Abstract

We study the influence of field diffusion on the spatial localized structures (cavity solitons) in bidirectional lasers. We find threefold positive role of the diffusion: 1) it allows for the existence of solitons in cavities with equal losses for the two fields; 2) it increases the stability range of the individual (isolated) solitons; and 3) it reduces the long-range interaction between cavity solitons, allowing for the independent manipulation (writing and erasing) of individual structures.

© 2009 Optical Society of America

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  1. M. C. Cross and P. C. Hohenberg, "Pattern Formation Out of Equilibrium," Rev. Mod. Phys. 65, 851-1112 (1993).
    [CrossRef]
  2. M. Tlidi, M. Taki, and Th. Kolokolnikov eds., Focus Issue: Dissipative Localized structures in extended systems, Chaos 17, Issue 3 (2007).
  3. P. Mandel and M. Tlidi, "Transverse dynamics in cavity nonlinear optics" (2000-2003),J. Opt. B: Quantum and Semiclass. Opt. 6, R60-R75 (2004).
    [CrossRef]
  4. K. Staliunas and V.J. Sánchez-Morcillo, Transverse Patterns in Nonlinear Optical Resonators, (Springer, Berlín, 2003)
  5. W .J. Firth and C. O. Weiss, "Cavity and feedback solitons," Opt. Photonic News 13, Issue 2, 54-58 (2002).
    [CrossRef]
  6. I. Pérez-Arjona, V. J. Sánchez-Morcillo, and E. Roldán, "Bidirectional ring laser cavity solitons," Opt. Lett. 32, 3221-3223 (2007).
    [CrossRef] [PubMed]
  7. G. Slekys, K. Staliunas, and C. O. Weiss, "Spatial localized structures in resonators with saturable absorber," Opt. Commun. 149, 113-116 (1998).
    [CrossRef]
  8. A. M. Dunlop, E. M. Wright, and W. J. Firth, "Spatial solitons laser," Opt. Commun. 147, 393-401 (1998).
    [CrossRef]
  9. X. Hachair, F. Pedaci, E. Caboche, S. Barland, M. Giudici, J. R. Tredicce, F. Prati, G. Tissoni, R. Kheradmand, L. A. Lugiato, I. Protsenko, and M. Brambilla, "Cavity solitons in a driven VCSEL above threshold," IEEE J. Sel. Top. Quantum Electron. 12, 339-351 (2006).
    [CrossRef]
  10. G. J. de Valcárcel and K. Staliunas, "Excitation of phase patterns and spatial solitons via two-frequency forcing of a 1:1 resonance," Phys. Rev. E 67, 026604 (2003).
    [CrossRef]
  11. A. Esteban-Martín, M. Martínez-Quesada, V. B. Taranenko, E. Roldán, and G. J. de Valcárcel, "Bistable Phase Locking of a Nonlinear Optical Cavity via Rocking: Transmuting Vortices into Phase Patterns," Phys. Rev. Lett. 97, 093903 (2006).
    [CrossRef] [PubMed]
  12. P. V. Paulau, A. J. Scroggie, A. Naumenko, T. Ackemann, N. A. Loiko, and W. J. Firth, "Localized traveling waves in vertical-cavity surface-emitting lasers with frequency-selective optical feedback," Phys. Rev. E 75, 056208 (2007).
    [CrossRef]
  13. H. Zeghlache, P. Mandel, N. B. Abraham, L. M. Hoffer, G. L. Lippi, and T. Mello, "Bidirectional ring laser: Stability analysis and time-dependent solutions," Phys. Rev. A 37, 470-497 (1988).
    [CrossRef] [PubMed]
  14. L. Columbo, L. Gil, and J. Tredicce, "Could cavity solitons exist in bidirectional ring lasers?" Opt. Lett. 33, 995-997 (2008).
    [CrossRef] [PubMed]
  15. M. Piché and P. Belánger, "On the loses of the counter-propagating modes of ring cavities," IEEE Journ. Quantm Electron. QE- 20, 1303-1307 (2008).
  16. A. M. Dunlop, W. J. Firth, and E. M. Wright, Opt. Commun. 138, 211 (1997).
    [CrossRef]
  17. M. San Miguel, "Phase instabilities in the Laser Vector Complex Ginzburg-Landau equation," Phys. Rev. Lett. 75, 425-428 (1995).
    [CrossRef] [PubMed]
  18. J. García-Ojalvo, R. Vilaseca, and M. C. Torrent, "Coupled pattern formation near threshold in a broad-area cascade laser," Phys. Rev. A 56, 5111-5120 (1997).
    [CrossRef]
  19. X. Hachair, G. Tissoni, H. Thienpont, and K. Panajotov, "Linearly polarized bistable localized structure in medium-size vertical-cavity surface-emitting lasers," Phys. Rev. A 79, 011801(R) (2009).
    [CrossRef]
  20. W. van Saarloos and P. C. Hohenberg, "Fronts, pulses, sources and sinks in generalized complex Ginzburg-Landau equations," Physica D 56, 306-367 (1992).
    [CrossRef]
  21. P. Coullet, T. Frisch and F. Plaza, "Sources and sinks of wave patterns," Physica D 62, 75-79 (1993).
    [CrossRef]

2008 (2)

M. Piché and P. Belánger, "On the loses of the counter-propagating modes of ring cavities," IEEE Journ. Quantm Electron. QE- 20, 1303-1307 (2008).

L. Columbo, L. Gil, and J. Tredicce, "Could cavity solitons exist in bidirectional ring lasers?" Opt. Lett. 33, 995-997 (2008).
[CrossRef] [PubMed]

2007 (2)

I. Pérez-Arjona, V. J. Sánchez-Morcillo, and E. Roldán, "Bidirectional ring laser cavity solitons," Opt. Lett. 32, 3221-3223 (2007).
[CrossRef] [PubMed]

P. V. Paulau, A. J. Scroggie, A. Naumenko, T. Ackemann, N. A. Loiko, and W. J. Firth, "Localized traveling waves in vertical-cavity surface-emitting lasers with frequency-selective optical feedback," Phys. Rev. E 75, 056208 (2007).
[CrossRef]

2006 (2)

X. Hachair, F. Pedaci, E. Caboche, S. Barland, M. Giudici, J. R. Tredicce, F. Prati, G. Tissoni, R. Kheradmand, L. A. Lugiato, I. Protsenko, and M. Brambilla, "Cavity solitons in a driven VCSEL above threshold," IEEE J. Sel. Top. Quantum Electron. 12, 339-351 (2006).
[CrossRef]

A. Esteban-Martín, M. Martínez-Quesada, V. B. Taranenko, E. Roldán, and G. J. de Valcárcel, "Bistable Phase Locking of a Nonlinear Optical Cavity via Rocking: Transmuting Vortices into Phase Patterns," Phys. Rev. Lett. 97, 093903 (2006).
[CrossRef] [PubMed]

2004 (1)

P. Mandel and M. Tlidi, "Transverse dynamics in cavity nonlinear optics" (2000-2003),J. Opt. B: Quantum and Semiclass. Opt. 6, R60-R75 (2004).
[CrossRef]

2003 (1)

G. J. de Valcárcel and K. Staliunas, "Excitation of phase patterns and spatial solitons via two-frequency forcing of a 1:1 resonance," Phys. Rev. E 67, 026604 (2003).
[CrossRef]

1998 (2)

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

A. M. Dunlop, E. M. Wright, and W. J. Firth, "Spatial solitons laser," Opt. Commun. 147, 393-401 (1998).
[CrossRef]

1997 (2)

A. M. Dunlop, W. J. Firth, and E. M. Wright, Opt. Commun. 138, 211 (1997).
[CrossRef]

J. García-Ojalvo, R. Vilaseca, and M. C. Torrent, "Coupled pattern formation near threshold in a broad-area cascade laser," Phys. Rev. A 56, 5111-5120 (1997).
[CrossRef]

1995 (1)

M. San Miguel, "Phase instabilities in the Laser Vector Complex Ginzburg-Landau equation," Phys. Rev. Lett. 75, 425-428 (1995).
[CrossRef] [PubMed]

1993 (2)

P. Coullet, T. Frisch and F. Plaza, "Sources and sinks of wave patterns," Physica D 62, 75-79 (1993).
[CrossRef]

M. C. Cross and P. C. Hohenberg, "Pattern Formation Out of Equilibrium," Rev. Mod. Phys. 65, 851-1112 (1993).
[CrossRef]

1992 (1)

W. van Saarloos and P. C. Hohenberg, "Fronts, pulses, sources and sinks in generalized complex Ginzburg-Landau equations," Physica D 56, 306-367 (1992).
[CrossRef]

1988 (1)

H. Zeghlache, P. Mandel, N. B. Abraham, L. M. Hoffer, G. L. Lippi, and T. Mello, "Bidirectional ring laser: Stability analysis and time-dependent solutions," Phys. Rev. A 37, 470-497 (1988).
[CrossRef] [PubMed]

Abraham, N. B.

H. Zeghlache, P. Mandel, N. B. Abraham, L. M. Hoffer, G. L. Lippi, and T. Mello, "Bidirectional ring laser: Stability analysis and time-dependent solutions," Phys. Rev. A 37, 470-497 (1988).
[CrossRef] [PubMed]

Ackemann, T.

P. V. Paulau, A. J. Scroggie, A. Naumenko, T. Ackemann, N. A. Loiko, and W. J. Firth, "Localized traveling waves in vertical-cavity surface-emitting lasers with frequency-selective optical feedback," Phys. Rev. E 75, 056208 (2007).
[CrossRef]

Barland, S.

X. Hachair, F. Pedaci, E. Caboche, S. Barland, M. Giudici, J. R. Tredicce, F. Prati, G. Tissoni, R. Kheradmand, L. A. Lugiato, I. Protsenko, and M. Brambilla, "Cavity solitons in a driven VCSEL above threshold," IEEE J. Sel. Top. Quantum Electron. 12, 339-351 (2006).
[CrossRef]

Belánger, P.

M. Piché and P. Belánger, "On the loses of the counter-propagating modes of ring cavities," IEEE Journ. Quantm Electron. QE- 20, 1303-1307 (2008).

Brambilla, M.

X. Hachair, F. Pedaci, E. Caboche, S. Barland, M. Giudici, J. R. Tredicce, F. Prati, G. Tissoni, R. Kheradmand, L. A. Lugiato, I. Protsenko, and M. Brambilla, "Cavity solitons in a driven VCSEL above threshold," IEEE J. Sel. Top. Quantum Electron. 12, 339-351 (2006).
[CrossRef]

Caboche, E.

X. Hachair, F. Pedaci, E. Caboche, S. Barland, M. Giudici, J. R. Tredicce, F. Prati, G. Tissoni, R. Kheradmand, L. A. Lugiato, I. Protsenko, and M. Brambilla, "Cavity solitons in a driven VCSEL above threshold," IEEE J. Sel. Top. Quantum Electron. 12, 339-351 (2006).
[CrossRef]

Columbo, L.

Coullet, P.

P. Coullet, T. Frisch and F. Plaza, "Sources and sinks of wave patterns," Physica D 62, 75-79 (1993).
[CrossRef]

Cross, M. C.

M. C. Cross and P. C. Hohenberg, "Pattern Formation Out of Equilibrium," Rev. Mod. Phys. 65, 851-1112 (1993).
[CrossRef]

de Valcárcel, G. J.

A. Esteban-Martín, M. Martínez-Quesada, V. B. Taranenko, E. Roldán, and G. J. de Valcárcel, "Bistable Phase Locking of a Nonlinear Optical Cavity via Rocking: Transmuting Vortices into Phase Patterns," Phys. Rev. Lett. 97, 093903 (2006).
[CrossRef] [PubMed]

G. J. de Valcárcel and K. Staliunas, "Excitation of phase patterns and spatial solitons via two-frequency forcing of a 1:1 resonance," Phys. Rev. E 67, 026604 (2003).
[CrossRef]

Dunlop, A. M.

A. M. Dunlop, E. M. Wright, and W. J. Firth, "Spatial solitons laser," Opt. Commun. 147, 393-401 (1998).
[CrossRef]

A. M. Dunlop, W. J. Firth, and E. M. Wright, Opt. Commun. 138, 211 (1997).
[CrossRef]

Esteban-Martín, A.

A. Esteban-Martín, M. Martínez-Quesada, V. B. Taranenko, E. Roldán, and G. J. de Valcárcel, "Bistable Phase Locking of a Nonlinear Optical Cavity via Rocking: Transmuting Vortices into Phase Patterns," Phys. Rev. Lett. 97, 093903 (2006).
[CrossRef] [PubMed]

Firth, W. J.

P. V. Paulau, A. J. Scroggie, A. Naumenko, T. Ackemann, N. A. Loiko, and W. J. Firth, "Localized traveling waves in vertical-cavity surface-emitting lasers with frequency-selective optical feedback," Phys. Rev. E 75, 056208 (2007).
[CrossRef]

A. M. Dunlop, E. M. Wright, and W. J. Firth, "Spatial solitons laser," Opt. Commun. 147, 393-401 (1998).
[CrossRef]

A. M. Dunlop, W. J. Firth, and E. M. Wright, Opt. Commun. 138, 211 (1997).
[CrossRef]

Frisch, T.

P. Coullet, T. Frisch and F. Plaza, "Sources and sinks of wave patterns," Physica D 62, 75-79 (1993).
[CrossRef]

García-Ojalvo, J.

J. García-Ojalvo, R. Vilaseca, and M. C. Torrent, "Coupled pattern formation near threshold in a broad-area cascade laser," Phys. Rev. A 56, 5111-5120 (1997).
[CrossRef]

Gil, L.

Giudici, M.

X. Hachair, F. Pedaci, E. Caboche, S. Barland, M. Giudici, J. R. Tredicce, F. Prati, G. Tissoni, R. Kheradmand, L. A. Lugiato, I. Protsenko, and M. Brambilla, "Cavity solitons in a driven VCSEL above threshold," IEEE J. Sel. Top. Quantum Electron. 12, 339-351 (2006).
[CrossRef]

Hachair, X.

X. Hachair, F. Pedaci, E. Caboche, S. Barland, M. Giudici, J. R. Tredicce, F. Prati, G. Tissoni, R. Kheradmand, L. A. Lugiato, I. Protsenko, and M. Brambilla, "Cavity solitons in a driven VCSEL above threshold," IEEE J. Sel. Top. Quantum Electron. 12, 339-351 (2006).
[CrossRef]

Hoffer, L. M.

H. Zeghlache, P. Mandel, N. B. Abraham, L. M. Hoffer, G. L. Lippi, and T. Mello, "Bidirectional ring laser: Stability analysis and time-dependent solutions," Phys. Rev. A 37, 470-497 (1988).
[CrossRef] [PubMed]

Hohenberg, P. C.

M. C. Cross and P. C. Hohenberg, "Pattern Formation Out of Equilibrium," Rev. Mod. Phys. 65, 851-1112 (1993).
[CrossRef]

Hohenberg, P.C.

W. van Saarloos and P. C. Hohenberg, "Fronts, pulses, sources and sinks in generalized complex Ginzburg-Landau equations," Physica D 56, 306-367 (1992).
[CrossRef]

Kheradmand, R.

X. Hachair, F. Pedaci, E. Caboche, S. Barland, M. Giudici, J. R. Tredicce, F. Prati, G. Tissoni, R. Kheradmand, L. A. Lugiato, I. Protsenko, and M. Brambilla, "Cavity solitons in a driven VCSEL above threshold," IEEE J. Sel. Top. Quantum Electron. 12, 339-351 (2006).
[CrossRef]

Lippi, G. L.

H. Zeghlache, P. Mandel, N. B. Abraham, L. M. Hoffer, G. L. Lippi, and T. Mello, "Bidirectional ring laser: Stability analysis and time-dependent solutions," Phys. Rev. A 37, 470-497 (1988).
[CrossRef] [PubMed]

Loiko, N. A.

P. V. Paulau, A. J. Scroggie, A. Naumenko, T. Ackemann, N. A. Loiko, and W. J. Firth, "Localized traveling waves in vertical-cavity surface-emitting lasers with frequency-selective optical feedback," Phys. Rev. E 75, 056208 (2007).
[CrossRef]

Lugiato, L.A.

X. Hachair, F. Pedaci, E. Caboche, S. Barland, M. Giudici, J. R. Tredicce, F. Prati, G. Tissoni, R. Kheradmand, L. A. Lugiato, I. Protsenko, and M. Brambilla, "Cavity solitons in a driven VCSEL above threshold," IEEE J. Sel. Top. Quantum Electron. 12, 339-351 (2006).
[CrossRef]

Mandel, P.

P. Mandel and M. Tlidi, "Transverse dynamics in cavity nonlinear optics" (2000-2003),J. Opt. B: Quantum and Semiclass. Opt. 6, R60-R75 (2004).
[CrossRef]

H. Zeghlache, P. Mandel, N. B. Abraham, L. M. Hoffer, G. L. Lippi, and T. Mello, "Bidirectional ring laser: Stability analysis and time-dependent solutions," Phys. Rev. A 37, 470-497 (1988).
[CrossRef] [PubMed]

Martínez-Quesada, M.

A. Esteban-Martín, M. Martínez-Quesada, V. B. Taranenko, E. Roldán, and G. J. de Valcárcel, "Bistable Phase Locking of a Nonlinear Optical Cavity via Rocking: Transmuting Vortices into Phase Patterns," Phys. Rev. Lett. 97, 093903 (2006).
[CrossRef] [PubMed]

Mello, T.

H. Zeghlache, P. Mandel, N. B. Abraham, L. M. Hoffer, G. L. Lippi, and T. Mello, "Bidirectional ring laser: Stability analysis and time-dependent solutions," Phys. Rev. A 37, 470-497 (1988).
[CrossRef] [PubMed]

Naumenko, A.

P. V. Paulau, A. J. Scroggie, A. Naumenko, T. Ackemann, N. A. Loiko, and W. J. Firth, "Localized traveling waves in vertical-cavity surface-emitting lasers with frequency-selective optical feedback," Phys. Rev. E 75, 056208 (2007).
[CrossRef]

Paulau, P. V.

P. V. Paulau, A. J. Scroggie, A. Naumenko, T. Ackemann, N. A. Loiko, and W. J. Firth, "Localized traveling waves in vertical-cavity surface-emitting lasers with frequency-selective optical feedback," Phys. Rev. E 75, 056208 (2007).
[CrossRef]

Pedaci, F.

X. Hachair, F. Pedaci, E. Caboche, S. Barland, M. Giudici, J. R. Tredicce, F. Prati, G. Tissoni, R. Kheradmand, L. A. Lugiato, I. Protsenko, and M. Brambilla, "Cavity solitons in a driven VCSEL above threshold," IEEE J. Sel. Top. Quantum Electron. 12, 339-351 (2006).
[CrossRef]

Pérez-Arjona, I.

Piché, M.

M. Piché and P. Belánger, "On the loses of the counter-propagating modes of ring cavities," IEEE Journ. Quantm Electron. QE- 20, 1303-1307 (2008).

Plaza, F.

P. Coullet, T. Frisch and F. Plaza, "Sources and sinks of wave patterns," Physica D 62, 75-79 (1993).
[CrossRef]

Prati, F.

X. Hachair, F. Pedaci, E. Caboche, S. Barland, M. Giudici, J. R. Tredicce, F. Prati, G. Tissoni, R. Kheradmand, L. A. Lugiato, I. Protsenko, and M. Brambilla, "Cavity solitons in a driven VCSEL above threshold," IEEE J. Sel. Top. Quantum Electron. 12, 339-351 (2006).
[CrossRef]

Protsenko, I.

X. Hachair, F. Pedaci, E. Caboche, S. Barland, M. Giudici, J. R. Tredicce, F. Prati, G. Tissoni, R. Kheradmand, L. A. Lugiato, I. Protsenko, and M. Brambilla, "Cavity solitons in a driven VCSEL above threshold," IEEE J. Sel. Top. Quantum Electron. 12, 339-351 (2006).
[CrossRef]

Roldán, E.

I. Pérez-Arjona, V. J. Sánchez-Morcillo, and E. Roldán, "Bidirectional ring laser cavity solitons," Opt. Lett. 32, 3221-3223 (2007).
[CrossRef] [PubMed]

A. Esteban-Martín, M. Martínez-Quesada, V. B. Taranenko, E. Roldán, and G. J. de Valcárcel, "Bistable Phase Locking of a Nonlinear Optical Cavity via Rocking: Transmuting Vortices into Phase Patterns," Phys. Rev. Lett. 97, 093903 (2006).
[CrossRef] [PubMed]

San Miguel, M.

M. San Miguel, "Phase instabilities in the Laser Vector Complex Ginzburg-Landau equation," Phys. Rev. Lett. 75, 425-428 (1995).
[CrossRef] [PubMed]

Sánchez-Morcillo, V. J.

Scroggie, A. J.

P. V. Paulau, A. J. Scroggie, A. Naumenko, T. Ackemann, N. A. Loiko, and W. J. Firth, "Localized traveling waves in vertical-cavity surface-emitting lasers with frequency-selective optical feedback," Phys. Rev. E 75, 056208 (2007).
[CrossRef]

Slekys, G.

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

Staliunas, K.

G. J. de Valcárcel and K. Staliunas, "Excitation of phase patterns and spatial solitons via two-frequency forcing of a 1:1 resonance," Phys. Rev. E 67, 026604 (2003).
[CrossRef]

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

Taranenko, V. B.

A. Esteban-Martín, M. Martínez-Quesada, V. B. Taranenko, E. Roldán, and G. J. de Valcárcel, "Bistable Phase Locking of a Nonlinear Optical Cavity via Rocking: Transmuting Vortices into Phase Patterns," Phys. Rev. Lett. 97, 093903 (2006).
[CrossRef] [PubMed]

Tissoni, G.

X. Hachair, F. Pedaci, E. Caboche, S. Barland, M. Giudici, J. R. Tredicce, F. Prati, G. Tissoni, R. Kheradmand, L. A. Lugiato, I. Protsenko, and M. Brambilla, "Cavity solitons in a driven VCSEL above threshold," IEEE J. Sel. Top. Quantum Electron. 12, 339-351 (2006).
[CrossRef]

Tlidi, M.

P. Mandel and M. Tlidi, "Transverse dynamics in cavity nonlinear optics" (2000-2003),J. Opt. B: Quantum and Semiclass. Opt. 6, R60-R75 (2004).
[CrossRef]

Torrent, M. C.

J. García-Ojalvo, R. Vilaseca, and M. C. Torrent, "Coupled pattern formation near threshold in a broad-area cascade laser," Phys. Rev. A 56, 5111-5120 (1997).
[CrossRef]

Tredicce, J.

Tredicce, J.R.

X. Hachair, F. Pedaci, E. Caboche, S. Barland, M. Giudici, J. R. Tredicce, F. Prati, G. Tissoni, R. Kheradmand, L. A. Lugiato, I. Protsenko, and M. Brambilla, "Cavity solitons in a driven VCSEL above threshold," IEEE J. Sel. Top. Quantum Electron. 12, 339-351 (2006).
[CrossRef]

van Saarloos, W.

W. van Saarloos and P. C. Hohenberg, "Fronts, pulses, sources and sinks in generalized complex Ginzburg-Landau equations," Physica D 56, 306-367 (1992).
[CrossRef]

Vilaseca, R.

J. García-Ojalvo, R. Vilaseca, and M. C. Torrent, "Coupled pattern formation near threshold in a broad-area cascade laser," Phys. Rev. A 56, 5111-5120 (1997).
[CrossRef]

Weiss, C.O.

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

Wright, E. M.

A. M. Dunlop, W. J. Firth, and E. M. Wright, Opt. Commun. 138, 211 (1997).
[CrossRef]

Wright, E.M.

A. M. Dunlop, E. M. Wright, and W. J. Firth, "Spatial solitons laser," Opt. Commun. 147, 393-401 (1998).
[CrossRef]

Zeghlache, H.

H. Zeghlache, P. Mandel, N. B. Abraham, L. M. Hoffer, G. L. Lippi, and T. Mello, "Bidirectional ring laser: Stability analysis and time-dependent solutions," Phys. Rev. A 37, 470-497 (1988).
[CrossRef] [PubMed]

IEEE J. Sel. Top. Quantum Electron. (1)

X. Hachair, F. Pedaci, E. Caboche, S. Barland, M. Giudici, J. R. Tredicce, F. Prati, G. Tissoni, R. Kheradmand, L. A. Lugiato, I. Protsenko, and M. Brambilla, "Cavity solitons in a driven VCSEL above threshold," IEEE J. Sel. Top. Quantum Electron. 12, 339-351 (2006).
[CrossRef]

IEEE Journ. Quantm Electron. QE (1)

M. Piché and P. Belánger, "On the loses of the counter-propagating modes of ring cavities," IEEE Journ. Quantm Electron. QE- 20, 1303-1307 (2008).

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

P. Mandel and M. Tlidi, "Transverse dynamics in cavity nonlinear optics" (2000-2003),J. Opt. B: Quantum and Semiclass. Opt. 6, R60-R75 (2004).
[CrossRef]

Opt. Commun. (3)

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

A. M. Dunlop, E. M. Wright, and W. J. Firth, "Spatial solitons laser," Opt. Commun. 147, 393-401 (1998).
[CrossRef]

A. M. Dunlop, W. J. Firth, and E. M. Wright, Opt. Commun. 138, 211 (1997).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (2)

J. García-Ojalvo, R. Vilaseca, and M. C. Torrent, "Coupled pattern formation near threshold in a broad-area cascade laser," Phys. Rev. A 56, 5111-5120 (1997).
[CrossRef]

H. Zeghlache, P. Mandel, N. B. Abraham, L. M. Hoffer, G. L. Lippi, and T. Mello, "Bidirectional ring laser: Stability analysis and time-dependent solutions," Phys. Rev. A 37, 470-497 (1988).
[CrossRef] [PubMed]

Phys. Rev. E (2)

G. J. de Valcárcel and K. Staliunas, "Excitation of phase patterns and spatial solitons via two-frequency forcing of a 1:1 resonance," Phys. Rev. E 67, 026604 (2003).
[CrossRef]

P. V. Paulau, A. J. Scroggie, A. Naumenko, T. Ackemann, N. A. Loiko, and W. J. Firth, "Localized traveling waves in vertical-cavity surface-emitting lasers with frequency-selective optical feedback," Phys. Rev. E 75, 056208 (2007).
[CrossRef]

Phys. Rev. Lett. (2)

A. Esteban-Martín, M. Martínez-Quesada, V. B. Taranenko, E. Roldán, and G. J. de Valcárcel, "Bistable Phase Locking of a Nonlinear Optical Cavity via Rocking: Transmuting Vortices into Phase Patterns," Phys. Rev. Lett. 97, 093903 (2006).
[CrossRef] [PubMed]

M. San Miguel, "Phase instabilities in the Laser Vector Complex Ginzburg-Landau equation," Phys. Rev. Lett. 75, 425-428 (1995).
[CrossRef] [PubMed]

Physica D (2)

W. van Saarloos and P. C. Hohenberg, "Fronts, pulses, sources and sinks in generalized complex Ginzburg-Landau equations," Physica D 56, 306-367 (1992).
[CrossRef]

P. Coullet, T. Frisch and F. Plaza, "Sources and sinks of wave patterns," Physica D 62, 75-79 (1993).
[CrossRef]

Rev. Mod. Phys. (1)

M. C. Cross and P. C. Hohenberg, "Pattern Formation Out of Equilibrium," Rev. Mod. Phys. 65, 851-1112 (1993).
[CrossRef]

Other (4)

M. Tlidi, M. Taki, and Th. Kolokolnikov eds., Focus Issue: Dissipative Localized structures in extended systems, Chaos 17, Issue 3 (2007).

K. Staliunas and V.J. Sánchez-Morcillo, Transverse Patterns in Nonlinear Optical Resonators, (Springer, Berlín, 2003)

W .J. Firth and C. O. Weiss, "Cavity and feedback solitons," Opt. Photonic News 13, Issue 2, 54-58 (2002).
[CrossRef]

X. Hachair, G. Tissoni, H. Thienpont, and K. Panajotov, "Linearly polarized bistable localized structure in medium-size vertical-cavity surface-emitting lasers," Phys. Rev. A 79, 011801(R) (2009).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Bidirectional laser localized structure as obtained from Eqs. (1) for σ= 1 (isotropic case), d = 0.3 and A = 1.4. In (a) the dashed (full) lines correspond to the transverse intensity distribution for the strong (weak) field. In (b) the phase is shown as a function of time.

Fig. 2.
Fig. 2.

Domain of existence of the LSs in the plane <σ,d> for a pump value A = 1.4. Shaded areas correspond to the regions the stable LSs are found.

Fig. 3.
Fig. 3.

Evolution of a cluster of eight LSs for σ = 1 for different values of the diffusion coefficient. From left to right: d = 0.1 (a), d = 0.2 (b) and d = 0.3 (c). Time span is 5000 and the transverse dimension L=707.

Fig. 4.
Fig. 4.

Evolution of a cluster of two LSs for σ = 1 and d = 0.1 (upper row) and d = 0.3 (lower row). Left column shows the full picture, with L = 316 and time span 5000. Central column shows a magnification of the red box in the left column, with L = 120 and time running from 750 to 2000. Right column shows the spatio-temporal distribution of the phase for the field distribution in the inset

Fig. 5.
Fig. 5.

Phase velocity as a function of diffusion d for σ = 1.020 (a), 1.010 (b), 1.005 (c), 1 (d). The velocity is calculated by evaluating the derivative of the phase with respect the time, at a point sufficiently far from the center of a single LS.

Equations (2)

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τ F 1 = ( A 1 F 1 2 2 F 2 2 ) F 1 + ( d + i ) ξ 2 F 1 ,
τ F 2 = ( A σ F 2 2 2 F 1 2 ) F 2 + ( d + i ) ξ 2 F 2 ,

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