Abstract

We predict the existence of a novel type of the flat-top dissipative solitonic pulses, “platicons”, in microresonators with normal group velocity dispersion (GVD). We propose methods to generate these platicons from cw pump. Their duration may be altered significantly by tuning the pump frequency. The transformation of a discrete energy spectrum of dark solitons of the Lugiato-Lefever equation into a quasicontinuous spectrum of platicons is demonstrated. Generation of similar structures is also possible with bi-harmonic, phase/amplitude modulated pump or via laser injection locking.

© 2015 Optical Society of America

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    [Crossref]
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    [Crossref] [PubMed]
  3. 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,” Nature Photon.  4, 37–40 (2010).
    [Crossref]
  4. L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nature Photon. 4, 41–45 (2010).
    [Crossref]
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  6. S. B. Papp, P. Del’Haye, and S. A. Diddams, “Mechanical control of a microrod-resonator optical frequency comb,” Phys. Rev. X 3, 031003 (2013).
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    [Crossref]
  8. P. Del’Haye, O. Arcizet, A. Schliesser, R. Holzwarth, and T. J. Kippenberg, “Full stabilization of a microresonator-based optical frequency comb,” Phys. Rev. Lett. 101, 053903 (2008).
    [Crossref]
  9. P. Del’Haye, S. B. Papp, and S. A. Diddams, “Hybrid electro-optically modulated microcombs,” Phys. Rev. Lett. 109, 263901 (2012).
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  27. Y. Liu, Y. Xuan, X. Xue, P.-H. Wang, S. Chen, A. J. Metcalf, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Investigation of mode coupling in normal-dispersion silicon nitride microresonators for Kerr frequency comb generation,” Optica 1, 137–144 (2014).
    [Crossref]
  28. B. Varlot, S. Wabnitz, J. Fatome, G. Millot, and C. Finot, “Experimental generation of optical flaticon pulses,” Opt. Lett. 38, 3899–3902 (2013).
    [Crossref] [PubMed]
  29. 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]
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  32. L. A. Lugiato and R. Lefever, “Spatial dissipative structures in passive optical-systems,” Phys. Rev. Lett. 58, 2209–2211 (1987).
    [Crossref] [PubMed]
  33. 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]
  34. C. Bao, L. Zhang, A. Matsko, Y. Yan, Z. Zhao, G. Xie, A. M. Agarwal, L. C. Kimerling, J. Michel, L. Maleki, and A. E. Willner, “Nonlinear conversion efficiency in Kerr frequency comb generation,” Opt. Lett. 39, 6126–6129 (2014).
    [Crossref] [PubMed]

2015 (1)

S. W. Huang, H. Zhou, J. Yang, J. F. McMillan, A. Matsko, M. Yu, D. L. Kwong, L. Maleki, and C. W. Wong, “Mode-Locked Ultrashort Pulse Generation from On-Chip Normal Dispersion Microresonators,” Phys. Rev. Lett. 114, 053901 (2015).
[Crossref] [PubMed]

2014 (7)

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

W. Liang, A. A. Savchenkov, V. S. Ilchenko, D. Eliyahu, D. Seidel, A. B. Matsko, and L. Maleki, “Generation of a coherent near-infrared Kerr frequency comb in a monolithic microresonator with normal GVD,” Opt. Lett. 39, 2920–2923 (2014).
[Crossref] [PubMed]

Y. Liu, Y. Xuan, X. Xue, P.-H. Wang, S. Chen, A. J. Metcalf, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Investigation of mode coupling in normal-dispersion silicon nitride microresonators for Kerr frequency comb generation,” Optica 1, 137–144 (2014).
[Crossref]

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

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

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

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

2013 (5)

A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. M. Dudley, C. R. Menyuk, and Y. K. Chembo, “Azimuthal Turing patterns, bright and dark cavity solitons in Kerr combs generated with whispering-gallery-mode resonators,” IEEE Photon. J. 5, 4, 6100409 (2013).
[Crossref]

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

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]

B. Varlot, S. Wabnitz, J. Fatome, G. Millot, and C. Finot, “Experimental generation of optical flaticon pulses,” Opt. Lett. 38, 3899–3902 (2013).
[Crossref] [PubMed]

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

2012 (5)

A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, “Kerr frequency comb generation in overmoded resonators,” Opt. Express 20, 27290–27298 (2012).
[Crossref] [PubMed]

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

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

A. B. Matsko, A. A. Savchenkov, and L. Maleki, “Normal group-velocity dispersion Kerr frequency comb,” Opt. Lett. 37, 43–45 (2012).
[Crossref] [PubMed]

P. Del’Haye, S. B. Papp, and S. A. Diddams, “Hybrid electro-optically modulated microcombs,” Phys. Rev. Lett. 109, 263901 (2012).
[Crossref]

2011 (4)

F. Ferdous, H. X. 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,” Nature Photon. 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]

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

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

2010 (3)

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,” Nature Photon.  4, 37–40 (2010).
[Crossref]

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

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

2008 (2)

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

P. Del’Haye, O. Arcizet, A. Schliesser, R. Holzwarth, and T. J. Kippenberg, “Full stabilization of a microresonator-based optical frequency comb,” Phys. Rev. Lett. 101, 053903 (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]

1987 (1)

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

Agarwal, A. M.

Arcizet, O.

P. Del’Haye, O. Arcizet, A. Schliesser, R. Holzwarth, and T. J. Kippenberg, “Full stabilization of a microresonator-based optical frequency comb,” Phys. Rev. Lett. 101, 053903 (2008).
[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]

Balakireva, I.

A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. M. Dudley, C. R. Menyuk, and Y. K. Chembo, “Azimuthal Turing patterns, bright and dark cavity solitons in Kerr combs generated with whispering-gallery-mode resonators,” IEEE Photon. J. 5, 4, 6100409 (2013).
[Crossref]

Balakireva, I. V.

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

Bao, C.

Brasch, V.

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

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

V. Brasch, T. Herr, M. Geiselmann, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip based optical frequency comb using soliton induced Cherenkov radiation,” (2014). http://arxiv.org/abs/1410.8598 .

J. D. Jost, T. Herr, C. Lecaplain, V. Brasch, M. H. P. Pfeiffer, and T. J. Kippenberg, “Microwave to optical link using an optical microresonator,” (2014). http://arxiv.org/abs/1411.1354 .

Chembo, Y. K.

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

A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. M. Dudley, C. R. Menyuk, and Y. K. Chembo, “Azimuthal Turing patterns, bright and dark cavity solitons in Kerr combs generated with whispering-gallery-mode resonators,” IEEE Photon. J. 5, 4, 6100409 (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]

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]

Chen, L.

F. Ferdous, H. X. 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,” Nature Photon. 5, 770–776 (2011).
[Crossref]

Chen, S.

Y. Liu, Y. Xuan, X. Xue, P.-H. Wang, S. Chen, A. J. Metcalf, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Investigation of mode coupling in normal-dispersion silicon nitride microresonators for Kerr frequency comb generation,” Optica 1, 137–144 (2014).
[Crossref]

X. Xue, Y. Xuan, Y. Liu, P. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode interaction aided self excitation of dark solitons and offset frequency tuning in microresonators constructed of normal dispersion waveguides,” (2014). http://arxiv.org/abs/1404.2865 .

Chen, T.

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

Chu, S.

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

Coillet, A.

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

A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. M. Dudley, C. R. Menyuk, and Y. K. Chembo, “Azimuthal Turing patterns, bright and dark cavity solitons in Kerr combs generated with whispering-gallery-mode resonators,” IEEE Photon. J. 5, 4, 6100409 (2013).
[Crossref]

Del’Haye, P.

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

P. Del’Haye, S. B. Papp, and S. A. Diddams, “Hybrid electro-optically modulated microcombs,” Phys. Rev. Lett. 109, 263901 (2012).
[Crossref]

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

P. Del’Haye, O. Arcizet, A. Schliesser, R. Holzwarth, and T. J. Kippenberg, “Full stabilization of a microresonator-based optical frequency comb,” Phys. Rev. Lett. 101, 053903 (2008).
[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. A.

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

P. Del’Haye, S. B. Papp, and S. A. Diddams, “Hybrid electro-optically modulated microcombs,” Phys. Rev. Lett. 109, 263901 (2012).
[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]

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

Duchesne, D.

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

Dudley, J. M.

A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. M. Dudley, C. R. Menyuk, and Y. K. Chembo, “Azimuthal Turing patterns, bright and dark cavity solitons in Kerr combs generated with whispering-gallery-mode resonators,” IEEE Photon. J. 5, 4, 6100409 (2013).
[Crossref]

Eliyahu, D.

W. Liang, A. A. Savchenkov, V. S. Ilchenko, D. Eliyahu, D. Seidel, A. B. Matsko, and L. Maleki, “Generation of a coherent near-infrared Kerr frequency comb in a monolithic microresonator with normal GVD,” Opt. Lett. 39, 2920–2923 (2014).
[Crossref] [PubMed]

W. Liang, D. Eliyahu, V. Ilchenko, A. Savchenkov, A. Matsko, and L. Maleki, “All-optical micro-clock,” in “Frequency Control Symposium (FCS), 2014 IEEE International,” pp. 1–4.

Fatome, J.

Ferdous, F.

F. Ferdous, H. X. 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,” Nature Photon. 5, 770–776 (2011).
[Crossref]

Ferrera, M.

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

Finot, C.

Foster, M. 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,” Nature Photon.  4, 37–40 (2010).
[Crossref]

Gaeta, A. L.

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,” Nature Photon.  4, 37–40 (2010).
[Crossref]

Gavartin, E.

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

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

Geiselmann, M.

V. Brasch, T. Herr, M. Geiselmann, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip based optical frequency comb using soliton induced Cherenkov radiation,” (2014). http://arxiv.org/abs/1410.8598 .

Godey, C.

C. Godey, I. V. Balakireva, A. Coillet, and Y. K. Chembo, “Stability analysis of the spatiotemporal Lugiato-Lefever model for Kerr optical frequency combs in the anomalous and normal dispersion regimes,” Phys. Rev. A 89, 063814 (2014).
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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,” Nature Photon.  4, 37–40 (2010).
[Crossref]

Gorodetsky, M. L.

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

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

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

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

G. V. Lihachev, T. Herr, T. J. Kippenberg, and M. L. Gorodetsky, “Tool for simulation of Kerr frequency combs,” in “Microresonator Frequency Combs and Applications, Ascona, Switzerland,” (code: http://www.rqc.ru/groups/gorodetsky/combgui.htm ).

V. Brasch, T. Herr, M. Geiselmann, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip based optical frequency comb using soliton induced Cherenkov radiation,” (2014). http://arxiv.org/abs/1410.8598 .

Hansson, T.

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

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

Hartinger, K.

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

Henriet, R.

A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. M. Dudley, C. R. Menyuk, and Y. K. Chembo, “Azimuthal Turing patterns, bright and dark cavity solitons in Kerr combs generated with whispering-gallery-mode resonators,” IEEE Photon. J. 5, 4, 6100409 (2013).
[Crossref]

Herr, T.

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

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

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

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

G. V. Lihachev, T. Herr, T. J. Kippenberg, and M. L. Gorodetsky, “Tool for simulation of Kerr frequency combs,” in “Microresonator Frequency Combs and Applications, Ascona, Switzerland,” (code: http://www.rqc.ru/groups/gorodetsky/combgui.htm ).

J. D. Jost, T. Herr, C. Lecaplain, V. Brasch, M. H. P. Pfeiffer, and T. J. Kippenberg, “Microwave to optical link using an optical microresonator,” (2014). http://arxiv.org/abs/1411.1354 .

V. Brasch, T. Herr, M. Geiselmann, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip based optical frequency comb using soliton induced Cherenkov radiation,” (2014). http://arxiv.org/abs/1410.8598 .

Holzwarth, R.

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

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

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

P. Del’Haye, O. Arcizet, A. Schliesser, R. Holzwarth, and T. J. Kippenberg, “Full stabilization of a microresonator-based optical frequency comb,” Phys. Rev. Lett. 101, 053903 (2008).
[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]

Huang, S. W.

S. W. Huang, H. Zhou, J. Yang, J. F. McMillan, A. Matsko, M. Yu, D. L. Kwong, L. Maleki, and C. W. Wong, “Mode-Locked Ultrashort Pulse Generation from On-Chip Normal Dispersion Microresonators,” Phys. Rev. Lett. 114, 053901 (2015).
[Crossref] [PubMed]

Ilchenko, V.

W. Liang, D. Eliyahu, V. Ilchenko, A. Savchenkov, A. Matsko, and L. Maleki, “All-optical micro-clock,” in “Frequency Control Symposium (FCS), 2014 IEEE International,” pp. 1–4.

Ilchenko, V. S.

Jost, J. D.

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

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

J. D. Jost, T. Herr, C. Lecaplain, V. Brasch, M. H. P. Pfeiffer, and T. J. Kippenberg, “Microwave to optical link using an optical microresonator,” (2014). http://arxiv.org/abs/1411.1354 .

Kimerling, L. C.

Kippenberg, T. J.

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

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

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

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

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

P. Del’Haye, O. Arcizet, A. Schliesser, R. Holzwarth, and T. J. Kippenberg, “Full stabilization of a microresonator-based optical frequency comb,” Phys. Rev. Lett. 101, 053903 (2008).
[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]

G. V. Lihachev, T. Herr, T. J. Kippenberg, and M. L. Gorodetsky, “Tool for simulation of Kerr frequency combs,” in “Microresonator Frequency Combs and Applications, Ascona, Switzerland,” (code: http://www.rqc.ru/groups/gorodetsky/combgui.htm ).

J. D. Jost, T. Herr, C. Lecaplain, V. Brasch, M. H. P. Pfeiffer, and T. J. Kippenberg, “Microwave to optical link using an optical microresonator,” (2014). http://arxiv.org/abs/1411.1354 .

V. Brasch, T. Herr, M. Geiselmann, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip based optical frequency comb using soliton induced Cherenkov radiation,” (2014). http://arxiv.org/abs/1410.8598 .

Kondratiev, N. M.

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

Kwong, D. L.

S. W. Huang, H. Zhou, J. Yang, J. F. McMillan, A. Matsko, M. Yu, D. L. Kwong, L. Maleki, and C. W. Wong, “Mode-Locked Ultrashort Pulse Generation from On-Chip Normal Dispersion Microresonators,” Phys. Rev. Lett. 114, 053901 (2015).
[Crossref] [PubMed]

Larger, L.

A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. M. Dudley, C. R. Menyuk, and Y. K. Chembo, “Azimuthal Turing patterns, bright and dark cavity solitons in Kerr combs generated with whispering-gallery-mode resonators,” IEEE Photon. J. 5, 4, 6100409 (2013).
[Crossref]

Leaird, D. E.

Y. Liu, Y. Xuan, X. Xue, P.-H. Wang, S. Chen, A. J. Metcalf, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Investigation of mode coupling in normal-dispersion silicon nitride microresonators for Kerr frequency comb generation,” Optica 1, 137–144 (2014).
[Crossref]

F. Ferdous, H. X. 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,” Nature Photon. 5, 770–776 (2011).
[Crossref]

X. Xue, Y. Xuan, Y. Liu, P. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode interaction aided self excitation of dark solitons and offset frequency tuning in microresonators constructed of normal dispersion waveguides,” (2014). http://arxiv.org/abs/1404.2865 .

Lecaplain, C.

J. D. Jost, T. Herr, C. Lecaplain, V. Brasch, M. H. P. Pfeiffer, and T. J. Kippenberg, “Microwave to optical link using an optical microresonator,” (2014). http://arxiv.org/abs/1411.1354 .

Lee, H.

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

Lefever, R.

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

Levy, J. S.

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,” Nature Photon.  4, 37–40 (2010).
[Crossref]

Li, J.

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

Liang, W.

Lihachev, G.

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

V. Brasch, T. Herr, M. Geiselmann, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip based optical frequency comb using soliton induced Cherenkov radiation,” (2014). http://arxiv.org/abs/1410.8598 .

Lihachev, G. V.

G. V. Lihachev, T. Herr, T. J. Kippenberg, and M. L. Gorodetsky, “Tool for simulation of Kerr frequency combs,” in “Microresonator Frequency Combs and Applications, Ascona, Switzerland,” (code: http://www.rqc.ru/groups/gorodetsky/combgui.htm ).

Lipson, M.

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,” Nature Photon.  4, 37–40 (2010).
[Crossref]

Little, B. E.

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

Liu, Y.

Y. Liu, Y. Xuan, X. Xue, P.-H. Wang, S. Chen, A. J. Metcalf, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Investigation of mode coupling in normal-dispersion silicon nitride microresonators for Kerr frequency comb generation,” Optica 1, 137–144 (2014).
[Crossref]

X. Xue, Y. Xuan, Y. Liu, P. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode interaction aided self excitation of dark solitons and offset frequency tuning in microresonators constructed of normal dispersion waveguides,” (2014). http://arxiv.org/abs/1404.2865 .

Lugiato, L. A.

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

Maleki, L.

S. W. Huang, H. Zhou, J. Yang, J. F. McMillan, A. Matsko, M. Yu, D. L. Kwong, L. Maleki, and C. W. Wong, “Mode-Locked Ultrashort Pulse Generation from On-Chip Normal Dispersion Microresonators,” Phys. Rev. Lett. 114, 053901 (2015).
[Crossref] [PubMed]

W. Liang, A. A. Savchenkov, V. S. Ilchenko, D. Eliyahu, D. Seidel, A. B. Matsko, and L. Maleki, “Generation of a coherent near-infrared Kerr frequency comb in a monolithic microresonator with normal GVD,” Opt. Lett. 39, 2920–2923 (2014).
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C. Bao, L. Zhang, A. Matsko, Y. Yan, Z. Zhao, G. Xie, A. M. Agarwal, L. C. Kimerling, J. Michel, L. Maleki, and A. E. Willner, “Nonlinear conversion efficiency in Kerr frequency comb generation,” Opt. Lett. 39, 6126–6129 (2014).
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A. B. Matsko, A. A. Savchenkov, and L. Maleki, “Normal group-velocity dispersion Kerr frequency comb,” Opt. Lett. 37, 43–45 (2012).
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A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, “Kerr frequency comb generation in overmoded resonators,” Opt. Express 20, 27290–27298 (2012).
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A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, “Tunable optical frequency comb with a crystalline whispering gallery mode resonator,” Phys. Rev. Lett. 101, 093902 (2008).
[Crossref] [PubMed]

W. Liang, D. Eliyahu, V. Ilchenko, A. Savchenkov, A. Matsko, and L. Maleki, “All-optical micro-clock,” in “Frequency Control Symposium (FCS), 2014 IEEE International,” pp. 1–4.

Matsko, A.

S. W. Huang, H. Zhou, J. Yang, J. F. McMillan, A. Matsko, M. Yu, D. L. Kwong, L. Maleki, and C. W. Wong, “Mode-Locked Ultrashort Pulse Generation from On-Chip Normal Dispersion Microresonators,” Phys. Rev. Lett. 114, 053901 (2015).
[Crossref] [PubMed]

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

W. Liang, D. Eliyahu, V. Ilchenko, A. Savchenkov, A. Matsko, and L. Maleki, “All-optical micro-clock,” in “Frequency Control Symposium (FCS), 2014 IEEE International,” pp. 1–4.

Matsko, A. B.

McMillan, J. F.

S. W. Huang, H. Zhou, J. Yang, J. F. McMillan, A. Matsko, M. Yu, D. L. Kwong, L. Maleki, and C. W. Wong, “Mode-Locked Ultrashort Pulse Generation from On-Chip Normal Dispersion Microresonators,” Phys. Rev. Lett. 114, 053901 (2015).
[Crossref] [PubMed]

Menyuk, C. R.

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]

A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. M. Dudley, C. R. Menyuk, and Y. K. Chembo, “Azimuthal Turing patterns, bright and dark cavity solitons in Kerr combs generated with whispering-gallery-mode resonators,” IEEE Photon. J. 5, 4, 6100409 (2013).
[Crossref]

Metcalf, A. J.

Miao, H. X.

F. Ferdous, H. X. 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,” Nature Photon. 5, 770–776 (2011).
[Crossref]

Michel, J.

Millot, G.

Mirgorodskiy, I.

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

Modotto, D.

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

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

Morandotti, R.

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

Moss, D. J.

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

Papp, S. B.

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

P. Del’Haye, S. B. Papp, and S. A. Diddams, “Hybrid electro-optically modulated microcombs,” Phys. Rev. Lett. 109, 263901 (2012).
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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]

Pfeiffer, M. H. P.

J. D. Jost, T. Herr, C. Lecaplain, V. Brasch, M. H. P. Pfeiffer, and T. J. Kippenberg, “Microwave to optical link using an optical microresonator,” (2014). http://arxiv.org/abs/1411.1354 .

V. Brasch, T. Herr, M. Geiselmann, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip based optical frequency comb using soliton induced Cherenkov radiation,” (2014). http://arxiv.org/abs/1410.8598 .

Qi, M.

Y. Liu, Y. Xuan, X. Xue, P.-H. Wang, S. Chen, A. J. Metcalf, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Investigation of mode coupling in normal-dispersion silicon nitride microresonators for Kerr frequency comb generation,” Optica 1, 137–144 (2014).
[Crossref]

X. Xue, Y. Xuan, Y. Liu, P. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode interaction aided self excitation of dark solitons and offset frequency tuning in microresonators constructed of normal dispersion waveguides,” (2014). http://arxiv.org/abs/1404.2865 .

Razzari, L.

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

Riemensberger, J.

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

Saleh, K.

A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. M. Dudley, C. R. Menyuk, and Y. K. Chembo, “Azimuthal Turing patterns, bright and dark cavity solitons in Kerr combs generated with whispering-gallery-mode resonators,” IEEE Photon. J. 5, 4, 6100409 (2013).
[Crossref]

Savchenkov, A.

W. Liang, D. Eliyahu, V. Ilchenko, A. Savchenkov, A. Matsko, and L. Maleki, “All-optical micro-clock,” in “Frequency Control Symposium (FCS), 2014 IEEE International,” pp. 1–4.

Savchenkov, A. A.

Schliesser, A.

P. Del’Haye, O. Arcizet, A. Schliesser, R. Holzwarth, and T. J. Kippenberg, “Full stabilization of a microresonator-based optical frequency comb,” Phys. Rev. Lett. 101, 053903 (2008).
[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]

Seidel, D.

Solomatine, I.

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

Srinivasan, K.

F. Ferdous, H. X. 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,” Nature Photon. 5, 770–776 (2011).
[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,” Nature Photon.  4, 37–40 (2010).
[Crossref]

Vahala, K. J.

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

Varghese, L. T.

F. Ferdous, H. X. 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,” Nature Photon. 5, 770–776 (2011).
[Crossref]

Varlot, B.

Wabnitz, S.

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

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

B. Varlot, S. Wabnitz, J. Fatome, G. Millot, and C. Finot, “Experimental generation of optical flaticon pulses,” Opt. Lett. 38, 3899–3902 (2013).
[Crossref] [PubMed]

Wang, C. Y.

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

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

Wang, J.

Y. Liu, Y. Xuan, X. Xue, P.-H. Wang, S. Chen, A. J. Metcalf, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Investigation of mode coupling in normal-dispersion silicon nitride microresonators for Kerr frequency comb generation,” Optica 1, 137–144 (2014).
[Crossref]

F. Ferdous, H. X. 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,” Nature Photon. 5, 770–776 (2011).
[Crossref]

X. Xue, Y. Xuan, Y. Liu, P. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode interaction aided self excitation of dark solitons and offset frequency tuning in microresonators constructed of normal dispersion waveguides,” (2014). http://arxiv.org/abs/1404.2865 .

Wang, P.

X. Xue, Y. Xuan, Y. Liu, P. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode interaction aided self excitation of dark solitons and offset frequency tuning in microresonators constructed of normal dispersion waveguides,” (2014). http://arxiv.org/abs/1404.2865 .

Wang, P.-H.

Weiner, A. M.

Y. Liu, Y. Xuan, X. Xue, P.-H. Wang, S. Chen, A. J. Metcalf, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Investigation of mode coupling in normal-dispersion silicon nitride microresonators for Kerr frequency comb generation,” Optica 1, 137–144 (2014).
[Crossref]

F. Ferdous, H. X. 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,” Nature Photon. 5, 770–776 (2011).
[Crossref]

X. Xue, Y. Xuan, Y. Liu, P. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode interaction aided self excitation of dark solitons and offset frequency tuning in microresonators constructed of normal dispersion waveguides,” (2014). http://arxiv.org/abs/1404.2865 .

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]

Willner, A. E.

Wong, C. W.

S. W. Huang, H. Zhou, J. Yang, J. F. McMillan, A. Matsko, M. Yu, D. L. Kwong, L. Maleki, and C. W. Wong, “Mode-Locked Ultrashort Pulse Generation from On-Chip Normal Dispersion Microresonators,” Phys. Rev. Lett. 114, 053901 (2015).
[Crossref] [PubMed]

Xie, G.

Xuan, Y.

Y. Liu, Y. Xuan, X. Xue, P.-H. Wang, S. Chen, A. J. Metcalf, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Investigation of mode coupling in normal-dispersion silicon nitride microresonators for Kerr frequency comb generation,” Optica 1, 137–144 (2014).
[Crossref]

X. Xue, Y. Xuan, Y. Liu, P. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode interaction aided self excitation of dark solitons and offset frequency tuning in microresonators constructed of normal dispersion waveguides,” (2014). http://arxiv.org/abs/1404.2865 .

Xue, X.

Y. Liu, Y. Xuan, X. Xue, P.-H. Wang, S. Chen, A. J. Metcalf, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Investigation of mode coupling in normal-dispersion silicon nitride microresonators for Kerr frequency comb generation,” Optica 1, 137–144 (2014).
[Crossref]

X. Xue, Y. Xuan, Y. Liu, P. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode interaction aided self excitation of dark solitons and offset frequency tuning in microresonators constructed of normal dispersion waveguides,” (2014). http://arxiv.org/abs/1404.2865 .

Yan, Y.

Yang, J.

S. W. Huang, H. Zhou, J. Yang, J. F. McMillan, A. Matsko, M. Yu, D. L. Kwong, L. Maleki, and C. W. Wong, “Mode-Locked Ultrashort Pulse Generation from On-Chip Normal Dispersion Microresonators,” Phys. Rev. Lett. 114, 053901 (2015).
[Crossref] [PubMed]

Yu, M.

S. W. Huang, H. Zhou, J. Yang, J. F. McMillan, A. Matsko, M. Yu, D. L. Kwong, L. Maleki, and C. W. Wong, “Mode-Locked Ultrashort Pulse Generation from On-Chip Normal Dispersion Microresonators,” Phys. Rev. Lett. 114, 053901 (2015).
[Crossref] [PubMed]

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]

Zhang, L.

Zhao, Z.

Zhou, H.

S. W. Huang, H. Zhou, J. Yang, J. F. McMillan, A. Matsko, M. Yu, D. L. Kwong, L. Maleki, and C. W. Wong, “Mode-Locked Ultrashort Pulse Generation from On-Chip Normal Dispersion Microresonators,” Phys. Rev. Lett. 114, 053901 (2015).
[Crossref] [PubMed]

IEEE Photon. J. (1)

A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. M. Dudley, C. R. Menyuk, and Y. K. Chembo, “Azimuthal Turing patterns, bright and dark cavity solitons in Kerr combs generated with whispering-gallery-mode resonators,” IEEE Photon. J. 5, 4, 6100409 (2013).
[Crossref]

Nature (1)

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

Nature Photon (1)

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,” Nature Photon.  4, 37–40 (2010).
[Crossref]

Nature Photon. (4)

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

F. Ferdous, H. X. 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,” Nature Photon. 5, 770–776 (2011).
[Crossref]

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

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

Opt. Commun. (1)

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

Opt. Express (1)

Opt. Lett. (4)

Optica (1)

Phys. Rev. A (5)

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

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

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

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]

Phys. Rev. Lett. (8)

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

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

P. Del’Haye, O. Arcizet, A. Schliesser, R. Holzwarth, and T. J. Kippenberg, “Full stabilization of a microresonator-based optical frequency comb,” Phys. Rev. Lett. 101, 053903 (2008).
[Crossref]

P. Del’Haye, S. B. Papp, and S. A. Diddams, “Hybrid electro-optically modulated microcombs,” Phys. Rev. Lett. 109, 263901 (2012).
[Crossref]

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

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

S. W. Huang, H. Zhou, J. Yang, J. F. McMillan, A. Matsko, M. Yu, D. L. Kwong, L. Maleki, and C. W. Wong, “Mode-Locked Ultrashort Pulse Generation from On-Chip Normal Dispersion Microresonators,” Phys. Rev. Lett. 114, 053901 (2015).
[Crossref] [PubMed]

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

Phys. Rev. X (1)

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

Science (1)

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

Other (5)

W. Liang, D. Eliyahu, V. Ilchenko, A. Savchenkov, A. Matsko, and L. Maleki, “All-optical micro-clock,” in “Frequency Control Symposium (FCS), 2014 IEEE International,” pp. 1–4.

V. Brasch, T. Herr, M. Geiselmann, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip based optical frequency comb using soliton induced Cherenkov radiation,” (2014). http://arxiv.org/abs/1410.8598 .

J. D. Jost, T. Herr, C. Lecaplain, V. Brasch, M. H. P. Pfeiffer, and T. J. Kippenberg, “Microwave to optical link using an optical microresonator,” (2014). http://arxiv.org/abs/1411.1354 .

X. Xue, Y. Xuan, Y. Liu, P. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode interaction aided self excitation of dark solitons and offset frequency tuning in microresonators constructed of normal dispersion waveguides,” (2014). http://arxiv.org/abs/1404.2865 .

G. V. Lihachev, T. Herr, T. J. Kippenberg, and M. L. Gorodetsky, “Tool for simulation of Kerr frequency combs,” in “Microresonator Frequency Combs and Applications, Ascona, Switzerland,” (code: http://www.rqc.ru/groups/gorodetsky/combgui.htm ).

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Figures (6)

Fig. 1
Fig. 1 Intracavity average intensity U vs. detuning ζ0 in normal GVD microresonators. Left: Same input power, different perturbations for 2Δ = 0 (no comb) and 2Δ = 4,10. Pin = 50mW. Right: 2Δ = 8, Pin = 25, 50 and 100 mW.
Fig. 2
Fig. 2 (Left: a, c, e) Numerically simulated shapes of optical platicons in normal GVD mi-croresonators for different values of laser detunings. (Right: b, d, f) Corresponding optical spectra for the same set of parameters (2Δ = 4, Pin = 50mW).
Fig. 3
Fig. 3 (Left) Numerical investigation of pulse formation in normal GVD microresonators. Color coded ratio of peak to average intensity in resonator, used as an indication of pulses, is mapped for different eigenmodes μs with eigenfrequencies shifted by Δ. Central bright straight vertical line corresponds to μs = 0 with platicons analyzed in this paper. Right: Existence (blue) and soft excitation (yellow) domains of platicons.
Fig. 4
Fig. 4 Transition of discrete spectrum of dark solitons into continuous platicons upon increased perturbation Δ of the pumped mode frequency at Pin = 50 mW (left). Several higher order dark dissipative solitons (right).
Fig. 5
Fig. 5 Families of platicons for different pump power (a,b). Families of platicons for different dispersion (c,d). In all cases 2Δ = 2.
Fig. 6
Fig. 6 Comparison of average pulse intensity for the same absolute values of normal (2Δ = 2, Pin = 12.5mW) and anomalous GVD combs. Insets show corresponding comb spectra.

Equations (1)

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a μ τ = [ 1 + i ζ μ ] a μ + i μ , μ a μ a μ a μ * + μ μ + δ 0 μ f ,

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