Abstract

Microresonator combs exploit parametric oscillation and nonlinear mixing in an ultrahigh-Q cavity. This new comb generator offers unique potential for chip integration and access to high repetition rates. However, time-domain studies reveal an intricate spectral coherence behavior in this type of platform. In particular, coherent, partially coherent or incoherent combs have been observed using the same microresonator under different pumping conditions. In this work, we provide a numerical analysis of the coherence dynamics that supports the above experimental findings and verify particular design rules to achieve spectrally coherent microresonator combs. A particular emphasis is placed in understanding the differences between so-called Type I and Type II combs.

© 2014 Optical Society of America

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2014 (3)

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

M. Erkintalo, S. Coen, “Coherence properties of Kerr frequency combs,” Opt. Lett. 39, 283–286 (2014).
[CrossRef]

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

2013 (13)

T. Godin, B. Wetzel, T. Sylvestre, L. Larger, A. Kudlinski, A. Mussot, A. Ben Salem, M. Zghal, G. Genty, F. Dias, J. M. Dudley, “Real time noise and wavelength correlations in octave-spanning supercontinuum generation,” Opt. Express 21, 18452–18460 (2013).
[CrossRef] [PubMed]

M. R. E. Lamont, Y. Okawachi, A. L. Gaeta, “Route to stabilized ultrabroadband microresonator-based frequency combs,” Opt. Lett. 38, 3478–3481 (2013).
[CrossRef] [PubMed]

K. Saha, Y. Okawachi, B. Shim, J. S. Levy, R. Salem, A. R. Johnson, M. A. Foster, M. R. E. Lamont, M. Lipson, A. L. Gaeta, “Modelocking and femtosecond pulse generation in chip-based frequency combs,” Opt. Express 21, 1335–1343 (2013).
[CrossRef] [PubMed]

S. B. Papp, P. Del’Haye, S. A. Diddams, “Parametric seeding of a microresonator optical frequency comb,” Opt. Express 21, 17615–17624 (2013).
[CrossRef] [PubMed]

F. Leo, L. Gelens, P. Emplit, M. Haelterman, S. Coen, “Dynamics of one-dimensional Kerr cavity solitons,” Opt. Express 21, 9180–9191 (2013).
[CrossRef] [PubMed]

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

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

D. J. Moss, R. Morandotti, A. L. Gaeta, M. Lipson, “New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics,” Nat. Photonics 7, 597–607 (2013).
[CrossRef]

Y. K. Chembo, C. R. Menyuk, “Spatiotemporal Lugiato-Lefever formalism for Kerr-comb generation in whispering gallery-mode resonators,” Phys. Rev. A 87, 053852 (2013).
[CrossRef]

S. Coen, H. G. Randle, T. Sylvestre, M. Erkintalo, “Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato-Lefever model,” Opt. Lett. 38, 37–39 (2013).
[CrossRef] [PubMed]

T. Hansson, D. Modotto, S. Wabnitz, “Dynamics of the modulation instability in microresonator frequency combs,” Phys. Rev. A 88, 023819 (2013).
[CrossRef]

S. Coen, M. Erkintalo, “Universal scaling laws of Kerr frequency combs,” Opt. Lett. 38, 1790–1792 (2013).
[CrossRef] [PubMed]

A. B. Matsko, W. Liang, A. A. Savchenko, L. Maleki, “Chaotic dynamics of frequency combs generated with continuously pumped nonlinear microresonators,” Opt. Lett. 38, 525–527 (2013).
[CrossRef] [PubMed]

2012 (9)

K. Saha, Y. Okawachi, J. S. Levy, R. K. W. Lau, K. Luke, M. A. Foster, M. Lipson, A. L. Gaeta, “Broadband parametric frequency comb generation with a 1 μm pump source,” Opt. Express 20, 26935–26941 (2012).
[CrossRef] [PubMed]

F. Ferdous, H. X. Miao, P. H. Wang, D. E. Leaird, K. Srinivasan, L. Chen, V. Aksyuk, A. M. Weiner, “Probing coherence in microcavity frequency combs via optical pulse shaping,” Opt. Express 20, 21033–21043 (2012).
[CrossRef] [PubMed]

P. H. Wang, F. Ferdous, H. X Miao, J. Wang, D. E. Leaird, K. Srinivasan, L. Chen, V. Aksyuk, A. M. Weiner, “Observation of correlation between route to formation, coherence, noise, and communication performance of Kerr combs,” Opt. Express 20, 29284–29295 (2012).
[CrossRef]

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

J. Riemensberger, K. Hartinger, T. Herr, V. Brasch, R. Holzwarth, T. J. Kippenberg, “Dispersion engineering of thick high-Q silicon nitride ring-resonators via atomic layer deposition,” Opt. Express 20, 27661–27669 (2012).
[CrossRef] [PubMed]

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

J. Li, H. Lee, T. Chen, 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]

A. B. Matsko, A. A. Savchenko, V. S. Ilchenko, D. Seidel, L. Maleki, “Hard and soft excitation regimes of Kerr frequency combs,” Phys. Rev. A 85, 023830 (2012).
[CrossRef]

M. Peccianti, A. Pasquazi, Y. Park, B. E. Little, S. T. Chu, D. J. Moss, R. Morandotti, “Demonstration of a stable ultrafast laser based on a nonlinear microcavity,” Nature Commun. 3, 765 (2012).
[CrossRef]

2011 (10)

A. A. Savchenko, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, L. Maleki, “Kerr combs with selectable central frequency,” Nature Photon. 5, 293–296 (2011).
[CrossRef]

Y. Okawachi, K. Saha, J. S. Levy, Y. H. Wen, M. Lipson, A. L. Gaeta, “Octave-spanning frequency comb generation in a silicon nitride chip,” Opt. Lett. 36, 3398–3400 (2011).
[CrossRef] [PubMed]

P. Del’Haye, T. Herr, E. Garvatin, M. L. Gorodetsky, R. Holzwarth, T. J. Kippenberg, “Octave spanning tunable frequency comb from a microresonator,” Phys. Rev. Lett. 107, 063901 (2011).
[CrossRef]

N. R. Newbury, “Searching for applications with a fine-tooth comb,” Nature Photon. 5, 186–188 (2011).
[CrossRef]

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

W. Liang, A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Seidel, L. Maleki, “Generation of near-infrared frequency combs from a MgF2 whispering gallery mode resonator,” Opt. Lett. 36, 2290–2292 (2011).
[CrossRef] [PubMed]

F. Ferdous, H. X Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, A. M. Weiner, “Spectral line-by-line pulse shaping of on-chip microresonator frequency combs,” Nat. Photonics 5, 770–776 (2011).
[CrossRef]

S. B. Papp, S. A. Diddams, “Spectral and temporal characterization of a fused-quartz-microresonator optical frequency comb,” Phys. Rev. A 84, 053833 (2011).
[CrossRef]

L. Zhang, Y. Yue, R. G. Beausoleil, A. E. Willner, “Analysis and engineering of chromatic dispersion in silicon waveguide bends and ring resonators,” Opt. Express 19, 8102–8107 (2011).
[CrossRef] [PubMed]

A. B. Matsko, A. A. Savchenko, W. Liang, V. S. Ilchenko, D. Seidel, L. Maleki, “Mode-locked Kerr frequency combs,” Opt. Lett. 36, 2845–2847 (2011).
[CrossRef] [PubMed]

2010 (8)

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

S. T. Cundiff, A. M. Weiner, “Optical arbitrary waveform generation,” Nat. Photonics 4, 760–766 (2010).
[CrossRef]

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, 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, M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4, 37–40 (2010).
[CrossRef]

G. Genty, M Surakka, J. Turunen, A. T. Friberg, “Second-order coherence of supercontinuum light,” Opt. Lett. 35, 3057–3059 (2010).
[CrossRef] [PubMed]

Y. K. Chembo, D. V. Strekalov, N. Yu, “Spectrum and dynamics of optical frequency combs generated with monolithic whispering gallery mode resonators,” Phys. Rev. Lett. 104, 103902 (2010).
[CrossRef] [PubMed]

F. Leo, S. Coen, P. Kockaert, S. P. Goza, P. Emplit, M. Haelterman, “Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,” Nat. Photonics 4, 471–476 (2010).
[CrossRef]

H. Lajunen, V. Torres-Company, J. Lancis, E. Silvestre, P. Andres, “Pulse-by-pulse method to characterize partially coherent pulse propagation in instantaneous nonlinear media,” Opt. Express 18, 14979–14991 (2010).
[CrossRef] [PubMed]

2008 (1)

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, 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, T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[CrossRef]

M. A. Foster, A. C. Turner, R. Salem, M. Lipson, A. L. Gaeta, “Broad-band continuous-wave parametric wavelength conversion in silicon nanowaveguides,” Opt. Express 15, 12949–12958 (2007).
[CrossRef] [PubMed]

2006 (2)

T. W. Hänsch, “Nobel Lecture: Passion for precision,” Rev. Mod. Phys. 78, 1297–1309 (2006).
[CrossRef]

J. M. Dudley, G. Genty, S. Coen, “Supercontinuum generation in photonic crystal fibers,” Rev. Mod. Phys. 78, 1135–1184 (2006).
[CrossRef]

2005 (1)

A. B. Matsko, A. A. Savchenko, D. Strekalov, V. S. Ilchenko, L. Maleki, “Optical hyperparametric oscillations in a whispering-gallery-mode resonator: Threshold and phase diffusion,” Phys. Rev. A 71, 033804 (2005).
[CrossRef]

2004 (1)

T. J. Kippenberg, S. M. Spillane, K. J. Vahala, “Kerr-nonlinearity optical parametric oscillation in ultrahigh-Q toroid microcavity,” Phys. Rev. Lett. 93, 083904 (2004).
[CrossRef]

2002 (1)

2000 (2)

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
[CrossRef] [PubMed]

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[CrossRef] [PubMed]

1996 (1)

I. V. Barashenkov, Y. S. Smirnov, “Existence and stability chart for the ac-driven, damped nonlinear Schrodinger solitons,” Phys. Rev. E 54, 5707–5725 (1996).
[CrossRef]

1992 (1)

1987 (1)

L. A. Lugiato, R. Lefever, “Spatial dissipative structures in passive optical systems,” Phys. Rev. Lett. 58, 2209–2211 (1987).
[CrossRef] [PubMed]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007).

Aksyuk, V.

Andres, P.

Arcizet, O.

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

Balakireva, I.

C. Godey, I. Balakireva, A. Colleit, Y. K Chembo, “Stability analysis of the Lugiato-Lefever model for Kerr optical frequency combs. Part I: case of normal dispersion,” arXiv: 1308.2539.

Barashenkov, I. V.

I. V. Barashenkov, Y. S. Smirnov, “Existence and stability chart for the ac-driven, damped nonlinear Schrodinger solitons,” Phys. Rev. E 54, 5707–5725 (1996).
[CrossRef]

Baumgartel, L.

Beausoleil, R. G.

Ben Salem, A.

Brasch, V.

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

J. Riemensberger, K. Hartinger, T. Herr, V. Brasch, R. Holzwarth, T. J. Kippenberg, “Dispersion engineering of thick high-Q silicon nitride ring-resonators via atomic layer deposition,” Opt. Express 20, 27661–27669 (2012).
[CrossRef] [PubMed]

Chembo, Y. K

C. Godey, I. Balakireva, A. Colleit, Y. K Chembo, “Stability analysis of the Lugiato-Lefever model for Kerr optical frequency combs. Part I: case of normal dispersion,” arXiv: 1308.2539.

Chembo, Y. K.

Y. K. Chembo, C. R. Menyuk, “Spatiotemporal Lugiato-Lefever formalism for Kerr-comb generation in whispering gallery-mode resonators,” Phys. Rev. A 87, 053852 (2013).
[CrossRef]

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

Y. K. Chembo, D. V. Strekalov, N. Yu, “Spectrum and dynamics of optical frequency combs generated with monolithic whispering gallery mode resonators,” Phys. Rev. Lett. 104, 103902 (2010).
[CrossRef] [PubMed]

Chen, L.

Chen, T.

J. Li, H. Lee, T. Chen, 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]

Chu, S.

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

Chu, S. T.

M. Peccianti, A. Pasquazi, Y. Park, B. E. Little, S. T. Chu, D. J. Moss, R. Morandotti, “Demonstration of a stable ultrafast laser based on a nonlinear microcavity,” Nature Commun. 3, 765 (2012).
[CrossRef]

Coen, S.

Colleit, A.

C. Godey, I. Balakireva, A. Colleit, Y. K Chembo, “Stability analysis of the Lugiato-Lefever model for Kerr optical frequency combs. Part I: case of normal dispersion,” arXiv: 1308.2539.

Cundiff, S. T.

S. T. Cundiff, A. M. Weiner, “Optical arbitrary waveform generation,” Nat. Photonics 4, 760–766 (2010).
[CrossRef]

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
[CrossRef] [PubMed]

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[CrossRef] [PubMed]

Del’Haye, P.

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

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

S. B. Papp, P. Del’Haye, S. A. Diddams, “Parametric seeding of a microresonator optical frequency comb,” Opt. Express 21, 17615–17624 (2013).
[CrossRef] [PubMed]

P. Del’Haye, T. Herr, E. Garvatin, M. L. Gorodetsky, R. Holzwarth, T. J. Kippenberg, “Octave spanning tunable frequency comb from a microresonator,” Phys. Rev. Lett. 107, 063901 (2011).
[CrossRef]

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

Dias, F.

Diddams, S. A.

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

S. B. Papp, P. Del’Haye, S. A. Diddams, “Parametric seeding of a microresonator optical frequency comb,” Opt. Express 21, 17615–17624 (2013).
[CrossRef] [PubMed]

S. B. Papp, S. A. Diddams, “Spectral and temporal characterization of a fused-quartz-microresonator optical frequency comb,” Phys. Rev. A 84, 053833 (2011).
[CrossRef]

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

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[CrossRef] [PubMed]

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
[CrossRef] [PubMed]

Duchesne, D.

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

Dudley, J. M.

Emplit, P.

F. Leo, L. Gelens, P. Emplit, M. Haelterman, S. Coen, “Dynamics of one-dimensional Kerr cavity solitons,” Opt. Express 21, 9180–9191 (2013).
[CrossRef] [PubMed]

F. Leo, S. Coen, P. Kockaert, S. P. Goza, P. Emplit, M. Haelterman, “Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,” Nat. Photonics 4, 471–476 (2010).
[CrossRef]

Erkintalo, M.

Ferdous, F.

Ferrera, M.

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

Fong, K. Y.

Foster, M. A.

Friberg, A. T.

Gaeta, A. L.

Garvatin, E.

P. Del’Haye, T. Herr, E. Garvatin, M. L. Gorodetsky, R. Holzwarth, T. J. Kippenberg, “Octave spanning tunable frequency comb from a microresonator,” Phys. Rev. Lett. 107, 063901 (2011).
[CrossRef]

Gavartin, E.

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

Gelens, L.

Genty, G.

Godey, C.

C. Godey, I. Balakireva, A. Colleit, Y. K Chembo, “Stability analysis of the Lugiato-Lefever model for Kerr optical frequency combs. Part I: case of normal dispersion,” arXiv: 1308.2539.

Godin, T.

Gondarenko, A.

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

Gorodetsky, M. L.

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

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

P. Del’Haye, T. Herr, E. Garvatin, M. L. Gorodetsky, R. Holzwarth, T. J. Kippenberg, “Octave spanning tunable frequency comb from a microresonator,” Phys. Rev. Lett. 107, 063901 (2011).
[CrossRef]

Goza, S. P.

F. Leo, S. Coen, P. Kockaert, S. P. Goza, P. Emplit, M. Haelterman, “Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,” Nat. Photonics 4, 471–476 (2010).
[CrossRef]

Grudinin, I. S.

Haelterman, M.

Hall, J. L.

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[CrossRef] [PubMed]

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
[CrossRef] [PubMed]

Hänsch, T. W.

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

T. W. Hänsch, “Nobel Lecture: Passion for precision,” Rev. Mod. Phys. 78, 1297–1309 (2006).
[CrossRef]

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[CrossRef] [PubMed]

Hansson, T.

T. Hansson, D. Modotto, S. Wabnitz, “Dynamics of the modulation instability in microresonator frequency combs,” Phys. Rev. A 88, 023819 (2013).
[CrossRef]

Hartinger, K.

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

J. Riemensberger, K. Hartinger, T. Herr, V. Brasch, R. Holzwarth, T. J. Kippenberg, “Dispersion engineering of thick high-Q silicon nitride ring-resonators via atomic layer deposition,” Opt. Express 20, 27661–27669 (2012).
[CrossRef] [PubMed]

Herr, T.

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

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

J. Riemensberger, K. Hartinger, T. Herr, V. Brasch, R. Holzwarth, T. J. Kippenberg, “Dispersion engineering of thick high-Q silicon nitride ring-resonators via atomic layer deposition,” Opt. Express 20, 27661–27669 (2012).
[CrossRef] [PubMed]

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

P. Del’Haye, T. Herr, E. Garvatin, M. L. Gorodetsky, R. Holzwarth, T. J. Kippenberg, “Octave spanning tunable frequency comb from a microresonator,” Phys. Rev. Lett. 107, 063901 (2011).
[CrossRef]

Hofer, J.

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

Holzwarth, R.

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

J. Riemensberger, K. Hartinger, T. Herr, V. Brasch, R. Holzwarth, T. J. Kippenberg, “Dispersion engineering of thick high-Q silicon nitride ring-resonators via atomic layer deposition,” Opt. Express 20, 27661–27669 (2012).
[CrossRef] [PubMed]

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

P. Del’Haye, T. Herr, E. Garvatin, M. L. Gorodetsky, R. Holzwarth, T. J. Kippenberg, “Octave spanning tunable frequency comb from a microresonator,” Phys. Rev. Lett. 107, 063901 (2011).
[CrossRef]

T. J. Kippenberg, R. Holzwarth, 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, T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[CrossRef]

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[CrossRef] [PubMed]

Ilchenko, V. S.

A. B. Matsko, A. A. Savchenko, V. S. Ilchenko, D. Seidel, L. Maleki, “Hard and soft excitation regimes of Kerr frequency combs,” Phys. Rev. A 85, 023830 (2012).
[CrossRef]

A. B. Matsko, A. A. Savchenko, W. Liang, V. S. Ilchenko, D. Seidel, L. Maleki, “Mode-locked Kerr frequency combs,” Opt. Lett. 36, 2845–2847 (2011).
[CrossRef] [PubMed]

W. Liang, A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Seidel, L. Maleki, “Generation of near-infrared frequency combs from a MgF2 whispering gallery mode resonator,” Opt. Lett. 36, 2290–2292 (2011).
[CrossRef] [PubMed]

A. A. Savchenko, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, L. Maleki, “Kerr combs with selectable central frequency,” Nature Photon. 5, 293–296 (2011).
[CrossRef]

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

A. B. Matsko, A. A. Savchenko, D. Strekalov, V. S. Ilchenko, L. Maleki, “Optical hyperparametric oscillations in a whispering-gallery-mode resonator: Threshold and phase diffusion,” Phys. Rev. A 71, 033804 (2005).
[CrossRef]

Johnson, A. R.

Jones, D. J.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
[CrossRef] [PubMed]

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[CrossRef] [PubMed]

Jost, J. D.

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

Jung, H.

Kippenberg, T. J.

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

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

J. Riemensberger, K. Hartinger, T. Herr, V. Brasch, R. Holzwarth, T. J. Kippenberg, “Dispersion engineering of thick high-Q silicon nitride ring-resonators via atomic layer deposition,” Opt. Express 20, 27661–27669 (2012).
[CrossRef] [PubMed]

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

P. Del’Haye, T. Herr, E. Garvatin, M. L. Gorodetsky, R. Holzwarth, T. J. Kippenberg, “Octave spanning tunable frequency comb from a microresonator,” Phys. Rev. Lett. 107, 063901 (2011).
[CrossRef]

T. J. Kippenberg, R. Holzwarth, 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, T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[CrossRef]

T. J. Kippenberg, S. M. Spillane, K. J. Vahala, “Kerr-nonlinearity optical parametric oscillation in ultrahigh-Q toroid microcavity,” Phys. Rev. Lett. 93, 083904 (2004).
[CrossRef]

Kockaert, P.

F. Leo, S. Coen, P. Kockaert, S. P. Goza, P. Emplit, M. Haelterman, “Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,” Nat. Photonics 4, 471–476 (2010).
[CrossRef]

Kondratiev, N. M.

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

Kudlinski, A.

Lajunen, H.

Lamont, M. R. E.

Lancis, J.

Larger, L.

Lau, R. K. W.

Leaird, D. E.

Lee, H.

J. Li, H. Lee, T. Chen, 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]

Lefever, R.

L. A. Lugiato, R. Lefever, “Spatial dissipative structures in passive optical systems,” Phys. Rev. Lett. 58, 2209–2211 (1987).
[CrossRef] [PubMed]

Leo, F.

F. Leo, L. Gelens, P. Emplit, M. Haelterman, S. Coen, “Dynamics of one-dimensional Kerr cavity solitons,” Opt. Express 21, 9180–9191 (2013).
[CrossRef] [PubMed]

F. Leo, S. Coen, P. Kockaert, S. P. Goza, P. Emplit, M. Haelterman, “Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,” Nat. Photonics 4, 471–476 (2010).
[CrossRef]

Levy, J. S.

Li, J.

J. Li, H. Lee, T. Chen, 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]

Liang, W.

Lipson, M.

Little, B. E.

M. Peccianti, A. Pasquazi, Y. Park, B. E. Little, S. T. Chu, D. J. Moss, R. Morandotti, “Demonstration of a stable ultrafast laser based on a nonlinear microcavity,” Nature Commun. 3, 765 (2012).
[CrossRef]

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

Lugiato, L. A.

L. A. Lugiato, R. Lefever, “Spatial dissipative structures in passive optical systems,” Phys. Rev. Lett. 58, 2209–2211 (1987).
[CrossRef] [PubMed]

Luke, K.

Maleki, L.

A. B. Matsko, W. Liang, A. A. Savchenko, L. Maleki, “Chaotic dynamics of frequency combs generated with continuously pumped nonlinear microresonators,” Opt. Lett. 38, 525–527 (2013).
[CrossRef] [PubMed]

A. B. Matsko, A. A. Savchenko, V. S. Ilchenko, D. Seidel, L. Maleki, “Hard and soft excitation regimes of Kerr frequency combs,” Phys. Rev. A 85, 023830 (2012).
[CrossRef]

A. B. Matsko, A. A. Savchenko, W. Liang, V. S. Ilchenko, D. Seidel, L. Maleki, “Mode-locked Kerr frequency combs,” Opt. Lett. 36, 2845–2847 (2011).
[CrossRef] [PubMed]

A. A. Savchenko, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, L. Maleki, “Kerr combs with selectable central frequency,” Nature Photon. 5, 293–296 (2011).
[CrossRef]

W. Liang, A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Seidel, L. Maleki, “Generation of near-infrared frequency combs from a MgF2 whispering gallery mode resonator,” Opt. Lett. 36, 2290–2292 (2011).
[CrossRef] [PubMed]

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

A. B. Matsko, A. A. Savchenko, D. Strekalov, V. S. Ilchenko, L. Maleki, “Optical hyperparametric oscillations in a whispering-gallery-mode resonator: Threshold and phase diffusion,” Phys. Rev. A 71, 033804 (2005).
[CrossRef]

Matsko, A. B.

A. B. Matsko, W. Liang, A. A. Savchenko, L. Maleki, “Chaotic dynamics of frequency combs generated with continuously pumped nonlinear microresonators,” Opt. Lett. 38, 525–527 (2013).
[CrossRef] [PubMed]

A. B. Matsko, A. A. Savchenko, V. S. Ilchenko, D. Seidel, L. Maleki, “Hard and soft excitation regimes of Kerr frequency combs,” Phys. Rev. A 85, 023830 (2012).
[CrossRef]

A. B. Matsko, A. A. Savchenko, W. Liang, V. S. Ilchenko, D. Seidel, L. Maleki, “Mode-locked Kerr frequency combs,” Opt. Lett. 36, 2845–2847 (2011).
[CrossRef] [PubMed]

W. Liang, A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Seidel, L. Maleki, “Generation of near-infrared frequency combs from a MgF2 whispering gallery mode resonator,” Opt. Lett. 36, 2290–2292 (2011).
[CrossRef] [PubMed]

A. A. Savchenko, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, L. Maleki, “Kerr combs with selectable central frequency,” Nature Photon. 5, 293–296 (2011).
[CrossRef]

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

A. B. Matsko, A. A. Savchenko, D. Strekalov, V. S. Ilchenko, L. Maleki, “Optical hyperparametric oscillations in a whispering-gallery-mode resonator: Threshold and phase diffusion,” Phys. Rev. A 71, 033804 (2005).
[CrossRef]

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Y. K. Chembo, C. R. Menyuk, “Spatiotemporal Lugiato-Lefever formalism for Kerr-comb generation in whispering gallery-mode resonators,” Phys. Rev. A 87, 053852 (2013).
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P. H. Wang, F. Ferdous, H. X Miao, J. Wang, D. E. Leaird, K. Srinivasan, L. Chen, V. Aksyuk, A. M. Weiner, “Observation of correlation between route to formation, coherence, noise, and communication performance of Kerr combs,” Opt. Express 20, 29284–29295 (2012).
[CrossRef]

F. Ferdous, H. X Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, A. M. Weiner, “Spectral line-by-line pulse shaping of on-chip microresonator frequency combs,” Nat. Photonics 5, 770–776 (2011).
[CrossRef]

Miao, H. X.

Modotto, D.

T. Hansson, D. Modotto, S. Wabnitz, “Dynamics of the modulation instability in microresonator frequency combs,” Phys. Rev. A 88, 023819 (2013).
[CrossRef]

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D. J. Moss, R. Morandotti, A. L. Gaeta, M. Lipson, “New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics,” Nat. Photonics 7, 597–607 (2013).
[CrossRef]

M. Peccianti, A. Pasquazi, Y. Park, B. E. Little, S. T. Chu, D. J. Moss, R. Morandotti, “Demonstration of a stable ultrafast laser based on a nonlinear microcavity,” Nature Commun. 3, 765 (2012).
[CrossRef]

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

Moss, D. J.

D. J. Moss, R. Morandotti, A. L. Gaeta, M. Lipson, “New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics,” Nat. Photonics 7, 597–607 (2013).
[CrossRef]

M. Peccianti, A. Pasquazi, Y. Park, B. E. Little, S. T. Chu, D. J. Moss, R. Morandotti, “Demonstration of a stable ultrafast laser based on a nonlinear microcavity,” Nature Commun. 3, 765 (2012).
[CrossRef]

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

Mussot, A.

Newbury, N. R.

N. R. Newbury, “Searching for applications with a fine-tooth comb,” Nature Photon. 5, 186–188 (2011).
[CrossRef]

Okawachi, Y.

Papp, S. B.

P. Del’Haye, S. B. Papp, 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, S. A. Diddams, “Parametric seeding of a microresonator optical frequency comb,” Opt. Express 21, 17615–17624 (2013).
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S. B. Papp, S. A. Diddams, “Spectral and temporal characterization of a fused-quartz-microresonator optical frequency comb,” Phys. Rev. A 84, 053833 (2011).
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M. Peccianti, A. Pasquazi, Y. Park, B. E. Little, S. T. Chu, D. J. Moss, R. Morandotti, “Demonstration of a stable ultrafast laser based on a nonlinear microcavity,” Nature Commun. 3, 765 (2012).
[CrossRef]

Pasquazi, A.

M. Peccianti, A. Pasquazi, Y. Park, B. E. Little, S. T. Chu, D. J. Moss, R. Morandotti, “Demonstration of a stable ultrafast laser based on a nonlinear microcavity,” Nature Commun. 3, 765 (2012).
[CrossRef]

Peccianti, M.

M. Peccianti, A. Pasquazi, Y. Park, B. E. Little, S. T. Chu, D. J. Moss, R. Morandotti, “Demonstration of a stable ultrafast laser based on a nonlinear microcavity,” Nature Commun. 3, 765 (2012).
[CrossRef]

Picque, N.

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

Randle, H. G.

Ranka, J. K.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
[CrossRef] [PubMed]

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[CrossRef] [PubMed]

Razzari, L.

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

Riemensberger, J.

Riemesberger, J.

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

Saha, K.

Salem, R.

Savchenko, A. A.

A. B. Matsko, W. Liang, A. A. Savchenko, L. Maleki, “Chaotic dynamics of frequency combs generated with continuously pumped nonlinear microresonators,” Opt. Lett. 38, 525–527 (2013).
[CrossRef] [PubMed]

A. B. Matsko, A. A. Savchenko, V. S. Ilchenko, D. Seidel, L. Maleki, “Hard and soft excitation regimes of Kerr frequency combs,” Phys. Rev. A 85, 023830 (2012).
[CrossRef]

A. B. Matsko, A. A. Savchenko, W. Liang, V. S. Ilchenko, D. Seidel, L. Maleki, “Mode-locked Kerr frequency combs,” Opt. Lett. 36, 2845–2847 (2011).
[CrossRef] [PubMed]

A. A. Savchenko, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, L. Maleki, “Kerr combs with selectable central frequency,” Nature Photon. 5, 293–296 (2011).
[CrossRef]

A. B. Matsko, A. A. Savchenko, D. Strekalov, V. S. Ilchenko, L. Maleki, “Optical hyperparametric oscillations in a whispering-gallery-mode resonator: Threshold and phase diffusion,” Phys. Rev. A 71, 033804 (2005).
[CrossRef]

Savchenkov, A. A.

W. Liang, A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Seidel, L. Maleki, “Generation of near-infrared frequency combs from a MgF2 whispering gallery mode resonator,” Opt. Lett. 36, 2290–2292 (2011).
[CrossRef] [PubMed]

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, 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. Picque, T. J. Kippenberg, “Mid-infrared optical frequency combs at 2.5 μm based on crystalline microresonators,” Nature Commun. 4, 1345 (2013).
[CrossRef]

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

Seidel, D.

A. B. Matsko, A. A. Savchenko, V. S. Ilchenko, D. Seidel, L. Maleki, “Hard and soft excitation regimes of Kerr frequency combs,” Phys. Rev. A 85, 023830 (2012).
[CrossRef]

A. B. Matsko, A. A. Savchenko, W. Liang, V. S. Ilchenko, D. Seidel, L. Maleki, “Mode-locked Kerr frequency combs,” Opt. Lett. 36, 2845–2847 (2011).
[CrossRef] [PubMed]

W. Liang, A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Seidel, L. Maleki, “Generation of near-infrared frequency combs from a MgF2 whispering gallery mode resonator,” Opt. Lett. 36, 2290–2292 (2011).
[CrossRef] [PubMed]

A. A. Savchenko, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, L. Maleki, “Kerr combs with selectable central frequency,” Nature Photon. 5, 293–296 (2011).
[CrossRef]

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

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I. V. Barashenkov, Y. S. Smirnov, “Existence and stability chart for the ac-driven, damped nonlinear Schrodinger solitons,” Phys. Rev. E 54, 5707–5725 (1996).
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A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, L. Maleki, “Tunable optical frequency comb with a crystalline whispering gallery mode resonator,” Phys. Rev. Lett. 101, 093902 (2008).
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T. J. Kippenberg, S. M. Spillane, K. J. Vahala, “Kerr-nonlinearity optical parametric oscillation in ultrahigh-Q toroid microcavity,” Phys. Rev. Lett. 93, 083904 (2004).
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Stentz, A.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
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Strekalov, D.

A. B. Matsko, A. A. Savchenko, D. Strekalov, V. S. Ilchenko, L. Maleki, “Optical hyperparametric oscillations in a whispering-gallery-mode resonator: Threshold and phase diffusion,” Phys. Rev. A 71, 033804 (2005).
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Strekalov, D. V.

Y. K. Chembo, D. V. Strekalov, N. Yu, “Spectrum and dynamics of optical frequency combs generated with monolithic whispering gallery mode resonators,” Phys. Rev. Lett. 104, 103902 (2010).
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Surakka, M

Sylvestre, T.

Tang, H. X.

Torres-Company, V.

H. Lajunen, V. Torres-Company, J. Lancis, E. Silvestre, P. Andres, “Pulse-by-pulse method to characterize partially coherent pulse propagation in instantaneous nonlinear media,” Opt. Express 18, 14979–14991 (2010).
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V. Torres-Company, A. M. Weiner, “Optical frequency comb technology for ultra-broadband radio-frequency photonics,” Laser and Photon. Rev. (in press, 2013). DOI .
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Turner, A. C.

Turner-Foster, A. C.

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

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
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J. Li, H. Lee, T. Chen, 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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T. J. Kippenberg, S. M. Spillane, K. J. Vahala, “Kerr-nonlinearity optical parametric oscillation in ultrahigh-Q toroid microcavity,” Phys. Rev. Lett. 93, 083904 (2004).
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F. Ferdous, H. X Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, A. M. Weiner, “Spectral line-by-line pulse shaping of on-chip microresonator frequency combs,” Nat. Photonics 5, 770–776 (2011).
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T. Hansson, D. Modotto, S. Wabnitz, “Dynamics of the modulation instability in microresonator frequency combs,” Phys. Rev. A 88, 023819 (2013).
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M. Haelterman, S. Trillo, S. Wabnitz, “Additive-modulation-instability ring laser in the normal dispersion regime of a fiber,” Opt. Lett. 17, 745–747 (1992).
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T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2014).
[CrossRef]

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

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

Wang, J.

P. H. Wang, F. Ferdous, H. X Miao, J. Wang, D. E. Leaird, K. Srinivasan, L. Chen, V. Aksyuk, A. M. Weiner, “Observation of correlation between route to formation, coherence, noise, and communication performance of Kerr combs,” Opt. Express 20, 29284–29295 (2012).
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F. Ferdous, H. X Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, A. M. Weiner, “Spectral line-by-line pulse shaping of on-chip microresonator frequency combs,” Nat. Photonics 5, 770–776 (2011).
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Wang, P. H.

Weiner, A. M.

P. H. Wang, F. Ferdous, H. X Miao, J. Wang, D. E. Leaird, K. Srinivasan, L. Chen, V. Aksyuk, A. M. Weiner, “Observation of correlation between route to formation, coherence, noise, and communication performance of Kerr combs,” Opt. Express 20, 29284–29295 (2012).
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F. Ferdous, H. X. Miao, P. H. Wang, D. E. Leaird, K. Srinivasan, L. Chen, V. Aksyuk, A. M. Weiner, “Probing coherence in microcavity frequency combs via optical pulse shaping,” Opt. Express 20, 21033–21043 (2012).
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F. Ferdous, H. X Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, A. M. Weiner, “Spectral line-by-line pulse shaping of on-chip microresonator frequency combs,” Nat. Photonics 5, 770–776 (2011).
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S. T. Cundiff, A. M. Weiner, “Optical arbitrary waveform generation,” Nat. Photonics 4, 760–766 (2010).
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V. Torres-Company, A. M. Weiner, “Optical frequency comb technology for ultra-broadband radio-frequency photonics,” Laser and Photon. Rev. (in press, 2013). DOI .
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Wetzel, B.

Wilken, T.

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

Willner, A. E.

Windeler, R. S.

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[CrossRef] [PubMed]

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
[CrossRef] [PubMed]

Xiong, C.

Ye, J.

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[CrossRef] [PubMed]

Yu, N.

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

Y. K. Chembo, D. V. Strekalov, N. Yu, “Spectrum and dynamics of optical frequency combs generated with monolithic whispering gallery mode resonators,” Phys. Rev. Lett. 104, 103902 (2010).
[CrossRef] [PubMed]

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

Zghal, M.

Zhang, L.

Zhang, X. F.

Nat. Photonics (8)

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, 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, M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4, 37–40 (2010).
[CrossRef]

D. J. Moss, R. Morandotti, A. L. Gaeta, M. Lipson, “New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics,” Nat. Photonics 7, 597–607 (2013).
[CrossRef]

F. Ferdous, H. X Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, A. M. Weiner, “Spectral line-by-line pulse shaping of on-chip microresonator frequency combs,” Nat. Photonics 5, 770–776 (2011).
[CrossRef]

S. T. Cundiff, A. M. Weiner, “Optical arbitrary waveform generation,” Nat. Photonics 4, 760–766 (2010).
[CrossRef]

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

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

F. Leo, S. Coen, P. Kockaert, S. P. Goza, P. Emplit, M. Haelterman, “Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,” Nat. Photonics 4, 471–476 (2010).
[CrossRef]

Nature (1)

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

Nature Commun. (2)

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

M. Peccianti, A. Pasquazi, Y. Park, B. E. Little, S. T. Chu, D. J. Moss, R. Morandotti, “Demonstration of a stable ultrafast laser based on a nonlinear microcavity,” Nature Commun. 3, 765 (2012).
[CrossRef]

Nature Photon. (2)

A. A. Savchenko, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, L. Maleki, “Kerr combs with selectable central frequency,” Nature Photon. 5, 293–296 (2011).
[CrossRef]

N. R. Newbury, “Searching for applications with a fine-tooth comb,” Nature Photon. 5, 186–188 (2011).
[CrossRef]

Opt. Express (12)

M. A. Foster, A. C. Turner, R. Salem, M. Lipson, A. L. Gaeta, “Broad-band continuous-wave parametric wavelength conversion in silicon nanowaveguides,” Opt. Express 15, 12949–12958 (2007).
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L. Zhang, Y. Yue, R. G. Beausoleil, A. E. Willner, “Analysis and engineering of chromatic dispersion in silicon waveguide bends and ring resonators,” Opt. Express 19, 8102–8107 (2011).
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J. Riemensberger, K. Hartinger, T. Herr, V. Brasch, R. Holzwarth, T. J. Kippenberg, “Dispersion engineering of thick high-Q silicon nitride ring-resonators via atomic layer deposition,” Opt. Express 20, 27661–27669 (2012).
[CrossRef] [PubMed]

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

K. Saha, Y. Okawachi, J. S. Levy, R. K. W. Lau, K. Luke, M. A. Foster, M. Lipson, A. L. Gaeta, “Broadband parametric frequency comb generation with a 1 μm pump source,” Opt. Express 20, 26935–26941 (2012).
[CrossRef] [PubMed]

F. Ferdous, H. X. Miao, P. H. Wang, D. E. Leaird, K. Srinivasan, L. Chen, V. Aksyuk, A. M. Weiner, “Probing coherence in microcavity frequency combs via optical pulse shaping,” Opt. Express 20, 21033–21043 (2012).
[CrossRef] [PubMed]

P. H. Wang, F. Ferdous, H. X Miao, J. Wang, D. E. Leaird, K. Srinivasan, L. Chen, V. Aksyuk, A. M. Weiner, “Observation of correlation between route to formation, coherence, noise, and communication performance of Kerr combs,” Opt. Express 20, 29284–29295 (2012).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Modulation instability (MI) is the underlying phenomenon that leads to parametric oscillation in microresonator frequency combs. In Type II combs, the MI sidebands generated by the CW pump lead to parametric growth of frequencies that are several FSRs away. These frequency components grow in power and nonlinear mix with the pump. This microresonator may lead to a spectrally partially coherent comb [29]. However, the comb dynamics can be altered by actively manipulating the CW pump settings in the course of comb formation. This may lead to the formation of stable combs [33, 39] and cavity solitons [42]. We show that these solutions are indeed stable and spectrally coherent, but they strongly depend on the particular initial conditions of the system. For Type I combs, the first oscillating modes are beside the pump and display a spectrally coherent behavior. These solutions are robust to the noise conditions.

Fig. 2
Fig. 2

Dynamics of a Type II microresonator comb in spectral domain (top row) and time domain (bottom row) for different detuning conditions. Corresponding average spectra, shot-to-shot fluctuations and spectral coherence are displayed in Fig. 3.

Fig. 3
Fig. 3

Spectral coherence and shot-to-shot fluctuations for the microresonator combs in Fig. 2.

Fig. 4
Fig. 4

(a)–(d) Average envelope spectra, degree of coherence and intensity profile for a Type I microresonator comb at different pump power leves. (e) MI gain bandwith shift for different power levels. At 0.2 W the maximum gain coincides with the FSR of the microresonator cavity.

Fig. 5
Fig. 5

Analysis of the universality of the stable solutions for Type I coherent combs. (Top) The different realizations calculated at a fixed instant time for different random seeds. (Bottom) the degree of coherence calculated at fixed time t over multiple noise seeds (blue dash curve) is however substantially different when compared to the one calculated at multiple instant times for a fixed seed (red dash curve). After compensating for a linear spectral phase ad hoc, the degree of coherence calculated at a fixed time for various noise seeds (blue solid line) is identical to the degree of coherence calculated for a fixed seed and various instant times.

Fig. 6
Fig. 6

Temporal cavity soliton formation in microresonators. (a) Dynamic evolution of detuning. Corresponding (b) spectral and (c) time domain evolutions. Note the difference in time scales at different stages. The detuning is changed dynamically in the course of the CS formation. In the first stage, it is kept constant. The points marked as A and C are indicated by the dashed white lines in (b) and (c). Once the cavity soliton is formed, the waveform appears stable and coherent (d). The average intensity indicates a pulse with 25 fs duration (e).

Fig. 7
Fig. 7

Analysis of cavity soliton formation under different noise conditions. The sweep and other parameters are identical to those in Fig. 6. The points A–C are indicated in Fig. 6(a).

Equations (7)

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t R E ( t , τ ) t = [ α i δ 0 + i L k 2 β k k ! ( i τ ) k + i γ L | E ( t , τ ) | 2 ] E ( t , τ ) + θ E in .
Ω m 2 = 2 L β 2 ( δ 0 2 γ LP 0 ) .
P in , th = 1 γ L [ α 2 + ( δ 0 α ) 2 ] ,
δ 0 α P in γ L α 2 .
β 2 = ( δ 0 2 γ LP 0 ) 2 L π 2 FSR 2 .
| g ( ω ; t 1 , t 2 ) | = | E ˜ * ( t 1 , ω ) E ˜ ( t 2 , ω ) | | E ˜ ( ω ) | 2 .
| g s ( ω ; t ) | = | E ˜ 1 * ( t , ω ) E ˜ 2 ( t , ω ) | | E ˜ 1 ( ω ) | 2 | E ˜ 2 ( ω ) | 2 .

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