Abstract

We present a quantitative analysis of the mode-pulling effect in microresonator-based comb (microcomb) generation. It is found that the initial dispersion of the microresonator can be ideally compensated or quasi-compensated by the Kerr effect. The ideal dispersion compensation leads to a stable comb, while the comb remains unstable in the quasi-compensation case. Four-wave mixing (FWM) is found to play a critical role in the mode-pulling effect. The influence of third-order dispersion is also analyzed and found to be insignificant. Additionally, the mode-pulling effect can also result in blue-shift of the cavity resonance due to the strong contribution from the phase-dependent FWM process.

© 2013 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  34. P. Grelu and N. Akhmediev, “Dissipative solitons for mode-locked lasers,” Nat. Photonics 6, 84–92 (2012).
    [CrossRef]

2013 (7)

C. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. Hänsch, N. Picqué, and T. Kippenberg, “Mid-infrared optical frequency combs at 2.5 μm based on crystalline microresonators,” Nat. Commun. 4, 1345–1351 (2013).
[CrossRef]

A. Pasquazi, L. Caspani, M. Peccianti, M. Clerici, M. Ferrera, L. Razzari, D. Duchesne, B. E. Little, S. T. Chu, and D. J. Moss, “Self-locked optical parametric oscillation in a CMOS compatible microring resonator: a route to robust optical frequency comb generation on a chip,” Opt. Express 21, 13333–13341 (2013).
[CrossRef]

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

C. Bao, X. Xiao, and C. Yang, “Manipulation of the generation dynamics of a microresonator-based frequency comb via selective mode filtering,” Phys. Rev. A 87, 053844 (2013).
[CrossRef]

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

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

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

2012 (3)

P. Grelu and N. Akhmediev, “Dissipative solitons for mode-locked lasers,” Nat. Photonics 6, 84–92 (2012).
[CrossRef]

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

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

2011 (6)

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

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

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

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

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and 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 and S. A. Diddams, “Spectral and temporal characterization of a fused-quartz-microresonator optical frequency comb,” Phys. Rev. A 84, 053833 (2011).
[CrossRef]

2010 (4)

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

S. A. Diddams, “The evolving optical frequency comb [Invited],” J. Opt. Soc. Am. B 27, B51–B62 (2010).
[CrossRef]

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

2009 (3)

I. H. Agha, Y. Okawachi, and A. L. Gaeta, “Theoretical and experimental investigation of broadband cascaded four-wave mixing in high-Q microspheres,” Opt. Express 17, 16209–16215 (2009).
[CrossRef]

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. Little, and D. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics 4, 41–45 (2009).
[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 (2009).
[CrossRef]

2008 (1)

C. H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kartner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s(−1),” Nature 452, 610–612 (2008).
[CrossRef]

2007 (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]

2006 (1)

2005 (1)

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

2004 (2)

B. R. Washburn, S. A. Diddams, N. R. Newbury, J. W. Nicholson, M. F. Yan, and C. G. Jrgensen, “Phase-locked, erbium-fiber-laser-based frequency comb in the near infrared,” Opt. Lett. 29, 250–252 (2004).
[CrossRef]

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

2002 (1)

S. T. Cundiff, “Phase stabilization of ultrashort optical pulses,” J. Phys. D 35, R43–R59 (2002).
[CrossRef]

2000 (1)

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

1992 (1)

M. Haelterman, S. Trillo, and S. Wabnitz, “Dissipative modulation instability in a nonlinear dispersive ring cavity,” Opt. Commun. 91, 401–407 (1992).
[CrossRef]

Agha, I. H.

Akhmediev, N.

P. Grelu and N. Akhmediev, “Dissipative solitons for mode-locked lasers,” Nat. Photonics 6, 84–92 (2012).
[CrossRef]

Aksyuk, V.

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]

Bao, C.

C. Bao, X. Xiao, and C. Yang, “Manipulation of the generation dynamics of a microresonator-based frequency comb via selective mode filtering,” Phys. Rev. A 87, 053844 (2013).
[CrossRef]

Benedick, A. J.

C. H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kartner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s(−1),” Nature 452, 610–612 (2008).
[CrossRef]

Brasch, V.

T. Herr, V. Brasch, J. Jost, C. Wang, N. Kondratiev, M. Gorodetsky, and T. Kippenberg, “Temporal solitons in optical microresonators,” arXiv:1211.0733 (2013).

J. Pfeifle, M. Lauermann, D. Wegner, V. Brasch, T. Herr, K. Hartinger, J. Li, D. Hillerkuss, R. Schmogrow, and R. Holzwarth, “Coherent data transmission with microresonator Kerr frequency combs,” arXiv:1307.1037 (2013).

Buckley, J.

Caspani, L.

Chembo, Y. K.

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

Chen, L.

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

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

Chong, A.

Chu, S.

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. Little, and D. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics 4, 41–45 (2009).
[CrossRef]

Chu, S. T.

Clerici, M.

Coen, S.

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

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

Cundiff, S. T.

S. T. Cundiff, “Phase stabilization of ultrashort optical pulses,” J. Phys. D 35, R43–R59 (2002).
[CrossRef]

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

Del’Haye, P.

C. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. Hänsch, N. Picqué, and T. Kippenberg, “Mid-infrared optical frequency combs at 2.5 μm based on crystalline microresonators,” Nat. Commun. 4, 1345–1351 (2013).
[CrossRef]

P. Del’Haye, T. Herr, E. Gavartin, M. Gorodetsky, R. Holzwarth, and T. 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, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[CrossRef]

Diddams, S.

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

Diddams, S. A.

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

S. A. Diddams, “The evolving optical frequency comb [Invited],” J. Opt. Soc. Am. B 27, B51–B62 (2010).
[CrossRef]

B. R. Washburn, S. A. Diddams, N. R. Newbury, J. W. Nicholson, M. F. Yan, and C. G. Jrgensen, “Phase-locked, erbium-fiber-laser-based frequency comb in the near infrared,” Opt. Lett. 29, 250–252 (2004).
[CrossRef]

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

Duchesne, D.

Emplit, P.

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, P. Emplit, and 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.

Fendel, P.

C. H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kartner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s(−1),” Nature 452, 610–612 (2008).
[CrossRef]

Ferdous, F.

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

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

Ferrera, M.

Foster, M. A.

K. Saha, Y. Okawachi, B. Shim, J. S. Levy, R. Salem, A. R. Johnson, M. A. Foster, M. R. E. Lamont, M. Lipson, and A. L. Gaeta, “Modelocking and femtosecond pulse generation in chip-based frequency combs,” Opt. Express 21, 1335–1343 (2013).
[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 (2009).
[CrossRef]

Gaeta, A. L.

Gavartin, E.

T. Herr, K. Hartinger, J. Riemensberger, C. Wang, E. Gavartin, R. Holzwarth, M. Gorodetsky, and T. 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. Gavartin, M. Gorodetsky, R. Holzwarth, and T. Kippenberg, “Octave spanning tunable frequency comb from a microresonator,” Phys. Rev. Lett. 107, 063901 (2011).
[CrossRef]

Glenday, A. G.

C. H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kartner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s(−1),” Nature 452, 610–612 (2008).
[CrossRef]

Gondarenko, A.

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 (2009).
[CrossRef]

Gorodetsky, M.

T. Herr, K. Hartinger, J. Riemensberger, C. Wang, E. Gavartin, R. Holzwarth, M. Gorodetsky, and T. 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. Gavartin, M. Gorodetsky, R. Holzwarth, and T. Kippenberg, “Octave spanning tunable frequency comb from a microresonator,” Phys. Rev. Lett. 107, 063901 (2011).
[CrossRef]

T. Herr, V. Brasch, J. Jost, C. Wang, N. Kondratiev, M. Gorodetsky, and T. Kippenberg, “Temporal solitons in optical microresonators,” arXiv:1211.0733 (2013).

Gorza, S.-P.

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

Grelu, P.

P. Grelu and N. Akhmediev, “Dissipative solitons for mode-locked lasers,” Nat. Photonics 6, 84–92 (2012).
[CrossRef]

Haelterman, M.

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

M. Haelterman, S. Trillo, and S. Wabnitz, “Dissipative modulation instability in a nonlinear dispersive ring cavity,” Opt. Commun. 91, 401–407 (1992).
[CrossRef]

Hall, J. L.

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

Hänsch, T.

C. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. Hänsch, N. Picqué, and T. Kippenberg, “Mid-infrared optical frequency combs at 2.5 μm based on crystalline microresonators,” Nat. Commun. 4, 1345–1351 (2013).
[CrossRef]

Hartinger, K.

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

J. Pfeifle, M. Lauermann, D. Wegner, V. Brasch, T. Herr, K. Hartinger, J. Li, D. Hillerkuss, R. Schmogrow, and R. Holzwarth, “Coherent data transmission with microresonator Kerr frequency combs,” arXiv:1307.1037 (2013).

Herr, T.

C. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. Hänsch, N. Picqué, and T. Kippenberg, “Mid-infrared optical frequency combs at 2.5 μm based on crystalline microresonators,” Nat. Commun. 4, 1345–1351 (2013).
[CrossRef]

T. Herr, K. Hartinger, J. Riemensberger, C. Wang, E. Gavartin, R. Holzwarth, M. Gorodetsky, and T. 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. Gavartin, M. Gorodetsky, R. Holzwarth, and T. Kippenberg, “Octave spanning tunable frequency comb from a microresonator,” Phys. Rev. Lett. 107, 063901 (2011).
[CrossRef]

J. Pfeifle, M. Lauermann, D. Wegner, V. Brasch, T. Herr, K. Hartinger, J. Li, D. Hillerkuss, R. Schmogrow, and R. Holzwarth, “Coherent data transmission with microresonator Kerr frequency combs,” arXiv:1307.1037 (2013).

T. Herr, V. Brasch, J. Jost, C. Wang, N. Kondratiev, M. Gorodetsky, and T. Kippenberg, “Temporal solitons in optical microresonators,” arXiv:1211.0733 (2013).

Hillerkuss, D.

J. Pfeifle, M. Lauermann, D. Wegner, V. Brasch, T. Herr, K. Hartinger, J. Li, D. Hillerkuss, R. Schmogrow, and R. Holzwarth, “Coherent data transmission with microresonator Kerr frequency combs,” arXiv:1307.1037 (2013).

Hofer, J.

C. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. Hänsch, N. Picqué, and T. Kippenberg, “Mid-infrared optical frequency combs at 2.5 μm based on crystalline microresonators,” Nat. Commun. 4, 1345–1351 (2013).
[CrossRef]

Holzwarth, R.

C. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. Hänsch, N. Picqué, and T. Kippenberg, “Mid-infrared optical frequency combs at 2.5 μm based on crystalline microresonators,” Nat. Commun. 4, 1345–1351 (2013).
[CrossRef]

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

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

P. Del’Haye, T. Herr, E. Gavartin, M. Gorodetsky, R. Holzwarth, and T. 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, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[CrossRef]

J. Pfeifle, M. Lauermann, D. Wegner, V. Brasch, T. Herr, K. Hartinger, J. Li, D. Hillerkuss, R. Schmogrow, and R. Holzwarth, “Coherent data transmission with microresonator Kerr frequency combs,” arXiv:1307.1037 (2013).

Ilchenko, V.

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

A. Matsko, A. Savchenkov, D. Strekalov, V. Ilchenko, and 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, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
[CrossRef]

Jost, J.

T. Herr, V. Brasch, J. Jost, C. Wang, N. Kondratiev, M. Gorodetsky, and T. Kippenberg, “Temporal solitons in optical microresonators,” arXiv:1211.0733 (2013).

Jrgensen, C. G.

Kartner, F. X.

C. H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kartner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s(−1),” Nature 452, 610–612 (2008).
[CrossRef]

Kippenberg, T.

C. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. Hänsch, N. Picqué, and T. Kippenberg, “Mid-infrared optical frequency combs at 2.5 μm based on crystalline microresonators,” Nat. Commun. 4, 1345–1351 (2013).
[CrossRef]

T. Herr, K. Hartinger, J. Riemensberger, C. Wang, E. Gavartin, R. Holzwarth, M. Gorodetsky, and T. 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. Gavartin, M. Gorodetsky, R. Holzwarth, and T. Kippenberg, “Octave spanning tunable frequency comb from a microresonator,” Phys. Rev. Lett. 107, 063901 (2011).
[CrossRef]

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

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

T. Herr, V. Brasch, J. Jost, C. Wang, N. Kondratiev, M. Gorodetsky, and T. Kippenberg, “Temporal solitons in optical microresonators,” arXiv:1211.0733 (2013).

Kippenberg, T. J.

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]

Kockaert, P.

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, P. Emplit, and 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.

T. Herr, V. Brasch, J. Jost, C. Wang, N. Kondratiev, M. Gorodetsky, and T. Kippenberg, “Temporal solitons in optical microresonators,” arXiv:1211.0733 (2013).

Lamont, M. R.

Lamont, M. R. E.

Lauermann, M.

J. Pfeifle, M. Lauermann, D. Wegner, V. Brasch, T. Herr, K. Hartinger, J. Li, D. Hillerkuss, R. Schmogrow, and R. Holzwarth, “Coherent data transmission with microresonator Kerr frequency combs,” arXiv:1307.1037 (2013).

Leaird, D. E.

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

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

Leo, F.

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, P. Emplit, and 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, C. H.

C. H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kartner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s(−1),” Nature 452, 610–612 (2008).
[CrossRef]

Li, J.

J. Pfeifle, M. Lauermann, D. Wegner, V. Brasch, T. Herr, K. Hartinger, J. Li, D. Hillerkuss, R. Schmogrow, and R. Holzwarth, “Coherent data transmission with microresonator Kerr frequency combs,” arXiv:1307.1037 (2013).

Liang, W.

Lipson, M.

Little, B.

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. Little, and D. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics 4, 41–45 (2009).
[CrossRef]

Little, B. E.

Maleki, L.

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

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

Matsko, A.

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

A. Matsko, A. Savchenkov, D. Strekalov, V. Ilchenko, and 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 and C. R. Menyuk, “Spatiotemporal Lugiato–Lefever formalism for Kerr-comb generation in whispering-gallery-mode resonators,” Phys. Rev. A 87, 053852 (2013).
[CrossRef]

Miao, H.

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

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

Morandotti, R.

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. Little, and D. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics 4, 41–45 (2009).
[CrossRef]

Moss, D.

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. Little, and D. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics 4, 41–45 (2009).
[CrossRef]

Moss, D. J.

Newbury, N. R.

Nicholson, J. W.

Okawachi, Y.

Papp, S. B.

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

Pasquazi, A.

Peccianti, M.

Pfeifle, J.

J. Pfeifle, M. Lauermann, D. Wegner, V. Brasch, T. Herr, K. Hartinger, J. Li, D. Hillerkuss, R. Schmogrow, and R. Holzwarth, “Coherent data transmission with microresonator Kerr frequency combs,” arXiv:1307.1037 (2013).

Phillips, D. F.

C. H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kartner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s(−1),” Nature 452, 610–612 (2008).
[CrossRef]

Picqué, N.

C. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. Hänsch, N. Picqué, and T. Kippenberg, “Mid-infrared optical frequency combs at 2.5 μm based on crystalline microresonators,” Nat. Commun. 4, 1345–1351 (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, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
[CrossRef]

Razzari, L.

Renninger, W.

Riemensberger, J.

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

Saha, K.

Salem, R.

Sasselov, D.

C. H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kartner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s(−1),” Nature 452, 610–612 (2008).
[CrossRef]

Savchenkov, A.

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

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

Schliesser, A.

C. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. Hänsch, N. Picqué, and T. Kippenberg, “Mid-infrared optical frequency combs at 2.5 μm based on crystalline microresonators,” Nat. Commun. 4, 1345–1351 (2013).
[CrossRef]

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]

Schmogrow, R.

J. Pfeifle, M. Lauermann, D. Wegner, V. Brasch, T. Herr, K. Hartinger, J. Li, D. Hillerkuss, R. Schmogrow, and R. Holzwarth, “Coherent data transmission with microresonator Kerr frequency combs,” arXiv:1307.1037 (2013).

Seidel, D.

Shim, B.

Spillane, S.

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

Srinivasan, K.

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

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

Stentz, A.

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

Strekalov, D.

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

Strekalov, D. V.

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

Sylvestre, T.

Szentgyorgyi, A.

C. H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kartner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s(−1),” Nature 452, 610–612 (2008).
[CrossRef]

Trillo, S.

M. Haelterman, S. Trillo, and S. Wabnitz, “Dissipative modulation instability in a nonlinear dispersive ring cavity,” Opt. Commun. 91, 401–407 (1992).
[CrossRef]

Turner-Foster, A. C.

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 (2009).
[CrossRef]

Vahala, K.

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

Varghese, L. T.

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

Wabnitz, S.

M. Haelterman, S. Trillo, and S. Wabnitz, “Dissipative modulation instability in a nonlinear dispersive ring cavity,” Opt. Commun. 91, 401–407 (1992).
[CrossRef]

Walsworth, R. L.

C. H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kartner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s(−1),” Nature 452, 610–612 (2008).
[CrossRef]

Wang, C.

C. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. Hänsch, N. Picqué, and T. Kippenberg, “Mid-infrared optical frequency combs at 2.5 μm based on crystalline microresonators,” Nat. Commun. 4, 1345–1351 (2013).
[CrossRef]

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

T. Herr, V. Brasch, J. Jost, C. Wang, N. Kondratiev, M. Gorodetsky, and T. Kippenberg, “Temporal solitons in optical microresonators,” arXiv:1211.0733 (2013).

Wang, J.

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

Wang, P. H.

Washburn, B. R.

Wegner, D.

J. Pfeifle, M. Lauermann, D. Wegner, V. Brasch, T. Herr, K. Hartinger, J. Li, D. Hillerkuss, R. Schmogrow, and R. Holzwarth, “Coherent data transmission with microresonator Kerr frequency combs,” arXiv:1307.1037 (2013).

Weiner, A. M.

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

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

Wen, Y. H.

Wilken, T.

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]

Windeler, R. S.

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

Wise, F.

Xiao, X.

C. Bao, X. Xiao, and C. Yang, “Manipulation of the generation dynamics of a microresonator-based frequency comb via selective mode filtering,” Phys. Rev. A 87, 053844 (2013).
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Yan, M. F.

Yang, C.

C. Bao, X. Xiao, and C. Yang, “Manipulation of the generation dynamics of a microresonator-based frequency comb via selective mode filtering,” Phys. Rev. A 87, 053844 (2013).
[CrossRef]

Yu, N.

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]

Y. K. Chembo, D. V. Strekalov, and 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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J. Opt. Soc. Am. B (1)

J. Phys. D (1)

S. T. Cundiff, “Phase stabilization of ultrashort optical pulses,” J. Phys. D 35, R43–R59 (2002).
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Nat. Commun. (1)

C. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. Hänsch, N. Picqué, and T. Kippenberg, “Mid-infrared optical frequency combs at 2.5 μm based on crystalline microresonators,” Nat. Commun. 4, 1345–1351 (2013).
[CrossRef]

Nat. Photonics (6)

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. Little, and D. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics 4, 41–45 (2009).
[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 (2009).
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Figures (9)

Fig. 1.
Fig. 1.

(a) Microcomb generation dynamics; the first pair is generated in ±1 modes. (b) Corresponding generated comb. The inset is the intensity evolution for mode 6 between 0.09 and 0.1 ms.

Fig. 2.
Fig. 2.

Mode-puling effect for the ideal dispersion compensation. The blue line is the initial cold cavity resonance from Eq. (4) with ω0 and ζ1 terms omitted. The red line is the resonance shift amount due to mode pulling. The black line is the final effective cavity resonance. The inset is a zoom-in of the black line.

Fig. 3.
Fig. 3.

(a) Microcomb generation dynamics; the first pair is generated in ±3 modes and the final state is still oscillating. (b) Corresponding generated comb. The inset is the intensity evolution for mode 6 between 4.5 and 5 ms.

Fig. 4.
Fig. 4.

Mode-pulling effect for quasi-dispersion compensation. The lines and inset have the same meaning as in Fig. 2.

Fig. 5.
Fig. 5.

Final cavity resonance at different moments, (a)–(d) for the ideal compensation case and (e)–(h) for the quasi-compensation case.

Fig. 6.
Fig. 6.

Contribution of mode-pulling effect from each Kerr effect pair for (a) mode 1 and (b) mode 5. The blue dotted lines show the contributions from XPM and SPM (cross points of dotted lines) pairs.

Fig. 7.
Fig. 7.

Mode-puling effect for type-I microcomb with TOD. Lines have the same meaning as in Fig. 2. The inset is a zoom-in of the black line and exhibits a nonzero slope for the excited modes.

Fig. 8.
Fig. 8.

(a) Microcomb generation dynamics with a large TOD. (b) Corresponding generated microcomb, with the inset showing the intensity evolution for mode 6 between 0.09 and 0.1 ms.

Fig. 9.
Fig. 9.

Mode-puling effect for type-I microcomb with large TOD. Lines and the inset have the same meaning as in Fig. 7.

Equations (4)

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dAηdt=12ΔωηAηig0α,β,μAαAβ*Aμei(ωαβμη+ωη)t+12ΔωηFeiΩ0tδ0η+iωηAη,
ig0α,β,μAαAβ*Aμei(ωαβμη+ωη)tAη=Mη+iNη,
dAηdt=12ΔωηAη+MηAη+Re(ΔωηFeiΩ0tδ0η2Aη)Aη+i[ωη+Nη+Im(ΔωηFeiΩ0tδ0η2Aη)]Aη,
ωη=ω0+2πς1η+12ς2η2+16ς3η3,

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