Abstract

We consider a bistable system consisting of all fiber cavity driven by an external injected continuous wave. We report on front propagation in a high finesse cavity. We study the asymptotic behavior of the front velocity. We show that the front velocity is affected by the distance from the critical point associated with bistability. We provide a scaling low governing its evolution near the up-switching point of the bistable curve. We show also that the velocity of front propagation obeys a generic power law when the front velocity approaches asymptotically its linear growing value.

© 2014 OSA

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    [CrossRef] [PubMed]
  2. M. Tlidi, R. Lefever, P. Mandel, “Pattern selection in optical bistability,” Quantum Semiclass. Opt. 8931–938 (1996).
    [CrossRef]
  3. F. Mitschke, G. Steinmeyer, A. Schwache, “Generation of one-dimensional optical turbulence,” Physica D 96, 251–258 (1996).
    [CrossRef]
  4. S. Coen, M. Haelterman, “Modulational instability induced by cavity boundary conditions in a normally dispersive optical fiber,” Phys. Rev. Lett. 79, 4139–4142 (1997).
    [CrossRef]
  5. M. Stratmann, T. Pagel, F. Mitschke, “Experimental observation of temporal soliton molecules,” Phys. Rev. Lett. 95, 143902 (2005).
    [CrossRef] [PubMed]
  6. M. Tlidi, M. Haelterman, P. Mandel, “3D patterns and pattern selection in optical bistability,” Europhys. Lett. 42, 505–509 (1998).
    [CrossRef]
  7. K. Staliunas, “Three-Dimensional Turing Structures and Spatial Solitons in Optical Parametric Oscillators,” Phys. Rev. Lett. 81, 81–85 (1998).
    [CrossRef]
  8. M. Tlidi, “Three-dimensional crystals and localized structures in diffractive and dispersive nonlinear ring cavities,” J. Opt. B: Quantum Semiclass. Opt. 2, 438–442 (2000).
    [CrossRef]
  9. M. Brambilla, T. Maggipinto, G. Patera, L. Columbo, “Cavity light bullets: Three-dimensional localized structures in a nonlinear optical resonator,” Phys. Rev. Lett. 93, 203901 (2004).
    [CrossRef] [PubMed]
  10. P. Tassin, G. Van der Sande, N. Veretenov, P. Kockaert, I. Veretennicoff, M. Tlidi, “Three-dimensional structures in nonlinear cavities containing left-handed materials”, Optics Express, 14, 9338–9343 (2006).
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  16. M. Tlidi, P. Mandel, R. Lefever, “Localized structures and localized patterns in optical bistability,” Phys. Rev. Lett. 73, 640–643 (1994).
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  17. G. Slekys, K. Staliunas, C.O. Weiss, “Spatial localized structures in resonators with saturable absorber,” Opt. Commun. 149, 113–116 (1998).
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  18. V.B. Taranenko, K. Staliunas, C. O. Weiss, “Spatial soliton laser: Localized structures in a laser with a saturable absorber in a self-imaging resonator,” Phys. Rev. A 56, 1582–1591 (1997).
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  20. 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,” Nature Photon. 4, 471–476 (2010).
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  21. F. Leo, L. Gelens, P. Emplit, M. Haelterman, S. Coen, “Dynamics of one-dimensional Kerr cavity solitons,” Opt. Express 21, 9180–9191 (2013).
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  22. D. Gomila, M. A. Matias, P. Colet, “Excitability mediated by localized structures in a dissipative nonlinear optical cavity,” Phys. Rev. Lett. 94, 063905 (2005).
    [CrossRef] [PubMed]
  23. D. Turaev, A. G. Vladimirov, S. Zelik, “Long-range interaction and synchronization of oscillating dissipative solitons”, Phys. Rev. Lett. 108, 263906–263909 (2012).
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  24. O.A Egorov, F. Lederer, “Spontaneously walking discrete cavity solitons,” Opt. Lett. 38, 1010–1012 (2013).
    [CrossRef] [PubMed]
  25. S. Coen, M. Tlidi, Ph. Emplit, M. Haelterman, “Convection versus dispersion in optical bistability,” Phys. Rev. Lett. 83, 2328–2331 (1999).
    [CrossRef]
  26. K. Staliunas, V.J. Sanchez-Morcillo, “Dynamics of phase domains in the Swift-Hohenberg equation,” Phys. Lett. A 24128–34 (1998).
    [CrossRef]
  27. M. Tlidi, P. Mandel, R. Lefever, “Kinetics of localized pattern formation in optical systems,” Phys. Rev. Lett. 81, 979–982 (1998).
    [CrossRef]
  28. M. Tlidi, Paul Mandel, M. Le Berre, E. Ressayre, A. Tallet, L. Di Menza, “Phase-separation dynamics of circular domain walls in the degenerate optical parametric oscillator,” Optics Lett. 25, 487–489 (2000).
    [CrossRef]
  29. V. B. Taranenko, K. Staliunas, C.O. Weiss, “Pattern formation and localized structures in degenerate optical parametric mixing”, Phys. Rev. Lett. 812236–2239 (1998).
    [CrossRef]
  30. G.T. Dee, J.S. Langer, “Propagating pattern selection,” Phys. Rev. Lett. 50, 383–386 (1983).
    [CrossRef]
  31. G.T. Dee, W. van Saarloos, “Bistable Systems with Propagating Fronts Leading to Pattern Formation,” Phys. Rev. Lett. 60, 2641–2644 (1988).
    [CrossRef] [PubMed]
  32. M. Taki, M. N. Ouarzazi, H. Ward, P. Glorieux, “Nonlinear front propagation in optical parametric oscillators,” J. Opt. Soc. Am. B 17, 997–1003 (2000).
    [CrossRef]
  33. W. van Saarloos, “Front propagation into unstable states,” Phys. Rep. 286, 29–222 (2003).
    [CrossRef]
  34. A. Mussot, E. Louvergneaux, N. Akhmediev, F. Reynaud, L. Delage, M. Taki, “Optical fiber systems are convectively unstable”, Phys. Rev. Lett. 101, 113904–113907 (2008).
    [CrossRef] [PubMed]
  35. Kestutis Staliunas, Oleg Egorov, Yuri S. Kivshar, Falk Lederer, “Bloch Cavity Solitons in Nonlinear Resonators with Intracavity Photonic Crystals,” Phys. Rev. Lett. 101, 153903–153906 (2008).
    [CrossRef] [PubMed]
  36. P. Kockaert, P. Tassin, G. Van der Sande, I. Veretennicoff, M. Tlidi, “Negative diffraction pattern dynamics in nonlinear cavities with left-handed materials,” Phys. Rev. A 74, 033822 (2006).
    [CrossRef]
  37. L. Gelens, G. Van der Sande, P. Tassin, M. Tlidi, P. Kockaert, D. Gomila, I. Veretennicoff, J. Danckaert, “Impact of nonlocal interactions in dissipative systems: Towards minimal-sized localized structures,” Phys. Rev. A 75, 063812 (2007).
    [CrossRef]
  38. M. Santagiustina, P. Colet, M. San Miguel, D. Walgraef, “Noise-sustained convective structures in nonlinear optics,” Phys. Rev. Lett. 79, 3633–3636 (1997).
    [CrossRef]
  39. S. Coulibaly, C. Durniak, M. Taki, “Spatial Dissipative Solitons Under Convective and Absolute Instabilities in Optical Parametric Oscillators,” Lecture Notes in Physics, 751, 261–285 (2008).
    [CrossRef]
  40. H. Ward, M. N. Ouarzazi, M. Taki, P. Glorieux, “Influence of walkoff on pattern formation in nondegenerate optical parametric oscillators,” Phys. Rev. E 63, 016604 (2000).
    [CrossRef]

2013 (2)

2012 (1)

D. Turaev, A. G. Vladimirov, S. Zelik, “Long-range interaction and synchronization of oscillating dissipative solitons”, Phys. Rev. Lett. 108, 263906–263909 (2012).
[CrossRef] [PubMed]

2011 (1)

V. Odent, M. Taki, E. Louvergneaux, “Experimental evidence of dissipative spatial solitons in an optical passive Kerr cavity,” New J. Phys. 13, 113026 (2011).
[CrossRef]

2010 (1)

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,” Nature Photon. 4, 471–476 (2010).
[CrossRef]

2008 (3)

S. Coulibaly, C. Durniak, M. Taki, “Spatial Dissipative Solitons Under Convective and Absolute Instabilities in Optical Parametric Oscillators,” Lecture Notes in Physics, 751, 261–285 (2008).
[CrossRef]

A. Mussot, E. Louvergneaux, N. Akhmediev, F. Reynaud, L. Delage, M. Taki, “Optical fiber systems are convectively unstable”, Phys. Rev. Lett. 101, 113904–113907 (2008).
[CrossRef] [PubMed]

Kestutis Staliunas, Oleg Egorov, Yuri S. Kivshar, Falk Lederer, “Bloch Cavity Solitons in Nonlinear Resonators with Intracavity Photonic Crystals,” Phys. Rev. Lett. 101, 153903–153906 (2008).
[CrossRef] [PubMed]

2007 (2)

L. Gelens, G. Van der Sande, P. Tassin, M. Tlidi, P. Kockaert, D. Gomila, I. Veretennicoff, J. Danckaert, “Impact of nonlocal interactions in dissipative systems: Towards minimal-sized localized structures,” Phys. Rev. A 75, 063812 (2007).
[CrossRef]

M. Tlidi, M. Taki, T. Kolokolnikov, “Introduction: Dissipative localized structures in extended systems”, Chaos 17, 037101 (2007).
[CrossRef] [PubMed]

2006 (2)

P. Kockaert, P. Tassin, G. Van der Sande, I. Veretennicoff, M. Tlidi, “Negative diffraction pattern dynamics in nonlinear cavities with left-handed materials,” Phys. Rev. A 74, 033822 (2006).
[CrossRef]

P. Tassin, G. Van der Sande, N. Veretenov, P. Kockaert, I. Veretennicoff, M. Tlidi, “Three-dimensional structures in nonlinear cavities containing left-handed materials”, Optics Express, 14, 9338–9343 (2006).
[CrossRef] [PubMed]

2005 (2)

D. Gomila, M. A. Matias, P. Colet, “Excitability mediated by localized structures in a dissipative nonlinear optical cavity,” Phys. Rev. Lett. 94, 063905 (2005).
[CrossRef] [PubMed]

M. Stratmann, T. Pagel, F. Mitschke, “Experimental observation of temporal soliton molecules,” Phys. Rev. Lett. 95, 143902 (2005).
[CrossRef] [PubMed]

2004 (1)

M. Brambilla, T. Maggipinto, G. Patera, L. Columbo, “Cavity light bullets: Three-dimensional localized structures in a nonlinear optical resonator,” Phys. Rev. Lett. 93, 203901 (2004).
[CrossRef] [PubMed]

2003 (1)

W. van Saarloos, “Front propagation into unstable states,” Phys. Rep. 286, 29–222 (2003).
[CrossRef]

2000 (4)

H. Ward, M. N. Ouarzazi, M. Taki, P. Glorieux, “Influence of walkoff on pattern formation in nondegenerate optical parametric oscillators,” Phys. Rev. E 63, 016604 (2000).
[CrossRef]

M. Taki, M. N. Ouarzazi, H. Ward, P. Glorieux, “Nonlinear front propagation in optical parametric oscillators,” J. Opt. Soc. Am. B 17, 997–1003 (2000).
[CrossRef]

M. Tlidi, Paul Mandel, M. Le Berre, E. Ressayre, A. Tallet, L. Di Menza, “Phase-separation dynamics of circular domain walls in the degenerate optical parametric oscillator,” Optics Lett. 25, 487–489 (2000).
[CrossRef]

M. Tlidi, “Three-dimensional crystals and localized structures in diffractive and dispersive nonlinear ring cavities,” J. Opt. B: Quantum Semiclass. Opt. 2, 438–442 (2000).
[CrossRef]

1999 (1)

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

1998 (6)

K. Staliunas, V.J. Sanchez-Morcillo, “Dynamics of phase domains in the Swift-Hohenberg equation,” Phys. Lett. A 24128–34 (1998).
[CrossRef]

M. Tlidi, P. Mandel, R. Lefever, “Kinetics of localized pattern formation in optical systems,” Phys. Rev. Lett. 81, 979–982 (1998).
[CrossRef]

G. Slekys, K. Staliunas, C.O. Weiss, “Spatial localized structures in resonators with saturable absorber,” Opt. Commun. 149, 113–116 (1998).
[CrossRef]

M. Tlidi, M. Haelterman, P. Mandel, “3D patterns and pattern selection in optical bistability,” Europhys. Lett. 42, 505–509 (1998).
[CrossRef]

K. Staliunas, “Three-Dimensional Turing Structures and Spatial Solitons in Optical Parametric Oscillators,” Phys. Rev. Lett. 81, 81–85 (1998).
[CrossRef]

V. B. Taranenko, K. Staliunas, C.O. Weiss, “Pattern formation and localized structures in degenerate optical parametric mixing”, Phys. Rev. Lett. 812236–2239 (1998).
[CrossRef]

1997 (3)

M. Santagiustina, P. Colet, M. San Miguel, D. Walgraef, “Noise-sustained convective structures in nonlinear optics,” Phys. Rev. Lett. 79, 3633–3636 (1997).
[CrossRef]

S. Coen, M. Haelterman, “Modulational instability induced by cavity boundary conditions in a normally dispersive optical fiber,” Phys. Rev. Lett. 79, 4139–4142 (1997).
[CrossRef]

V.B. Taranenko, K. Staliunas, C. O. Weiss, “Spatial soliton laser: Localized structures in a laser with a saturable absorber in a self-imaging resonator,” Phys. Rev. A 56, 1582–1591 (1997).
[CrossRef]

1996 (2)

M. Tlidi, R. Lefever, P. Mandel, “Pattern selection in optical bistability,” Quantum Semiclass. Opt. 8931–938 (1996).
[CrossRef]

F. Mitschke, G. Steinmeyer, A. Schwache, “Generation of one-dimensional optical turbulence,” Physica D 96, 251–258 (1996).
[CrossRef]

1994 (2)

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 and Fractals 4, 1323–1354 (1994).
[CrossRef]

M. Tlidi, P. Mandel, R. Lefever, “Localized structures and localized patterns in optical bistability,” Phys. Rev. Lett. 73, 640–643 (1994).
[CrossRef] [PubMed]

1988 (1)

G.T. Dee, W. van Saarloos, “Bistable Systems with Propagating Fronts Leading to Pattern Formation,” Phys. Rev. Lett. 60, 2641–2644 (1988).
[CrossRef] [PubMed]

1987 (1)

L.A. Lugiato, R. Lefever, “Spatial Dissipative Structures in Passive Optical Systems,” Phys. Rev. Lett. 58, 2209–2211 (1987).
[CrossRef] [PubMed]

1983 (1)

G.T. Dee, J.S. Langer, “Propagating pattern selection,” Phys. Rev. Lett. 50, 383–386 (1983).
[CrossRef]

Akhmediev, N.

A. Mussot, E. Louvergneaux, N. Akhmediev, F. Reynaud, L. Delage, M. Taki, “Optical fiber systems are convectively unstable”, Phys. Rev. Lett. 101, 113904–113907 (2008).
[CrossRef] [PubMed]

Assanto, G.

O. Descalzi, M.G. Clerc, S. Residori, G. Assanto, Localized States in Physics: Solitons and Patterns (Springer, 2010).

Brambilla, M.

M. Brambilla, T. Maggipinto, G. Patera, L. Columbo, “Cavity light bullets: Three-dimensional localized structures in a nonlinear optical resonator,” Phys. Rev. Lett. 93, 203901 (2004).
[CrossRef] [PubMed]

Clerc, M.G.

O. Descalzi, M.G. Clerc, S. Residori, G. Assanto, Localized States in Physics: Solitons and Patterns (Springer, 2010).

Coen, S.

F. Leo, L. Gelens, P. Emplit, M. Haelterman, S. Coen, “Dynamics of one-dimensional Kerr cavity solitons,” Opt. Express 21, 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,” Nature Photon. 4, 471–476 (2010).
[CrossRef]

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

S. Coen, M. Haelterman, “Modulational instability induced by cavity boundary conditions in a normally dispersive optical fiber,” Phys. Rev. Lett. 79, 4139–4142 (1997).
[CrossRef]

Colet, P.

D. Gomila, M. A. Matias, P. Colet, “Excitability mediated by localized structures in a dissipative nonlinear optical cavity,” Phys. Rev. Lett. 94, 063905 (2005).
[CrossRef] [PubMed]

M. Santagiustina, P. Colet, M. San Miguel, D. Walgraef, “Noise-sustained convective structures in nonlinear optics,” Phys. Rev. Lett. 79, 3633–3636 (1997).
[CrossRef]

Columbo, L.

M. Brambilla, T. Maggipinto, G. Patera, L. Columbo, “Cavity light bullets: Three-dimensional localized structures in a nonlinear optical resonator,” Phys. Rev. Lett. 93, 203901 (2004).
[CrossRef] [PubMed]

Coulibaly, S.

S. Coulibaly, C. Durniak, M. Taki, “Spatial Dissipative Solitons Under Convective and Absolute Instabilities in Optical Parametric Oscillators,” Lecture Notes in Physics, 751, 261–285 (2008).
[CrossRef]

Danckaert, J.

L. Gelens, G. Van der Sande, P. Tassin, M. Tlidi, P. Kockaert, D. Gomila, I. Veretennicoff, J. Danckaert, “Impact of nonlocal interactions in dissipative systems: Towards minimal-sized localized structures,” Phys. Rev. A 75, 063812 (2007).
[CrossRef]

Dee, G.T.

G.T. Dee, W. van Saarloos, “Bistable Systems with Propagating Fronts Leading to Pattern Formation,” Phys. Rev. Lett. 60, 2641–2644 (1988).
[CrossRef] [PubMed]

G.T. Dee, J.S. Langer, “Propagating pattern selection,” Phys. Rev. Lett. 50, 383–386 (1983).
[CrossRef]

Delage, L.

A. Mussot, E. Louvergneaux, N. Akhmediev, F. Reynaud, L. Delage, M. Taki, “Optical fiber systems are convectively unstable”, Phys. Rev. Lett. 101, 113904–113907 (2008).
[CrossRef] [PubMed]

Descalzi, O.

O. Descalzi, M.G. Clerc, S. Residori, G. Assanto, Localized States in Physics: Solitons and Patterns (Springer, 2010).

Di Menza, L.

M. Tlidi, Paul Mandel, M. Le Berre, E. Ressayre, A. Tallet, L. Di Menza, “Phase-separation dynamics of circular domain walls in the degenerate optical parametric oscillator,” Optics Lett. 25, 487–489 (2000).
[CrossRef]

Durniak, C.

S. Coulibaly, C. Durniak, M. Taki, “Spatial Dissipative Solitons Under Convective and Absolute Instabilities in Optical Parametric Oscillators,” Lecture Notes in Physics, 751, 261–285 (2008).
[CrossRef]

Egorov, O.A

Egorov, Oleg

Kestutis Staliunas, Oleg Egorov, Yuri S. Kivshar, Falk Lederer, “Bloch Cavity Solitons in Nonlinear Resonators with Intracavity Photonic Crystals,” Phys. Rev. Lett. 101, 153903–153906 (2008).
[CrossRef] [PubMed]

Emplit, P.

F. Leo, L. Gelens, P. Emplit, M. Haelterman, S. Coen, “Dynamics of one-dimensional Kerr cavity solitons,” Opt. Express 21, 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,” Nature Photon. 4, 471–476 (2010).
[CrossRef]

Emplit, Ph.

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

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 and Fractals 4, 1323–1354 (1994).
[CrossRef]

Gelens, L.

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

L. Gelens, G. Van der Sande, P. Tassin, M. Tlidi, P. Kockaert, D. Gomila, I. Veretennicoff, J. Danckaert, “Impact of nonlocal interactions in dissipative systems: Towards minimal-sized localized structures,” Phys. Rev. A 75, 063812 (2007).
[CrossRef]

Glorieux, P.

M. Taki, M. N. Ouarzazi, H. Ward, P. Glorieux, “Nonlinear front propagation in optical parametric oscillators,” J. Opt. Soc. Am. B 17, 997–1003 (2000).
[CrossRef]

H. Ward, M. N. Ouarzazi, M. Taki, P. Glorieux, “Influence of walkoff on pattern formation in nondegenerate optical parametric oscillators,” Phys. Rev. E 63, 016604 (2000).
[CrossRef]

Gomila, D.

L. Gelens, G. Van der Sande, P. Tassin, M. Tlidi, P. Kockaert, D. Gomila, I. Veretennicoff, J. Danckaert, “Impact of nonlocal interactions in dissipative systems: Towards minimal-sized localized structures,” Phys. Rev. A 75, 063812 (2007).
[CrossRef]

D. Gomila, M. A. Matias, P. Colet, “Excitability mediated by localized structures in a dissipative nonlinear optical cavity,” Phys. Rev. Lett. 94, 063905 (2005).
[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,” Nature Photon. 4, 471–476 (2010).
[CrossRef]

Haelterman, M.

F. Leo, L. Gelens, P. Emplit, M. Haelterman, S. Coen, “Dynamics of one-dimensional Kerr cavity solitons,” Opt. Express 21, 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,” Nature Photon. 4, 471–476 (2010).
[CrossRef]

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

M. Tlidi, M. Haelterman, P. Mandel, “3D patterns and pattern selection in optical bistability,” Europhys. Lett. 42, 505–509 (1998).
[CrossRef]

S. Coen, M. Haelterman, “Modulational instability induced by cavity boundary conditions in a normally dispersive optical fiber,” Phys. Rev. Lett. 79, 4139–4142 (1997).
[CrossRef]

Kivshar, Yuri S.

Kestutis Staliunas, Oleg Egorov, Yuri S. Kivshar, Falk Lederer, “Bloch Cavity Solitons in Nonlinear Resonators with Intracavity Photonic Crystals,” Phys. Rev. Lett. 101, 153903–153906 (2008).
[CrossRef] [PubMed]

Kockaert, 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,” Nature Photon. 4, 471–476 (2010).
[CrossRef]

L. Gelens, G. Van der Sande, P. Tassin, M. Tlidi, P. Kockaert, D. Gomila, I. Veretennicoff, J. Danckaert, “Impact of nonlocal interactions in dissipative systems: Towards minimal-sized localized structures,” Phys. Rev. A 75, 063812 (2007).
[CrossRef]

P. Kockaert, P. Tassin, G. Van der Sande, I. Veretennicoff, M. Tlidi, “Negative diffraction pattern dynamics in nonlinear cavities with left-handed materials,” Phys. Rev. A 74, 033822 (2006).
[CrossRef]

P. Tassin, G. Van der Sande, N. Veretenov, P. Kockaert, I. Veretennicoff, M. Tlidi, “Three-dimensional structures in nonlinear cavities containing left-handed materials”, Optics Express, 14, 9338–9343 (2006).
[CrossRef] [PubMed]

Kolokolnikov, T.

M. Tlidi, M. Taki, T. Kolokolnikov, “Introduction: Dissipative localized structures in extended systems”, Chaos 17, 037101 (2007).
[CrossRef] [PubMed]

Langer, J.S.

G.T. Dee, J.S. Langer, “Propagating pattern selection,” Phys. Rev. Lett. 50, 383–386 (1983).
[CrossRef]

Le Berre, M.

M. Tlidi, Paul Mandel, M. Le Berre, E. Ressayre, A. Tallet, L. Di Menza, “Phase-separation dynamics of circular domain walls in the degenerate optical parametric oscillator,” Optics Lett. 25, 487–489 (2000).
[CrossRef]

Lederer, F.

Lederer, Falk

Kestutis Staliunas, Oleg Egorov, Yuri S. Kivshar, Falk Lederer, “Bloch Cavity Solitons in Nonlinear Resonators with Intracavity Photonic Crystals,” Phys. Rev. Lett. 101, 153903–153906 (2008).
[CrossRef] [PubMed]

Lefever, R.

M. Tlidi, P. Mandel, R. Lefever, “Kinetics of localized pattern formation in optical systems,” Phys. Rev. Lett. 81, 979–982 (1998).
[CrossRef]

M. Tlidi, R. Lefever, P. Mandel, “Pattern selection in optical bistability,” Quantum Semiclass. Opt. 8931–938 (1996).
[CrossRef]

M. Tlidi, P. Mandel, R. Lefever, “Localized structures and localized patterns in optical bistability,” Phys. Rev. Lett. 73, 640–643 (1994).
[CrossRef] [PubMed]

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 and Fractals 4, 1323–1354 (1994).
[CrossRef]

L.A. Lugiato, R. Lefever, “Spatial Dissipative Structures in Passive Optical Systems,” Phys. Rev. Lett. 58, 2209–2211 (1987).
[CrossRef] [PubMed]

Leo, F.

F. Leo, L. Gelens, P. Emplit, M. Haelterman, S. Coen, “Dynamics of one-dimensional Kerr cavity solitons,” Opt. Express 21, 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,” Nature Photon. 4, 471–476 (2010).
[CrossRef]

Louvergneaux, E.

V. Odent, M. Taki, E. Louvergneaux, “Experimental evidence of dissipative spatial solitons in an optical passive Kerr cavity,” New J. Phys. 13, 113026 (2011).
[CrossRef]

A. Mussot, E. Louvergneaux, N. Akhmediev, F. Reynaud, L. Delage, M. Taki, “Optical fiber systems are convectively unstable”, Phys. Rev. Lett. 101, 113904–113907 (2008).
[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 and Fractals 4, 1323–1354 (1994).
[CrossRef]

Lugiato, L.A.

L.A. Lugiato, R. Lefever, “Spatial Dissipative Structures in Passive Optical Systems,” Phys. Rev. Lett. 58, 2209–2211 (1987).
[CrossRef] [PubMed]

Maggipinto, T.

M. Brambilla, T. Maggipinto, G. Patera, L. Columbo, “Cavity light bullets: Three-dimensional localized structures in a nonlinear optical resonator,” Phys. Rev. Lett. 93, 203901 (2004).
[CrossRef] [PubMed]

Mandel, P.

M. Tlidi, P. Mandel, R. Lefever, “Kinetics of localized pattern formation in optical systems,” Phys. Rev. Lett. 81, 979–982 (1998).
[CrossRef]

M. Tlidi, M. Haelterman, P. Mandel, “3D patterns and pattern selection in optical bistability,” Europhys. Lett. 42, 505–509 (1998).
[CrossRef]

M. Tlidi, R. Lefever, P. Mandel, “Pattern selection in optical bistability,” Quantum Semiclass. Opt. 8931–938 (1996).
[CrossRef]

M. Tlidi, P. Mandel, R. Lefever, “Localized structures and localized patterns in optical bistability,” Phys. Rev. Lett. 73, 640–643 (1994).
[CrossRef] [PubMed]

Mandel, Paul

M. Tlidi, Paul Mandel, M. Le Berre, E. Ressayre, A. Tallet, L. Di Menza, “Phase-separation dynamics of circular domain walls in the degenerate optical parametric oscillator,” Optics Lett. 25, 487–489 (2000).
[CrossRef]

Matias, M. A.

D. Gomila, M. A. Matias, P. Colet, “Excitability mediated by localized structures in a dissipative nonlinear optical cavity,” Phys. Rev. Lett. 94, 063905 (2005).
[CrossRef] [PubMed]

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 and Fractals 4, 1323–1354 (1994).
[CrossRef]

Mitschke, F.

M. Stratmann, T. Pagel, F. Mitschke, “Experimental observation of temporal soliton molecules,” Phys. Rev. Lett. 95, 143902 (2005).
[CrossRef] [PubMed]

F. Mitschke, G. Steinmeyer, A. Schwache, “Generation of one-dimensional optical turbulence,” Physica D 96, 251–258 (1996).
[CrossRef]

Mussot, A.

A. Mussot, E. Louvergneaux, N. Akhmediev, F. Reynaud, L. Delage, M. Taki, “Optical fiber systems are convectively unstable”, Phys. Rev. Lett. 101, 113904–113907 (2008).
[CrossRef] [PubMed]

Odent, V.

V. Odent, M. Taki, E. Louvergneaux, “Experimental evidence of dissipative spatial solitons in an optical passive Kerr cavity,” New J. Phys. 13, 113026 (2011).
[CrossRef]

Ouarzazi, M. N.

H. Ward, M. N. Ouarzazi, M. Taki, P. Glorieux, “Influence of walkoff on pattern formation in nondegenerate optical parametric oscillators,” Phys. Rev. E 63, 016604 (2000).
[CrossRef]

M. Taki, M. N. Ouarzazi, H. Ward, P. Glorieux, “Nonlinear front propagation in optical parametric oscillators,” J. Opt. Soc. Am. B 17, 997–1003 (2000).
[CrossRef]

Pagel, T.

M. Stratmann, T. Pagel, F. Mitschke, “Experimental observation of temporal soliton molecules,” Phys. Rev. Lett. 95, 143902 (2005).
[CrossRef] [PubMed]

Patera, G.

M. Brambilla, T. Maggipinto, G. Patera, L. Columbo, “Cavity light bullets: Three-dimensional localized structures in a nonlinear optical resonator,” Phys. Rev. Lett. 93, 203901 (2004).
[CrossRef] [PubMed]

Residori, S.

O. Descalzi, M.G. Clerc, S. Residori, G. Assanto, Localized States in Physics: Solitons and Patterns (Springer, 2010).

Ressayre, E.

M. Tlidi, Paul Mandel, M. Le Berre, E. Ressayre, A. Tallet, L. Di Menza, “Phase-separation dynamics of circular domain walls in the degenerate optical parametric oscillator,” Optics Lett. 25, 487–489 (2000).
[CrossRef]

Reynaud, F.

A. Mussot, E. Louvergneaux, N. Akhmediev, F. Reynaud, L. Delage, M. Taki, “Optical fiber systems are convectively unstable”, Phys. Rev. Lett. 101, 113904–113907 (2008).
[CrossRef] [PubMed]

San Miguel, M.

M. Santagiustina, P. Colet, M. San Miguel, D. Walgraef, “Noise-sustained convective structures in nonlinear optics,” Phys. Rev. Lett. 79, 3633–3636 (1997).
[CrossRef]

Sanchez-Morcillo, V.J.

K. Staliunas, V.J. Sanchez-Morcillo, “Dynamics of phase domains in the Swift-Hohenberg equation,” Phys. Lett. A 24128–34 (1998).
[CrossRef]

K. Staliunas, V.J. Sanchez-Morcillo, “Transverse Patterns in Nonlinear Optical Resonators” Springer Verlag, Springer Tracts in Modern Physics, 2003, Vol. 183.

Santagiustina, M.

M. Santagiustina, P. Colet, M. San Miguel, D. Walgraef, “Noise-sustained convective structures in nonlinear optics,” Phys. Rev. Lett. 79, 3633–3636 (1997).
[CrossRef]

Schwache, A.

F. Mitschke, G. Steinmeyer, A. Schwache, “Generation of one-dimensional optical turbulence,” Physica D 96, 251–258 (1996).
[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 and Fractals 4, 1323–1354 (1994).
[CrossRef]

Slekys, G.

G. Slekys, K. Staliunas, C.O. Weiss, “Spatial localized structures in resonators with saturable absorber,” Opt. Commun. 149, 113–116 (1998).
[CrossRef]

Staliunas, K.

G. Slekys, K. Staliunas, C.O. Weiss, “Spatial localized structures in resonators with saturable absorber,” Opt. Commun. 149, 113–116 (1998).
[CrossRef]

V. B. Taranenko, K. Staliunas, C.O. Weiss, “Pattern formation and localized structures in degenerate optical parametric mixing”, Phys. Rev. Lett. 812236–2239 (1998).
[CrossRef]

K. Staliunas, V.J. Sanchez-Morcillo, “Dynamics of phase domains in the Swift-Hohenberg equation,” Phys. Lett. A 24128–34 (1998).
[CrossRef]

K. Staliunas, “Three-Dimensional Turing Structures and Spatial Solitons in Optical Parametric Oscillators,” Phys. Rev. Lett. 81, 81–85 (1998).
[CrossRef]

V.B. Taranenko, K. Staliunas, C. O. Weiss, “Spatial soliton laser: Localized structures in a laser with a saturable absorber in a self-imaging resonator,” Phys. Rev. A 56, 1582–1591 (1997).
[CrossRef]

K. Staliunas, V.J. Sanchez-Morcillo, “Transverse Patterns in Nonlinear Optical Resonators” Springer Verlag, Springer Tracts in Modern Physics, 2003, Vol. 183.

Staliunas, Kestutis

Kestutis Staliunas, Oleg Egorov, Yuri S. Kivshar, Falk Lederer, “Bloch Cavity Solitons in Nonlinear Resonators with Intracavity Photonic Crystals,” Phys. Rev. Lett. 101, 153903–153906 (2008).
[CrossRef] [PubMed]

Steinmeyer, G.

F. Mitschke, G. Steinmeyer, A. Schwache, “Generation of one-dimensional optical turbulence,” Physica D 96, 251–258 (1996).
[CrossRef]

Stratmann, M.

M. Stratmann, T. Pagel, F. Mitschke, “Experimental observation of temporal soliton molecules,” Phys. Rev. Lett. 95, 143902 (2005).
[CrossRef] [PubMed]

Taki, M.

V. Odent, M. Taki, E. Louvergneaux, “Experimental evidence of dissipative spatial solitons in an optical passive Kerr cavity,” New J. Phys. 13, 113026 (2011).
[CrossRef]

A. Mussot, E. Louvergneaux, N. Akhmediev, F. Reynaud, L. Delage, M. Taki, “Optical fiber systems are convectively unstable”, Phys. Rev. Lett. 101, 113904–113907 (2008).
[CrossRef] [PubMed]

S. Coulibaly, C. Durniak, M. Taki, “Spatial Dissipative Solitons Under Convective and Absolute Instabilities in Optical Parametric Oscillators,” Lecture Notes in Physics, 751, 261–285 (2008).
[CrossRef]

M. Tlidi, M. Taki, T. Kolokolnikov, “Introduction: Dissipative localized structures in extended systems”, Chaos 17, 037101 (2007).
[CrossRef] [PubMed]

M. Taki, M. N. Ouarzazi, H. Ward, P. Glorieux, “Nonlinear front propagation in optical parametric oscillators,” J. Opt. Soc. Am. B 17, 997–1003 (2000).
[CrossRef]

H. Ward, M. N. Ouarzazi, M. Taki, P. Glorieux, “Influence of walkoff on pattern formation in nondegenerate optical parametric oscillators,” Phys. Rev. E 63, 016604 (2000).
[CrossRef]

Tallet, A.

M. Tlidi, Paul Mandel, M. Le Berre, E. Ressayre, A. Tallet, L. Di Menza, “Phase-separation dynamics of circular domain walls in the degenerate optical parametric oscillator,” Optics Lett. 25, 487–489 (2000).
[CrossRef]

Taranenko, V. B.

V. B. Taranenko, K. Staliunas, C.O. Weiss, “Pattern formation and localized structures in degenerate optical parametric mixing”, Phys. Rev. Lett. 812236–2239 (1998).
[CrossRef]

Taranenko, V.B.

V.B. Taranenko, K. Staliunas, C. O. Weiss, “Spatial soliton laser: Localized structures in a laser with a saturable absorber in a self-imaging resonator,” Phys. Rev. A 56, 1582–1591 (1997).
[CrossRef]

Tassin, P.

L. Gelens, G. Van der Sande, P. Tassin, M. Tlidi, P. Kockaert, D. Gomila, I. Veretennicoff, J. Danckaert, “Impact of nonlocal interactions in dissipative systems: Towards minimal-sized localized structures,” Phys. Rev. A 75, 063812 (2007).
[CrossRef]

P. Kockaert, P. Tassin, G. Van der Sande, I. Veretennicoff, M. Tlidi, “Negative diffraction pattern dynamics in nonlinear cavities with left-handed materials,” Phys. Rev. A 74, 033822 (2006).
[CrossRef]

P. Tassin, G. Van der Sande, N. Veretenov, P. Kockaert, I. Veretennicoff, M. Tlidi, “Three-dimensional structures in nonlinear cavities containing left-handed materials”, Optics Express, 14, 9338–9343 (2006).
[CrossRef] [PubMed]

Tlidi, M.

M. Tlidi, M. Taki, T. Kolokolnikov, “Introduction: Dissipative localized structures in extended systems”, Chaos 17, 037101 (2007).
[CrossRef] [PubMed]

L. Gelens, G. Van der Sande, P. Tassin, M. Tlidi, P. Kockaert, D. Gomila, I. Veretennicoff, J. Danckaert, “Impact of nonlocal interactions in dissipative systems: Towards minimal-sized localized structures,” Phys. Rev. A 75, 063812 (2007).
[CrossRef]

P. Kockaert, P. Tassin, G. Van der Sande, I. Veretennicoff, M. Tlidi, “Negative diffraction pattern dynamics in nonlinear cavities with left-handed materials,” Phys. Rev. A 74, 033822 (2006).
[CrossRef]

P. Tassin, G. Van der Sande, N. Veretenov, P. Kockaert, I. Veretennicoff, M. Tlidi, “Three-dimensional structures in nonlinear cavities containing left-handed materials”, Optics Express, 14, 9338–9343 (2006).
[CrossRef] [PubMed]

M. Tlidi, “Three-dimensional crystals and localized structures in diffractive and dispersive nonlinear ring cavities,” J. Opt. B: Quantum Semiclass. Opt. 2, 438–442 (2000).
[CrossRef]

M. Tlidi, Paul Mandel, M. Le Berre, E. Ressayre, A. Tallet, L. Di Menza, “Phase-separation dynamics of circular domain walls in the degenerate optical parametric oscillator,” Optics Lett. 25, 487–489 (2000).
[CrossRef]

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

M. Tlidi, M. Haelterman, P. Mandel, “3D patterns and pattern selection in optical bistability,” Europhys. Lett. 42, 505–509 (1998).
[CrossRef]

M. Tlidi, P. Mandel, R. Lefever, “Kinetics of localized pattern formation in optical systems,” Phys. Rev. Lett. 81, 979–982 (1998).
[CrossRef]

M. Tlidi, R. Lefever, P. Mandel, “Pattern selection in optical bistability,” Quantum Semiclass. Opt. 8931–938 (1996).
[CrossRef]

M. Tlidi, P. Mandel, R. Lefever, “Localized structures and localized patterns in optical bistability,” Phys. Rev. Lett. 73, 640–643 (1994).
[CrossRef] [PubMed]

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 and Fractals 4, 1323–1354 (1994).
[CrossRef]

Turaev, D.

D. Turaev, A. G. Vladimirov, S. Zelik, “Long-range interaction and synchronization of oscillating dissipative solitons”, Phys. Rev. Lett. 108, 263906–263909 (2012).
[CrossRef] [PubMed]

Van der Sande, G.

L. Gelens, G. Van der Sande, P. Tassin, M. Tlidi, P. Kockaert, D. Gomila, I. Veretennicoff, J. Danckaert, “Impact of nonlocal interactions in dissipative systems: Towards minimal-sized localized structures,” Phys. Rev. A 75, 063812 (2007).
[CrossRef]

P. Kockaert, P. Tassin, G. Van der Sande, I. Veretennicoff, M. Tlidi, “Negative diffraction pattern dynamics in nonlinear cavities with left-handed materials,” Phys. Rev. A 74, 033822 (2006).
[CrossRef]

P. Tassin, G. Van der Sande, N. Veretenov, P. Kockaert, I. Veretennicoff, M. Tlidi, “Three-dimensional structures in nonlinear cavities containing left-handed materials”, Optics Express, 14, 9338–9343 (2006).
[CrossRef] [PubMed]

van Saarloos, W.

W. van Saarloos, “Front propagation into unstable states,” Phys. Rep. 286, 29–222 (2003).
[CrossRef]

G.T. Dee, W. van Saarloos, “Bistable Systems with Propagating Fronts Leading to Pattern Formation,” Phys. Rev. Lett. 60, 2641–2644 (1988).
[CrossRef] [PubMed]

Veretennicoff, I.

L. Gelens, G. Van der Sande, P. Tassin, M. Tlidi, P. Kockaert, D. Gomila, I. Veretennicoff, J. Danckaert, “Impact of nonlocal interactions in dissipative systems: Towards minimal-sized localized structures,” Phys. Rev. A 75, 063812 (2007).
[CrossRef]

P. Kockaert, P. Tassin, G. Van der Sande, I. Veretennicoff, M. Tlidi, “Negative diffraction pattern dynamics in nonlinear cavities with left-handed materials,” Phys. Rev. A 74, 033822 (2006).
[CrossRef]

P. Tassin, G. Van der Sande, N. Veretenov, P. Kockaert, I. Veretennicoff, M. Tlidi, “Three-dimensional structures in nonlinear cavities containing left-handed materials”, Optics Express, 14, 9338–9343 (2006).
[CrossRef] [PubMed]

Veretenov, N.

P. Tassin, G. Van der Sande, N. Veretenov, P. Kockaert, I. Veretennicoff, M. Tlidi, “Three-dimensional structures in nonlinear cavities containing left-handed materials”, Optics Express, 14, 9338–9343 (2006).
[CrossRef] [PubMed]

Vladimirov, A. G.

D. Turaev, A. G. Vladimirov, S. Zelik, “Long-range interaction and synchronization of oscillating dissipative solitons”, Phys. Rev. Lett. 108, 263906–263909 (2012).
[CrossRef] [PubMed]

Walgraef, D.

M. Santagiustina, P. Colet, M. San Miguel, D. Walgraef, “Noise-sustained convective structures in nonlinear optics,” Phys. Rev. Lett. 79, 3633–3636 (1997).
[CrossRef]

Ward, H.

H. Ward, M. N. Ouarzazi, M. Taki, P. Glorieux, “Influence of walkoff on pattern formation in nondegenerate optical parametric oscillators,” Phys. Rev. E 63, 016604 (2000).
[CrossRef]

M. Taki, M. N. Ouarzazi, H. Ward, P. Glorieux, “Nonlinear front propagation in optical parametric oscillators,” J. Opt. Soc. Am. B 17, 997–1003 (2000).
[CrossRef]

Weiss, C. O.

V.B. Taranenko, K. Staliunas, C. O. Weiss, “Spatial soliton laser: Localized structures in a laser with a saturable absorber in a self-imaging resonator,” Phys. Rev. A 56, 1582–1591 (1997).
[CrossRef]

Weiss, C.O.

V. B. Taranenko, K. Staliunas, C.O. Weiss, “Pattern formation and localized structures in degenerate optical parametric mixing”, Phys. Rev. Lett. 812236–2239 (1998).
[CrossRef]

G. Slekys, K. Staliunas, C.O. Weiss, “Spatial localized structures in resonators with saturable absorber,” Opt. Commun. 149, 113–116 (1998).
[CrossRef]

Zelik, S.

D. Turaev, A. G. Vladimirov, S. Zelik, “Long-range interaction and synchronization of oscillating dissipative solitons”, Phys. Rev. Lett. 108, 263906–263909 (2012).
[CrossRef] [PubMed]

Chaos (1)

M. Tlidi, M. Taki, T. Kolokolnikov, “Introduction: Dissipative localized structures in extended systems”, Chaos 17, 037101 (2007).
[CrossRef] [PubMed]

Chaos, Solitons and 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 and Fractals 4, 1323–1354 (1994).
[CrossRef]

Europhys. Lett. (1)

M. Tlidi, M. Haelterman, P. Mandel, “3D patterns and pattern selection in optical bistability,” Europhys. Lett. 42, 505–509 (1998).
[CrossRef]

J. Opt. B: Quantum Semiclass. Opt. (1)

M. Tlidi, “Three-dimensional crystals and localized structures in diffractive and dispersive nonlinear ring cavities,” J. Opt. B: Quantum Semiclass. Opt. 2, 438–442 (2000).
[CrossRef]

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

Lecture Notes in Physics (1)

S. Coulibaly, C. Durniak, M. Taki, “Spatial Dissipative Solitons Under Convective and Absolute Instabilities in Optical Parametric Oscillators,” Lecture Notes in Physics, 751, 261–285 (2008).
[CrossRef]

Nature Photon. (1)

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,” Nature Photon. 4, 471–476 (2010).
[CrossRef]

New J. Phys. (1)

V. Odent, M. Taki, E. Louvergneaux, “Experimental evidence of dissipative spatial solitons in an optical passive Kerr cavity,” New J. Phys. 13, 113026 (2011).
[CrossRef]

Opt. Commun. (1)

G. Slekys, K. Staliunas, C.O. Weiss, “Spatial localized structures in resonators with saturable absorber,” Opt. Commun. 149, 113–116 (1998).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Optics Express (1)

P. Tassin, G. Van der Sande, N. Veretenov, P. Kockaert, I. Veretennicoff, M. Tlidi, “Three-dimensional structures in nonlinear cavities containing left-handed materials”, Optics Express, 14, 9338–9343 (2006).
[CrossRef] [PubMed]

Optics Lett. (1)

M. Tlidi, Paul Mandel, M. Le Berre, E. Ressayre, A. Tallet, L. Di Menza, “Phase-separation dynamics of circular domain walls in the degenerate optical parametric oscillator,” Optics Lett. 25, 487–489 (2000).
[CrossRef]

Phys. Lett. A (1)

K. Staliunas, V.J. Sanchez-Morcillo, “Dynamics of phase domains in the Swift-Hohenberg equation,” Phys. Lett. A 24128–34 (1998).
[CrossRef]

Phys. Rep. (1)

W. van Saarloos, “Front propagation into unstable states,” Phys. Rep. 286, 29–222 (2003).
[CrossRef]

Phys. Rev. A (3)

V.B. Taranenko, K. Staliunas, C. O. Weiss, “Spatial soliton laser: Localized structures in a laser with a saturable absorber in a self-imaging resonator,” Phys. Rev. A 56, 1582–1591 (1997).
[CrossRef]

P. Kockaert, P. Tassin, G. Van der Sande, I. Veretennicoff, M. Tlidi, “Negative diffraction pattern dynamics in nonlinear cavities with left-handed materials,” Phys. Rev. A 74, 033822 (2006).
[CrossRef]

L. Gelens, G. Van der Sande, P. Tassin, M. Tlidi, P. Kockaert, D. Gomila, I. Veretennicoff, J. Danckaert, “Impact of nonlocal interactions in dissipative systems: Towards minimal-sized localized structures,” Phys. Rev. A 75, 063812 (2007).
[CrossRef]

Phys. Rev. E (1)

H. Ward, M. N. Ouarzazi, M. Taki, P. Glorieux, “Influence of walkoff on pattern formation in nondegenerate optical parametric oscillators,” Phys. Rev. E 63, 016604 (2000).
[CrossRef]

Phys. Rev. Lett. (16)

D. Gomila, M. A. Matias, P. Colet, “Excitability mediated by localized structures in a dissipative nonlinear optical cavity,” Phys. Rev. Lett. 94, 063905 (2005).
[CrossRef] [PubMed]

D. Turaev, A. G. Vladimirov, S. Zelik, “Long-range interaction and synchronization of oscillating dissipative solitons”, Phys. Rev. Lett. 108, 263906–263909 (2012).
[CrossRef] [PubMed]

A. Mussot, E. Louvergneaux, N. Akhmediev, F. Reynaud, L. Delage, M. Taki, “Optical fiber systems are convectively unstable”, Phys. Rev. Lett. 101, 113904–113907 (2008).
[CrossRef] [PubMed]

Kestutis Staliunas, Oleg Egorov, Yuri S. Kivshar, Falk Lederer, “Bloch Cavity Solitons in Nonlinear Resonators with Intracavity Photonic Crystals,” Phys. Rev. Lett. 101, 153903–153906 (2008).
[CrossRef] [PubMed]

M. Tlidi, P. Mandel, R. Lefever, “Kinetics of localized pattern formation in optical systems,” Phys. Rev. Lett. 81, 979–982 (1998).
[CrossRef]

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

V. B. Taranenko, K. Staliunas, C.O. Weiss, “Pattern formation and localized structures in degenerate optical parametric mixing”, Phys. Rev. Lett. 812236–2239 (1998).
[CrossRef]

G.T. Dee, J.S. Langer, “Propagating pattern selection,” Phys. Rev. Lett. 50, 383–386 (1983).
[CrossRef]

G.T. Dee, W. van Saarloos, “Bistable Systems with Propagating Fronts Leading to Pattern Formation,” Phys. Rev. Lett. 60, 2641–2644 (1988).
[CrossRef] [PubMed]

M. Tlidi, P. Mandel, R. Lefever, “Localized structures and localized patterns in optical bistability,” Phys. Rev. Lett. 73, 640–643 (1994).
[CrossRef] [PubMed]

M. Brambilla, T. Maggipinto, G. Patera, L. Columbo, “Cavity light bullets: Three-dimensional localized structures in a nonlinear optical resonator,” Phys. Rev. Lett. 93, 203901 (2004).
[CrossRef] [PubMed]

K. Staliunas, “Three-Dimensional Turing Structures and Spatial Solitons in Optical Parametric Oscillators,” Phys. Rev. Lett. 81, 81–85 (1998).
[CrossRef]

L.A. Lugiato, R. Lefever, “Spatial Dissipative Structures in Passive Optical Systems,” Phys. Rev. Lett. 58, 2209–2211 (1987).
[CrossRef] [PubMed]

S. Coen, M. Haelterman, “Modulational instability induced by cavity boundary conditions in a normally dispersive optical fiber,” Phys. Rev. Lett. 79, 4139–4142 (1997).
[CrossRef]

M. Stratmann, T. Pagel, F. Mitschke, “Experimental observation of temporal soliton molecules,” Phys. Rev. Lett. 95, 143902 (2005).
[CrossRef] [PubMed]

M. Santagiustina, P. Colet, M. San Miguel, D. Walgraef, “Noise-sustained convective structures in nonlinear optics,” Phys. Rev. Lett. 79, 3633–3636 (1997).
[CrossRef]

Physica D (1)

F. Mitschke, G. Steinmeyer, A. Schwache, “Generation of one-dimensional optical turbulence,” Physica D 96, 251–258 (1996).
[CrossRef]

Quantum Semiclass. Opt. (1)

M. Tlidi, R. Lefever, P. Mandel, “Pattern selection in optical bistability,” Quantum Semiclass. Opt. 8931–938 (1996).
[CrossRef]

Other (3)

N. Akhmediev, A. Ankiewicz, eds. Dissipative Solitons: From Optics to Biology and Medicine (Springer-Verlag, Berlin, Heidelberg, 2008).

O. Descalzi, M.G. Clerc, S. Residori, G. Assanto, Localized States in Physics: Solitons and Patterns (Springer, 2010).

K. Staliunas, V.J. Sanchez-Morcillo, “Transverse Patterns in Nonlinear Optical Resonators” Springer Verlag, Springer Tracts in Modern Physics, 2003, Vol. 183.

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Figures (2)

Figure 1
Figure 1

Left panel: lower figure represents tξ map that shows the dynamics of a flat propagating front spreading into an unstable HSS. The black color indicates the intermediate unstable state and the white color represents the stable lower HSS solution. The up figure shows a cross section at a fixed time t as indicated in the figure. Right panel: top figure shows the bistability cycle with the branches connected by the front. The lower figure display the transient evolution of the front before reaching its asymptotic velocity. The parameters are α = 1, S = 1.27, and Δ = 1.78.

Figure 2
Figure 2

(a) Transient velocity as a function of time that approaches for a long time evolution its asymptotic value v* obtained from numerical simulation of Eq. (1). (b) Asymptotic front velocity v* vs the intensity distance to critical point IIc. Dots are measured velocities and solid line reproduces the predicted velocities by Eq. (8). The parameters are the same as in Fig. 1.

Equations (10)

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E ( t , ξ ) t = S + [ 1 i ( Δ | E ( t , ξ ) | 2 ) i α 2 ξ 2 ] E ( t , ξ )
λ = i [ 1 + I 2 ( ( Δ 2 I ) α Ω 2 ) 2 ] .
( λ Ω ) = 0 ,
( λ Ω ) = ( λ ) ( Ω ) and ( λ ) ( Ω ) = v .
λ i 2 [ I 2 1 ( δ α Ω 2 ) 2 ] ,
( λ Ω ) = 2 α Ω i [ δ α ( 3 Ω r 2 + Ω i 2 ) ] ,
v = 2 α Ω i ( δ + α Ω i ± 2 ) with
Ω i ± 2 = 1 3 α [ δ ± 13 I 2 16 Δ I + 4 Δ 2 + 3 ] .
Ω i , 2 = I u α [ 2 Δ 3 I u 2 I u Δ ] ε + O ( ε ε )
v * = ± 2 α ( Δ 2 3 ) 1 / 4 ( 2 I u Δ ) 1 / 2 I I u .

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