Abstract

We generalize the coupled mode formalism to study the generation of frequency combs in microresonators with simultaneous Raman and Kerr nonlinearities and investigate an impact of the former on the formation of frequency combs and dynamics of platicons in the regime of the normal group velocity dispersion. We demonstrate that the Raman effect initiates generation of sidebands, which cascade further in four-wave mixing and reshape into the Raman-Kerr frequency combs. We reveal that the Raman scattering induces a strong instability of the platicon pulses associated with the Kerr effect and normal dispersion. This instability results in branching of platicons and complex spatiotemporal dynamics.

© 2017 Optical Society of America

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References

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]

2017 (4)

2016 (7)

P. Parra-Rivas, D. Gomila, E. Knobloch, S. Coen, and L. Gelens, “Origin and stability of dark pulse Kerr combs in normal dispersion resonators,” Opt. Lett. 41, 2402–2405 (2016).
[Crossref] [PubMed]

G. Lin, S. Diallo, J. M. Dudley, and Y. K. Chembo, “Universal nonlinear scattering in ultra-high Q whispering gallery-mode resonators,” Opt. Express 24, 14880–14894 (2016).
[Crossref] [PubMed]

X. Yi, Q.-F. Yang, K. Y. Yang, and K. Vahala, “Theory and measurement of the soliton self-frequency shift and efficiency in optical microcavities,” Opt. Lett. 41, 3419–3422 (2016).
[Crossref] [PubMed]

M. Karpov, H. Guo, A. Kordts, V. Brasch, M. H. P. Pfeiffer, M. Zervas, M. Geiselmann, and T. J. Kippenberg, “Raman self-frequency shift of dissipative Kerr solitons in an optical microresonator,” Phys. Rev. Lett. 116, 103902 (2016).
[Crossref] [PubMed]

P. Parra-Rivas, E. Knobloch, D. Gomila, and L. Gelens, “Dark solitons in the Lugiato-Lefever equation with normal dispersion,” Phys. Rev. A 93, 063839 (2016).
[Crossref]

Q.-F. Yang, X. Yi, K. Y. Yang, and K. Vahala, “Stokes solitons in optical microcavities,” Nat. Phys. 13(1), 3875 (2016).
[Crossref]

X. Xue, M. Qi, and A. M. Weiner, “Normal-dispersion microresonator Kerr frequency combs,” Nanophotonics 5, 244–262 (2016).
[Crossref]

2015 (6)

X. Xue, Y. Xuan, Y. Liu, P.-H. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode-locked dark pulse Kerr combs in normal-dispersion microresonators,” Nat. Photon. 9, 594–600 (2015).
[Crossref]

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

X. Xue, Y. Xuan, P.-H. Wang, Y. Liu, D. E. Leaird, M. Qi, and A. M. Weiner, “Normal-dispersion microcombs enabled by controllable mode interactions,” Las. Photon. Rev. 9, L23–L28 (2015).

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

Y. K. Chembo, I. S. Grudinin, and N. Yu, “Spatiotemporal dynamics of Kerr-Raman optical frequency combs,” Phys. Rev. A 92, 043818 (2015).
[Crossref]

V. Lobanov, G. Lihachev, T. J. Kippenberg, and M. Gorodetsky, “Frequency combs and platicons in optical microresonators with normal GVD,” Opt. Express 23, 7713–7721 (2015).
[Crossref] [PubMed]

2014 (5)

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, “Mid-infrared soliton and Raman frequency comb generation in silicon microrings,” Opt. Lett. 39, 6747–6750 (2014).
[Crossref] [PubMed]

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

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. 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]

2013 (2)

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]

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] [PubMed]

2012 (1)

2011 (3)

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] [PubMed]

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 (1)

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]

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)

2004 (1)

A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, “Low threshold optical oscillations in a whispering gallery mode CaF2 resonator,” Phys. Rev. Lett. 93, 243905 (2004).
[Crossref]

1990 (1)

B. A. Malomed and A. A. Nepomnyashchy, “Kinks and solitons in the generalized Ginzburg-Landau equation,”, Phys. Rev. A 42, 6009–6014 (1990).
[Crossref] [PubMed]

1987 (1)

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

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.

Bilenko, I. A.

V. E. Lobanov, A. V. Cherenkov, A. E. Shitikov, I. A. Bilenko, and M. L. Gorodetsky, “Dynamics of platicons due to third-order dispersion,” Eur. Phys. J. D 71, 1–5 (2017).
[Crossref]

Brasch, V.

M. Karpov, H. Guo, A. Kordts, V. Brasch, M. H. P. Pfeiffer, M. Zervas, M. Geiselmann, and T. J. Kippenberg, “Raman self-frequency shift of dissipative Kerr solitons in an optical microresonator,” Phys. Rev. Lett. 116, 103902 (2016).
[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]

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

Chembo, Y. K.

G. Lin, S. Diallo, J. M. Dudley, and Y. K. Chembo, “Universal nonlinear scattering in ultra-high Q whispering gallery-mode resonators,” Opt. Express 24, 14880–14894 (2016).
[Crossref] [PubMed]

Y. K. Chembo, I. S. Grudinin, and N. Yu, “Spatiotemporal dynamics of Kerr-Raman optical frequency combs,” Phys. Rev. A 92, 043818 (2015).
[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, S.

X. Xue, Y. Xuan, Y. Liu, P.-H. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode-locked dark pulse Kerr combs in normal-dispersion microresonators,” Nat. Photon. 9, 594–600 (2015).
[Crossref]

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]

Cherenkov, A. V.

V. E. Lobanov, A. V. Cherenkov, A. E. Shitikov, I. A. Bilenko, and M. L. Gorodetsky, “Dynamics of platicons due to third-order dispersion,” Eur. Phys. J. D 71, 1–5 (2017).
[Crossref]

Coen, S.

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]

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]

Diallo, S.

Diddams, S. A.

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

Dudley, J. M.

Erkintalo, M.

Gaeta, A. L.

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.

M. Karpov, H. Guo, A. Kordts, V. Brasch, M. H. P. Pfeiffer, M. Zervas, M. Geiselmann, and T. J. Kippenberg, “Raman self-frequency shift of dissipative Kerr solitons in an optical microresonator,” Phys. Rev. Lett. 116, 103902 (2016).
[Crossref] [PubMed]

Gelens, L.

P. Parra-Rivas, E. Knobloch, D. Gomila, and L. Gelens, “Dark solitons in the Lugiato-Lefever equation with normal dispersion,” Phys. Rev. A 93, 063839 (2016).
[Crossref]

P. Parra-Rivas, D. Gomila, E. Knobloch, S. Coen, and L. Gelens, “Origin and stability of dark pulse Kerr combs in normal dispersion resonators,” Opt. Lett. 41, 2402–2405 (2016).
[Crossref] [PubMed]

Gomila, D.

P. Parra-Rivas, D. Gomila, E. Knobloch, S. Coen, and L. Gelens, “Origin and stability of dark pulse Kerr combs in normal dispersion resonators,” Opt. Lett. 41, 2402–2405 (2016).
[Crossref] [PubMed]

P. Parra-Rivas, E. Knobloch, D. Gomila, and L. Gelens, “Dark solitons in the Lugiato-Lefever equation with normal dispersion,” Phys. Rev. A 93, 063839 (2016).
[Crossref]

Gorbach, A. V.

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

Gorodetsky, M.

Gorodetsky, M. L.

V. E. Lobanov, A. V. Cherenkov, A. E. Shitikov, I. A. Bilenko, and M. L. Gorodetsky, “Dynamics of platicons due to third-order dispersion,” Eur. Phys. J. D 71, 1–5 (2017).
[Crossref]

V. E. Lobanov, G. Lihachev, and M. L. Gorodetsky, “Generation of platicons and frequency combs in optical microresonators with normal GVD by modulated pump,” Europhysics Letters 112, 54008 (2015).
[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, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photon. 8, 145–152 (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]

Griffith, A. G.

Grudinin, I. S.

Y. K. Chembo, I. S. Grudinin, and N. Yu, “Spatiotemporal dynamics of Kerr-Raman optical frequency combs,” Phys. Rev. A 92, 043818 (2015).
[Crossref]

Guo, H.

M. Karpov, H. Guo, A. Kordts, V. Brasch, M. H. P. Pfeiffer, M. Zervas, M. Geiselmann, and T. J. Kippenberg, “Raman self-frequency shift of dissipative Kerr solitons in an optical microresonator,” Phys. Rev. Lett. 116, 103902 (2016).
[Crossref] [PubMed]

Guo, H. R.

Hansson, T.

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

T. Hansson, D. Modotto, and S. Wabnitz, “Mid-infrared soliton and Raman frequency comb generation in silicon microrings,” Opt. Lett. 39, 6747–6750 (2014).
[Crossref] [PubMed]

Herkommer, C.

Herr, T.

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. 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]

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]

Holzwarth, R.

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, 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]

Ilchenko, V. S.

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]

A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, “Low threshold optical oscillations in a whispering gallery mode CaF2 resonator,” Phys. Rev. Lett. 93, 243905 (2004).
[Crossref]

Jaramillo-Villegas, J. A.

Jost, J. D.

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

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

Karpov, M.

M. H. P. Pfeiffer, C. Herkommer, J. Q. Liu, H. R. Guo, M. Karpov, E. Lucas, M. Zervas, and T. J. Kippenberg, “Octave-spanning dissipative Kerr soliton frequency combs in Si3N4 microresonators,” Optica 4, 684–691 (2017).
[Crossref]

M. Karpov, H. Guo, A. Kordts, V. Brasch, M. H. P. Pfeiffer, M. Zervas, M. Geiselmann, and T. J. Kippenberg, “Raman self-frequency shift of dissipative Kerr solitons in an optical microresonator,” Phys. Rev. Lett. 116, 103902 (2016).
[Crossref] [PubMed]

Kippenberg, T. J.

M. H. P. Pfeiffer, C. Herkommer, J. Q. Liu, H. R. Guo, M. Karpov, E. Lucas, M. Zervas, and T. J. Kippenberg, “Octave-spanning dissipative Kerr soliton frequency combs in Si3N4 microresonators,” Optica 4, 684–691 (2017).
[Crossref]

M. Karpov, H. Guo, A. Kordts, V. Brasch, M. H. P. Pfeiffer, M. Zervas, M. Geiselmann, and T. J. Kippenberg, “Raman self-frequency shift of dissipative Kerr solitons in an optical microresonator,” Phys. Rev. Lett. 116, 103902 (2016).
[Crossref] [PubMed]

V. Lobanov, G. Lihachev, T. J. Kippenberg, and M. Gorodetsky, “Frequency combs and platicons in optical microresonators with normal GVD,” Opt. Express 23, 7713–7721 (2015).
[Crossref] [PubMed]

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. 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]

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, 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]

Knobloch, E.

P. Parra-Rivas, D. Gomila, E. Knobloch, S. Coen, and L. Gelens, “Origin and stability of dark pulse Kerr combs in normal dispersion resonators,” Opt. Lett. 41, 2402–2405 (2016).
[Crossref] [PubMed]

P. Parra-Rivas, E. Knobloch, D. Gomila, and L. Gelens, “Dark solitons in the Lugiato-Lefever equation with normal dispersion,” Phys. Rev. A 93, 063839 (2016).
[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,” Nat. Photon. 8, 145–152 (2014).
[Crossref]

Kordts, A.

M. Karpov, H. Guo, A. Kordts, V. Brasch, M. H. P. Pfeiffer, M. Zervas, M. Geiselmann, and T. J. Kippenberg, “Raman self-frequency shift of dissipative Kerr solitons in an optical microresonator,” Phys. Rev. Lett. 116, 103902 (2016).
[Crossref] [PubMed]

Latawiec, P. M.

Leaird, D. E.

C. Bao, Y. Xuan, C. Wang, J. A. Jaramillo-Villegas, D. E. Leaird, M. Qi, and A. M. Weiner, “Soliton repetition rate in a silicon-nitride microresonator,” Opt. Lett. 42, 759–762 (2017).
[Crossref] [PubMed]

X. Xue, Y. Xuan, P.-H. Wang, Y. Liu, D. E. Leaird, M. Qi, and A. M. Weiner, “Normal-dispersion microcombs enabled by controllable mode interactions,” Las. Photon. Rev. 9, L23–L28 (2015).

X. Xue, Y. Xuan, Y. Liu, P.-H. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode-locked dark pulse Kerr combs in normal-dispersion microresonators,” Nat. Photon. 9, 594–600 (2015).
[Crossref]

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]

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.

Liang, W.

Lihachev, G.

V. Lobanov, G. Lihachev, T. J. Kippenberg, and M. Gorodetsky, “Frequency combs and platicons in optical microresonators with normal GVD,” Opt. Express 23, 7713–7721 (2015).
[Crossref] [PubMed]

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

Lin, G.

Lipson, M.

Liu, J. Q.

Liu, Y.

X. Xue, Y. Xuan, Y. Liu, P.-H. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode-locked dark pulse Kerr combs in normal-dispersion microresonators,” Nat. Photon. 9, 594–600 (2015).
[Crossref]

X. Xue, Y. Xuan, P.-H. Wang, Y. Liu, D. E. Leaird, M. Qi, and A. M. Weiner, “Normal-dispersion microcombs enabled by controllable mode interactions,” Las. Photon. Rev. 9, L23–L28 (2015).

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]

Lobanov, V.

Lobanov, V. E.

V. E. Lobanov, A. V. Cherenkov, A. E. Shitikov, I. A. Bilenko, and M. L. Gorodetsky, “Dynamics of platicons due to third-order dispersion,” Eur. Phys. J. D 71, 1–5 (2017).
[Crossref]

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

Loncar, M.

Lucas, E.

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.

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]

A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, “Low threshold optical oscillations in a whispering gallery mode CaF2 resonator,” Phys. Rev. Lett. 93, 243905 (2004).
[Crossref]

Malomed, B. A.

B. A. Malomed and A. A. Nepomnyashchy, “Kinks and solitons in the generalized Ginzburg-Landau equation,”, Phys. Rev. A 42, 6009–6014 (1990).
[Crossref] [PubMed]

Matsko, A. B.

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]

A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, “Low threshold optical oscillations in a whispering gallery mode CaF2 resonator,” Phys. Rev. Lett. 93, 243905 (2004).
[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]

Metcalf, A. J.

Milián, C.

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

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. Comm. 312, 134–136 (2014).
[Crossref]

T. Hansson, D. Modotto, and S. Wabnitz, “Mid-infrared soliton and Raman frequency comb generation in silicon microrings,” Opt. Lett. 39, 6747–6750 (2014).
[Crossref] [PubMed]

Mohageg, M.

A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, “Low threshold optical oscillations in a whispering gallery mode CaF2 resonator,” Phys. Rev. Lett. 93, 243905 (2004).
[Crossref]

Nepomnyashchy, A. A.

B. A. Malomed and A. A. Nepomnyashchy, “Kinks and solitons in the generalized Ginzburg-Landau equation,”, Phys. Rev. A 42, 6009–6014 (1990).
[Crossref] [PubMed]

Okawachi, Y.

Parra-Rivas, P.

P. Parra-Rivas, E. Knobloch, D. Gomila, and L. Gelens, “Dark solitons in the Lugiato-Lefever equation with normal dispersion,” Phys. Rev. A 93, 063839 (2016).
[Crossref]

P. Parra-Rivas, D. Gomila, E. Knobloch, S. Coen, and L. Gelens, “Origin and stability of dark pulse Kerr combs in normal dispersion resonators,” Opt. Lett. 41, 2402–2405 (2016).
[Crossref] [PubMed]

Pfeiffer, M. H. P.

M. H. P. Pfeiffer, C. Herkommer, J. Q. Liu, H. R. Guo, M. Karpov, E. Lucas, M. Zervas, and T. J. Kippenberg, “Octave-spanning dissipative Kerr soliton frequency combs in Si3N4 microresonators,” Optica 4, 684–691 (2017).
[Crossref]

M. Karpov, H. Guo, A. Kordts, V. Brasch, M. H. P. Pfeiffer, M. Zervas, M. Geiselmann, and T. J. Kippenberg, “Raman self-frequency shift of dissipative Kerr solitons in an optical microresonator,” Phys. Rev. Lett. 116, 103902 (2016).
[Crossref] [PubMed]

Qi, M.

C. Bao, Y. Xuan, C. Wang, J. A. Jaramillo-Villegas, D. E. Leaird, M. Qi, and A. M. Weiner, “Soliton repetition rate in a silicon-nitride microresonator,” Opt. Lett. 42, 759–762 (2017).
[Crossref] [PubMed]

X. Xue, M. Qi, and A. M. Weiner, “Normal-dispersion microresonator Kerr frequency combs,” Nanophotonics 5, 244–262 (2016).
[Crossref]

X. Xue, Y. Xuan, Y. Liu, P.-H. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode-locked dark pulse Kerr combs in normal-dispersion microresonators,” Nat. Photon. 9, 594–600 (2015).
[Crossref]

X. Xue, Y. Xuan, P.-H. Wang, Y. Liu, D. E. Leaird, M. Qi, and A. M. Weiner, “Normal-dispersion microcombs enabled by controllable mode interactions,” Las. Photon. Rev. 9, L23–L28 (2015).

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]

Randle, H. G.

Saha, K.

Savchenkov, A. A.

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]

A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, “Low threshold optical oscillations in a whispering gallery mode CaF2 resonator,” Phys. Rev. Lett. 93, 243905 (2004).
[Crossref]

Schliesser, A.

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.

Shitikov, A. E.

V. E. Lobanov, A. V. Cherenkov, A. E. Shitikov, I. A. Bilenko, and M. L. Gorodetsky, “Dynamics of platicons due to third-order dispersion,” Eur. Phys. J. D 71, 1–5 (2017).
[Crossref]

Skryabin, D. V.

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

A. V. Yulin and D. V. Skryabin, “Slowing down of solitons by intrapulse Raman scattering in fibers with frequency cutoff,” Opt. Lett. 31, 3092–3094 (2006).
[Crossref] [PubMed]

Strekalov, D.

A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, “Low threshold optical oscillations in a whispering gallery mode CaF2 resonator,” Phys. Rev. Lett. 93, 243905 (2004).
[Crossref]

Sylvestre, T.

Taki, M.

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

Vahala, K.

Venkataraman, V.

Wabnitz, S.

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

T. Hansson, D. Modotto, and S. Wabnitz, “Mid-infrared soliton and Raman frequency comb generation in silicon microrings,” Opt. Lett. 39, 6747–6750 (2014).
[Crossref] [PubMed]

Wang, C.

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,” Nat. Photon. 8, 145–152 (2014).
[Crossref]

Wang, J.

X. Xue, Y. Xuan, Y. Liu, P.-H. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode-locked dark pulse Kerr combs in normal-dispersion microresonators,” Nat. Photon. 9, 594–600 (2015).
[Crossref]

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]

Wang, P.-H.

X. Xue, Y. Xuan, Y. Liu, P.-H. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode-locked dark pulse Kerr combs in normal-dispersion microresonators,” Nat. Photon. 9, 594–600 (2015).
[Crossref]

X. Xue, Y. Xuan, P.-H. Wang, Y. Liu, D. E. Leaird, M. Qi, and A. M. Weiner, “Normal-dispersion microcombs enabled by controllable mode interactions,” Las. Photon. Rev. 9, L23–L28 (2015).

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]

Weiner, A. M.

C. Bao, Y. Xuan, C. Wang, J. A. Jaramillo-Villegas, D. E. Leaird, M. Qi, and A. M. Weiner, “Soliton repetition rate in a silicon-nitride microresonator,” Opt. Lett. 42, 759–762 (2017).
[Crossref] [PubMed]

X. Xue, M. Qi, and A. M. Weiner, “Normal-dispersion microresonator Kerr frequency combs,” Nanophotonics 5, 244–262 (2016).
[Crossref]

X. Xue, Y. Xuan, Y. Liu, P.-H. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode-locked dark pulse Kerr combs in normal-dispersion microresonators,” Nat. Photon. 9, 594–600 (2015).
[Crossref]

X. Xue, Y. Xuan, P.-H. Wang, Y. Liu, D. E. Leaird, M. Qi, and A. M. Weiner, “Normal-dispersion microcombs enabled by controllable mode interactions,” Las. Photon. Rev. 9, L23–L28 (2015).

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]

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]

Xuan, Y.

C. Bao, Y. Xuan, C. Wang, J. A. Jaramillo-Villegas, D. E. Leaird, M. Qi, and A. M. Weiner, “Soliton repetition rate in a silicon-nitride microresonator,” Opt. Lett. 42, 759–762 (2017).
[Crossref] [PubMed]

X. Xue, Y. Xuan, P.-H. Wang, Y. Liu, D. E. Leaird, M. Qi, and A. M. Weiner, “Normal-dispersion microcombs enabled by controllable mode interactions,” Las. Photon. Rev. 9, L23–L28 (2015).

X. Xue, Y. Xuan, Y. Liu, P.-H. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode-locked dark pulse Kerr combs in normal-dispersion microresonators,” Nat. Photon. 9, 594–600 (2015).
[Crossref]

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]

Xue, X.

X. Xue, M. Qi, and A. M. Weiner, “Normal-dispersion microresonator Kerr frequency combs,” Nanophotonics 5, 244–262 (2016).
[Crossref]

X. Xue, Y. Xuan, Y. Liu, P.-H. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode-locked dark pulse Kerr combs in normal-dispersion microresonators,” Nat. Photon. 9, 594–600 (2015).
[Crossref]

X. Xue, Y. Xuan, P.-H. Wang, Y. Liu, D. E. Leaird, M. Qi, and A. M. Weiner, “Normal-dispersion microcombs enabled by controllable mode interactions,” Las. Photon. Rev. 9, L23–L28 (2015).

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]

Yang, K. Y.

Yang, Q.-F.

Yi, X.

Yu, M.

Yu, N.

Y. K. Chembo, I. S. Grudinin, and N. Yu, “Spatiotemporal dynamics of Kerr-Raman optical frequency combs,” Phys. Rev. A 92, 043818 (2015).
[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]

Yulin, A. V.

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

A. V. Yulin and D. V. Skryabin, “Slowing down of solitons by intrapulse Raman scattering in fibers with frequency cutoff,” Opt. Lett. 31, 3092–3094 (2006).
[Crossref] [PubMed]

Zervas, M.

M. H. P. Pfeiffer, C. Herkommer, J. Q. Liu, H. R. Guo, M. Karpov, E. Lucas, M. Zervas, and T. J. Kippenberg, “Octave-spanning dissipative Kerr soliton frequency combs in Si3N4 microresonators,” Optica 4, 684–691 (2017).
[Crossref]

M. Karpov, H. Guo, A. Kordts, V. Brasch, M. H. P. Pfeiffer, M. Zervas, M. Geiselmann, and T. J. Kippenberg, “Raman self-frequency shift of dissipative Kerr solitons in an optical microresonator,” Phys. Rev. Lett. 116, 103902 (2016).
[Crossref] [PubMed]

Eur. Phys. J. D (1)

V. E. Lobanov, A. V. Cherenkov, A. E. Shitikov, I. A. Bilenko, and M. L. Gorodetsky, “Dynamics of platicons due to third-order dispersion,” Eur. Phys. J. D 71, 1–5 (2017).
[Crossref]

Europhysics Letters (1)

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

Las. Photon. Rev. (1)

X. Xue, Y. Xuan, P.-H. Wang, Y. Liu, D. E. Leaird, M. Qi, and A. M. Weiner, “Normal-dispersion microcombs enabled by controllable mode interactions,” Las. Photon. Rev. 9, L23–L28 (2015).

Nanophotonics (1)

X. Xue, M. Qi, and A. M. Weiner, “Normal-dispersion microresonator Kerr frequency combs,” Nanophotonics 5, 244–262 (2016).
[Crossref]

Nat. Photon. (2)

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Figures (6)

Fig. 1
Fig. 1 A schematic representation of Raman scattering in microresonators. The Raman peak covers several free spectral ranges (FSR) in a large diameter microresonator. ΩR is the detuning of the Raman peak from the pump frequency ( Ω R 2 π = 9.66 THzfor CaF2 and 12.3 THz for MgF2).
Fig. 2
Fig. 2 Optical spectrum for the primary Stokes line formation for GR = 120 (a) and GR = 160 (b). The Raman peak overlaps the mode with μs = −198, the width of the Raman gain γ̃ = 1.5, ζ = 0.02. The anti-Stokes line is strongly suppressed. The Raman FWM between the pump mode and the Stokes mode creates an anti-Stokes peak at the mode number μas = 202 and cascades a peak with frequency such as ωcascade is divisible by the Raman frequency. Spectral lines around the Raman peak are shown in the insets.
Fig. 3
Fig. 3 The comb spectrum is generated by a combination of the Raman scattering, which downshifts its frequency and nondegenerate four-wave mixing processes in which all four photons have different frequencies. Insets show energy level diagrams for the Raman scattering and four-wave mixing processes. The Raman part of the FWM plays a dominant role in the spectrum formation.
Fig. 4
Fig. 4 Wide platicon (ζ0 = 0.02) evolution for different values of the Raman gain: (a) GR = 150; (b) GR = 175; (c) GR = 200; (d) GR = 220; (e) GR = 300; (f) GR = 575.
Fig. 5
Fig. 5 Platicon dynamics for intermediate width (ζ0 = 0.03, a–c) and narrow (ζ0 = 0.04, d–f) platicon with different values of the Raman gain: (a) GR = 200; (b) GR = 250; (c) GR = 300, (d) GR = 400; (e) GR = 575; (f) GR = 700.
Fig. 6
Fig. 6 Degradation of the platicon optical spectra for ζ0 = 0.02, GR = 175: (a) τ = 0; (b) τ = 5000. The Stokes mode corresponds to μ ≈ 100. The waveforms for the corresponding spectra are shown in the (c) and (d).

Equations (16)

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χ ( 1 ) = χ 0 ( 1 ) + χ ( 1 ) q q ,
d 2 q d t 2 + 2 γ d q d t + Ω 0 2 q = w F q ,
F q = 0 2 χ ( 1 ) q | E | 2 V eff ,
× × E + n 2 c 2 2 E t 2 = 1 0 c 2 2 P p t 2 1 c 2 χ ( 1 ) q 2 t 2 q E χ ( 3 ) c 2 2 ( E | E | 2 ) t 2 ,
E ( r , t ) = ( e i ω t μ A μ ( t ) e μ ( r ) ) ,
× × e μ n 2 ω μ 2 c 2 e μ = 0
F q = 0 4 χ ( 1 ) q μ ν ( e μ e ν A μ A ν e 2 i ω t + e μ e ν * A μ A ν * ) V eff .
d 2 q ν ν d t 2 + 2 γ d q ν ν d t + Ω 0 2 q ν ν = w 0 4 V eff χ ( 1 ) q A ν A ν * .
A ˙ μ = i ω μ 2 ω 2 2 ω A μ + i ω f μ χ ( 1 ) 2 n 2 δ μ 0 + i 3 χ ( 3 ) ω 8 n 2 μ μ μ Λ μ μ μ μ A μ A μ A μ * + i w 2 n 2 χ ( 1 ) q ω ν ν μ Λ μ μ ν ν q ν ν ( t ) A μ .
A μ t = i ( ω μ ω ) A μ κ μ 2 A μ + i G ω μ q μ μ ( t ) A μ + i g μ = μ + μ μ A μ A μ A μ * + F δ μ 0
d 2 q μ μ d t 2 + 2 γ d q μ μ d t + Ω 0 2 q μ μ = G ω ν A ν A ν + μ μ * .
A t = i [ ( ω 0 ω ) i κ 2 ] A D 1 A ϕ + i D 2 2 2 A ϕ 2 + i g A | A | 2 + i G q ω A + F ,
d 2 q ( ϕ , t ) d t 2 + 2 γ d q ( ϕ , t ) d t + Ω 0 2 q ( ϕ , t ) = G ω | A ( ϕ , t ) | 2 .
a μ τ = ( κ 2 D 1 + i ζ μ ) a μ + R μ + i μ μ ( 2 δ μ μ ) a μ a μ a μ + μ μ * + f δ μ 0 ,
d 2 q ¯ d τ 2 + 2 γ ˜ d q ¯ d τ + Ω ˜ 0 2 q ¯ = η D 1 Ω 0 + 2 γ , ν a ν a ν η * e i η τ ,
R μ = i G R q ¯ μ a μ e i η τ ,

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