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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  6. 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).
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    [CrossRef]
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  19. 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).
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  28. H. A. Haus, “Mode-locking of lasers,” IEEE J. Quantum Electron. 6(6), 1173–1185 (2000).
    [CrossRef]
  29. P. Elleaume, “Microtemporal and spectral structure of storage ring free-electron lasers,” IEEE J. Quantum Electron. 21(7), 1012–1022 (1985).
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  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)

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]

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]

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]

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]

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]

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)

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]

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]

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]

2010 (2)

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

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)

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]

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

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]

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]

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.

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, 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]

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, 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]

Erkintalo, M.

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]

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]

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, 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]

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.

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]

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, 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]

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)

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

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]

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]

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]

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]

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]

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]

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]

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]

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Figures (5)

Fig. 1
Fig. 1

Bifurcation diagrams of the normalized pulse energy N with respect to the normalized temporal walk-off δ corresponding to a delay range from −200 to 200 fs, simulated with (a) the IMF and (b) Eq. (1). Each value of δ contains 200 values of N. Vertical dashed lines represent dynamical transitions. The evolution diagrams in Fig. 2 correspond to the slice highlighted in green, which is labeled “Fig. 2”.

Fig. 2
Fig. 2

Comparison of temporal (left column) and spectral (right column) pulse evolution simulated with the IMF (top) and Eq. (1) (bottom) for δ = 12. The simulation corresponds to the green region labeled “Fig. 2” in Fig. 1. The time window for θ corresponds to 6 ps in physical units and k = 1/θ.

Fig. 3
Fig. 3

(a) Bifurcation diagram of the normalized pulse energy Ν for the stationary solutions of Eq. (2) with respect to the pump strength ξ, where solid branches are linearly stable and dashed branches unstable. i, ii, and iii indicate regions where the system is monostable, bistable and multistable. (b,c) Close-ups of the bistable and multistable regions. In (b), the symmetric and asymmetric sections are labeled “s” and “as”, while the states outside the dark blue area are symmetric. (d,e) Power and phase of the two solutions in the inset of (c). The vertical grey dashed line in (c) indicates the states discussed in Fig. 4.

Fig. 4
Fig. 4

Evolution of the (a) normalized pulse energy, (b) temporal shape and (c) asymmetry of the cavity pulse when seeding with an unstable symmetric solution at ξ = 3.66 as indicated by the vertical grey dashed line in Fig. 3(c).

Fig. 5
Fig. 5

Hydrodynamical representation of the (a) energy generation S and (b) internal energy flow J for the AS presented in Fig. 3(e) at ξ ≈3.4. (c) shows the temporal shape of the complex envelope of the pump pulses |Âp(θ)|2.

Equations (6)

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[ T +δ θ ]A(T,θ)=A+ L f κ T p k=2 i k+1 k! t 0 k β k θ k A+i L f κ T p F(A)+ξ A p ^ ( θ ) e i φ p
T A( T,θ )=Ai L f β 2 2κ T p t 0 2 θ 2 A+i L f κ T p F( A )+ R P 0 κ T p A p ^ ( θ )
T ρ+J=2ξf( θ ) ρ cos( ΨΦ )ρ=S
E n+1 ( t )=A( T+κ T p ,θ+ τ wo t 0 )A( T,θ )+κ T p T A( T,θ )+ τ wo t 0 θ A( T,θ )
E n+1 ( t ) E n ( t )=κ τ wo E n ( t )+ L f k=2 i k+1 k! β k t k E n ( t ) +i L f F( E n ( t ) )+ R E p ( t ) e i φ p
[ T +δ θ ]A(T,θ)=A+ L f κ T p k=2 i k+1 k! t 0 k β k θ k A+i L f κ T p F(A)+ξ A p ^ ( θ ) e i φ p

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