Abstract

We consider a passive optical cavity containing a photonic crystal and a purely absorptive two-level medium. The cavity is driven by a superposition of two coherent beams forming a periodically modulated pump. Using a coupled mode reduction and direct numerical modeling of the full system we demonstrate the existence of bistability between uniformly periodic states, modulational instabilities and localized structures of light. All are found to exist within the conduction band of the photonic material. Moreover, contrary to similar previously found intra-band structures, we show that these localized structures can be truly stationary states.

© 2006 Optical Society of America

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  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]
  2. N. Akhmediev and A. Ankiewicz, Dissipative Solitons, Series: Lecture Notes in Physics, Vol. 661 (Springer, 2005).
  3. N. N. Rosanov, Spatial hysteresis and optical patterns (Springer, Berlin2002).
  4. L. A. Lugiato and R. Lefever, “Spatial dissipative structures in passive optical systems,” Phys. Rev. Lett. 58, 2209–2211 (1987).
    [CrossRef] [PubMed]
  5. V. B. Taranenko, K. Staliunas, and 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]
  6. Y. F. Chen and Y. P. Lan, “Formation of repetitively nanosecond spatial solitons in a saturable absorber Q-switched laser,” Phys. Rev. Lett. 93, 013901 (2004).
    [CrossRef]
  7. J. Tredicce, M. Guidici, and P. Glorieux, “Comment on “Formation of repetitively nanosecond spatial solitons in a saturable absorber Q-switched laser,” Phys. Rev. Lett. 94, 249401 (2005).
    [CrossRef]
  8. A. Schreiber, B. Thuring, M. Kreuzer, and T. Tschudi, “Experimental investigation of solitary structures in a nonlinear optical feedback system,” Opt. Commun. 136, 415–418 (1997).
    [CrossRef]
  9. P. L. Ramazza, S. Ducci, S. Boccaletti, and F. T. Arecchi, “Localized versus delocalized patterns in a nonlinear optical interferometer,” J. Opt. B: Quantum and semiclass. Opt. 2, 399–405 (2000).
    [CrossRef]
  10. U. Bortolozzo, L. Pastur, P. L. Ramazza, M. Tlidi, and G. Kozyreff “Bistability between different localized structures in nonlinear optics,” Phys. Rev. Lett. 93, 253901 (2004).
    [CrossRef]
  11. M. Pesch, E. Große Westhoff, T. Ackemann, and W. Lange, “Observation of a discrete family of dissipative solitons in a nonlinear optical system,” Phys. Rev. Lett. 95, 143906 (2005).
    [CrossRef] [PubMed]
  12. S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger “Cavity solitons as pixels in semiconductor microcavities,” Nature (London) 419, 699–702 (2002).
    [CrossRef]
  13. K. Staliunas, “Midband dissipative spatial solitons,” Phys. Rev. Lett. 91, 053901 (2003).
    [CrossRef] [PubMed]
  14. K. Staliunas, “Midband solitons in nonlinear photonic crystal resonators,” Phys. Rev. E 70, 016602 (2004).
    [CrossRef]
  15. N.K. Efremidis and D.N. Christodoulides, “Discrete Ginzburg-Landau solitons,” Phys. Rev. E 67, 026606 (2003).
    [CrossRef]
  16. K. Maruno, A. Ankiewicz, and N. Akhmediev, “Exact localized and periodic solutions of the discrete complex Ginzburg-Landau equation,” Opt. Commun. 221, 199–209 (2003).
    [CrossRef]
  17. U. Peschel, O. Egorov, and F. Lederer, “Discrete cavity solitons,” Opt. Lett. 29, 1909–1911 (2004).
    [CrossRef] [PubMed]
  18. A. V. Yulin, D. V. Skryabin, and P. St. J. Russell, “Dissipative localized structures of light in photonic crystal films,” Opt. Express 13, 3529–3534 (2005). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-9-3529
    [CrossRef] [PubMed]
  19. E.A. Ultanir, G.I. Stegeman, and D.N. Christodoulides, “Dissipative photonic lattice solitons,” Opt. Lett. 29, 845–847 (2004).
    [CrossRef] [PubMed]
  20. D. Gomila, R. Zambrini, and G.L. Oppo, “Photonic band-gap inhibition of modulational instabilities,” Phys. Rev. Lett. 92, 253904 (2004).
    [CrossRef] [PubMed]
  21. D. Gomila and G.L. Oppo, “Coupled-mode theory for photonic band-gap inhibition of spatial instabilities,” Phys. Rev. E 72, 016614 (2005).
    [CrossRef]
  22. L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L.A. Lugiato, “Spatial solitons in semiconductor microcavities,” Phys. Rev. A 58, 2542–2559 (1998).
    [CrossRef]
  23. Y.S. Kivshar and G.P. Agrawal, Optical solitons: from a fiber to photonic crystals (Academic Press, 2003).

2005 (4)

J. Tredicce, M. Guidici, and P. Glorieux, “Comment on “Formation of repetitively nanosecond spatial solitons in a saturable absorber Q-switched laser,” Phys. Rev. Lett. 94, 249401 (2005).
[CrossRef]

M. Pesch, E. Große Westhoff, T. Ackemann, and W. Lange, “Observation of a discrete family of dissipative solitons in a nonlinear optical system,” Phys. Rev. Lett. 95, 143906 (2005).
[CrossRef] [PubMed]

D. Gomila and G.L. Oppo, “Coupled-mode theory for photonic band-gap inhibition of spatial instabilities,” Phys. Rev. E 72, 016614 (2005).
[CrossRef]

A. V. Yulin, D. V. Skryabin, and P. St. J. Russell, “Dissipative localized structures of light in photonic crystal films,” Opt. Express 13, 3529–3534 (2005). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-9-3529
[CrossRef] [PubMed]

2004 (7)

E.A. Ultanir, G.I. Stegeman, and D.N. Christodoulides, “Dissipative photonic lattice solitons,” Opt. Lett. 29, 845–847 (2004).
[CrossRef] [PubMed]

U. Peschel, O. Egorov, and F. Lederer, “Discrete cavity solitons,” Opt. Lett. 29, 1909–1911 (2004).
[CrossRef] [PubMed]

D. Gomila, R. Zambrini, and G.L. Oppo, “Photonic band-gap inhibition of modulational instabilities,” Phys. Rev. Lett. 92, 253904 (2004).
[CrossRef] [PubMed]

K. Staliunas, “Midband solitons in nonlinear photonic crystal resonators,” Phys. Rev. E 70, 016602 (2004).
[CrossRef]

U. Bortolozzo, L. Pastur, P. L. Ramazza, M. Tlidi, and G. Kozyreff “Bistability between different localized structures in nonlinear optics,” Phys. Rev. Lett. 93, 253901 (2004).
[CrossRef]

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]

Y. F. Chen and Y. P. Lan, “Formation of repetitively nanosecond spatial solitons in a saturable absorber Q-switched laser,” Phys. Rev. Lett. 93, 013901 (2004).
[CrossRef]

2003 (3)

N.K. Efremidis and D.N. Christodoulides, “Discrete Ginzburg-Landau solitons,” Phys. Rev. E 67, 026606 (2003).
[CrossRef]

K. Maruno, A. Ankiewicz, and N. Akhmediev, “Exact localized and periodic solutions of the discrete complex Ginzburg-Landau equation,” Opt. Commun. 221, 199–209 (2003).
[CrossRef]

K. Staliunas, “Midband dissipative spatial solitons,” Phys. Rev. Lett. 91, 053901 (2003).
[CrossRef] [PubMed]

2002 (1)

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger “Cavity solitons as pixels in semiconductor microcavities,” Nature (London) 419, 699–702 (2002).
[CrossRef]

2000 (1)

P. L. Ramazza, S. Ducci, S. Boccaletti, and F. T. Arecchi, “Localized versus delocalized patterns in a nonlinear optical interferometer,” J. Opt. B: Quantum and semiclass. Opt. 2, 399–405 (2000).
[CrossRef]

1998 (1)

L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L.A. Lugiato, “Spatial solitons in semiconductor microcavities,” Phys. Rev. A 58, 2542–2559 (1998).
[CrossRef]

1997 (2)

A. Schreiber, B. Thuring, M. Kreuzer, and T. Tschudi, “Experimental investigation of solitary structures in a nonlinear optical feedback system,” Opt. Commun. 136, 415–418 (1997).
[CrossRef]

V. B. Taranenko, K. Staliunas, and 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]

1987 (1)

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

Ackemann, T.

M. Pesch, E. Große Westhoff, T. Ackemann, and W. Lange, “Observation of a discrete family of dissipative solitons in a nonlinear optical system,” Phys. Rev. Lett. 95, 143906 (2005).
[CrossRef] [PubMed]

Agrawal, G.P.

Y.S. Kivshar and G.P. Agrawal, Optical solitons: from a fiber to photonic crystals (Academic Press, 2003).

Akhmediev, N.

K. Maruno, A. Ankiewicz, and N. Akhmediev, “Exact localized and periodic solutions of the discrete complex Ginzburg-Landau equation,” Opt. Commun. 221, 199–209 (2003).
[CrossRef]

N. Akhmediev and A. Ankiewicz, Dissipative Solitons, Series: Lecture Notes in Physics, Vol. 661 (Springer, 2005).

Ankiewicz, A.

K. Maruno, A. Ankiewicz, and N. Akhmediev, “Exact localized and periodic solutions of the discrete complex Ginzburg-Landau equation,” Opt. Commun. 221, 199–209 (2003).
[CrossRef]

N. Akhmediev and A. Ankiewicz, Dissipative Solitons, Series: Lecture Notes in Physics, Vol. 661 (Springer, 2005).

Arecchi, F. T.

P. L. Ramazza, S. Ducci, S. Boccaletti, and F. T. Arecchi, “Localized versus delocalized patterns in a nonlinear optical interferometer,” J. Opt. B: Quantum and semiclass. Opt. 2, 399–405 (2000).
[CrossRef]

Balle, S.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger “Cavity solitons as pixels in semiconductor microcavities,” Nature (London) 419, 699–702 (2002).
[CrossRef]

Barland, S.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger “Cavity solitons as pixels in semiconductor microcavities,” Nature (London) 419, 699–702 (2002).
[CrossRef]

Boccaletti, S.

P. L. Ramazza, S. Ducci, S. Boccaletti, and F. T. Arecchi, “Localized versus delocalized patterns in a nonlinear optical interferometer,” J. Opt. B: Quantum and semiclass. Opt. 2, 399–405 (2000).
[CrossRef]

Bortolozzo, U.

U. Bortolozzo, L. Pastur, P. L. Ramazza, M. Tlidi, and G. Kozyreff “Bistability between different localized structures in nonlinear optics,” Phys. Rev. Lett. 93, 253901 (2004).
[CrossRef]

Brambilla, M.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger “Cavity solitons as pixels in semiconductor microcavities,” Nature (London) 419, 699–702 (2002).
[CrossRef]

L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L.A. Lugiato, “Spatial solitons in semiconductor microcavities,” Phys. Rev. A 58, 2542–2559 (1998).
[CrossRef]

Chen, Y. F.

Y. F. Chen and Y. P. Lan, “Formation of repetitively nanosecond spatial solitons in a saturable absorber Q-switched laser,” Phys. Rev. Lett. 93, 013901 (2004).
[CrossRef]

Christodoulides, D.N.

E.A. Ultanir, G.I. Stegeman, and D.N. Christodoulides, “Dissipative photonic lattice solitons,” Opt. Lett. 29, 845–847 (2004).
[CrossRef] [PubMed]

N.K. Efremidis and D.N. Christodoulides, “Discrete Ginzburg-Landau solitons,” Phys. Rev. E 67, 026606 (2003).
[CrossRef]

Ducci, S.

P. L. Ramazza, S. Ducci, S. Boccaletti, and F. T. Arecchi, “Localized versus delocalized patterns in a nonlinear optical interferometer,” J. Opt. B: Quantum and semiclass. Opt. 2, 399–405 (2000).
[CrossRef]

Efremidis, N.K.

N.K. Efremidis and D.N. Christodoulides, “Discrete Ginzburg-Landau solitons,” Phys. Rev. E 67, 026606 (2003).
[CrossRef]

Egorov, O.

Giudici, M.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger “Cavity solitons as pixels in semiconductor microcavities,” Nature (London) 419, 699–702 (2002).
[CrossRef]

Glorieux, P.

J. Tredicce, M. Guidici, and P. Glorieux, “Comment on “Formation of repetitively nanosecond spatial solitons in a saturable absorber Q-switched laser,” Phys. Rev. Lett. 94, 249401 (2005).
[CrossRef]

Gomila, D.

D. Gomila and G.L. Oppo, “Coupled-mode theory for photonic band-gap inhibition of spatial instabilities,” Phys. Rev. E 72, 016614 (2005).
[CrossRef]

D. Gomila, R. Zambrini, and G.L. Oppo, “Photonic band-gap inhibition of modulational instabilities,” Phys. Rev. Lett. 92, 253904 (2004).
[CrossRef] [PubMed]

Große Westhoff, E.

M. Pesch, E. Große Westhoff, T. Ackemann, and W. Lange, “Observation of a discrete family of dissipative solitons in a nonlinear optical system,” Phys. Rev. Lett. 95, 143906 (2005).
[CrossRef] [PubMed]

Guidici, M.

J. Tredicce, M. Guidici, and P. Glorieux, “Comment on “Formation of repetitively nanosecond spatial solitons in a saturable absorber Q-switched laser,” Phys. Rev. Lett. 94, 249401 (2005).
[CrossRef]

Jäger, R.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger “Cavity solitons as pixels in semiconductor microcavities,” Nature (London) 419, 699–702 (2002).
[CrossRef]

Kivshar, Y.S.

Y.S. Kivshar and G.P. Agrawal, Optical solitons: from a fiber to photonic crystals (Academic Press, 2003).

Knödl, T.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger “Cavity solitons as pixels in semiconductor microcavities,” Nature (London) 419, 699–702 (2002).
[CrossRef]

Kozyreff, G.

U. Bortolozzo, L. Pastur, P. L. Ramazza, M. Tlidi, and G. Kozyreff “Bistability between different localized structures in nonlinear optics,” Phys. Rev. Lett. 93, 253901 (2004).
[CrossRef]

Kreuzer, M.

A. Schreiber, B. Thuring, M. Kreuzer, and T. Tschudi, “Experimental investigation of solitary structures in a nonlinear optical feedback system,” Opt. Commun. 136, 415–418 (1997).
[CrossRef]

Lan, Y. P.

Y. F. Chen and Y. P. Lan, “Formation of repetitively nanosecond spatial solitons in a saturable absorber Q-switched laser,” Phys. Rev. Lett. 93, 013901 (2004).
[CrossRef]

Lange, W.

M. Pesch, E. Große Westhoff, T. Ackemann, and W. Lange, “Observation of a discrete family of dissipative solitons in a nonlinear optical system,” Phys. Rev. Lett. 95, 143906 (2005).
[CrossRef] [PubMed]

Lederer, F.

Lefever, R.

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

Lugiato, L. A.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger “Cavity solitons as pixels in semiconductor microcavities,” Nature (London) 419, 699–702 (2002).
[CrossRef]

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

Lugiato, L.A.

L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L.A. Lugiato, “Spatial solitons in semiconductor microcavities,” Phys. Rev. A 58, 2542–2559 (1998).
[CrossRef]

Maggipinto, T.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger “Cavity solitons as pixels in semiconductor microcavities,” Nature (London) 419, 699–702 (2002).
[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]

Maruno, K.

K. Maruno, A. Ankiewicz, and N. Akhmediev, “Exact localized and periodic solutions of the discrete complex Ginzburg-Landau equation,” Opt. Commun. 221, 199–209 (2003).
[CrossRef]

Miller, M.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger “Cavity solitons as pixels in semiconductor microcavities,” Nature (London) 419, 699–702 (2002).
[CrossRef]

Oppo, G.L.

D. Gomila and G.L. Oppo, “Coupled-mode theory for photonic band-gap inhibition of spatial instabilities,” Phys. Rev. E 72, 016614 (2005).
[CrossRef]

D. Gomila, R. Zambrini, and G.L. Oppo, “Photonic band-gap inhibition of modulational instabilities,” Phys. Rev. Lett. 92, 253904 (2004).
[CrossRef] [PubMed]

Pastur, L.

U. Bortolozzo, L. Pastur, P. L. Ramazza, M. Tlidi, and G. Kozyreff “Bistability between different localized structures in nonlinear optics,” Phys. Rev. Lett. 93, 253901 (2004).
[CrossRef]

Pesch, M.

M. Pesch, E. Große Westhoff, T. Ackemann, and W. Lange, “Observation of a discrete family of dissipative solitons in a nonlinear optical system,” Phys. Rev. Lett. 95, 143906 (2005).
[CrossRef] [PubMed]

Peschel, U.

Prati, F.

L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L.A. Lugiato, “Spatial solitons in semiconductor microcavities,” Phys. Rev. A 58, 2542–2559 (1998).
[CrossRef]

Ramazza, P. L.

U. Bortolozzo, L. Pastur, P. L. Ramazza, M. Tlidi, and G. Kozyreff “Bistability between different localized structures in nonlinear optics,” Phys. Rev. Lett. 93, 253901 (2004).
[CrossRef]

P. L. Ramazza, S. Ducci, S. Boccaletti, and F. T. Arecchi, “Localized versus delocalized patterns in a nonlinear optical interferometer,” J. Opt. B: Quantum and semiclass. Opt. 2, 399–405 (2000).
[CrossRef]

Rosanov, N. N.

N. N. Rosanov, Spatial hysteresis and optical patterns (Springer, Berlin2002).

Russell, P. St. J.

Schreiber, A.

A. Schreiber, B. Thuring, M. Kreuzer, and T. Tschudi, “Experimental investigation of solitary structures in a nonlinear optical feedback system,” Opt. Commun. 136, 415–418 (1997).
[CrossRef]

Skryabin, D. V.

Spinelli, L.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger “Cavity solitons as pixels in semiconductor microcavities,” Nature (London) 419, 699–702 (2002).
[CrossRef]

L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L.A. Lugiato, “Spatial solitons in semiconductor microcavities,” Phys. Rev. A 58, 2542–2559 (1998).
[CrossRef]

Staliunas, K.

K. Staliunas, “Midband solitons in nonlinear photonic crystal resonators,” Phys. Rev. E 70, 016602 (2004).
[CrossRef]

K. Staliunas, “Midband dissipative spatial solitons,” Phys. Rev. Lett. 91, 053901 (2003).
[CrossRef] [PubMed]

V. B. Taranenko, K. Staliunas, and 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]

Stegeman, G.I.

Taranenko, V. B.

V. B. Taranenko, K. Staliunas, and 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]

Thuring, B.

A. Schreiber, B. Thuring, M. Kreuzer, and T. Tschudi, “Experimental investigation of solitary structures in a nonlinear optical feedback system,” Opt. Commun. 136, 415–418 (1997).
[CrossRef]

Tissoni, G.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger “Cavity solitons as pixels in semiconductor microcavities,” Nature (London) 419, 699–702 (2002).
[CrossRef]

L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L.A. Lugiato, “Spatial solitons in semiconductor microcavities,” Phys. Rev. A 58, 2542–2559 (1998).
[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]

U. Bortolozzo, L. Pastur, P. L. Ramazza, M. Tlidi, and G. Kozyreff “Bistability between different localized structures in nonlinear optics,” Phys. Rev. Lett. 93, 253901 (2004).
[CrossRef]

Tredicce, J.

J. Tredicce, M. Guidici, and P. Glorieux, “Comment on “Formation of repetitively nanosecond spatial solitons in a saturable absorber Q-switched laser,” Phys. Rev. Lett. 94, 249401 (2005).
[CrossRef]

Tredicce, J. R.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger “Cavity solitons as pixels in semiconductor microcavities,” Nature (London) 419, 699–702 (2002).
[CrossRef]

Tschudi, T.

A. Schreiber, B. Thuring, M. Kreuzer, and T. Tschudi, “Experimental investigation of solitary structures in a nonlinear optical feedback system,” Opt. Commun. 136, 415–418 (1997).
[CrossRef]

Ultanir, E.A.

Weiss, C. O.

V. B. Taranenko, K. Staliunas, and 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]

Yulin, A. V.

Zambrini, R.

D. Gomila, R. Zambrini, and G.L. Oppo, “Photonic band-gap inhibition of modulational instabilities,” Phys. Rev. Lett. 92, 253904 (2004).
[CrossRef] [PubMed]

J. Opt. B: Quantum and semiclass. Opt. (2)

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]

P. L. Ramazza, S. Ducci, S. Boccaletti, and F. T. Arecchi, “Localized versus delocalized patterns in a nonlinear optical interferometer,” J. Opt. B: Quantum and semiclass. Opt. 2, 399–405 (2000).
[CrossRef]

Nature (London) (1)

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger “Cavity solitons as pixels in semiconductor microcavities,” Nature (London) 419, 699–702 (2002).
[CrossRef]

Opt. Commun. (2)

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Opt. Express (1)

Opt. Lett. (2)

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V. B. Taranenko, K. Staliunas, and 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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N. Akhmediev and A. Ankiewicz, Dissipative Solitons, Series: Lecture Notes in Physics, Vol. 661 (Springer, 2005).

N. N. Rosanov, Spatial hysteresis and optical patterns (Springer, Berlin2002).

Y.S. Kivshar and G.P. Agrawal, Optical solitons: from a fiber to photonic crystals (Academic Press, 2003).

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Figures (5)

Fig. 1.
Fig. 1.

Schematic setup of the nonlinear cavity filled with a passive two-level medium (PM) and a photonic crystal film (PCF). The Fabry-Perot cavity with flat Mirrors (M) is driven by two pumping beam P 1,2.

Fig. 2.
Fig. 2.

Instability boundaries as a function of the effective detuning parameter Ω. (a) Pump P 1 = P 2 = P versus Ω. The solid curve is the modulational instability boundary. The bistability region is delimited by the three dashed curves. Grey region indicates photonic band gap (BG). (b) Critical wavenumber at the modulational instability versus Ω. Parameters are γ = 0.01, C = 0.4, δ = 0, and q = 0.

Fig. 3.
Fig. 3.

Stationary localized structures. Ω=1.05. Other parameters are the same as in Fig. 2. (a) Real and imaginary parts of the field amplitudes A 1,2 for P 1 = P 2 = 0.225. Solid (broken) lines correspond to A 1 (A 2). (b) Bifurcation diagram. LS: localized structures, HSS: homogeneous steady state. Broken lines correspond to unstable solutions.

Fig. 4.
Fig. 4.

Stationary localized structure obtained by direct numerical simulation of Eqs. (1,2). Parameters are γ = 0.05, C = 2.0, δ = 0, ϕ = 0, P 1 = P 2 = 1.2, km = 2.5 √ Δε k 0, and ωc −ω0 = -0.3125 ω0 Δε.

Fig. 5.
Fig. 5.

Transverse velocity v = dξ/dt of a localized structure as a function of (a) the phase shift δ, (b) pump imbalance δP= (P 2-P 1)/(P 2+P 1), where P 2+P 1 = 0.45, (c) incidence angle ϕ. Other parameters are the same as in Fig. 3.

Equations (12)

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F t = P ( x ) κF i ( ω c ω 0 ) F αcNF + ic 2 k 0 2 F x 2 + i ω 0 Δ ε cos ( k m x ) F ,
N t = Γ [ 1 N ( 1 + F 2 ) ] .
P ( x ) = ω 0 Δ ε 2 [ P 1 e i 2 ( k m ( 1 + ϕ ) x δ ) + P 2 e i 2 ( k m ( 1 ϕ ) x δ ) ] ,
Δ x ~ 1 k 0 ω 0 2 κ = 2 L k 0 T .
F ( x , t ) = A 1 ( x , t ) e i 2 ( k m x δ ) + A 2 ( x , t ) e i 2 ( k m x δ )
N 0 = 1 + A 1 2 + A 2 2 S , N 1 = A 1 A 2 * S , N 2 = A 1 * A 2 S ,
S = ( 1 + A 1 2 + A 2 2 ) 2 2 A 1 2 A 2 2 .
A 1 τ = P 1 exp iqξ ( γ + i Ω ) A 1 + i A 2 e + A 1 ξ 2 C 1 + A 1 2 S A 1 ,
A 2 τ = P 2 exp iqξ ( γ + i Ω ) A 2 + i A 1 e A 2 ξ 2 C 1 + A 2 2 S A 2 ,
γ = 2 κ ω 0 Δ ε , Ω = 1 ω 0 Δ ε ( ω c ω 0 + c k m 2 4 k 0 ) , C = αc ω 0 Δ ε , q = k m 2 ϕ 2 k 0 2 Δ ε .
Δ x B = k m k 0 2 Δ ε Δ ξ B ~ ω 0 2 κ Δ ε k m k 0 2 = k m k 0 Δ ε Δ x .
Δ εγ k m 2 k 0 2 1 ,

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