref]

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4, 37–40 (2010).
[Crossref]

Y. K. Chembo and N. Yu, “Modal expansion approach to optical-frequency-comb generation with monolithic whispering-gallery-mode resonators,” Phys. Rev. A 82, 033801 (2010).
[Crossref]

2008 (1)

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, “Tunable optical frequency comb with a crystalline whispering gallery mode resonator,” Phys. Rev. Lett. 101, 093902 (2008).
[Crossref] [PubMed]

2007 (2)

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[Crossref]

I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Four-wave-mixing parametric oscillations in dispersion-compensated high-Q silica microspheres,” Phys. Rev. A 76, 043837 (2007).
[Crossref]

2005 (1)

2004 (1)

1992 (1)

V. S. Il’chenko and M. L. Gorodetskii, “Thermal nonlinear effects in optical whispering gallery microresonators,” Laser Phys. 2, 1004–1009 (1992).

1989 (1)

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137, 393–397 (1989).
[Crossref]

Adibi, A.

H. Taheri, A. A. Eftekhar, K. Wiesenfeld, and A. Adibi, “Soliton formation in whispering-gallery-mode resonators via input phase modulation,” IEEE Photonics J. 7, 9 (2015).
[Crossref]

Agarwal, A. M.

Agha, I. H.

I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Four-wave-mixing parametric oscillations in dispersion-compensated high-Q silica microspheres,” Phys. Rev. A 76, 043837 (2007).
[Crossref]

Arcizet, O.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[Crossref]

Balakireva, I. V.

C. Godey, I. V. Balakireva, A. Coillet, and Y. K. Chembo, “Stability analysis of the spatiotemporal Lugiato-Lefever model for Kerr optical frequency combs in the anomalous and normal dispersion regimes,” Phys. Rev. A 89, 063814 (2014).
[Crossref]

Bao, C.

C. Bao, L. Zhang, A. Matsko, Y. Yan, Z. Zhao, G. Xie, A. M. Agarwal, L. C. Kimerling, J. Michel, L. Maleki, and A. E. Willner, “Nonlinear conversion efficiency in Kerr frequency comb generation,” Opt. Lett. 39, 6126–6129 (2014).
[Crossref] [PubMed]

C. Bao, J. Jaramillo-Villegas, Y. Xuan, D. E. Leaird, M. Qi, and A. M. Weiner, “Observation of Fermi-Pasta-Ulam recurrence in an on-chip optical microresonator,” arXiv:1606.06788 (2016).

Baumgartel, L.

Beha, K.

P. Del’Haye, K. Beha, S. B. Papp, and S. A. Diddams, “Self-injection locking and phase-locked states in microresonator-based optical frequency combs,” Phys. Rev. Lett. 112, 043905 (2014).
[Crossref]

Braginsky, V. B.

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V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip based optical frequency comb using soliton Cherenkov radiation,” Science 351, 357–360 (2016).
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T. Herr, V. Brasch, J. D. Jost, I. Mirgorodskiy, G. Lihachev, M. L. Gorodetsky, and T. J. Kippenberg, “Mode spectrum and temporal soliton formation in optical microresonators,” Phys. Rev. Lett. 113, 123901 (2014).
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J. K. Jang, M. Erkintalo, S. G. Murdoch, and S. Coen, “Writing and erasing of temporal cavity solitons by direct phase modulation of the cavity driving field,” Opt. Lett. 40, 4755–4758 (2015).
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C. Godey, I. V. Balakireva, A. Coillet, and Y. K. Chembo, “Stability analysis of the spatiotemporal Lugiato-Lefever model for Kerr optical frequency combs in the anomalous and normal dispersion regimes,” Phys. Rev. A 89, 063814 (2014).
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S. B. Papp, P. Del’Haye, and S. A. Diddams, “Mechanical control of a microrod-resonator optical frequency comb,” Phys. Rev. X 3, 031003 (2013).

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B. J. M. Hausmann, I. Bulu, V. Venkataraman, P. Deotare, and M. Loncar, “Diamond nonlinear photonics,” Nat. Photonics 8, 369–374 (2014).
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Diallo, S.

Diddams, S. A.

P. Del’Haye, K. Beha, S. B. Papp, and S. A. Diddams, “Self-injection locking and phase-locked states in microresonator-based optical frequency combs,” Phys. Rev. Lett. 112, 043905 (2014).
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S. B. Papp, P. Del’Haye, and S. A. Diddams, “Mechanical control of a microrod-resonator optical frequency comb,” Phys. Rev. X 3, 031003 (2013).

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L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics 4, 41–45 (2010).
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J. K. Jang, M. Erkintalo, K. Luo, G.-L. Oppo, S. Coen, and S. G. Murdoch, “Controlled merging and annihilation of localised dissipative structures in an ac-driven damped nonlinear schrödinger system,” New J. Phys. 18, 033034 (2016).
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J. K. Jang, M. Erkintalo, S. Coen, and S. G. Murdoch, “Temporal tweezing of light through the trapping and manipulation of temporal cavity solitons,” Nat. Commun. 6, 7370 (2015).
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K. Luo, J. K. Jang, S. Coen, S. G. Murdoch, and M. Erkintalo, “Spontaneous creation and annihilation of temporal cavity solitons in a coherently driven passive fiber resonator,” Opt. Lett. 40, 3735–3738 (2015).
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J. K. Jang, M. Erkintalo, S. G. Murdoch, and S. Coen, “Writing and erasing of temporal cavity solitons by direct phase modulation of the cavity driving field,” Opt. Lett. 40, 4755–4758 (2015).
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A. G. Griffith, R. K. W. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. J. Yu, C. T. Phare, C. B. Poitras, A. L. Gaeta, and M. Lipson, “Silicon-chip mid-infrared frequency comb generation,” Nat. Commun. 6, 5 (2015).
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L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics 4, 41–45 (2010).
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Fong, K. Y.

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A. G. Griffith, R. K. W. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. J. Yu, C. T. Phare, C. B. Poitras, A. L. Gaeta, and M. Lipson, “Silicon-chip mid-infrared frequency comb generation,” Nat. Commun. 6, 5 (2015).
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I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Four-wave-mixing parametric oscillations in dispersion-compensated high-Q silica microspheres,” Phys. Rev. A 76, 043837 (2007).
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M. Yu, J. K. Jang, Y. Okawachi, A. G. Griffith, K. Luke, S. A. Miller, X. Ji, M. Lipson, and A. L. Gaeta, “Breather soliton dynamics in microresonators,” arXiv:1609.01760 (2016).

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T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photonics 6, 480–487 (2012).
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V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip based optical frequency comb using soliton Cherenkov radiation,” Science 351, 357–360 (2016).
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C. Godey, I. V. Balakireva, A. Coillet, and Y. K. Chembo, “Stability analysis of the spatiotemporal Lugiato-Lefever model for Kerr optical frequency combs in the anomalous and normal dispersion regimes,” Phys. Rev. A 89, 063814 (2014).
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J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4, 37–40 (2010).
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C. Milián, A. V. Gorbach, M. Taki, A. V. Yulin, and D. V. Skryabin, “Solitons and frequency combs in silica microring resonators: Interplay of the raman and higher-order dispersion effects,” Phys. Rev. A 92, 033851 (2015).
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V. S. Il’chenko and M. L. Gorodetskii, “Thermal nonlinear effects in optical whispering gallery microresonators,” Laser Phys. 2, 1004–1009 (1992).

Gorodetsky, M. L.

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip based optical frequency comb using soliton Cherenkov radiation,” Science 351, 357–360 (2016).
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T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2014).
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T. Herr, V. Brasch, J. D. Jost, I. Mirgorodskiy, G. Lihachev, M. L. Gorodetsky, and T. J. Kippenberg, “Mode spectrum and temporal soliton formation in optical microresonators,” Phys. Rev. Lett. 113, 123901 (2014).
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T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photonics 6, 480–487 (2012).
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A. E. Fomin, M. L. Gorodetsky, I. S. Grudinin, and V. S. Ilchenko, “Nonstationary nonlinear effects in optical microspheres,” J. Opt. Soc. Am. B 22, 459–465 (2005).
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V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137, 393–397 (1989).
[Crossref]

H. Guo, M. Karpov, E. Lucas, A. Kordts, M. H. P. Pfeiffer, V. Brasch, G. Lihachev, V. E. Lobanov, M. L. Gorodetsky, and T. J. Kippenberg, “Universal dynamics and deterministic switching of dissipative Kerr solitons in optical microresonators,” Nat. Phys., advance online publication (2016).
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Griffith, A. G.

M. Yu, Y. Okawachi, A. G. Griffith, M. Lipson, and A. L. Gaeta, “Mode-locked mid-infrared frequency combs in a silicon microresonator,” Optica 3, 854–860 (2016).
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A. G. Griffith, R. K. W. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. J. Yu, C. T. Phare, C. B. Poitras, A. L. Gaeta, and M. Lipson, “Silicon-chip mid-infrared frequency comb generation,” Nat. Commun. 6, 5 (2015).
[Crossref]

M. Yu, J. K. Jang, Y. Okawachi, A. G. Griffith, K. Luke, S. A. Miller, X. Ji, M. Lipson, and A. L. Gaeta, “Breather soliton dynamics in microresonators,” arXiv:1609.01760 (2016).

Grudinin, I. S.

Guo, H.

H. Guo, M. Karpov, E. Lucas, A. Kordts, M. H. P. Pfeiffer, V. Brasch, G. Lihachev, V. E. Lobanov, M. L. Gorodetsky, and T. J. Kippenberg, “Universal dynamics and deterministic switching of dissipative Kerr solitons in optical microresonators,” Nat. Phys., advance online publication (2016).
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C. Y. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. W. Hänsch, N. Picquè, and T. J. Kippenberg, “Mid-infrared optical frequency combs at 2.5 um based on crystalline microresonators,” Nat. Commun. 4, 1345 (2013).
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[Crossref]

Hausmann, B. J. M.

B. J. M. Hausmann, I. Bulu, V. Venkataraman, P. Deotare, and M. Loncar, “Diamond nonlinear photonics,” Nat. Photonics 8, 369–374 (2014).
[Crossref]

Herr, T.

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip based optical frequency comb using soliton Cherenkov radiation,” Science 351, 357–360 (2016).
[Crossref] [PubMed]

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2014).
[Crossref]

T. Herr, V. Brasch, J. D. Jost, I. Mirgorodskiy, G. Lihachev, M. L. Gorodetsky, and T. J. Kippenberg, “Mode spectrum and temporal soliton formation in optical microresonators,” Phys. Rev. Lett. 113, 123901 (2014).
[Crossref] [PubMed]

C. Y. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. W. Hänsch, N. Picquè, and T. J. Kippenberg, “Mid-infrared optical frequency combs at 2.5 um based on crystalline microresonators,” Nat. Commun. 4, 1345 (2013).
[Crossref]

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photonics 6, 480–487 (2012).
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Hofer, J.

C. Y. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. W. Hänsch, N. Picquè, and T. J. Kippenberg, “Mid-infrared optical frequency combs at 2.5 um based on crystalline microresonators,” Nat. Commun. 4, 1345 (2013).
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Holzwarth, R.

C. Y. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. W. Hänsch, N. Picquè, and T. J. Kippenberg, “Mid-infrared optical frequency combs at 2.5 um based on crystalline microresonators,” Nat. Commun. 4, 1345 (2013).
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T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photonics 6, 480–487 (2012).
[Crossref]

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332, 555–559 (2011).
[Crossref] [PubMed]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[Crossref]

Il’chenko, V. S.

V. S. Il’chenko and M. L. Gorodetskii, “Thermal nonlinear effects in optical whispering gallery microresonators,” Laser Phys. 2, 1004–1009 (1992).

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V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, “Generation of Kerr frequency combs in a sapphire whispering gallery mode microresonator,” Opt. Eng. 53, 122607 (2014).
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[Crossref]

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137, 393–397 (1989).
[Crossref]

Itobe, H.

T. Kobatake, T. Kato, H. Itobe, Y. Nakagawa, and T. Tanabe, “Thermal effects on Kerr comb generation in a CaF2 whispering gallery mode microcavity,” IEEE Photonics J. 8, 4501109 (2016).
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Jang, J. K.

J. K. Jang, M. Erkintalo, K. Luo, G.-L. Oppo, S. Coen, and S. G. Murdoch, “Controlled merging and annihilation of localised dissipative structures in an ac-driven damped nonlinear schrödinger system,” New J. Phys. 18, 033034 (2016).
[Crossref]

C. Joshi, J. K. Jang, K. Luke, X. Ji, S. A. Miller, A. Klenner, Y. Okawachi, M. Lipson, and A. L. Gaeta, “Thermally controlled comb generation and soliton modelocking in microresonators,” Opt. Lett. 41, 2565–2568 (2016).
[Crossref] [PubMed]

J. K. Jang, M. Erkintalo, S. G. Murdoch, and S. Coen, “Writing and erasing of temporal cavity solitons by direct phase modulation of the cavity driving field,” Opt. Lett. 40, 4755–4758 (2015).
[Crossref] [PubMed]

K. Luo, J. K. Jang, S. Coen, S. G. Murdoch, and M. Erkintalo, “Spontaneous creation and annihilation of temporal cavity solitons in a coherently driven passive fiber resonator,” Opt. Lett. 40, 3735–3738 (2015).
[Crossref] [PubMed]

J. K. Jang, M. Erkintalo, S. Coen, and S. G. Murdoch, “Temporal tweezing of light through the trapping and manipulation of temporal cavity solitons,” Nat. Commun. 6, 7370 (2015).
[Crossref] [PubMed]

M. Yu, J. K. Jang, Y. Okawachi, A. G. Griffith, K. Luke, S. A. Miller, X. Ji, M. Lipson, and A. L. Gaeta, “Breather soliton dynamics in microresonators,” arXiv:1609.01760 (2016).

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C. Bao, J. Jaramillo-Villegas, Y. Xuan, D. E. Leaird, M. Qi, and A. M. Weiner, “Observation of Fermi-Pasta-Ulam recurrence in an on-chip optical microresonator,” arXiv:1606.06788 (2016).

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Ji, X.

C. Joshi, J. K. Jang, K. Luke, X. Ji, S. A. Miller, A. Klenner, Y. Okawachi, M. Lipson, and A. L. Gaeta, “Thermally controlled comb generation and soliton modelocking in microresonators,” Opt. Lett. 41, 2565–2568 (2016).
[Crossref] [PubMed]

M. Yu, J. K. Jang, Y. Okawachi, A. G. Griffith, K. Luke, S. A. Miller, X. Ji, M. Lipson, and A. L. Gaeta, “Breather soliton dynamics in microresonators,” arXiv:1609.01760 (2016).

Joshi, C.

Jost, J. D.

T. Herr, V. Brasch, J. D. Jost, I. Mirgorodskiy, G. Lihachev, M. L. Gorodetsky, and T. J. Kippenberg, “Mode spectrum and temporal soliton formation in optical microresonators,” Phys. Rev. Lett. 113, 123901 (2014).
[Crossref] [PubMed]

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2014).
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Jung, H.

Karpov, M.

H. Guo, M. Karpov, E. Lucas, A. Kordts, M. H. P. Pfeiffer, V. Brasch, G. Lihachev, V. E. Lobanov, M. L. Gorodetsky, and T. J. Kippenberg, “Universal dynamics and deterministic switching of dissipative Kerr solitons in optical microresonators,” Nat. Phys., advance online publication (2016).
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T. Kobatake, T. Kato, H. Itobe, Y. Nakagawa, and T. Tanabe, “Thermal effects on Kerr comb generation in a CaF2 whispering gallery mode microcavity,” IEEE Photonics J. 8, 4501109 (2016).
[Crossref]

Kimerling, L. C.

Kippenberg, T. J.

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip based optical frequency comb using soliton Cherenkov radiation,” Science 351, 357–360 (2016).
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T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2014).
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T. Herr, V. Brasch, J. D. Jost, I. Mirgorodskiy, G. Lihachev, M. L. Gorodetsky, and T. J. Kippenberg, “Mode spectrum and temporal soliton formation in optical microresonators,” Phys. Rev. Lett. 113, 123901 (2014).
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C. Y. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. W. Hänsch, N. Picquè, and T. J. Kippenberg, “Mid-infrared optical frequency combs at 2.5 um based on crystalline microresonators,” Nat. Commun. 4, 1345 (2013).
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T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photonics 6, 480–487 (2012).
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T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332, 555–559 (2011).
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P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
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H. Guo, M. Karpov, E. Lucas, A. Kordts, M. H. P. Pfeiffer, V. Brasch, G. Lihachev, V. E. Lobanov, M. L. Gorodetsky, and T. J. Kippenberg, “Universal dynamics and deterministic switching of dissipative Kerr solitons in optical microresonators,” Nat. Phys., advance online publication (2016).
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Klenner, A.

Kobatake, T.

T. Kobatake, T. Kato, H. Itobe, Y. Nakagawa, and T. Tanabe, “Thermal effects on Kerr comb generation in a CaF2 whispering gallery mode microcavity,” IEEE Photonics J. 8, 4501109 (2016).
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T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2014).
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Kordts, A.

H. Guo, M. Karpov, E. Lucas, A. Kordts, M. H. P. Pfeiffer, V. Brasch, G. Lihachev, V. E. Lobanov, M. L. Gorodetsky, and T. J. Kippenberg, “Universal dynamics and deterministic switching of dissipative Kerr solitons in optical microresonators,” Nat. Phys., advance online publication (2016).
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A. G. Griffith, R. K. W. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. J. Yu, C. T. Phare, C. B. Poitras, A. L. Gaeta, and M. Lipson, “Silicon-chip mid-infrared frequency comb generation,” Nat. Commun. 6, 5 (2015).
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J. A. Jaramillo-Villegas, X. X. Xue, P. H. Wang, D. E. Leaird, and A. M. Weiner, “Deterministic single soliton generation and compression in microring resonators avoiding the chaotic region,” Opt. Express 23, 9618–9626 (2015).
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C. Bao, J. Jaramillo-Villegas, Y. Xuan, D. E. Leaird, M. Qi, and A. M. Weiner, “Observation of Fermi-Pasta-Ulam recurrence in an on-chip optical microresonator,” arXiv:1606.06788 (2016).

Lee, H.

J. Li, H. Lee, T. Chen, and K. J. Vahala, “Low-pump-power, low-phase-noise, and microwave to millimeter-wave repetition rate operation in microcombs,” Phys. Rev. Lett. 109, 233901 (2012).
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A. G. Griffith, R. K. W. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. J. Yu, C. T. Phare, C. B. Poitras, A. L. Gaeta, and M. Lipson, “Silicon-chip mid-infrared frequency comb generation,” Nat. Commun. 6, 5 (2015).
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J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4, 37–40 (2010).
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J. Li, H. Lee, T. Chen, and K. J. Vahala, “Low-pump-power, low-phase-noise, and microwave to millimeter-wave repetition rate operation in microcombs,” Phys. Rev. Lett. 109, 233901 (2012).
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V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip based optical frequency comb using soliton Cherenkov radiation,” Science 351, 357–360 (2016).
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V. E. Lobanov, G. Lihachev, and M. L. Gorodetsky, “Generation of platicons and frequency combs in optical microresonators with normal GVD by modulated pump,” EPL 112, 54008 (2015).
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T. Herr, V. Brasch, J. D. Jost, I. Mirgorodskiy, G. Lihachev, M. L. Gorodetsky, and T. J. Kippenberg, “Mode spectrum and temporal soliton formation in optical microresonators,” Phys. Rev. Lett. 113, 123901 (2014).
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H. Guo, M. Karpov, E. Lucas, A. Kordts, M. H. P. Pfeiffer, V. Brasch, G. Lihachev, V. E. Lobanov, M. L. Gorodetsky, and T. J. Kippenberg, “Universal dynamics and deterministic switching of dissipative Kerr solitons in optical microresonators,” Nat. Phys., advance online publication (2016).
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Lin, G. P.

Lipson, M.

M. Yu, Y. Okawachi, A. G. Griffith, M. Lipson, and A. L. Gaeta, “Mode-locked mid-infrared frequency combs in a silicon microresonator,” Optica 3, 854–860 (2016).
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C. Joshi, J. K. Jang, K. Luke, X. Ji, S. A. Miller, A. Klenner, Y. Okawachi, M. Lipson, and A. L. Gaeta, “Thermally controlled comb generation and soliton modelocking in microresonators,” Opt. Lett. 41, 2565–2568 (2016).
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A. G. Griffith, R. K. W. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. J. Yu, C. T. Phare, C. B. Poitras, A. L. Gaeta, and M. Lipson, “Silicon-chip mid-infrared frequency comb generation,” Nat. Commun. 6, 5 (2015).
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J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4, 37–40 (2010).
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M. Yu, J. K. Jang, Y. Okawachi, A. G. Griffith, K. Luke, S. A. Miller, X. Ji, M. Lipson, and A. L. Gaeta, “Breather soliton dynamics in microresonators,” arXiv:1609.01760 (2016).

Little, B. E.

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics 4, 41–45 (2010).
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Lobanov, V. E.

V. E. Lobanov, G. Lihachev, and M. L. Gorodetsky, “Generation of platicons and frequency combs in optical microresonators with normal GVD by modulated pump,” EPL 112, 54008 (2015).
[Crossref]

H. Guo, M. Karpov, E. Lucas, A. Kordts, M. H. P. Pfeiffer, V. Brasch, G. Lihachev, V. E. Lobanov, M. L. Gorodetsky, and T. J. Kippenberg, “Universal dynamics and deterministic switching of dissipative Kerr solitons in optical microresonators,” Nat. Phys., advance online publication (2016).
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B. J. M. Hausmann, I. Bulu, V. Venkataraman, P. Deotare, and M. Loncar, “Diamond nonlinear photonics,” Nat. Photonics 8, 369–374 (2014).
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H. Guo, M. Karpov, E. Lucas, A. Kordts, M. H. P. Pfeiffer, V. Brasch, G. Lihachev, V. E. Lobanov, M. L. Gorodetsky, and T. J. Kippenberg, “Universal dynamics and deterministic switching of dissipative Kerr solitons in optical microresonators,” Nat. Phys., advance online publication (2016).
[Crossref]

Luke, K.

C. Joshi, J. K. Jang, K. Luke, X. Ji, S. A. Miller, A. Klenner, Y. Okawachi, M. Lipson, and A. L. Gaeta, “Thermally controlled comb generation and soliton modelocking in microresonators,” Opt. Lett. 41, 2565–2568 (2016).
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M. Yu, J. K. Jang, Y. Okawachi, A. G. Griffith, K. Luke, S. A. Miller, X. Ji, M. Lipson, and A. L. Gaeta, “Breather soliton dynamics in microresonators,” arXiv:1609.01760 (2016).

Luo, K.

J. K. Jang, M. Erkintalo, K. Luo, G.-L. Oppo, S. Coen, and S. G. Murdoch, “Controlled merging and annihilation of localised dissipative structures in an ac-driven damped nonlinear schrödinger system,” New J. Phys. 18, 033034 (2016).
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K. Luo, J. K. Jang, S. Coen, S. G. Murdoch, and M. Erkintalo, “Spontaneous creation and annihilation of temporal cavity solitons in a coherently driven passive fiber resonator,” Opt. Lett. 40, 3735–3738 (2015).
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A. A. Savchenkov, A. B. Matsko, and L. Maleki, “On frequency combs in monolithic resonators,” Nanophotonics 5, 363 (2016).
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V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, “Generation of Kerr frequency combs in a sapphire whispering gallery mode microresonator,” Opt. Eng. 53, 122607 (2014).
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C. Bao, L. Zhang, A. Matsko, Y. Yan, Z. Zhao, G. Xie, A. M. Agarwal, L. C. Kimerling, J. Michel, L. Maleki, and A. E. Willner, “Nonlinear conversion efficiency in Kerr frequency comb generation,” Opt. Lett. 39, 6126–6129 (2014).
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A. B. Matsko, A. A. Savchenkov, and L. Maleki, “On excitation of breather solitons in an optical microresonator,” Opt. Lett. 37, 4856–4858 (2012).
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A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, “Tunable optical frequency comb with a crystalline whispering gallery mode resonator,” Phys. Rev. Lett. 101, 093902 (2008).
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Matsko, A.

Matsko, A. B.

A. A. Savchenkov, A. B. Matsko, and L. Maleki, “On frequency combs in monolithic resonators,” Nanophotonics 5, 363 (2016).
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V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, “Generation of Kerr frequency combs in a sapphire whispering gallery mode microresonator,” Opt. Eng. 53, 122607 (2014).
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A. B. Matsko, A. A. Savchenkov, and L. Maleki, “On excitation of breather solitons in an optical microresonator,” Opt. Lett. 37, 4856–4858 (2012).
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A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, “Tunable optical frequency comb with a crystalline whispering gallery mode resonator,” Phys. Rev. Lett. 101, 093902 (2008).
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Michel, J.

Milián, C.

C. Milián, A. V. Gorbach, M. Taki, A. V. Yulin, and D. V. Skryabin, “Solitons and frequency combs in silica microring resonators: Interplay of the raman and higher-order dispersion effects,” Phys. Rev. A 92, 033851 (2015).
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Miller, S. A.

C. Joshi, J. K. Jang, K. Luke, X. Ji, S. A. Miller, A. Klenner, Y. Okawachi, M. Lipson, and A. L. Gaeta, “Thermally controlled comb generation and soliton modelocking in microresonators,” Opt. Lett. 41, 2565–2568 (2016).
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M. Yu, J. K. Jang, Y. Okawachi, A. G. Griffith, K. Luke, S. A. Miller, X. Ji, M. Lipson, and A. L. Gaeta, “Breather soliton dynamics in microresonators,” arXiv:1609.01760 (2016).

Mirgorodskiy, I.

T. Herr, V. Brasch, J. D. Jost, I. Mirgorodskiy, G. Lihachev, M. L. Gorodetsky, and T. J. Kippenberg, “Mode spectrum and temporal soliton formation in optical microresonators,” Phys. Rev. Lett. 113, 123901 (2014).
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T. Hansson, D. Modotto, and S. Wabnitz, “On the numerical simulation of Kerr frequency combs using coupled mode equations,” Opt. Commun. 312, 134–136 (2014).
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A. G. Griffith, R. K. W. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. J. Yu, C. T. Phare, C. B. Poitras, A. L. Gaeta, and M. Lipson, “Silicon-chip mid-infrared frequency comb generation,” Nat. Commun. 6, 5 (2015).
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L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics 4, 41–45 (2010).
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Moss, D. J.

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics 4, 41–45 (2010).
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Murdoch, S. G.

J. K. Jang, M. Erkintalo, K. Luo, G.-L. Oppo, S. Coen, and S. G. Murdoch, “Controlled merging and annihilation of localised dissipative structures in an ac-driven damped nonlinear schrödinger system,” New J. Phys. 18, 033034 (2016).
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J. K. Jang, M. Erkintalo, S. Coen, and S. G. Murdoch, “Temporal tweezing of light through the trapping and manipulation of temporal cavity solitons,” Nat. Commun. 6, 7370 (2015).
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K. Luo, J. K. Jang, S. Coen, S. G. Murdoch, and M. Erkintalo, “Spontaneous creation and annihilation of temporal cavity solitons in a coherently driven passive fiber resonator,” Opt. Lett. 40, 3735–3738 (2015).
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J. K. Jang, M. Erkintalo, S. G. Murdoch, and S. Coen, “Writing and erasing of temporal cavity solitons by direct phase modulation of the cavity driving field,” Opt. Lett. 40, 4755–4758 (2015).
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Nakagawa, Y.

T. Kobatake, T. Kato, H. Itobe, Y. Nakagawa, and T. Tanabe, “Thermal effects on Kerr comb generation in a CaF2 whispering gallery mode microcavity,” IEEE Photonics J. 8, 4501109 (2016).
[Crossref]

Okawachi, Y.

M. Yu, Y. Okawachi, A. G. Griffith, M. Lipson, and A. L. Gaeta, “Mode-locked mid-infrared frequency combs in a silicon microresonator,” Optica 3, 854–860 (2016).
[Crossref]

C. Joshi, J. K. Jang, K. Luke, X. Ji, S. A. Miller, A. Klenner, Y. Okawachi, M. Lipson, and A. L. Gaeta, “Thermally controlled comb generation and soliton modelocking in microresonators,” Opt. Lett. 41, 2565–2568 (2016).
[Crossref] [PubMed]

A. G. Griffith, R. K. W. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. J. Yu, C. T. Phare, C. B. Poitras, A. L. Gaeta, and M. Lipson, “Silicon-chip mid-infrared frequency comb generation,” Nat. Commun. 6, 5 (2015).
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I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Four-wave-mixing parametric oscillations in dispersion-compensated high-Q silica microspheres,” Phys. Rev. A 76, 043837 (2007).
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M. Yu, J. K. Jang, Y. Okawachi, A. G. Griffith, K. Luke, S. A. Miller, X. Ji, M. Lipson, and A. L. Gaeta, “Breather soliton dynamics in microresonators,” arXiv:1609.01760 (2016).

Oppo, G.-L.

J. K. Jang, M. Erkintalo, K. Luo, G.-L. Oppo, S. Coen, and S. G. Murdoch, “Controlled merging and annihilation of localised dissipative structures in an ac-driven damped nonlinear schrödinger system,” New J. Phys. 18, 033034 (2016).
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P. Del’Haye, K. Beha, S. B. Papp, and S. A. Diddams, “Self-injection locking and phase-locked states in microresonator-based optical frequency combs,” Phys. Rev. Lett. 112, 043905 (2014).
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S. B. Papp, P. Del’Haye, and S. A. Diddams, “Mechanical control of a microrod-resonator optical frequency comb,” Phys. Rev. X 3, 031003 (2013).

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V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip based optical frequency comb using soliton Cherenkov radiation,” Science 351, 357–360 (2016).
[Crossref] [PubMed]

H. Guo, M. Karpov, E. Lucas, A. Kordts, M. H. P. Pfeiffer, V. Brasch, G. Lihachev, V. E. Lobanov, M. L. Gorodetsky, and T. J. Kippenberg, “Universal dynamics and deterministic switching of dissipative Kerr solitons in optical microresonators,” Nat. Phys., advance online publication (2016).
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A. G. Griffith, R. K. W. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. J. Yu, C. T. Phare, C. B. Poitras, A. L. Gaeta, and M. Lipson, “Silicon-chip mid-infrared frequency comb generation,” Nat. Commun. 6, 5 (2015).
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Picquè, N.

C. Y. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. W. Hänsch, N. Picquè, and T. J. Kippenberg, “Mid-infrared optical frequency combs at 2.5 um based on crystalline microresonators,” Nat. Commun. 4, 1345 (2013).
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Poitras, C. B.

A. G. Griffith, R. K. W. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. J. Yu, C. T. Phare, C. B. Poitras, A. L. Gaeta, and M. Lipson, “Silicon-chip mid-infrared frequency comb generation,” Nat. Commun. 6, 5 (2015).
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Qi, M.

C. Bao, J. Jaramillo-Villegas, Y. Xuan, D. E. Leaird, M. Qi, and A. M. Weiner, “Observation of Fermi-Pasta-Ulam recurrence in an on-chip optical microresonator,” arXiv:1606.06788 (2016).

Razzari, L.

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics 4, 41–45 (2010).
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Riemensberger, J.

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photonics 6, 480–487 (2012).
[Crossref]

Saleh, K.

Savchenkov, A. A.

A. A. Savchenkov, A. B. Matsko, and L. Maleki, “On frequency combs in monolithic resonators,” Nanophotonics 5, 363 (2016).
[Crossref]

V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, “Generation of Kerr frequency combs in a sapphire whispering gallery mode microresonator,” Opt. Eng. 53, 122607 (2014).
[Crossref]

A. B. Matsko, A. A. Savchenkov, and L. Maleki, “On excitation of breather solitons in an optical microresonator,” Opt. Lett. 37, 4856–4858 (2012).
[Crossref] [PubMed]

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, “Tunable optical frequency comb with a crystalline whispering gallery mode resonator,” Phys. Rev. Lett. 101, 093902 (2008).
[Crossref] [PubMed]

Schliesser, A.

C. Y. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. W. Hänsch, N. Picquè, and T. J. Kippenberg, “Mid-infrared optical frequency combs at 2.5 um based on crystalline microresonators,” Nat. Commun. 4, 1345 (2013).
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P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
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Seidel, D.

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, “Tunable optical frequency comb with a crystalline whispering gallery mode resonator,” Phys. Rev. Lett. 101, 093902 (2008).
[Crossref] [PubMed]

Sharping, J. E.

I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Four-wave-mixing parametric oscillations in dispersion-compensated high-Q silica microspheres,” Phys. Rev. A 76, 043837 (2007).
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Skryabin, D. V.

C. Milián, A. V. Gorbach, M. Taki, A. V. Yulin, and D. V. Skryabin, “Solitons and frequency combs in silica microring resonators: Interplay of the raman and higher-order dispersion effects,” Phys. Rev. A 92, 033851 (2015).
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Solomatine, I.

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, “Tunable optical frequency comb with a crystalline whispering gallery mode resonator,” Phys. Rev. Lett. 101, 093902 (2008).
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X. Yi, Q.-F. Yang, K. Y. Yang, M.-G. Suh, and K. Vahala, “Soliton frequency comb at microwave rates in a high-Q silica microresonator,” Optica 2, 1078–1085 (2015).
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M.-G. Suh, Q.-F. Yang, K. Y. Yang, X. Yi, and K. Vahala, “Microresonator soliton dual-comb spectroscopy,” arXiv:1607.08222 (2016).

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H. Taheri, A. A. Eftekhar, K. Wiesenfeld, and A. Adibi, “Soliton formation in whispering-gallery-mode resonators via input phase modulation,” IEEE Photonics J. 7, 9 (2015).
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Taki, M.

C. Milián, A. V. Gorbach, M. Taki, A. V. Yulin, and D. V. Skryabin, “Solitons and frequency combs in silica microring resonators: Interplay of the raman and higher-order dispersion effects,” Phys. Rev. A 92, 033851 (2015).
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Tanabe, T.

T. Kobatake, T. Kato, H. Itobe, Y. Nakagawa, and T. Tanabe, “Thermal effects on Kerr comb generation in a CaF2 whispering gallery mode microcavity,” IEEE Photonics J. 8, 4501109 (2016).
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J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4, 37–40 (2010).
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Vahala, K.

X. Yi, Q.-F. Yang, K. Y. Yang, M.-G. Suh, and K. Vahala, “Soliton frequency comb at microwave rates in a high-Q silica microresonator,” Optica 2, 1078–1085 (2015).
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M.-G. Suh, Q.-F. Yang, K. Y. Yang, X. Yi, and K. Vahala, “Microresonator soliton dual-comb spectroscopy,” arXiv:1607.08222 (2016).

Vahala, K. J.

J. Li, H. Lee, T. Chen, and K. J. Vahala, “Low-pump-power, low-phase-noise, and microwave to millimeter-wave repetition rate operation in microcombs,” Phys. Rev. Lett. 109, 233901 (2012).
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Appl. Opt. (1)

EPL (1)

V. E. Lobanov, G. Lihachev, and M. L. Gorodetsky, “Generation of platicons and frequency combs in optical microresonators with normal GVD by modulated pump,” EPL 112, 54008 (2015).
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Front. Optoelectron. (1)

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T. Hansson and S. Wabnitz, “Dynamics of microresonator frequency comb generation: models and stability,” Nanophotonics 5, 231–243 (2016).
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A. A. Savchenkov, A. B. Matsko, and L. Maleki, “On frequency combs in monolithic resonators,” Nanophotonics 5, 363 (2016).
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Nat. Commun. (3)

A. G. Griffith, R. K. W. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. J. Yu, C. T. Phare, C. B. Poitras, A. L. Gaeta, and M. Lipson, “Silicon-chip mid-infrared frequency comb generation,” Nat. Commun. 6, 5 (2015).
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C. Y. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. W. Hänsch, N. Picquè, and T. J. Kippenberg, “Mid-infrared optical frequency combs at 2.5 um based on crystalline microresonators,” Nat. Commun. 4, 1345 (2013).
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T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photonics 6, 480–487 (2012).
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T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2014).
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Nature (1)

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
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Other (5)

M.-G. Suh, Q.-F. Yang, K. Y. Yang, X. Yi, and K. Vahala, “Microresonator soliton dual-comb spectroscopy,” arXiv:1607.08222 (2016).

H. Guo, M. Karpov, E. Lucas, A. Kordts, M. H. P. Pfeiffer, V. Brasch, G. Lihachev, V. E. Lobanov, M. L. Gorodetsky, and T. J. Kippenberg, “Universal dynamics and deterministic switching of dissipative Kerr solitons in optical microresonators,” Nat. Phys., advance online publication (2016).
[Crossref]

J. Ye and S. T. Cundiff, Femtosecond Optical Frequency Comb: Principle, Operation and Applications (Springer, 2016).

M. Yu, J. K. Jang, Y. Okawachi, A. G. Griffith, K. Luke, S. A. Miller, X. Ji, M. Lipson, and A. L. Gaeta, “Breather soliton dynamics in microresonators,” arXiv:1609.01760 (2016).

C. Bao, J. Jaramillo-Villegas, Y. Xuan, D. E. Leaird, M. Qi, and A. M. Weiner, “Observation of Fermi-Pasta-Ulam recurrence in an on-chip optical microresonator,” arXiv:1606.06788 (2016).

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Figures (6)

Fig. 1
Fig. 1 Probability p of the final number of solitons distribution for different modulation amplitudes ε and scan speeds α. Final detuning is ζ0 = 18 for the phase and ζ0 = 15 for the amplitude modulation. In each case F ≈ 4.11 and 100 realizations were generated.

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Fig. 2
Fig. 2 Field distribution evolution inside microresonator for different values of phase modulation depth (α = 0.002, F ≈ 4.11): (a) ε = 0 (no modulation); (b,c) ε = 0.04; (d) ε = 0.08; (e) ε = 0.5; (f) fractional modulation frequency Ω = D1/3, ε = 1.5, α = 0.0004, F = 5.

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Fig. 3
Fig. 3 Field distribution evolution inside microresonator for different values of amplitude modulation depth (α = 0.002): (a,b) ε = 0.04; (c) ε = 0.08; (d,e) ε = 0.5; (f) ε = 1.0. Dashed line indicates the halt of frequency scan.

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Fig. 4
Fig. 4 Distribution of number of solitons generated by phase-modulated pump for different values of Δ and ε at α = 0.001, D 2 κ ≈ 0.01. Final detuning is ζ0 = 18: (a) ε = 0.3; (b) ε = 0.6; (c) ε = 1.0.

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Fig. 5
Fig. 5 Probabilities of realizations obtained via pump phase modulation resulting in generation of 1 or 0 solitons (a) vs. thermal nonlinearity coefficient, (b–c) vs. modulation depth and (d) vs thermal relaxation time. In all cases D 2 κ ≈ 0.01, α = 0.002 and Δ = 0. Final detuning is ζ0 = 18.

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Fig. 6
Fig. 6 Experimental measurement of soliton formation upon phase modulation and laser detuning. (a) experimental setup (AFG, arbitrary function generator; CW laser, continuous wave narrow linewidth tunable laser; FPC, fiber polarization controller, EDFA, Erbium-doped fiber amplifier; WGM, whispering gallery mode MgF2 crystalline microresonator; FBG, Fiber Bragg grating filter; PD, photodiode; OSA, optical spectrum analyzer; OSC, oscilloscope); (b) statistics for 100 oscilloscope traces at scan repetition rate of 100 Hz for the output power versus laser detuning without modulation. (c) statistics of traces at 100 Hz with phase modulation, the zero soliton probability is 0.5, one soliton – 0.4, two solitons – 0.1; the inset shows one-soliton spectrum with sech2(x) envelope, spectrum width is 35 nm, line spacing is 12.1 GHz; (d) statistics of 100 traces with amplitude modulation, scan repetition rate is 5 Hz, zero soliton probability – 0.4, one soliton – 0.6.

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Equations (2)

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∂ a μ ∂ τ = − ( 1 + ζ μ ) a μ + i ∑ μ ′ , μ ″ a μ ′ a μ ″ a μ ′ + μ ″ − μ * + f μ exp ( i μ Δ τ ) .
∂ a μ ∂ τ = − ( 1 + i ( ζ μ − Θ ) ) a μ + i ∑ μ ′ , μ ″ a μ ′ a μ ″ a μ ′ + μ ″ − μ * + f μ exp ( i μ Δ τ ) , ∂ Θ ∂ τ = 2 κ τ T ( n 2 T n 2 ∑ μ | a μ | 2 − Θ ) ,

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