Abstract

We investigate frequency comb generation in the presence of polarization effects induced by nonlinear mode coupling in microresonator devices. A set of coupled temporal Lugiato–Lefever equations are derived to model the propagation dynamics, and an in-depth study is made of the modulational instability of their multistable homogeneous steady-state solutions. It is shown that new kinds of instabilities can occur for co-propagating fields that interact through nonlinear cross-phase modulation. These instabilities display properties that differ from their scalar counterpart, and are shown to result in the generation of new types of incoherently coupled frequency comb states.

© 2018 Optical Society of America

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References

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  1. T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332, 555–559 (2011).
    [Crossref]
  2. A. Pasquazi, M. Peccianti, L. Razzari, D. J. Moss, S. Coen, M. Erkintalo, Y. K. Chembo, T. Hansson, S. Wabnitz, P. Del’Haye, X. Xue, A. M. Weiner, and R. Morandotti, “Micro-combs: a novel generation of optical sources,” Phys. Rep. 729, 1–81 (2018).
    [Crossref]
  3. A. Matsko, A. Savchenkov, D. Strekalov, V. Ilchenko, and L. Maleki, “Optical hyperparametric oscillations in a whispering-gallery-mode resonator: threshold and phase diffusion,” Phys. Rev. A 71, 033804 (2005).
    [Crossref]
  4. T. Hansson, D. Modotto, and S. Wabnitz, “Dynamics of the modulational instability in microresonator frequency combs,” Phys. Rev. A 88, 023819 (2013).
    [Crossref]
  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, 6100409 (2013).
    [Crossref]
  6. Z. Qi, G. D’Aguanno, and C. R. Menyuk, “Nonlinear frequency combs generated by cnoidal waves in microring resonators,” J. Opt. Soc. Am. B 34, 785–794 (2017).
    [Crossref]
  7. L. A. Lugiato and R. Lefever, “Spatial dissipative structures in passive optical systems,” Phys. Rev. Lett. 58, 2209–2211 (1987).
    [Crossref]
  8. 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]
  9. 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, 1259–1266 (2015).
    [Crossref]
  10. G. P. Agrawal, “Modulation instability induced by cross-phase modulation,” Phys. Rev. Lett. 59, 880–883 (1987).
    [Crossref]
  11. S. Wabnitz, “Modulational polarization instability of light in a nonlinear birefringent dispersive medium,” Phys. Rev. A 38, 2018–2021 (1988).
    [Crossref]
  12. J. E. Rothenberg, “Modulational instability for normal dispersion,” Phys. Rev. A 42, 682–685 (1990).
    [Crossref]
  13. 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]
  14. 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]
  15. D. C. Cole, E. S. Lamb, P. Del’Haye, S. A. Diddams, and S. B. Papp, “Soliton crystals in Kerr resonators,” Nat. Photonics 11, 671–676 (2017).
    [Crossref]
  16. M. Haelterman, S. Trillo, and S. Wabnitz, “Polarization multistability and instability in a nonlinear dispersive ring cavity,” J. Opt. Soc. Am. B 11, 446–456 (1994).
    [Crossref]
  17. G. D’Aguanno and C. R. Menyuk, “Nonlinear mode coupling in whispering-gallery-mode resonators,” Phys. Rev. A 93, 043820 (2016).
    [Crossref]
  18. G. D’Aguanno and C. R. Menyuk, “Coupled Lugiato-Lefever equation for nonlinear frequency comb generation at an avoided crossing of a microresonator,” Eur. Phys. J. D 71, 74 (2017).
    [Crossref]
  19. E. Averlant, M. Tlidi, K. Panajotov, and L. Weicker, “Coexistence of cavity solitons with different polarization states and different power peaks in all-fiber resonators,” Opt. Lett. 42, 2750–2753 (2017).
    [Crossref]
  20. C. Bao, P. Liao, A. Kordts, L. Zhang, A. Matsko, M. Karpov, M. H. P. Pfeiffer, G. Xie, Y. Cao, Y. Yan, A. Almaiman, Z. Zhao, A. Mohajerin-Ariaei, A. Fallahpour, F. Alishahi, M. Tur, L. Maleki, T. J. Kippenberg, and A. E. Willner, “Orthogonally polarized Kerr frequency combs,” arXiv:1705.05045 (2017).
  21. Y. Wang, F. Leo, J. Fatome, M. Erkintalo, S. G. Murdoch, and S. Coen, “Universal mechanism for the binding of temporal cavity solitons,” Optica 4, 855–863 (2017).
    [Crossref]
  22. G. P. Agrawal, Nonlinear Fiber Optics, 5th ed. (Academic, 2012).
  23. M. Haelterman, S. Trillo, and S. Wabnitz, “Dissipative modulation instability in a nonlinear dispersive ring cavity,” Opt. Commun. 91, 401–407 (1992).
    [Crossref]
  24. A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, D. Seidel, and L. Maleki, “Hard and soft excitation regimes of Kerr frequency combs,” Phys. Rev. A 85, 023830 (2012).
    [Crossref]
  25. A. Mussot, E. Louvergneaux, N. Akhmediev, F. Reynaud, L. Delage, and M. Taki, “Optical fiber systems are convectively unstable,” Phys. Rev. Lett. 101, 113904 (2008).
    [Crossref]
  26. H. Guo, E. Lucas, M. H. P. Pfeiffer, M. Karpov, M. Anderson, J. Liu, M. Geiselmann, J. D. Jost, and T. J. Kippenberg, “Intermode breather solitons in optical microresonators,” Phys. Rev. X 7, 041055 (2017).
    [Crossref]

2018 (1)

A. Pasquazi, M. Peccianti, L. Razzari, D. J. Moss, S. Coen, M. Erkintalo, Y. K. Chembo, T. Hansson, S. Wabnitz, P. Del’Haye, X. Xue, A. M. Weiner, and R. Morandotti, “Micro-combs: a novel generation of optical sources,” Phys. Rep. 729, 1–81 (2018).
[Crossref]

2017 (6)

D. C. Cole, E. S. Lamb, P. Del’Haye, S. A. Diddams, and S. B. Papp, “Soliton crystals in Kerr resonators,” Nat. Photonics 11, 671–676 (2017).
[Crossref]

G. D’Aguanno and C. R. Menyuk, “Coupled Lugiato-Lefever equation for nonlinear frequency comb generation at an avoided crossing of a microresonator,” Eur. Phys. J. D 71, 74 (2017).
[Crossref]

H. Guo, E. Lucas, M. H. P. Pfeiffer, M. Karpov, M. Anderson, J. Liu, M. Geiselmann, J. D. Jost, and T. J. Kippenberg, “Intermode breather solitons in optical microresonators,” Phys. Rev. X 7, 041055 (2017).
[Crossref]

Z. Qi, G. D’Aguanno, and C. R. Menyuk, “Nonlinear frequency combs generated by cnoidal waves in microring resonators,” J. Opt. Soc. Am. B 34, 785–794 (2017).
[Crossref]

E. Averlant, M. Tlidi, K. Panajotov, and L. Weicker, “Coexistence of cavity solitons with different polarization states and different power peaks in all-fiber resonators,” Opt. Lett. 42, 2750–2753 (2017).
[Crossref]

Y. Wang, F. Leo, J. Fatome, M. Erkintalo, S. G. Murdoch, and S. Coen, “Universal mechanism for the binding of temporal cavity solitons,” Optica 4, 855–863 (2017).
[Crossref]

2016 (1)

G. D’Aguanno and C. R. Menyuk, “Nonlinear mode coupling in whispering-gallery-mode resonators,” Phys. Rev. A 93, 043820 (2016).
[Crossref]

2015 (1)

2014 (1)

2013 (3)

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]

T. Hansson, D. Modotto, and S. Wabnitz, “Dynamics of the modulational instability in microresonator frequency combs,” Phys. Rev. A 88, 023819 (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, 6100409 (2013).
[Crossref]

2012 (2)

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

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]

2011 (1)

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

2008 (1)

A. Mussot, E. Louvergneaux, N. Akhmediev, F. Reynaud, L. Delage, and M. Taki, “Optical fiber systems are convectively unstable,” Phys. Rev. Lett. 101, 113904 (2008).
[Crossref]

2005 (1)

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

1994 (1)

1992 (1)

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

1990 (1)

J. E. Rothenberg, “Modulational instability for normal dispersion,” Phys. Rev. A 42, 682–685 (1990).
[Crossref]

1988 (1)

S. Wabnitz, “Modulational polarization instability of light in a nonlinear birefringent dispersive medium,” Phys. Rev. A 38, 2018–2021 (1988).
[Crossref]

1987 (2)

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

G. P. Agrawal, “Modulation instability induced by cross-phase modulation,” Phys. Rev. Lett. 59, 880–883 (1987).
[Crossref]

Agrawal, G. P.

G. P. Agrawal, “Modulation instability induced by cross-phase modulation,” Phys. Rev. Lett. 59, 880–883 (1987).
[Crossref]

G. P. Agrawal, Nonlinear Fiber Optics, 5th ed. (Academic, 2012).

Akhmediev, N.

A. Mussot, E. Louvergneaux, N. Akhmediev, F. Reynaud, L. Delage, and M. Taki, “Optical fiber systems are convectively unstable,” Phys. Rev. Lett. 101, 113904 (2008).
[Crossref]

Alishahi, F.

C. Bao, P. Liao, A. Kordts, L. Zhang, A. Matsko, M. Karpov, M. H. P. Pfeiffer, G. Xie, Y. Cao, Y. Yan, A. Almaiman, Z. Zhao, A. Mohajerin-Ariaei, A. Fallahpour, F. Alishahi, M. Tur, L. Maleki, T. J. Kippenberg, and A. E. Willner, “Orthogonally polarized Kerr frequency combs,” arXiv:1705.05045 (2017).

Almaiman, A.

C. Bao, P. Liao, A. Kordts, L. Zhang, A. Matsko, M. Karpov, M. H. P. Pfeiffer, G. Xie, Y. Cao, Y. Yan, A. Almaiman, Z. Zhao, A. Mohajerin-Ariaei, A. Fallahpour, F. Alishahi, M. Tur, L. Maleki, T. J. Kippenberg, and A. E. Willner, “Orthogonally polarized Kerr frequency combs,” arXiv:1705.05045 (2017).

Anderson, M.

H. Guo, E. Lucas, M. H. P. Pfeiffer, M. Karpov, M. Anderson, J. Liu, M. Geiselmann, J. D. Jost, and T. J. Kippenberg, “Intermode breather solitons in optical microresonators,” Phys. Rev. X 7, 041055 (2017).
[Crossref]

Averlant, E.

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, 6100409 (2013).
[Crossref]

Bao, C.

C. Bao, P. Liao, A. Kordts, L. Zhang, A. Matsko, M. Karpov, M. H. P. Pfeiffer, G. Xie, Y. Cao, Y. Yan, A. Almaiman, Z. Zhao, A. Mohajerin-Ariaei, A. Fallahpour, F. Alishahi, M. Tur, L. Maleki, T. J. Kippenberg, and A. E. Willner, “Orthogonally polarized Kerr frequency combs,” arXiv:1705.05045 (2017).

Cao, Y.

C. Bao, P. Liao, A. Kordts, L. Zhang, A. Matsko, M. Karpov, M. H. P. Pfeiffer, G. Xie, Y. Cao, Y. Yan, A. Almaiman, Z. Zhao, A. Mohajerin-Ariaei, A. Fallahpour, F. Alishahi, M. Tur, L. Maleki, T. J. Kippenberg, and A. E. Willner, “Orthogonally polarized Kerr frequency combs,” arXiv:1705.05045 (2017).

Chembo, Y. K.

A. Pasquazi, M. Peccianti, L. Razzari, D. J. Moss, S. Coen, M. Erkintalo, Y. K. Chembo, T. Hansson, S. Wabnitz, P. Del’Haye, X. Xue, A. M. Weiner, and R. Morandotti, “Micro-combs: a novel generation of optical sources,” Phys. Rep. 729, 1–81 (2018).
[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, 6100409 (2013).
[Crossref]

Chen, S.

Coen, S.

Coillet, A.

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, 6100409 (2013).
[Crossref]

Cole, D. C.

D. C. Cole, E. S. Lamb, P. Del’Haye, S. A. Diddams, and S. B. Papp, “Soliton crystals in Kerr resonators,” Nat. Photonics 11, 671–676 (2017).
[Crossref]

D’Aguanno, G.

G. D’Aguanno and C. R. Menyuk, “Coupled Lugiato-Lefever equation for nonlinear frequency comb generation at an avoided crossing of a microresonator,” Eur. Phys. J. D 71, 74 (2017).
[Crossref]

Z. Qi, G. D’Aguanno, and C. R. Menyuk, “Nonlinear frequency combs generated by cnoidal waves in microring resonators,” J. Opt. Soc. Am. B 34, 785–794 (2017).
[Crossref]

G. D’Aguanno and C. R. Menyuk, “Nonlinear mode coupling in whispering-gallery-mode resonators,” Phys. Rev. A 93, 043820 (2016).
[Crossref]

Del’Haye, P.

A. Pasquazi, M. Peccianti, L. Razzari, D. J. Moss, S. Coen, M. Erkintalo, Y. K. Chembo, T. Hansson, S. Wabnitz, P. Del’Haye, X. Xue, A. M. Weiner, and R. Morandotti, “Micro-combs: a novel generation of optical sources,” Phys. Rep. 729, 1–81 (2018).
[Crossref]

D. C. Cole, E. S. Lamb, P. Del’Haye, S. A. Diddams, and S. B. Papp, “Soliton crystals in Kerr resonators,” Nat. Photonics 11, 671–676 (2017).
[Crossref]

Delage, L.

A. Mussot, E. Louvergneaux, N. Akhmediev, F. Reynaud, L. Delage, and M. Taki, “Optical fiber systems are convectively unstable,” Phys. Rev. Lett. 101, 113904 (2008).
[Crossref]

Diddams, S. A.

D. C. Cole, E. S. Lamb, P. Del’Haye, S. A. Diddams, and S. B. Papp, “Soliton crystals in Kerr resonators,” Nat. Photonics 11, 671–676 (2017).
[Crossref]

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332, 555–559 (2011).
[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, 6100409 (2013).
[Crossref]

Erkintalo, M.

Fallahpour, A.

C. Bao, P. Liao, A. Kordts, L. Zhang, A. Matsko, M. Karpov, M. H. P. Pfeiffer, G. Xie, Y. Cao, Y. Yan, A. Almaiman, Z. Zhao, A. Mohajerin-Ariaei, A. Fallahpour, F. Alishahi, M. Tur, L. Maleki, T. J. Kippenberg, and A. E. Willner, “Orthogonally polarized Kerr frequency combs,” arXiv:1705.05045 (2017).

Fatome, J.

Geiselmann, M.

H. Guo, E. Lucas, M. H. P. Pfeiffer, M. Karpov, M. Anderson, J. Liu, M. Geiselmann, J. D. Jost, and T. J. Kippenberg, “Intermode breather solitons in optical microresonators,” Phys. Rev. X 7, 041055 (2017).
[Crossref]

Guo, H.

H. Guo, E. Lucas, M. H. P. Pfeiffer, M. Karpov, M. Anderson, J. Liu, M. Geiselmann, J. D. Jost, and T. J. Kippenberg, “Intermode breather solitons in optical microresonators,” Phys. Rev. X 7, 041055 (2017).
[Crossref]

Haelterman, M.

M. Haelterman, S. Trillo, and S. Wabnitz, “Polarization multistability and instability in a nonlinear dispersive ring cavity,” J. Opt. Soc. Am. B 11, 446–456 (1994).
[Crossref]

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

Hansson, T.

A. Pasquazi, M. Peccianti, L. Razzari, D. J. Moss, S. Coen, M. Erkintalo, Y. K. Chembo, T. Hansson, S. Wabnitz, P. Del’Haye, X. Xue, A. M. Weiner, and R. Morandotti, “Micro-combs: a novel generation of optical sources,” Phys. Rep. 729, 1–81 (2018).
[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, 1259–1266 (2015).
[Crossref]

T. Hansson, D. Modotto, and S. Wabnitz, “Dynamics of the modulational instability in microresonator frequency combs,” Phys. Rev. A 88, 023819 (2013).
[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, 6100409 (2013).
[Crossref]

Holzwarth, R.

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

Ilchenko, V.

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

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]

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

Jost, J. D.

H. Guo, E. Lucas, M. H. P. Pfeiffer, M. Karpov, M. Anderson, J. Liu, M. Geiselmann, J. D. Jost, and T. J. Kippenberg, “Intermode breather solitons in optical microresonators,” Phys. Rev. X 7, 041055 (2017).
[Crossref]

Karpov, M.

H. Guo, E. Lucas, M. H. P. Pfeiffer, M. Karpov, M. Anderson, J. Liu, M. Geiselmann, J. D. Jost, and T. J. Kippenberg, “Intermode breather solitons in optical microresonators,” Phys. Rev. X 7, 041055 (2017).
[Crossref]

C. Bao, P. Liao, A. Kordts, L. Zhang, A. Matsko, M. Karpov, M. H. P. Pfeiffer, G. Xie, Y. Cao, Y. Yan, A. Almaiman, Z. Zhao, A. Mohajerin-Ariaei, A. Fallahpour, F. Alishahi, M. Tur, L. Maleki, T. J. Kippenberg, and A. E. Willner, “Orthogonally polarized Kerr frequency combs,” arXiv:1705.05045 (2017).

Kippenberg, T. J.

H. Guo, E. Lucas, M. H. P. Pfeiffer, M. Karpov, M. Anderson, J. Liu, M. Geiselmann, J. D. Jost, and T. J. Kippenberg, “Intermode breather solitons in optical microresonators,” Phys. Rev. X 7, 041055 (2017).
[Crossref]

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

C. Bao, P. Liao, A. Kordts, L. Zhang, A. Matsko, M. Karpov, M. H. P. Pfeiffer, G. Xie, Y. Cao, Y. Yan, A. Almaiman, Z. Zhao, A. Mohajerin-Ariaei, A. Fallahpour, F. Alishahi, M. Tur, L. Maleki, T. J. Kippenberg, and A. E. Willner, “Orthogonally polarized Kerr frequency combs,” arXiv:1705.05045 (2017).

Kordts, A.

C. Bao, P. Liao, A. Kordts, L. Zhang, A. Matsko, M. Karpov, M. H. P. Pfeiffer, G. Xie, Y. Cao, Y. Yan, A. Almaiman, Z. Zhao, A. Mohajerin-Ariaei, A. Fallahpour, F. Alishahi, M. Tur, L. Maleki, T. J. Kippenberg, and A. E. Willner, “Orthogonally polarized Kerr frequency combs,” arXiv:1705.05045 (2017).

Lamb, E. S.

D. C. Cole, E. S. Lamb, P. Del’Haye, S. A. Diddams, and S. B. Papp, “Soliton crystals in Kerr resonators,” Nat. Photonics 11, 671–676 (2017).
[Crossref]

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, 6100409 (2013).
[Crossref]

Leaird, D. E.

Lefever, R.

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

Leo, F.

Liang, W.

Liao, P.

C. Bao, P. Liao, A. Kordts, L. Zhang, A. Matsko, M. Karpov, M. H. P. Pfeiffer, G. Xie, Y. Cao, Y. Yan, A. Almaiman, Z. Zhao, A. Mohajerin-Ariaei, A. Fallahpour, F. Alishahi, M. Tur, L. Maleki, T. J. Kippenberg, and A. E. Willner, “Orthogonally polarized Kerr frequency combs,” arXiv:1705.05045 (2017).

Liu, J.

H. Guo, E. Lucas, M. H. P. Pfeiffer, M. Karpov, M. Anderson, J. Liu, M. Geiselmann, J. D. Jost, and T. J. Kippenberg, “Intermode breather solitons in optical microresonators,” Phys. Rev. X 7, 041055 (2017).
[Crossref]

Liu, Y.

Louvergneaux, E.

A. Mussot, E. Louvergneaux, N. Akhmediev, F. Reynaud, L. Delage, and M. Taki, “Optical fiber systems are convectively unstable,” Phys. Rev. Lett. 101, 113904 (2008).
[Crossref]

Lucas, E.

H. Guo, E. Lucas, M. H. P. Pfeiffer, M. Karpov, M. Anderson, J. Liu, M. Geiselmann, J. D. Jost, and T. J. Kippenberg, “Intermode breather solitons in optical microresonators,” Phys. Rev. X 7, 041055 (2017).
[Crossref]

Lugiato, L. A.

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

Maleki, L.

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

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]

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

C. Bao, P. Liao, A. Kordts, L. Zhang, A. Matsko, M. Karpov, M. H. P. Pfeiffer, G. Xie, Y. Cao, Y. Yan, A. Almaiman, Z. Zhao, A. Mohajerin-Ariaei, A. Fallahpour, F. Alishahi, M. Tur, L. Maleki, T. J. Kippenberg, and A. E. Willner, “Orthogonally polarized Kerr frequency combs,” arXiv:1705.05045 (2017).

Matsko, A.

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

C. Bao, P. Liao, A. Kordts, L. Zhang, A. Matsko, M. Karpov, M. H. P. Pfeiffer, G. Xie, Y. Cao, Y. Yan, A. Almaiman, Z. Zhao, A. Mohajerin-Ariaei, A. Fallahpour, F. Alishahi, M. Tur, L. Maleki, T. J. Kippenberg, and A. E. Willner, “Orthogonally polarized Kerr frequency combs,” arXiv:1705.05045 (2017).

Matsko, A. B.

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

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]

Menyuk, C. R.

Z. Qi, G. D’Aguanno, and C. R. Menyuk, “Nonlinear frequency combs generated by cnoidal waves in microring resonators,” J. Opt. Soc. Am. B 34, 785–794 (2017).
[Crossref]

G. D’Aguanno and C. R. Menyuk, “Coupled Lugiato-Lefever equation for nonlinear frequency comb generation at an avoided crossing of a microresonator,” Eur. Phys. J. D 71, 74 (2017).
[Crossref]

G. D’Aguanno and C. R. Menyuk, “Nonlinear mode coupling in whispering-gallery-mode resonators,” Phys. Rev. A 93, 043820 (2016).
[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, 6100409 (2013).
[Crossref]

Metcalf, A. J.

Modotto, D.

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

Mohajerin-Ariaei, A.

C. Bao, P. Liao, A. Kordts, L. Zhang, A. Matsko, M. Karpov, M. H. P. Pfeiffer, G. Xie, Y. Cao, Y. Yan, A. Almaiman, Z. Zhao, A. Mohajerin-Ariaei, A. Fallahpour, F. Alishahi, M. Tur, L. Maleki, T. J. Kippenberg, and A. E. Willner, “Orthogonally polarized Kerr frequency combs,” arXiv:1705.05045 (2017).

Morandotti, R.

A. Pasquazi, M. Peccianti, L. Razzari, D. J. Moss, S. Coen, M. Erkintalo, Y. K. Chembo, T. Hansson, S. Wabnitz, P. Del’Haye, X. Xue, A. M. Weiner, and R. Morandotti, “Micro-combs: a novel generation of optical sources,” Phys. Rep. 729, 1–81 (2018).
[Crossref]

Moss, D. J.

A. Pasquazi, M. Peccianti, L. Razzari, D. J. Moss, S. Coen, M. Erkintalo, Y. K. Chembo, T. Hansson, S. Wabnitz, P. Del’Haye, X. Xue, A. M. Weiner, and R. Morandotti, “Micro-combs: a novel generation of optical sources,” Phys. Rep. 729, 1–81 (2018).
[Crossref]

Murdoch, S. G.

Mussot, A.

A. Mussot, E. Louvergneaux, N. Akhmediev, F. Reynaud, L. Delage, and M. Taki, “Optical fiber systems are convectively unstable,” Phys. Rev. Lett. 101, 113904 (2008).
[Crossref]

Panajotov, K.

Papp, S. B.

D. C. Cole, E. S. Lamb, P. Del’Haye, S. A. Diddams, and S. B. Papp, “Soliton crystals in Kerr resonators,” Nat. Photonics 11, 671–676 (2017).
[Crossref]

Pasquazi, A.

A. Pasquazi, M. Peccianti, L. Razzari, D. J. Moss, S. Coen, M. Erkintalo, Y. K. Chembo, T. Hansson, S. Wabnitz, P. Del’Haye, X. Xue, A. M. Weiner, and R. Morandotti, “Micro-combs: a novel generation of optical sources,” Phys. Rep. 729, 1–81 (2018).
[Crossref]

Peccianti, M.

A. Pasquazi, M. Peccianti, L. Razzari, D. J. Moss, S. Coen, M. Erkintalo, Y. K. Chembo, T. Hansson, S. Wabnitz, P. Del’Haye, X. Xue, A. M. Weiner, and R. Morandotti, “Micro-combs: a novel generation of optical sources,” Phys. Rep. 729, 1–81 (2018).
[Crossref]

Pfeiffer, M. H. P.

H. Guo, E. Lucas, M. H. P. Pfeiffer, M. Karpov, M. Anderson, J. Liu, M. Geiselmann, J. D. Jost, and T. J. Kippenberg, “Intermode breather solitons in optical microresonators,” Phys. Rev. X 7, 041055 (2017).
[Crossref]

C. Bao, P. Liao, A. Kordts, L. Zhang, A. Matsko, M. Karpov, M. H. P. Pfeiffer, G. Xie, Y. Cao, Y. Yan, A. Almaiman, Z. Zhao, A. Mohajerin-Ariaei, A. Fallahpour, F. Alishahi, M. Tur, L. Maleki, T. J. Kippenberg, and A. E. Willner, “Orthogonally polarized Kerr frequency combs,” arXiv:1705.05045 (2017).

Qi, M.

Qi, Z.

Randle, H. G.

Razzari, L.

A. Pasquazi, M. Peccianti, L. Razzari, D. J. Moss, S. Coen, M. Erkintalo, Y. K. Chembo, T. Hansson, S. Wabnitz, P. Del’Haye, X. Xue, A. M. Weiner, and R. Morandotti, “Micro-combs: a novel generation of optical sources,” Phys. Rep. 729, 1–81 (2018).
[Crossref]

Reynaud, F.

A. Mussot, E. Louvergneaux, N. Akhmediev, F. Reynaud, L. Delage, and M. Taki, “Optical fiber systems are convectively unstable,” Phys. Rev. Lett. 101, 113904 (2008).
[Crossref]

Rothenberg, J. E.

J. E. Rothenberg, “Modulational instability for normal dispersion,” Phys. Rev. A 42, 682–685 (1990).
[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, 6100409 (2013).
[Crossref]

Savchenkov, A.

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

Savchenkov, A. A.

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

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]

Seidel, D.

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]

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

Strekalov, D.

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

Sylvestre, T.

Taki, M.

A. Mussot, E. Louvergneaux, N. Akhmediev, F. Reynaud, L. Delage, and M. Taki, “Optical fiber systems are convectively unstable,” Phys. Rev. Lett. 101, 113904 (2008).
[Crossref]

Tlidi, M.

Trillo, S.

M. Haelterman, S. Trillo, and S. Wabnitz, “Polarization multistability and instability in a nonlinear dispersive ring cavity,” J. Opt. Soc. Am. B 11, 446–456 (1994).
[Crossref]

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

Tur, M.

C. Bao, P. Liao, A. Kordts, L. Zhang, A. Matsko, M. Karpov, M. H. P. Pfeiffer, G. Xie, Y. Cao, Y. Yan, A. Almaiman, Z. Zhao, A. Mohajerin-Ariaei, A. Fallahpour, F. Alishahi, M. Tur, L. Maleki, T. J. Kippenberg, and A. E. Willner, “Orthogonally polarized Kerr frequency combs,” arXiv:1705.05045 (2017).

Wabnitz, S.

A. Pasquazi, M. Peccianti, L. Razzari, D. J. Moss, S. Coen, M. Erkintalo, Y. K. Chembo, T. Hansson, S. Wabnitz, P. Del’Haye, X. Xue, A. M. Weiner, and R. Morandotti, “Micro-combs: a novel generation of optical sources,” Phys. Rep. 729, 1–81 (2018).
[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, 1259–1266 (2015).
[Crossref]

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

M. Haelterman, S. Trillo, and S. Wabnitz, “Polarization multistability and instability in a nonlinear dispersive ring cavity,” J. Opt. Soc. Am. B 11, 446–456 (1994).
[Crossref]

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

S. Wabnitz, “Modulational polarization instability of light in a nonlinear birefringent dispersive medium,” Phys. Rev. A 38, 2018–2021 (1988).
[Crossref]

Wang, J.

Wang, P.-H.

Wang, Y.

Weicker, L.

Weiner, A. M.

A. Pasquazi, M. Peccianti, L. Razzari, D. J. Moss, S. Coen, M. Erkintalo, Y. K. Chembo, T. Hansson, S. Wabnitz, P. Del’Haye, X. Xue, A. M. Weiner, and R. Morandotti, “Micro-combs: a novel generation of optical sources,” Phys. Rep. 729, 1–81 (2018).
[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]

Willner, A. E.

C. Bao, P. Liao, A. Kordts, L. Zhang, A. Matsko, M. Karpov, M. H. P. Pfeiffer, G. Xie, Y. Cao, Y. Yan, A. Almaiman, Z. Zhao, A. Mohajerin-Ariaei, A. Fallahpour, F. Alishahi, M. Tur, L. Maleki, T. J. Kippenberg, and A. E. Willner, “Orthogonally polarized Kerr frequency combs,” arXiv:1705.05045 (2017).

Xie, G.

C. Bao, P. Liao, A. Kordts, L. Zhang, A. Matsko, M. Karpov, M. H. P. Pfeiffer, G. Xie, Y. Cao, Y. Yan, A. Almaiman, Z. Zhao, A. Mohajerin-Ariaei, A. Fallahpour, F. Alishahi, M. Tur, L. Maleki, T. J. Kippenberg, and A. E. Willner, “Orthogonally polarized Kerr frequency combs,” arXiv:1705.05045 (2017).

Xuan, Y.

Xue, X.

A. Pasquazi, M. Peccianti, L. Razzari, D. J. Moss, S. Coen, M. Erkintalo, Y. K. Chembo, T. Hansson, S. Wabnitz, P. Del’Haye, X. Xue, A. M. Weiner, and R. Morandotti, “Micro-combs: a novel generation of optical sources,” Phys. Rep. 729, 1–81 (2018).
[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]

Yan, Y.

C. Bao, P. Liao, A. Kordts, L. Zhang, A. Matsko, M. Karpov, M. H. P. Pfeiffer, G. Xie, Y. Cao, Y. Yan, A. Almaiman, Z. Zhao, A. Mohajerin-Ariaei, A. Fallahpour, F. Alishahi, M. Tur, L. Maleki, T. J. Kippenberg, and A. E. Willner, “Orthogonally polarized Kerr frequency combs,” arXiv:1705.05045 (2017).

Zhang, L.

C. Bao, P. Liao, A. Kordts, L. Zhang, A. Matsko, M. Karpov, M. H. P. Pfeiffer, G. Xie, Y. Cao, Y. Yan, A. Almaiman, Z. Zhao, A. Mohajerin-Ariaei, A. Fallahpour, F. Alishahi, M. Tur, L. Maleki, T. J. Kippenberg, and A. E. Willner, “Orthogonally polarized Kerr frequency combs,” arXiv:1705.05045 (2017).

Zhao, Z.

C. Bao, P. Liao, A. Kordts, L. Zhang, A. Matsko, M. Karpov, M. H. P. Pfeiffer, G. Xie, Y. Cao, Y. Yan, A. Almaiman, Z. Zhao, A. Mohajerin-Ariaei, A. Fallahpour, F. Alishahi, M. Tur, L. Maleki, T. J. Kippenberg, and A. E. Willner, “Orthogonally polarized Kerr frequency combs,” arXiv:1705.05045 (2017).

Eur. Phys. J. D (1)

G. D’Aguanno and C. R. Menyuk, “Coupled Lugiato-Lefever equation for nonlinear frequency comb generation at an avoided crossing of a microresonator,” Eur. Phys. J. D 71, 74 (2017).
[Crossref]

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, 6100409 (2013).
[Crossref]

J. Opt. Soc. Am. B (3)

Nat. Photonics (1)

D. C. Cole, E. S. Lamb, P. Del’Haye, S. A. Diddams, and S. B. Papp, “Soliton crystals in Kerr resonators,” Nat. Photonics 11, 671–676 (2017).
[Crossref]

Opt. Commun. (1)

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

Opt. Express (1)

Opt. Lett. (2)

Optica (2)

Phys. Rep. (1)

A. Pasquazi, M. Peccianti, L. Razzari, D. J. Moss, S. Coen, M. Erkintalo, Y. K. Chembo, T. Hansson, S. Wabnitz, P. Del’Haye, X. Xue, A. M. Weiner, and R. Morandotti, “Micro-combs: a novel generation of optical sources,” Phys. Rep. 729, 1–81 (2018).
[Crossref]

Phys. Rev. A (6)

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

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

G. D’Aguanno and C. R. Menyuk, “Nonlinear mode coupling in whispering-gallery-mode resonators,” Phys. Rev. A 93, 043820 (2016).
[Crossref]

S. Wabnitz, “Modulational polarization instability of light in a nonlinear birefringent dispersive medium,” Phys. Rev. A 38, 2018–2021 (1988).
[Crossref]

J. E. Rothenberg, “Modulational instability for normal dispersion,” Phys. Rev. A 42, 682–685 (1990).
[Crossref]

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

Phys. Rev. Lett. (3)

A. Mussot, E. Louvergneaux, N. Akhmediev, F. Reynaud, L. Delage, and M. Taki, “Optical fiber systems are convectively unstable,” Phys. Rev. Lett. 101, 113904 (2008).
[Crossref]

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

G. P. Agrawal, “Modulation instability induced by cross-phase modulation,” Phys. Rev. Lett. 59, 880–883 (1987).
[Crossref]

Phys. Rev. X (1)

H. Guo, E. Lucas, M. H. P. Pfeiffer, M. Karpov, M. Anderson, J. Liu, M. Geiselmann, J. D. Jost, and T. J. Kippenberg, “Intermode breather solitons in optical microresonators,” Phys. Rev. X 7, 041055 (2017).
[Crossref]

Science (1)

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

Other (2)

C. Bao, P. Liao, A. Kordts, L. Zhang, A. Matsko, M. Karpov, M. H. P. Pfeiffer, G. Xie, Y. Cao, Y. Yan, A. Almaiman, Z. Zhao, A. Mohajerin-Ariaei, A. Fallahpour, F. Alishahi, M. Tur, L. Maleki, T. J. Kippenberg, and A. E. Willner, “Orthogonally polarized Kerr frequency combs,” arXiv:1705.05045 (2017).

G. P. Agrawal, Nonlinear Fiber Optics, 5th ed. (Academic, 2012).

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Figures (7)

Fig. 1.
Fig. 1. Homogeneous steady-state solutions showing Kerr tilts for Px=Py=4, σ=2/3, and αx=αy=1 with δ0=0 (blue solid), δ0=1.5 (red dashed), and δ0=4 (orange dash-dotted). The intermediate case of δ0=1.5 is seen to display tristability. The positive slope branches on the right-hand side of each tilted resonance are unstable to CW perturbations.
Fig. 2.
Fig. 2. Top: density plot of MI growth rate for parameters Px=Py=4, αx=αy=1, and δ0=1.5, with β2,x=2 and β2,y=1. The regions A1, A2, and A3 that satisfy the MI conditions are denoted with red, green, and blue dashed lines, respectively. The solid black line marks the contour for zero gain, while the dotted lines mark the phase-matching conditions. Bottom: parameterization of detuning values for the tristable resonance curve.
Fig. 3.
Fig. 3. Density plot of MI growth rate for the same parameters as Fig. 2, except with β2,x=1 and β2,y=2. Here the A3 type of instability is not observed, and it is the A2 type that is the first to occur as the detuning increases.
Fig. 4.
Fig. 4. Top: density plot of MI growth rate for Px=Py=3, αx=αy=1, and δ0=0, with normal dispersion β2,x=β2,y=1 and GVM coefficient Δβ1=3. The regions B1, B2, and B3 that satisfy the MI conditions are denoted with red, green, and blue dashed lines, respectively. Bottom: parameterization of bistable detuning values.
Fig. 5.
Fig. 5. Top: temporal intracavity power at t=1000, with |Ex|2 in blue and |Ey|2 in orange. Comb generation occurs due to an instability of the A3 type. Parameters as in Fig. 2 with ξ=0.44 (δx=2.5). Middle: corresponding normalized spectrum on a decibel (dB) scale. Bottom: temporal evolution showing periodicity of the vector state.
Fig. 6.
Fig. 6. Top: temporal intracavity power showing stationary pattern state at t=1000 due to an instability of the A2 type. The parameters are the same as in Fig. 3 with initial conditions given by the CW solution for ξ=0.5 (δx=3.3). Bottom: normalized spectrum on a dB scale.
Fig. 7.
Fig. 7. Top: temporal intracavity power of stationary pattern state at t=1000 resulting from normal dispersion comb generation with GVM. Parameters as in Fig. 4 with ξ=0.6 (δx=4.5). Bottom: normalized spectrum on a dB scale.

Equations (16)

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

Axmz+β1,xAxmτ+iβ2,x22Axmτ2+αi,x2Axm=iγ(|Axm|2+23|Aym|2)Axm+iγ3(Axm)*(Aym)2ei2Δβz,
Aymz+β1,yAymτ+iβ2,y22Aymτ2+αi,y2Aym=iγ(|Aym|2+23|Axm|2)Aym+iγ3(Aym)*(Axm)2ei2Δβz.
Ajm+1(z=0,τ)=θjEjin+1θjeiδjAjm(z=L,τ).
Ext=[(αx+iδx)+Δβ1τiβ2,x22τ2]Ex+i(|Ex|2+σ|Ey|2)Ex+Sx,
Eyt=[(αy+iδy)Δβ1τiβ2,y22τ2]Ey+i(|Ey|2+σ|Ex|2)Ey+Sy,
Px=[(δxIxσIy)2+αx2]Ix,
Py=[(δyIyσIx)2+αy2]Iy,
(IxIy)[(Ix+Iy)2IxIy(1σ)22δx(Ix+Iy)+(α2+δx2)]=0,
A=[iqxαxiΔβ1ωiIxiσIxIyiσIxIyiIxiqxαxiΔβ1ωiσIxIyiσIxIyiσIxIyiσIxIyiqyαy+iΔβ1ωiIyiσIxIyiσIxIyiIyiqyαy+iΔβ1ω],
qx=2Ix+σIyδx+β2,x2ω2,qy=2Iy+σIxδy+β2,y2ω2.
[(λ+αx+iΔβ1ω)2fx][(λ+αyiΔβ1ω)2fy]=p,
p=4σ2IxIy(Ixqx)(Iyqy).
λ=α±12(fx+fy)±p+14(fxfy)2.
A1: fx+fy>0,A2: p>fxfy,A3: p<14(fxfy)2.
λ=12(αx+αy)±(f014ζ2)±p0f0ζ2,
B1: f0>14ζ2,B2: p0>(f0+14ζ2)2,B3: p0<f0ζ2.

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