Abstract

We describe the spatio-temporal evolution of ultrashort pulses propagating in a fiber ring cavity using an extension of the Lugiato-Lefever model. The model predicts the appearance of multistability and spontaneous symmetry breaking in temporal pulse shape. We also use a hydrodynamical approach to explain the stability of the observed regimes of asymmetry.

© 2014 Optical Society of America

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    [CrossRef]
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  28. H. A. Haus, “Mode-locking of lasers,” IEEE J. Quantum Electron. 6(6), 1173–1185 (2000).
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    [CrossRef]
  30. C. Bruni, T. Legrand, C. Szwaj, S. Bielawski, M. E. Couprie, “Equivalence between free-electron-laser oscillators and actively-mode-locked lasers: Detailed studies of temporal, spatiotemporal, and spectrotemporal dynamics,” Phys. Rev. A 84(6), 063804 (2011).
    [CrossRef]
  31. S. Coen, H. G. Randle, T. Sylvestre, M. Erkintalo, “Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato-Lefever model,” Opt. Lett. 38(1), 37–39 (2013).
    [CrossRef] [PubMed]
  32. M. Tlidi, L. Gelens, “High-order dispersion stabilizes dark dissipative solitons in all-fiber cavities,” Opt. Lett. 35(3), 306–308 (2010).
    [CrossRef] [PubMed]
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    [CrossRef]
  35. E. Doedel, H. B. Keller, J. P. Kernevez, “Numerical analysis and control of bifurcation problems (II): Bifurcation in infinite dimensions,” Int. J. Bifurcat. Chaos 01(04), 745–772 (1991).
    [CrossRef]
  36. A. Alexandrescu, J. R. Salgueiro, “Efficient numerical method for linear stability analysis of solitary waves,” Comput. Phys. Commun. 182(12), 2479–2485 (2011).
    [CrossRef]
  37. J. M. Soto-Crespo, D. R. Heatley, E. M. Wright, N. N. Akhmediev, “Stability of the higher-bound states in a saturable self-focusing medium,” Phys. Rev. A 44(1), 636–644 (1991).
    [CrossRef] [PubMed]
  38. F. Leo, L. Gelens, P. Emplit, M. Haelterman, S. Coen, “Dynamics of one-dimensional Kerr cavity solitons,” Opt. Express 21(7), 9180–9191 (2013).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

2013 (9)

M. Tlidi, L. Bahloul, L. Cherbi, A. Hariz, S. Coulibaly, “Drift of dark cavity solitons in a photonic-crystal fiber resonator,” Phys. Rev. A 88(3), 035802 (2013).
[CrossRef]

J. K. Jang, M. Erkintalo, S. G. Murdoch, S. Coen, “Ultraweak long-range interactions of solitons observed over astronomical distances,” Nat. Photonics 7(8), 657–663 (2013).
[CrossRef]

Y. K. Chembo, C. R. Menyuk, “Spatiotemporal Lugiato-Lefever formalism for Kerr-comb generation in whispering-gallery-mode resonators,” Phys. Rev. A 87(5), 053852 (2013).
[CrossRef]

R. W. Bowman, G. M. Gibson, M. J. Padgett, F. Saglimbeni, R. Di Leonardo, “Optical trapping at gigapascal pressures,” Phys. Rev. Lett. 110(9), 095902 (2013).
[CrossRef] [PubMed]

F. Leo, A. Mussot, P. Kockaert, P. Emplit, M. Haelterman, M. Taki, “Nonlinear symmetry breaking induced by third-order dispersion in optical fiber cavities,” Phys. Rev. Lett. 110(10), 104103 (2013).
[CrossRef] [PubMed]

Y. Li, J. Liu, W. Pang, B. A. Malomed, “Symmetry breaking in dipolar matter-wave solitons in dual-core couplers,” Phys. Rev. A 87(1), 013604 (2013).
[CrossRef]

M. Azhar, N. Y. Joly, J. C. Travers, P. S. J. Russell, “Nonlinear optics in Xe-filled hollow-core PCF in high pressure and supercritical regimes,” Appl. Phys. B 112(4), 457–460 (2013).
[CrossRef]

S. Coen, H. G. Randle, T. Sylvestre, M. Erkintalo, “Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato-Lefever model,” Opt. Lett. 38(1), 37–39 (2013).
[CrossRef] [PubMed]

F. Leo, L. Gelens, P. Emplit, M. Haelterman, S. Coen, “Dynamics of one-dimensional Kerr cavity solitons,” Opt. Express 21(7), 9180–9191 (2013).
[CrossRef] [PubMed]

2012 (1)

2011 (5)

N. Brauckmann, M. Kues, P. Gross, C. Fallnich, “Noise reduction of supercontinua via optical feedback,” Opt. Express 19(16), 14763–14778 (2011).
[CrossRef] [PubMed]

C. Bruni, T. Legrand, C. Szwaj, S. Bielawski, M. E. Couprie, “Equivalence between free-electron-laser oscillators and actively-mode-locked lasers: Detailed studies of temporal, spatiotemporal, and spectrotemporal dynamics,” Phys. Rev. A 84(6), 063804 (2011).
[CrossRef]

M. Kues, N. Brauckmann, P. Groß, C. Fallnich, “Basic prerequisites for limit-cycle oscillations within a synchronously pumped passive optical nonlinear fiber-ring resonator,” Phys. Rev. A 84(3), 033833 (2011).
[CrossRef]

A. Alexandrescu, J. R. Salgueiro, “Efficient numerical method for linear stability analysis of solitary waves,” Comput. Phys. Commun. 182(12), 2479–2485 (2011).
[CrossRef]

A. E. Miroshnichenko, B. A. Malomed, Y. S. Kivshar, “Nonlinearly PT-symmetric systems: Spontaneous symmetry breaking and transmission resonances,” Phys. Rev. A 84(1), 012123 (2011).
[CrossRef]

2010 (2)

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, P. Emplit, M. Haelterman, “Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,” Nat. Photonics 4(7), 471–476 (2010).
[CrossRef]

M. Tlidi, L. Gelens, “High-order dispersion stabilizes dark dissipative solitons in all-fiber cavities,” Opt. Lett. 35(3), 306–308 (2010).
[CrossRef] [PubMed]

2009 (2)

G. Kozyreff, M. Tlidi, A. Mussot, E. Louvergneaux, M. Taki, A. G. Vladimirov, “Localized beating between dynamically generated frequencies,” Phys. Rev. Lett. 102(4), 043905 (2009).
[CrossRef] [PubMed]

D. Novoa, H. Michinel, D. Tommasini, “Pressure, surface tension, and dripping of self-trapped laser beams,” Phys. Rev. Lett. 103(2), 023903 (2009).
[CrossRef] [PubMed]

2007 (1)

2006 (1)

2005 (1)

2002 (1)

I. S. Aranson, L. Kramer, “The world of the complex Ginzburg-Landau equation,” Rev. Mod. Phys. 74(1), 99–143 (2002).
[CrossRef]

2000 (1)

H. A. Haus, “Mode-locking of lasers,” IEEE J. Quantum Electron. 6(6), 1173–1185 (2000).
[CrossRef]

1999 (2)

S. Coen, M. Tlidi, P. Emplit, M. Haelterman, “Convection versus dispersion in optical bistability,” Phys. Rev. Lett. 83(12), 2328–2331 (1999).
[CrossRef]

H. U. Voss, A. Schwache, J. Kurths, F. Mitschke, “Equations of motion from chaotic data: A driven optical fiber ring resonator,” Phys. Lett. A 256(1), 47–54 (1999).
[CrossRef]

1997 (1)

1996 (1)

G. Steinmeyer, F. Mitschke, “Longitudinal structure formation in a nonlinear resonator,” Appl. Phys. B 62(4), 367–374 (1996).
[CrossRef]

1995 (1)

J. García-Mateos, F. C. Bienzobas, M. Haelterman, “Optical bistability and temporal symmetry-breaking instability in nonlinear fiber resonators,” Fiber Integr. Opt. 14(4), 337–346 (1995).
[CrossRef]

1994 (1)

A. J. Scroggie, W. J. Firth, G. S. McDonald, M. Tlidi, R. Lefever, L. A. Lugiato, “Pattern formation in a passive Kerr cavity,” Chaos Solitons Fractals 4(8–9), 1323–1354 (1994).
[CrossRef]

1991 (3)

E. Doedel, H. B. Keller, J. P. Kernevez, “Numerical analysis and control of bifurcation problems (II): Bifurcation in infinite dimensions,” Int. J. Bifurcat. Chaos 01(04), 745–772 (1991).
[CrossRef]

J. M. Soto-Crespo, D. R. Heatley, E. M. Wright, N. N. Akhmediev, “Stability of the higher-bound states in a saturable self-focusing medium,” Phys. Rev. A 44(1), 636–644 (1991).
[CrossRef] [PubMed]

R. Vallée, “Temporal instabilities in the output of an all-fiber ring cavity,” Opt. Commun. 81(6), 419–426 (1991).
[CrossRef]

1990 (1)

C. Green, G. B. Mindlin, E. J. D’Angelo, H. G. Solari, J. R. Tredicce, “Spontaneous symmetry breaking in a laser: The experimental side,” Phys. Rev. Lett. 65(25), 3124–3127 (1990).
[CrossRef] [PubMed]

1987 (1)

L. A. Lugiato, R. Lefever, “Spatial dissipative structures in passive optical systems,” Phys. Rev. Lett. 58(21), 2209–2211 (1987).
[CrossRef] [PubMed]

1985 (1)

P. Elleaume, “Microtemporal and spectral structure of storage ring free-electron lasers,” IEEE J. Quantum Electron. 21(7), 1012–1022 (1985).
[CrossRef]

1979 (1)

K. Ikeda, “Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system,” Opt. Commun. 30(2), 257–261 (1979).
[CrossRef]

1964 (1)

P. W. Higgs, “Broken symmetries and the masses of gauge bosons,” Phys. Rev. Lett. 13(16), 508–509 (1964).
[CrossRef]

Akhmediev, N. N.

J. M. Soto-Crespo, D. R. Heatley, E. M. Wright, N. N. Akhmediev, “Stability of the higher-bound states in a saturable self-focusing medium,” Phys. Rev. A 44(1), 636–644 (1991).
[CrossRef] [PubMed]

Alexandrescu, A.

A. Alexandrescu, J. R. Salgueiro, “Efficient numerical method for linear stability analysis of solitary waves,” Comput. Phys. Commun. 182(12), 2479–2485 (2011).
[CrossRef]

Aranson, I. S.

I. S. Aranson, L. Kramer, “The world of the complex Ginzburg-Landau equation,” Rev. Mod. Phys. 74(1), 99–143 (2002).
[CrossRef]

Azhar, M.

M. Azhar, N. Y. Joly, J. C. Travers, P. S. J. Russell, “Nonlinear optics in Xe-filled hollow-core PCF in high pressure and supercritical regimes,” Appl. Phys. B 112(4), 457–460 (2013).
[CrossRef]

Bahloul, L.

M. Tlidi, L. Bahloul, L. Cherbi, A. Hariz, S. Coulibaly, “Drift of dark cavity solitons in a photonic-crystal fiber resonator,” Phys. Rev. A 88(3), 035802 (2013).
[CrossRef]

Biancalana, F.

M. J. Schmidberger, F. Biancalana, P. St. J. Russell, N. Y. Joly, “Semi-analytical model for the evolution of femtosecond pulses during supercontinuum generation in synchronously pumped ring cavities,” in The European Conference on Lasers and Electro-Optics (OSA, 2013).

Bielawski, S.

C. Bruni, T. Legrand, C. Szwaj, S. Bielawski, M. E. Couprie, “Equivalence between free-electron-laser oscillators and actively-mode-locked lasers: Detailed studies of temporal, spatiotemporal, and spectrotemporal dynamics,” Phys. Rev. A 84(6), 063804 (2011).
[CrossRef]

Bienzobas, F. C.

J. García-Mateos, F. C. Bienzobas, M. Haelterman, “Optical bistability and temporal symmetry-breaking instability in nonlinear fiber resonators,” Fiber Integr. Opt. 14(4), 337–346 (1995).
[CrossRef]

Birks, T. A.

Bowman, R. W.

R. W. Bowman, G. M. Gibson, M. J. Padgett, F. Saglimbeni, R. Di Leonardo, “Optical trapping at gigapascal pressures,” Phys. Rev. Lett. 110(9), 095902 (2013).
[CrossRef] [PubMed]

Brauckmann, N.

N. Brauckmann, M. Kues, P. Gross, C. Fallnich, “Noise reduction of supercontinua via optical feedback,” Opt. Express 19(16), 14763–14778 (2011).
[CrossRef] [PubMed]

M. Kues, N. Brauckmann, P. Groß, C. Fallnich, “Basic prerequisites for limit-cycle oscillations within a synchronously pumped passive optical nonlinear fiber-ring resonator,” Phys. Rev. A 84(3), 033833 (2011).
[CrossRef]

Bruni, C.

C. Bruni, T. Legrand, C. Szwaj, S. Bielawski, M. E. Couprie, “Equivalence between free-electron-laser oscillators and actively-mode-locked lasers: Detailed studies of temporal, spatiotemporal, and spectrotemporal dynamics,” Phys. Rev. A 84(6), 063804 (2011).
[CrossRef]

Chang, W.

Chembo, Y. K.

Y. K. Chembo, C. R. Menyuk, “Spatiotemporal Lugiato-Lefever formalism for Kerr-comb generation in whispering-gallery-mode resonators,” Phys. Rev. A 87(5), 053852 (2013).
[CrossRef]

Cherbi, L.

M. Tlidi, L. Bahloul, L. Cherbi, A. Hariz, S. Coulibaly, “Drift of dark cavity solitons in a photonic-crystal fiber resonator,” Phys. Rev. A 88(3), 035802 (2013).
[CrossRef]

Coen, S.

F. Leo, L. Gelens, P. Emplit, M. Haelterman, S. Coen, “Dynamics of one-dimensional Kerr cavity solitons,” Opt. Express 21(7), 9180–9191 (2013).
[CrossRef] [PubMed]

J. K. Jang, M. Erkintalo, S. G. Murdoch, S. Coen, “Ultraweak long-range interactions of solitons observed over astronomical distances,” Nat. Photonics 7(8), 657–663 (2013).
[CrossRef]

S. Coen, H. G. Randle, T. Sylvestre, M. Erkintalo, “Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato-Lefever model,” Opt. Lett. 38(1), 37–39 (2013).
[CrossRef] [PubMed]

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, P. Emplit, M. Haelterman, “Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,” Nat. Photonics 4(7), 471–476 (2010).
[CrossRef]

S. Coen, M. Tlidi, P. Emplit, M. Haelterman, “Convection versus dispersion in optical bistability,” Phys. Rev. Lett. 83(12), 2328–2331 (1999).
[CrossRef]

Coulibaly, S.

M. Tlidi, L. Bahloul, L. Cherbi, A. Hariz, S. Coulibaly, “Drift of dark cavity solitons in a photonic-crystal fiber resonator,” Phys. Rev. A 88(3), 035802 (2013).
[CrossRef]

Couprie, M. E.

C. Bruni, T. Legrand, C. Szwaj, S. Bielawski, M. E. Couprie, “Equivalence between free-electron-laser oscillators and actively-mode-locked lasers: Detailed studies of temporal, spatiotemporal, and spectrotemporal dynamics,” Phys. Rev. A 84(6), 063804 (2011).
[CrossRef]

D’Angelo, E. J.

C. Green, G. B. Mindlin, E. J. D’Angelo, H. G. Solari, J. R. Tredicce, “Spontaneous symmetry breaking in a laser: The experimental side,” Phys. Rev. Lett. 65(25), 3124–3127 (1990).
[CrossRef] [PubMed]

Di Leonardo, R.

R. W. Bowman, G. M. Gibson, M. J. Padgett, F. Saglimbeni, R. Di Leonardo, “Optical trapping at gigapascal pressures,” Phys. Rev. Lett. 110(9), 095902 (2013).
[CrossRef] [PubMed]

Doedel, E.

E. Doedel, H. B. Keller, J. P. Kernevez, “Numerical analysis and control of bifurcation problems (II): Bifurcation in infinite dimensions,” Int. J. Bifurcat. Chaos 01(04), 745–772 (1991).
[CrossRef]

Elleaume, P.

P. Elleaume, “Microtemporal and spectral structure of storage ring free-electron lasers,” IEEE J. Quantum Electron. 21(7), 1012–1022 (1985).
[CrossRef]

Emplit, P.

F. Leo, A. Mussot, P. Kockaert, P. Emplit, M. Haelterman, M. Taki, “Nonlinear symmetry breaking induced by third-order dispersion in optical fiber cavities,” Phys. Rev. Lett. 110(10), 104103 (2013).
[CrossRef] [PubMed]

F. Leo, L. Gelens, P. Emplit, M. Haelterman, S. Coen, “Dynamics of one-dimensional Kerr cavity solitons,” Opt. Express 21(7), 9180–9191 (2013).
[CrossRef] [PubMed]

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, P. Emplit, M. Haelterman, “Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,” Nat. Photonics 4(7), 471–476 (2010).
[CrossRef]

S. Coen, M. Tlidi, P. Emplit, M. Haelterman, “Convection versus dispersion in optical bistability,” Phys. Rev. Lett. 83(12), 2328–2331 (1999).
[CrossRef]

Erkintalo, M.

J. K. Jang, M. Erkintalo, S. G. Murdoch, S. Coen, “Ultraweak long-range interactions of solitons observed over astronomical distances,” Nat. Photonics 7(8), 657–663 (2013).
[CrossRef]

S. Coen, H. G. Randle, T. Sylvestre, M. Erkintalo, “Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato-Lefever model,” Opt. Lett. 38(1), 37–39 (2013).
[CrossRef] [PubMed]

Fallnich, C.

M. Kues, N. Brauckmann, P. Groß, C. Fallnich, “Basic prerequisites for limit-cycle oscillations within a synchronously pumped passive optical nonlinear fiber-ring resonator,” Phys. Rev. A 84(3), 033833 (2011).
[CrossRef]

N. Brauckmann, M. Kues, P. Gross, C. Fallnich, “Noise reduction of supercontinua via optical feedback,” Opt. Express 19(16), 14763–14778 (2011).
[CrossRef] [PubMed]

Firth, W. J.

A. J. Scroggie, W. J. Firth, G. S. McDonald, M. Tlidi, R. Lefever, L. A. Lugiato, “Pattern formation in a passive Kerr cavity,” Chaos Solitons Fractals 4(8–9), 1323–1354 (1994).
[CrossRef]

García-Mateos, J.

J. García-Mateos, F. C. Bienzobas, M. Haelterman, “Optical bistability and temporal symmetry-breaking instability in nonlinear fiber resonators,” Fiber Integr. Opt. 14(4), 337–346 (1995).
[CrossRef]

Gelens, L.

Gibson, G. M.

R. W. Bowman, G. M. Gibson, M. J. Padgett, F. Saglimbeni, R. Di Leonardo, “Optical trapping at gigapascal pressures,” Phys. Rev. Lett. 110(9), 095902 (2013).
[CrossRef] [PubMed]

Gorza, S.-P.

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, P. Emplit, M. Haelterman, “Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,” Nat. Photonics 4(7), 471–476 (2010).
[CrossRef]

Green, C.

C. Green, G. B. Mindlin, E. J. D’Angelo, H. G. Solari, J. R. Tredicce, “Spontaneous symmetry breaking in a laser: The experimental side,” Phys. Rev. Lett. 65(25), 3124–3127 (1990).
[CrossRef] [PubMed]

Groß, P.

M. Kues, N. Brauckmann, P. Groß, C. Fallnich, “Basic prerequisites for limit-cycle oscillations within a synchronously pumped passive optical nonlinear fiber-ring resonator,” Phys. Rev. A 84(3), 033833 (2011).
[CrossRef]

Gross, P.

Haelterman, M.

F. Leo, L. Gelens, P. Emplit, M. Haelterman, S. Coen, “Dynamics of one-dimensional Kerr cavity solitons,” Opt. Express 21(7), 9180–9191 (2013).
[CrossRef] [PubMed]

F. Leo, A. Mussot, P. Kockaert, P. Emplit, M. Haelterman, M. Taki, “Nonlinear symmetry breaking induced by third-order dispersion in optical fiber cavities,” Phys. Rev. Lett. 110(10), 104103 (2013).
[CrossRef] [PubMed]

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, P. Emplit, M. Haelterman, “Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,” Nat. Photonics 4(7), 471–476 (2010).
[CrossRef]

S. Coen, M. Tlidi, P. Emplit, M. Haelterman, “Convection versus dispersion in optical bistability,” Phys. Rev. Lett. 83(12), 2328–2331 (1999).
[CrossRef]

J. García-Mateos, F. C. Bienzobas, M. Haelterman, “Optical bistability and temporal symmetry-breaking instability in nonlinear fiber resonators,” Fiber Integr. Opt. 14(4), 337–346 (1995).
[CrossRef]

Hariz, A.

M. Tlidi, L. Bahloul, L. Cherbi, A. Hariz, S. Coulibaly, “Drift of dark cavity solitons in a photonic-crystal fiber resonator,” Phys. Rev. A 88(3), 035802 (2013).
[CrossRef]

Haus, H. A.

H. A. Haus, “Mode-locking of lasers,” IEEE J. Quantum Electron. 6(6), 1173–1185 (2000).
[CrossRef]

Heatley, D. R.

J. M. Soto-Crespo, D. R. Heatley, E. M. Wright, N. N. Akhmediev, “Stability of the higher-bound states in a saturable self-focusing medium,” Phys. Rev. A 44(1), 636–644 (1991).
[CrossRef] [PubMed]

Higgs, P. W.

P. W. Higgs, “Broken symmetries and the masses of gauge bosons,” Phys. Rev. Lett. 13(16), 508–509 (1964).
[CrossRef]

Ikeda, K.

K. Ikeda, “Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system,” Opt. Commun. 30(2), 257–261 (1979).
[CrossRef]

Jang, J. K.

J. K. Jang, M. Erkintalo, S. G. Murdoch, S. Coen, “Ultraweak long-range interactions of solitons observed over astronomical distances,” Nat. Photonics 7(8), 657–663 (2013).
[CrossRef]

Joly, N. Y.

M. Azhar, N. Y. Joly, J. C. Travers, P. S. J. Russell, “Nonlinear optics in Xe-filled hollow-core PCF in high pressure and supercritical regimes,” Appl. Phys. B 112(4), 457–460 (2013).
[CrossRef]

M. Schmidberger, W. Chang, P. St. J. Russell, N. Y. Joly, “Influence of timing jitter on nonlinear dynamics of a photonic crystal fiber ring cavity,” Opt. Lett. 37(17), 3576–3578 (2012).
[CrossRef] [PubMed]

M. J. Schmidberger, F. Biancalana, P. St. J. Russell, N. Y. Joly, “Semi-analytical model for the evolution of femtosecond pulses during supercontinuum generation in synchronously pumped ring cavities,” in The European Conference on Lasers and Electro-Optics (OSA, 2013).

Keller, H. B.

E. Doedel, H. B. Keller, J. P. Kernevez, “Numerical analysis and control of bifurcation problems (II): Bifurcation in infinite dimensions,” Int. J. Bifurcat. Chaos 01(04), 745–772 (1991).
[CrossRef]

Kernevez, J. P.

E. Doedel, H. B. Keller, J. P. Kernevez, “Numerical analysis and control of bifurcation problems (II): Bifurcation in infinite dimensions,” Int. J. Bifurcat. Chaos 01(04), 745–772 (1991).
[CrossRef]

Kivshar, Y. S.

A. E. Miroshnichenko, B. A. Malomed, Y. S. Kivshar, “Nonlinearly PT-symmetric systems: Spontaneous symmetry breaking and transmission resonances,” Phys. Rev. A 84(1), 012123 (2011).
[CrossRef]

J. R. Salgueiro, Y. S. Kivshar, “Nonlinear dual-core photonic crystal fiber couplers,” Opt. Lett. 30(14), 1858–1860 (2005).
[CrossRef] [PubMed]

Knight, J. C.

Kockaert, P.

F. Leo, A. Mussot, P. Kockaert, P. Emplit, M. Haelterman, M. Taki, “Nonlinear symmetry breaking induced by third-order dispersion in optical fiber cavities,” Phys. Rev. Lett. 110(10), 104103 (2013).
[CrossRef] [PubMed]

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, P. Emplit, M. Haelterman, “Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,” Nat. Photonics 4(7), 471–476 (2010).
[CrossRef]

Kozyreff, G.

G. Kozyreff, M. Tlidi, A. Mussot, E. Louvergneaux, M. Taki, A. G. Vladimirov, “Localized beating between dynamically generated frequencies,” Phys. Rev. Lett. 102(4), 043905 (2009).
[CrossRef] [PubMed]

M. Tlidi, A. Mussot, E. Louvergneaux, G. Kozyreff, A. G. Vladimirov, M. Taki, “Control and removal of modulational instabilities in low-dispersion photonic crystal fiber cavities,” Opt. Lett. 32(6), 662–664 (2007).
[CrossRef] [PubMed]

Kramer, L.

I. S. Aranson, L. Kramer, “The world of the complex Ginzburg-Landau equation,” Rev. Mod. Phys. 74(1), 99–143 (2002).
[CrossRef]

Kues, M.

N. Brauckmann, M. Kues, P. Gross, C. Fallnich, “Noise reduction of supercontinua via optical feedback,” Opt. Express 19(16), 14763–14778 (2011).
[CrossRef] [PubMed]

M. Kues, N. Brauckmann, P. Groß, C. Fallnich, “Basic prerequisites for limit-cycle oscillations within a synchronously pumped passive optical nonlinear fiber-ring resonator,” Phys. Rev. A 84(3), 033833 (2011).
[CrossRef]

Kurths, J.

H. U. Voss, A. Schwache, J. Kurths, F. Mitschke, “Equations of motion from chaotic data: A driven optical fiber ring resonator,” Phys. Lett. A 256(1), 47–54 (1999).
[CrossRef]

Lefever, R.

A. J. Scroggie, W. J. Firth, G. S. McDonald, M. Tlidi, R. Lefever, L. A. Lugiato, “Pattern formation in a passive Kerr cavity,” Chaos Solitons Fractals 4(8–9), 1323–1354 (1994).
[CrossRef]

L. A. Lugiato, R. Lefever, “Spatial dissipative structures in passive optical systems,” Phys. Rev. Lett. 58(21), 2209–2211 (1987).
[CrossRef] [PubMed]

Legrand, T.

C. Bruni, T. Legrand, C. Szwaj, S. Bielawski, M. E. Couprie, “Equivalence between free-electron-laser oscillators and actively-mode-locked lasers: Detailed studies of temporal, spatiotemporal, and spectrotemporal dynamics,” Phys. Rev. A 84(6), 063804 (2011).
[CrossRef]

Leo, F.

F. Leo, A. Mussot, P. Kockaert, P. Emplit, M. Haelterman, M. Taki, “Nonlinear symmetry breaking induced by third-order dispersion in optical fiber cavities,” Phys. Rev. Lett. 110(10), 104103 (2013).
[CrossRef] [PubMed]

F. Leo, L. Gelens, P. Emplit, M. Haelterman, S. Coen, “Dynamics of one-dimensional Kerr cavity solitons,” Opt. Express 21(7), 9180–9191 (2013).
[CrossRef] [PubMed]

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, P. Emplit, M. Haelterman, “Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,” Nat. Photonics 4(7), 471–476 (2010).
[CrossRef]

Li, Y.

Y. Li, J. Liu, W. Pang, B. A. Malomed, “Symmetry breaking in dipolar matter-wave solitons in dual-core couplers,” Phys. Rev. A 87(1), 013604 (2013).
[CrossRef]

Liu, J.

Y. Li, J. Liu, W. Pang, B. A. Malomed, “Symmetry breaking in dipolar matter-wave solitons in dual-core couplers,” Phys. Rev. A 87(1), 013604 (2013).
[CrossRef]

Louvergneaux, E.

G. Kozyreff, M. Tlidi, A. Mussot, E. Louvergneaux, M. Taki, A. G. Vladimirov, “Localized beating between dynamically generated frequencies,” Phys. Rev. Lett. 102(4), 043905 (2009).
[CrossRef] [PubMed]

M. Tlidi, A. Mussot, E. Louvergneaux, G. Kozyreff, A. G. Vladimirov, M. Taki, “Control and removal of modulational instabilities in low-dispersion photonic crystal fiber cavities,” Opt. Lett. 32(6), 662–664 (2007).
[CrossRef] [PubMed]

Lugiato, L. A.

A. J. Scroggie, W. J. Firth, G. S. McDonald, M. Tlidi, R. Lefever, L. A. Lugiato, “Pattern formation in a passive Kerr cavity,” Chaos Solitons Fractals 4(8–9), 1323–1354 (1994).
[CrossRef]

L. A. Lugiato, R. Lefever, “Spatial dissipative structures in passive optical systems,” Phys. Rev. Lett. 58(21), 2209–2211 (1987).
[CrossRef] [PubMed]

Malomed, B. A.

Y. Li, J. Liu, W. Pang, B. A. Malomed, “Symmetry breaking in dipolar matter-wave solitons in dual-core couplers,” Phys. Rev. A 87(1), 013604 (2013).
[CrossRef]

A. E. Miroshnichenko, B. A. Malomed, Y. S. Kivshar, “Nonlinearly PT-symmetric systems: Spontaneous symmetry breaking and transmission resonances,” Phys. Rev. A 84(1), 012123 (2011).
[CrossRef]

McDonald, G. S.

A. J. Scroggie, W. J. Firth, G. S. McDonald, M. Tlidi, R. Lefever, L. A. Lugiato, “Pattern formation in a passive Kerr cavity,” Chaos Solitons Fractals 4(8–9), 1323–1354 (1994).
[CrossRef]

Menyuk, C. R.

Y. K. Chembo, C. R. Menyuk, “Spatiotemporal Lugiato-Lefever formalism for Kerr-comb generation in whispering-gallery-mode resonators,” Phys. Rev. A 87(5), 053852 (2013).
[CrossRef]

Michinel, H.

D. Novoa, H. Michinel, D. Tommasini, “Pressure, surface tension, and dripping of self-trapped laser beams,” Phys. Rev. Lett. 103(2), 023903 (2009).
[CrossRef] [PubMed]

Mindlin, G. B.

C. Green, G. B. Mindlin, E. J. D’Angelo, H. G. Solari, J. R. Tredicce, “Spontaneous symmetry breaking in a laser: The experimental side,” Phys. Rev. Lett. 65(25), 3124–3127 (1990).
[CrossRef] [PubMed]

Miroshnichenko, A. E.

A. E. Miroshnichenko, B. A. Malomed, Y. S. Kivshar, “Nonlinearly PT-symmetric systems: Spontaneous symmetry breaking and transmission resonances,” Phys. Rev. A 84(1), 012123 (2011).
[CrossRef]

Mitschke, F.

H. U. Voss, A. Schwache, J. Kurths, F. Mitschke, “Equations of motion from chaotic data: A driven optical fiber ring resonator,” Phys. Lett. A 256(1), 47–54 (1999).
[CrossRef]

G. Steinmeyer, F. Mitschke, “Longitudinal structure formation in a nonlinear resonator,” Appl. Phys. B 62(4), 367–374 (1996).
[CrossRef]

Murdoch, S. G.

J. K. Jang, M. Erkintalo, S. G. Murdoch, S. Coen, “Ultraweak long-range interactions of solitons observed over astronomical distances,” Nat. Photonics 7(8), 657–663 (2013).
[CrossRef]

Mussot, A.

F. Leo, A. Mussot, P. Kockaert, P. Emplit, M. Haelterman, M. Taki, “Nonlinear symmetry breaking induced by third-order dispersion in optical fiber cavities,” Phys. Rev. Lett. 110(10), 104103 (2013).
[CrossRef] [PubMed]

G. Kozyreff, M. Tlidi, A. Mussot, E. Louvergneaux, M. Taki, A. G. Vladimirov, “Localized beating between dynamically generated frequencies,” Phys. Rev. Lett. 102(4), 043905 (2009).
[CrossRef] [PubMed]

M. Tlidi, A. Mussot, E. Louvergneaux, G. Kozyreff, A. G. Vladimirov, M. Taki, “Control and removal of modulational instabilities in low-dispersion photonic crystal fiber cavities,” Opt. Lett. 32(6), 662–664 (2007).
[CrossRef] [PubMed]

Novoa, D.

D. Novoa, H. Michinel, D. Tommasini, “Pressure, surface tension, and dripping of self-trapped laser beams,” Phys. Rev. Lett. 103(2), 023903 (2009).
[CrossRef] [PubMed]

Padgett, M. J.

R. W. Bowman, G. M. Gibson, M. J. Padgett, F. Saglimbeni, R. Di Leonardo, “Optical trapping at gigapascal pressures,” Phys. Rev. Lett. 110(9), 095902 (2013).
[CrossRef] [PubMed]

Pang, W.

Y. Li, J. Liu, W. Pang, B. A. Malomed, “Symmetry breaking in dipolar matter-wave solitons in dual-core couplers,” Phys. Rev. A 87(1), 013604 (2013).
[CrossRef]

Randle, H. G.

Russell, P. S. J.

M. Azhar, N. Y. Joly, J. C. Travers, P. S. J. Russell, “Nonlinear optics in Xe-filled hollow-core PCF in high pressure and supercritical regimes,” Appl. Phys. B 112(4), 457–460 (2013).
[CrossRef]

Russell, P. St. J.

Saglimbeni, F.

R. W. Bowman, G. M. Gibson, M. J. Padgett, F. Saglimbeni, R. Di Leonardo, “Optical trapping at gigapascal pressures,” Phys. Rev. Lett. 110(9), 095902 (2013).
[CrossRef] [PubMed]

Salgueiro, J. R.

A. Alexandrescu, J. R. Salgueiro, “Efficient numerical method for linear stability analysis of solitary waves,” Comput. Phys. Commun. 182(12), 2479–2485 (2011).
[CrossRef]

J. R. Salgueiro, Y. S. Kivshar, “Nonlinear dual-core photonic crystal fiber couplers,” Opt. Lett. 30(14), 1858–1860 (2005).
[CrossRef] [PubMed]

Schmidberger, M.

Schmidberger, M. J.

M. J. Schmidberger, F. Biancalana, P. St. J. Russell, N. Y. Joly, “Semi-analytical model for the evolution of femtosecond pulses during supercontinuum generation in synchronously pumped ring cavities,” in The European Conference on Lasers and Electro-Optics (OSA, 2013).

Schwache, A.

H. U. Voss, A. Schwache, J. Kurths, F. Mitschke, “Equations of motion from chaotic data: A driven optical fiber ring resonator,” Phys. Lett. A 256(1), 47–54 (1999).
[CrossRef]

Scroggie, A. J.

A. J. Scroggie, W. J. Firth, G. S. McDonald, M. Tlidi, R. Lefever, L. A. Lugiato, “Pattern formation in a passive Kerr cavity,” Chaos Solitons Fractals 4(8–9), 1323–1354 (1994).
[CrossRef]

Solari, H. G.

C. Green, G. B. Mindlin, E. J. D’Angelo, H. G. Solari, J. R. Tredicce, “Spontaneous symmetry breaking in a laser: The experimental side,” Phys. Rev. Lett. 65(25), 3124–3127 (1990).
[CrossRef] [PubMed]

Soto-Crespo, J. M.

J. M. Soto-Crespo, D. R. Heatley, E. M. Wright, N. N. Akhmediev, “Stability of the higher-bound states in a saturable self-focusing medium,” Phys. Rev. A 44(1), 636–644 (1991).
[CrossRef] [PubMed]

Steinmeyer, G.

G. Steinmeyer, F. Mitschke, “Longitudinal structure formation in a nonlinear resonator,” Appl. Phys. B 62(4), 367–374 (1996).
[CrossRef]

Sylvestre, T.

Szwaj, C.

C. Bruni, T. Legrand, C. Szwaj, S. Bielawski, M. E. Couprie, “Equivalence between free-electron-laser oscillators and actively-mode-locked lasers: Detailed studies of temporal, spatiotemporal, and spectrotemporal dynamics,” Phys. Rev. A 84(6), 063804 (2011).
[CrossRef]

Taki, M.

F. Leo, A. Mussot, P. Kockaert, P. Emplit, M. Haelterman, M. Taki, “Nonlinear symmetry breaking induced by third-order dispersion in optical fiber cavities,” Phys. Rev. Lett. 110(10), 104103 (2013).
[CrossRef] [PubMed]

G. Kozyreff, M. Tlidi, A. Mussot, E. Louvergneaux, M. Taki, A. G. Vladimirov, “Localized beating between dynamically generated frequencies,” Phys. Rev. Lett. 102(4), 043905 (2009).
[CrossRef] [PubMed]

M. Tlidi, A. Mussot, E. Louvergneaux, G. Kozyreff, A. G. Vladimirov, M. Taki, “Control and removal of modulational instabilities in low-dispersion photonic crystal fiber cavities,” Opt. Lett. 32(6), 662–664 (2007).
[CrossRef] [PubMed]

Tlidi, M.

M. Tlidi, L. Bahloul, L. Cherbi, A. Hariz, S. Coulibaly, “Drift of dark cavity solitons in a photonic-crystal fiber resonator,” Phys. Rev. A 88(3), 035802 (2013).
[CrossRef]

M. Tlidi, L. Gelens, “High-order dispersion stabilizes dark dissipative solitons in all-fiber cavities,” Opt. Lett. 35(3), 306–308 (2010).
[CrossRef] [PubMed]

G. Kozyreff, M. Tlidi, A. Mussot, E. Louvergneaux, M. Taki, A. G. Vladimirov, “Localized beating between dynamically generated frequencies,” Phys. Rev. Lett. 102(4), 043905 (2009).
[CrossRef] [PubMed]

M. Tlidi, A. Mussot, E. Louvergneaux, G. Kozyreff, A. G. Vladimirov, M. Taki, “Control and removal of modulational instabilities in low-dispersion photonic crystal fiber cavities,” Opt. Lett. 32(6), 662–664 (2007).
[CrossRef] [PubMed]

S. Coen, M. Tlidi, P. Emplit, M. Haelterman, “Convection versus dispersion in optical bistability,” Phys. Rev. Lett. 83(12), 2328–2331 (1999).
[CrossRef]

A. J. Scroggie, W. J. Firth, G. S. McDonald, M. Tlidi, R. Lefever, L. A. Lugiato, “Pattern formation in a passive Kerr cavity,” Chaos Solitons Fractals 4(8–9), 1323–1354 (1994).
[CrossRef]

Tommasini, D.

D. Novoa, H. Michinel, D. Tommasini, “Pressure, surface tension, and dripping of self-trapped laser beams,” Phys. Rev. Lett. 103(2), 023903 (2009).
[CrossRef] [PubMed]

Travers, J. C.

M. Azhar, N. Y. Joly, J. C. Travers, P. S. J. Russell, “Nonlinear optics in Xe-filled hollow-core PCF in high pressure and supercritical regimes,” Appl. Phys. B 112(4), 457–460 (2013).
[CrossRef]

Tredicce, J. R.

C. Green, G. B. Mindlin, E. J. D’Angelo, H. G. Solari, J. R. Tredicce, “Spontaneous symmetry breaking in a laser: The experimental side,” Phys. Rev. Lett. 65(25), 3124–3127 (1990).
[CrossRef] [PubMed]

Vallée, R.

R. Vallée, “Temporal instabilities in the output of an all-fiber ring cavity,” Opt. Commun. 81(6), 419–426 (1991).
[CrossRef]

Vladimirov, A. G.

G. Kozyreff, M. Tlidi, A. Mussot, E. Louvergneaux, M. Taki, A. G. Vladimirov, “Localized beating between dynamically generated frequencies,” Phys. Rev. Lett. 102(4), 043905 (2009).
[CrossRef] [PubMed]

M. Tlidi, A. Mussot, E. Louvergneaux, G. Kozyreff, A. G. Vladimirov, M. Taki, “Control and removal of modulational instabilities in low-dispersion photonic crystal fiber cavities,” Opt. Lett. 32(6), 662–664 (2007).
[CrossRef] [PubMed]

Voss, H. U.

H. U. Voss, A. Schwache, J. Kurths, F. Mitschke, “Equations of motion from chaotic data: A driven optical fiber ring resonator,” Phys. Lett. A 256(1), 47–54 (1999).
[CrossRef]

Wright, E. M.

J. M. Soto-Crespo, D. R. Heatley, E. M. Wright, N. N. Akhmediev, “Stability of the higher-bound states in a saturable self-focusing medium,” Phys. Rev. A 44(1), 636–644 (1991).
[CrossRef] [PubMed]

Appl. Phys. B (2)

G. Steinmeyer, F. Mitschke, “Longitudinal structure formation in a nonlinear resonator,” Appl. Phys. B 62(4), 367–374 (1996).
[CrossRef]

M. Azhar, N. Y. Joly, J. C. Travers, P. S. J. Russell, “Nonlinear optics in Xe-filled hollow-core PCF in high pressure and supercritical regimes,” Appl. Phys. B 112(4), 457–460 (2013).
[CrossRef]

Chaos Solitons Fractals (1)

A. J. Scroggie, W. J. Firth, G. S. McDonald, M. Tlidi, R. Lefever, L. A. Lugiato, “Pattern formation in a passive Kerr cavity,” Chaos Solitons Fractals 4(8–9), 1323–1354 (1994).
[CrossRef]

Comput. Phys. Commun. (1)

A. Alexandrescu, J. R. Salgueiro, “Efficient numerical method for linear stability analysis of solitary waves,” Comput. Phys. Commun. 182(12), 2479–2485 (2011).
[CrossRef]

Fiber Integr. Opt. (1)

J. García-Mateos, F. C. Bienzobas, M. Haelterman, “Optical bistability and temporal symmetry-breaking instability in nonlinear fiber resonators,” Fiber Integr. Opt. 14(4), 337–346 (1995).
[CrossRef]

IEEE J. Quantum Electron. (2)

H. A. Haus, “Mode-locking of lasers,” IEEE J. Quantum Electron. 6(6), 1173–1185 (2000).
[CrossRef]

P. Elleaume, “Microtemporal and spectral structure of storage ring free-electron lasers,” IEEE J. Quantum Electron. 21(7), 1012–1022 (1985).
[CrossRef]

Int. J. Bifurcat. Chaos (1)

E. Doedel, H. B. Keller, J. P. Kernevez, “Numerical analysis and control of bifurcation problems (II): Bifurcation in infinite dimensions,” Int. J. Bifurcat. Chaos 01(04), 745–772 (1991).
[CrossRef]

J. Lightwave Technol. (1)

Nat. Photonics (2)

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, P. Emplit, M. Haelterman, “Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,” Nat. Photonics 4(7), 471–476 (2010).
[CrossRef]

J. K. Jang, M. Erkintalo, S. G. Murdoch, S. Coen, “Ultraweak long-range interactions of solitons observed over astronomical distances,” Nat. Photonics 7(8), 657–663 (2013).
[CrossRef]

Opt. Commun. (2)

K. Ikeda, “Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system,” Opt. Commun. 30(2), 257–261 (1979).
[CrossRef]

R. Vallée, “Temporal instabilities in the output of an all-fiber ring cavity,” Opt. Commun. 81(6), 419–426 (1991).
[CrossRef]

Opt. Express (2)

Opt. Lett. (6)

Phys. Lett. A (1)

H. U. Voss, A. Schwache, J. Kurths, F. Mitschke, “Equations of motion from chaotic data: A driven optical fiber ring resonator,” Phys. Lett. A 256(1), 47–54 (1999).
[CrossRef]

Phys. Rev. A (7)

M. Tlidi, L. Bahloul, L. Cherbi, A. Hariz, S. Coulibaly, “Drift of dark cavity solitons in a photonic-crystal fiber resonator,” Phys. Rev. A 88(3), 035802 (2013).
[CrossRef]

Y. K. Chembo, C. R. Menyuk, “Spatiotemporal Lugiato-Lefever formalism for Kerr-comb generation in whispering-gallery-mode resonators,” Phys. Rev. A 87(5), 053852 (2013).
[CrossRef]

A. E. Miroshnichenko, B. A. Malomed, Y. S. Kivshar, “Nonlinearly PT-symmetric systems: Spontaneous symmetry breaking and transmission resonances,” Phys. Rev. A 84(1), 012123 (2011).
[CrossRef]

Y. Li, J. Liu, W. Pang, B. A. Malomed, “Symmetry breaking in dipolar matter-wave solitons in dual-core couplers,” Phys. Rev. A 87(1), 013604 (2013).
[CrossRef]

M. Kues, N. Brauckmann, P. Groß, C. Fallnich, “Basic prerequisites for limit-cycle oscillations within a synchronously pumped passive optical nonlinear fiber-ring resonator,” Phys. Rev. A 84(3), 033833 (2011).
[CrossRef]

C. Bruni, T. Legrand, C. Szwaj, S. Bielawski, M. E. Couprie, “Equivalence between free-electron-laser oscillators and actively-mode-locked lasers: Detailed studies of temporal, spatiotemporal, and spectrotemporal dynamics,” Phys. Rev. A 84(6), 063804 (2011).
[CrossRef]

J. M. Soto-Crespo, D. R. Heatley, E. M. Wright, N. N. Akhmediev, “Stability of the higher-bound states in a saturable self-focusing medium,” Phys. Rev. A 44(1), 636–644 (1991).
[CrossRef] [PubMed]

Phys. Rev. Lett. (8)

P. W. Higgs, “Broken symmetries and the masses of gauge bosons,” Phys. Rev. Lett. 13(16), 508–509 (1964).
[CrossRef]

C. Green, G. B. Mindlin, E. J. D’Angelo, H. G. Solari, J. R. Tredicce, “Spontaneous symmetry breaking in a laser: The experimental side,” Phys. Rev. Lett. 65(25), 3124–3127 (1990).
[CrossRef] [PubMed]

S. Coen, M. Tlidi, P. Emplit, M. Haelterman, “Convection versus dispersion in optical bistability,” Phys. Rev. Lett. 83(12), 2328–2331 (1999).
[CrossRef]

L. A. Lugiato, R. Lefever, “Spatial dissipative structures in passive optical systems,” Phys. Rev. Lett. 58(21), 2209–2211 (1987).
[CrossRef] [PubMed]

R. W. Bowman, G. M. Gibson, M. J. Padgett, F. Saglimbeni, R. Di Leonardo, “Optical trapping at gigapascal pressures,” Phys. Rev. Lett. 110(9), 095902 (2013).
[CrossRef] [PubMed]

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