Abstract

We are reporting that the Lugiato-Lefever equation describing the frequency comb generation in ring resonators with the localized pump and loss terms also describes the simultaneous nonlinear resonances leading to the multistability of nonlinear modes and coexisting solitons that are associated with the spectrally distinct frequency combs.

© 2017 Optical Society of America

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References

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  1. 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]
  2. 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 (2014).
    [Crossref]
  3. V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip-based optical frequency comb using soliton Cherenkov radiation,” Science 351357–360 (2016).
    [Crossref] [PubMed]
  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,” Nature Photon. 4, 471 (2010).
    [Crossref]
  5. J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J.S. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T.J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photon. 8, 375–380 (2014).
    [Crossref]
  6. M. G. Suh, Q. F. Yang, K. Y. Yang, X. Yi, and K. J. Vahala, “Microresonator soliton dual-comb spectroscopy,” Science 354, 600–603 (2016).
    [Crossref] [PubMed]
  7. D. V. Skryabin and A. V. Gorbach, “Looking at a soliton through the prism of optical supercontinuum,” Rev. Mod. Phys. 82, 1287–1299 (2010).
    [Crossref]
  8. L. A. Lugiato and R. Lefever, “Spatial dissipative structures in passive optical systems,” Phys. Rev. Lett. 58, 2209 (1987).
    [Crossref] [PubMed]
  9. 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]
  10. 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]
  11. C. Milian, A. V. Gorbach, M. Taki, A. V. Yulin, and D. V. Skryabin, “Solitons and frequency combs in silica microring resonators: Interplay of the Ramanand higher-order dispersion effect,” Phys. Rev. A 92, 033851 (2015).
    [Crossref]
  12. D. W. McLaughlin, J. V. Moloney, and A. C. Newell, “Solitary waves as fixed points of infinitely dimensional maps in an optical bistable ring cavity,” Phys. Rev. Lett. 51, 75–78 (1983).
    [Crossref]
  13. S. Coen and M. Haelterman, “Modulational instability induced by cavity boundary conditions in a normally dispersive optical fiber,” Phys. Rev. Lett. 79, 4139 (1997).
    [Crossref]
  14. T. Hansson and S. Wabnitz, “Frequency comb generation beyond the Lugiato-Lefever equation: multi-stability and super cavity solitons,” J. Opt. Soc. Am. B 32, 1259 (2015).
    [Crossref]
  15. M. Anderson, Y. Wang, F. Leo, M. Erkintalo, S. Coen, and S. G. Murdoch, “Coexistence of distinct cavity soliton states in a tristable passive Kerr resonator,” in Photonics and Fiber Technology 2016 (ACOFT, BGPP, NP), OSA Technical Digest (online) (Optical Society of America, 2016), paper NW3B.1.
  16. W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. DeVos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6, 47–73 (2012).
    [Crossref]
  17. J. K. Jang, M. Erkintalo, S. G. Murdoch, and S. Coen, “Ultraweak long-range interactions of solitons observed over astronomical distances,” Nat. Photon. 7, 657–663 (2013).
    [Crossref]

2016 (2)

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip-based optical frequency comb using soliton Cherenkov radiation,” Science 351357–360 (2016).
[Crossref] [PubMed]

M. G. Suh, Q. F. Yang, K. Y. Yang, X. Yi, and K. J. Vahala, “Microresonator soliton dual-comb spectroscopy,” Science 354, 600–603 (2016).
[Crossref] [PubMed]

2015 (2)

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

T. Hansson and S. Wabnitz, “Frequency comb generation beyond the Lugiato-Lefever equation: multi-stability and super cavity solitons,” J. Opt. Soc. Am. B 32, 1259 (2015).
[Crossref]

2014 (2)

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J.S. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T.J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photon. 8, 375–380 (2014).
[Crossref]

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

2013 (2)

J. K. Jang, M. Erkintalo, S. G. Murdoch, and S. Coen, “Ultraweak long-range interactions of solitons observed over astronomical distances,” Nat. Photon. 7, 657–663 (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]

2012 (1)

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. DeVos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6, 47–73 (2012).
[Crossref]

2011 (1)

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]

2010 (3)

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,” Nature Photon. 4, 471 (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]

D. V. Skryabin and A. V. Gorbach, “Looking at a soliton through the prism of optical supercontinuum,” Rev. Mod. Phys. 82, 1287–1299 (2010).
[Crossref]

1997 (1)

S. Coen and M. Haelterman, “Modulational instability induced by cavity boundary conditions in a normally dispersive optical fiber,” Phys. Rev. Lett. 79, 4139 (1997).
[Crossref]

1987 (1)

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

1983 (1)

D. W. McLaughlin, J. V. Moloney, and A. C. Newell, “Solitary waves as fixed points of infinitely dimensional maps in an optical bistable ring cavity,” Phys. Rev. Lett. 51, 75–78 (1983).
[Crossref]

Anderson, M.

M. Anderson, Y. Wang, F. Leo, M. Erkintalo, S. Coen, and S. G. Murdoch, “Coexistence of distinct cavity soliton states in a tristable passive Kerr resonator,” in Photonics and Fiber Technology 2016 (ACOFT, BGPP, NP), OSA Technical Digest (online) (Optical Society of America, 2016), paper NW3B.1.

Baets, R.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. DeVos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6, 47–73 (2012).
[Crossref]

Bienstman, P.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. DeVos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6, 47–73 (2012).
[Crossref]

Bogaerts, W.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. DeVos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6, 47–73 (2012).
[Crossref]

Brasch, V.

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip-based optical frequency comb using soliton Cherenkov radiation,” Science 351357–360 (2016).
[Crossref] [PubMed]

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

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J.S. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T.J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photon. 8, 375–380 (2014).
[Crossref]

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]

Claes, T.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. DeVos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6, 47–73 (2012).
[Crossref]

Coen, S.

J. K. Jang, M. Erkintalo, S. G. Murdoch, and S. Coen, “Ultraweak long-range interactions of solitons observed over astronomical distances,” Nat. Photon. 7, 657–663 (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,” Nature Photon. 4, 471 (2010).
[Crossref]

S. Coen and M. Haelterman, “Modulational instability induced by cavity boundary conditions in a normally dispersive optical fiber,” Phys. Rev. Lett. 79, 4139 (1997).
[Crossref]

M. Anderson, Y. Wang, F. Leo, M. Erkintalo, S. Coen, and S. G. Murdoch, “Coexistence of distinct cavity soliton states in a tristable passive Kerr resonator,” in Photonics and Fiber Technology 2016 (ACOFT, BGPP, NP), OSA Technical Digest (online) (Optical Society of America, 2016), paper NW3B.1.

Del’Haye, P.

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]

DeVos, K.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. DeVos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6, 47–73 (2012).
[Crossref]

Dumon, P.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. DeVos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6, 47–73 (2012).
[Crossref]

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,” Nature Photon. 4, 471 (2010).
[Crossref]

Erkintalo, M.

J. K. Jang, M. Erkintalo, S. G. Murdoch, and S. Coen, “Ultraweak long-range interactions of solitons observed over astronomical distances,” Nat. Photon. 7, 657–663 (2013).
[Crossref]

M. Anderson, Y. Wang, F. Leo, M. Erkintalo, S. Coen, and S. G. Murdoch, “Coexistence of distinct cavity soliton states in a tristable passive Kerr resonator,” in Photonics and Fiber Technology 2016 (ACOFT, BGPP, NP), OSA Technical Digest (online) (Optical Society of America, 2016), paper NW3B.1.

Freude, W.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J.S. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T.J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photon. 8, 375–380 (2014).
[Crossref]

Gavartin, E.

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, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip-based optical frequency comb using soliton Cherenkov radiation,” Science 351357–360 (2016).
[Crossref] [PubMed]

Gorbach, A. V.

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

D. V. Skryabin and A. V. Gorbach, “Looking at a soliton through the prism of optical supercontinuum,” Rev. Mod. Phys. 82, 1287–1299 (2010).
[Crossref]

Gorodetsky, M. L.

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip-based optical frequency comb using soliton Cherenkov radiation,” Science 351357–360 (2016).
[Crossref] [PubMed]

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

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,” Nature Photon. 4, 471 (2010).
[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,” Nature Photon. 4, 471 (2010).
[Crossref]

S. Coen and M. Haelterman, “Modulational instability induced by cavity boundary conditions in a normally dispersive optical fiber,” Phys. Rev. Lett. 79, 4139 (1997).
[Crossref]

Hansson, T.

Hartinger, K.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J.S. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T.J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photon. 8, 375–380 (2014).
[Crossref]

Herr, T.

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip-based optical frequency comb using soliton Cherenkov radiation,” Science 351357–360 (2016).
[Crossref] [PubMed]

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

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J.S. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T.J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photon. 8, 375–380 (2014).
[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]

Heyn, P. De

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. DeVos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6, 47–73 (2012).
[Crossref]

Hillerkuss, D.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J.S. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T.J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photon. 8, 375–380 (2014).
[Crossref]

Holzwarth, R.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J.S. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T.J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photon. 8, 375–380 (2014).
[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]

Jang, J. K.

J. K. Jang, M. Erkintalo, S. G. Murdoch, and S. Coen, “Ultraweak long-range interactions of solitons observed over astronomical distances,” Nat. Photon. 7, 657–663 (2013).
[Crossref]

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 (2014).
[Crossref]

Kippenberg, T. J.

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip-based optical frequency comb using soliton Cherenkov radiation,” Science 351357–360 (2016).
[Crossref] [PubMed]

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

Kippenberg, T.J.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J.S. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T.J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photon. 8, 375–380 (2014).
[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,” Nature Photon. 4, 471 (2010).
[Crossref]

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 (2014).
[Crossref]

Koos, C.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J.S. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T.J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photon. 8, 375–380 (2014).
[Crossref]

Lauermann, M.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J.S. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T.J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photon. 8, 375–380 (2014).
[Crossref]

Lefever, R.

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

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,” Nature Photon. 4, 471 (2010).
[Crossref]

M. Anderson, Y. Wang, F. Leo, M. Erkintalo, S. Coen, and S. G. Murdoch, “Coexistence of distinct cavity soliton states in a tristable passive Kerr resonator,” in Photonics and Fiber Technology 2016 (ACOFT, BGPP, NP), OSA Technical Digest (online) (Optical Society of America, 2016), paper NW3B.1.

Leuthold, J.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J.S. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T.J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photon. 8, 375–380 (2014).
[Crossref]

Li, J.S.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J.S. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T.J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photon. 8, 375–380 (2014).
[Crossref]

Lihachev, G.

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip-based optical frequency comb using soliton Cherenkov radiation,” Science 351357–360 (2016).
[Crossref] [PubMed]

Lugiato, L. A.

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

McLaughlin, D. W.

D. W. McLaughlin, J. V. Moloney, and A. C. Newell, “Solitary waves as fixed points of infinitely dimensional maps in an optical bistable ring cavity,” Phys. Rev. Lett. 51, 75–78 (1983).
[Crossref]

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]

Milian, C.

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

Moloney, J. V.

D. W. McLaughlin, J. V. Moloney, and A. C. Newell, “Solitary waves as fixed points of infinitely dimensional maps in an optical bistable ring cavity,” Phys. Rev. Lett. 51, 75–78 (1983).
[Crossref]

Murdoch, S. G.

J. K. Jang, M. Erkintalo, S. G. Murdoch, and S. Coen, “Ultraweak long-range interactions of solitons observed over astronomical distances,” Nat. Photon. 7, 657–663 (2013).
[Crossref]

M. Anderson, Y. Wang, F. Leo, M. Erkintalo, S. Coen, and S. G. Murdoch, “Coexistence of distinct cavity soliton states in a tristable passive Kerr resonator,” in Photonics and Fiber Technology 2016 (ACOFT, BGPP, NP), OSA Technical Digest (online) (Optical Society of America, 2016), paper NW3B.1.

Newell, A. C.

D. W. McLaughlin, J. V. Moloney, and A. C. Newell, “Solitary waves as fixed points of infinitely dimensional maps in an optical bistable ring cavity,” Phys. Rev. Lett. 51, 75–78 (1983).
[Crossref]

Pfeiffer, M. H. P.

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip-based optical frequency comb using soliton Cherenkov radiation,” Science 351357–360 (2016).
[Crossref] [PubMed]

Pfeifle, J.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J.S. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T.J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photon. 8, 375–380 (2014).
[Crossref]

Schindler, P.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J.S. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T.J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photon. 8, 375–380 (2014).
[Crossref]

Schmogrow, R.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J.S. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T.J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photon. 8, 375–380 (2014).
[Crossref]

Selvaraja, S. K.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. DeVos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6, 47–73 (2012).
[Crossref]

Skryabin, D. V.

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

D. V. Skryabin and A. V. Gorbach, “Looking at a soliton through the prism of optical supercontinuum,” Rev. Mod. Phys. 82, 1287–1299 (2010).
[Crossref]

Suh, M. G.

M. G. Suh, Q. F. Yang, K. Y. Yang, X. Yi, and K. J. Vahala, “Microresonator soliton dual-comb spectroscopy,” Science 354, 600–603 (2016).
[Crossref] [PubMed]

Taki, M.

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

Vahala, K. J.

M. G. Suh, Q. F. Yang, K. Y. Yang, X. Yi, and K. J. Vahala, “Microresonator soliton dual-comb spectroscopy,” Science 354, 600–603 (2016).
[Crossref] [PubMed]

Van Thourhout, D.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. DeVos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6, 47–73 (2012).
[Crossref]

Van Vaerenbergh, T.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. DeVos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6, 47–73 (2012).
[Crossref]

Wabnitz, S.

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 (2014).
[Crossref]

Wang, Y.

M. Anderson, Y. Wang, F. Leo, M. Erkintalo, S. Coen, and S. G. Murdoch, “Coexistence of distinct cavity soliton states in a tristable passive Kerr resonator,” in Photonics and Fiber Technology 2016 (ACOFT, BGPP, NP), OSA Technical Digest (online) (Optical Society of America, 2016), paper NW3B.1.

Wegner, D.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J.S. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T.J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photon. 8, 375–380 (2014).
[Crossref]

Weimann, C.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J.S. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T.J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photon. 8, 375–380 (2014).
[Crossref]

Yang, K. Y.

M. G. Suh, Q. F. Yang, K. Y. Yang, X. Yi, and K. J. Vahala, “Microresonator soliton dual-comb spectroscopy,” Science 354, 600–603 (2016).
[Crossref] [PubMed]

Yang, Q. F.

M. G. Suh, Q. F. Yang, K. Y. Yang, X. Yi, and K. J. Vahala, “Microresonator soliton dual-comb spectroscopy,” Science 354, 600–603 (2016).
[Crossref] [PubMed]

Yi, X.

M. G. Suh, Q. F. Yang, K. Y. Yang, X. Yi, and K. J. Vahala, “Microresonator soliton dual-comb spectroscopy,” Science 354, 600–603 (2016).
[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]

Yu, Y.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J.S. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T.J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photon. 8, 375–380 (2014).
[Crossref]

Yulin, A. V.

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

J. Opt. Soc. Am. B (1)

Laser Photon. Rev. (1)

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. DeVos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6, 47–73 (2012).
[Crossref]

Nat. Photon. (2)

J. K. Jang, M. Erkintalo, S. G. Murdoch, and S. Coen, “Ultraweak long-range interactions of solitons observed over astronomical distances,” Nat. Photon. 7, 657–663 (2013).
[Crossref]

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J.S. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T.J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photon. 8, 375–380 (2014).
[Crossref]

Nature Photon. (2)

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 (2014).
[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,” Nature Photon. 4, 471 (2010).
[Crossref]

Phys. Rev. A (3)

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]

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

Phys. Rev. Lett. (4)

D. W. McLaughlin, J. V. Moloney, and A. C. Newell, “Solitary waves as fixed points of infinitely dimensional maps in an optical bistable ring cavity,” Phys. Rev. Lett. 51, 75–78 (1983).
[Crossref]

S. Coen and M. Haelterman, “Modulational instability induced by cavity boundary conditions in a normally dispersive optical fiber,” Phys. Rev. Lett. 79, 4139 (1997).
[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]

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

Rev. Mod. Phys. (1)

D. V. Skryabin and A. V. Gorbach, “Looking at a soliton through the prism of optical supercontinuum,” Rev. Mod. Phys. 82, 1287–1299 (2010).
[Crossref]

Science (2)

M. G. Suh, Q. F. Yang, K. Y. Yang, X. Yi, and K. J. Vahala, “Microresonator soliton dual-comb spectroscopy,” Science 354, 600–603 (2016).
[Crossref] [PubMed]

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip-based optical frequency comb using soliton Cherenkov radiation,” Science 351357–360 (2016).
[Crossref] [PubMed]

Other (1)

M. Anderson, Y. Wang, F. Leo, M. Erkintalo, S. Coen, and S. G. Murdoch, “Coexistence of distinct cavity soliton states in a tristable passive Kerr resonator,” in Photonics and Fiber Technology 2016 (ACOFT, BGPP, NP), OSA Technical Digest (online) (Optical Society of America, 2016), paper NW3B.1.

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Figures (3)

Fig. 1
Fig. 1 (a) Spectra of the pump H (empty circles) and of the nonlinear solution ψ ˜ ( θ ) = m ψ m e i θ m (red dots) corresponding to the upper branch of the m = 0 resonance calculated for h = 5, δ = 3, θ0 = π/50, and γ = 0.05, see Fig. 1(c). (b,c) Multiple nonlinear resonances: max θ | ψ ˜ ( θ ) | vs the detuning parameter δ. h = 5 in (b) and 9 in (c). (c) shows the nonlinear resonance tilts exceeding 2π and the associated multistability. (d) Spectra of the maximally unstable solutions of Eqs. (5), { u ( θ ) , v ( θ ) } = m { u m , v m } e i θ m , that drives the instability of the nonlinear state shown in (a). Note the log scales in (a) and (d).
Fig. 2
Fig. 2 (a) Spatiotemporal dynamics of comb formation observed in numerical modeling of Eq. (2) initialized by the highest amplitude solution in the multistability regime shown in Fig. 1(c) at δ = 8:4. (b) shows a zoom of the θ ∈ [−0:75π; −0:57π] interval. (c) shows the associated comb spectrum at τ = 200.
Fig. 3
Fig. 3 (a) A zoomed interval of θ from Fig. 2(a) showing the coexisting comb solitons with the different widths and amplitudes. (b) Breathing of the amplitude of the larger soliton from (a) as it makes round trips around the resonator. (c,d) The comb spectra of the isolated low (c) and high (d) amplitude solitons from (a).

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

i T Ψ = ( ω 0 i ω Z 1 2 ω Z 2 ) Ψ i κ Ψ T r 1 | Ψ | 2 Ψ P e i ω p t .
i τ ψ = ( δ i 2 π θ d θ 2 ) ψ i Γ ( θ ) ψ | ψ | 2 ψ H ( θ ) ,
i τ ψ = δ ψ d x 2 ψ i Γ ( x + 2 π τ ) ψ | ψ | 2 ψ H ( x + 2 π τ ) , x θ 2 π τ .
( δ + 2 π m + d m 2 ) ψ m = i n γ n ψ m n + k n ψ k ψ n ψ m k + n * + h m .
λ u = i δ u 2 π θ u + i d θ 2 u Γ u + 2 i | ψ ˜ | 2 u + i ψ ˜ 2 v λ v = i δ v 2 π θ v i d θ 2 v Γ v 2 i | ψ ˜ | 2 v i ψ ˜   2 u

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