Abstract

We show that coupling diffraction and chromatic dispersion lead to body-centered cubic and hexagonally packed cylinders of dissipative optical crystals in a degenerate optical parametric oscillator. The stabilization of these crystals is a direct consequence of the interaction between the modulational and the quasi-neutral modes.

© 2003 Optical Society of America

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  1. G. L. Oppo, M. Brambilla, and L. A. Lugiato, Phys. Rev. A 49, 2028 (1994).
    [CrossRef] [PubMed]
  2. S. Trillo, M. Haelterman, and A. Sheppard, Opt. Lett. 22, 970 (1997).
    [CrossRef] [PubMed]
  3. K. Staliunas and V. J. Sánchez-Morcillo, Phys. Lett. A 241, 28 (1998).
    [CrossRef]
  4. G. L. Oppo, A. J. Scroggie, and W. J. Firth, J. Opt. B 1, 133 (1999).
    [CrossRef]
  5. M. Tlidi, P. Mandel, and R. Lefever, Phys. Rev. Lett. 81, 979 (1998).
    [CrossRef]
  6. M. Tlidi and P. Mandel, Phys. Rev. A 59, R2575 (1999).
    [CrossRef]
  7. D. V. Skryabin and W. J. Firth, Opt. Lett. 24, 1056 (1999).
    [CrossRef]
  8. D. V. Skryabin, Phys. Rev. E 60, R3508 (1999).
    [CrossRef]
  9. S. Fedorov, D. Michaelis, U. Peschel, C. Etrich, D. V. Skryabin, N. Rosanov, and F. Lederer, Phys. Rev. E 64, 036610 (2001).
    [CrossRef]
  10. P. Lodahl, M. Bache, and M. Saffman, Phys. Rev. A 63, 023815 (2001).
    [CrossRef]
  11. M. Le Berre, E. Ressayre, and A. Tallet, J. Opt. B 1, 153 (1999).
    [CrossRef]
  12. M. Le Berre, E. Ressayre, and A. Tallet, J. Opt. B 2, 347 (2000).
    [CrossRef]
  13. M. Le Berre, D. Leduc, S. Patrascu, E. Ressayre, and A. Tallet, Chaos Solitons Fractals 10, 627 (1999).
    [CrossRef]
  14. M. Tlidi, P. Mandel, M. Le Berre, E. Ressayre, A. Tallet, and L. Di Menza, Opt. Lett. 25, 487 (2000).
    [CrossRef]
  15. D. T. Reid, J. M. Dudley, M. Ebrahimzadeh, and W. Sibbett, Opt. Lett. 19, 825 (1994).
    [CrossRef] [PubMed]
  16. S. Longhi, Opt. Lett. 20, 1628 (1995).
    [CrossRef] [PubMed]
  17. S. Trillo and M. Haelterman, Opt. Lett. 21, 1114 (1996).
    [CrossRef] [PubMed]
  18. M. Tlidi and M. Haelterman, Phys. Lett. A 239, 59 (1998).
    [CrossRef]
  19. M. Tlidi, M. Haelterman, and P. Mandel, Europhys. Lett. 42, 505 (1998).
    [CrossRef]
  20. M. Tlidi and P. Mandel, Phys. Rev. Lett. 83, 4995 (1999).
    [CrossRef]
  21. M. Tlidi, J. Opt. B 2, 438 (2000).
    [CrossRef]
  22. K. Staliunas, Phys. Rev. Lett. 81, 81 (1998).
    [CrossRef]
  23. M. Tlidi, M’F. Hilali, and P. Mandel, Europhys. Lett. 55, 26 (2001).
    [CrossRef]
  24. P. M. Lushnikov and M. Saffman, Phys. Rev. E 62, 5793 (2000).
    [CrossRef]
  25. S. Longhi and A. Geraci, Phys. Rev. A 54, 4581 (1996).
    [CrossRef] [PubMed]
  26. G. J. de Valcárcel, K. Staliunas, E. Roldán, and V. J. Sánchez-Morcillo, Phys. Rev. A 54, 1609 (1996).
    [CrossRef]
  27. Z. H. Musslimani, Physica A 249, 141 (1998).
    [CrossRef]
  28. M. Tlidi, R. Lefever, and P. Mandel, Quantum Semiclassic. Opt. 8, 931 (1996).
    [CrossRef]

2001 (3)

S. Fedorov, D. Michaelis, U. Peschel, C. Etrich, D. V. Skryabin, N. Rosanov, and F. Lederer, Phys. Rev. E 64, 036610 (2001).
[CrossRef]

P. Lodahl, M. Bache, and M. Saffman, Phys. Rev. A 63, 023815 (2001).
[CrossRef]

M. Tlidi, M’F. Hilali, and P. Mandel, Europhys. Lett. 55, 26 (2001).
[CrossRef]

2000 (4)

P. M. Lushnikov and M. Saffman, Phys. Rev. E 62, 5793 (2000).
[CrossRef]

M. Tlidi, J. Opt. B 2, 438 (2000).
[CrossRef]

M. Le Berre, E. Ressayre, and A. Tallet, J. Opt. B 2, 347 (2000).
[CrossRef]

M. Tlidi, P. Mandel, M. Le Berre, E. Ressayre, A. Tallet, and L. Di Menza, Opt. Lett. 25, 487 (2000).
[CrossRef]

1999 (7)

G. L. Oppo, A. J. Scroggie, and W. J. Firth, J. Opt. B 1, 133 (1999).
[CrossRef]

M. Tlidi and P. Mandel, Phys. Rev. A 59, R2575 (1999).
[CrossRef]

D. V. Skryabin and W. J. Firth, Opt. Lett. 24, 1056 (1999).
[CrossRef]

M. Le Berre, D. Leduc, S. Patrascu, E. Ressayre, and A. Tallet, Chaos Solitons Fractals 10, 627 (1999).
[CrossRef]

M. Le Berre, E. Ressayre, and A. Tallet, J. Opt. B 1, 153 (1999).
[CrossRef]

D. V. Skryabin, Phys. Rev. E 60, R3508 (1999).
[CrossRef]

M. Tlidi and P. Mandel, Phys. Rev. Lett. 83, 4995 (1999).
[CrossRef]

1998 (6)

M. Tlidi and M. Haelterman, Phys. Lett. A 239, 59 (1998).
[CrossRef]

M. Tlidi, M. Haelterman, and P. Mandel, Europhys. Lett. 42, 505 (1998).
[CrossRef]

K. Staliunas, Phys. Rev. Lett. 81, 81 (1998).
[CrossRef]

Z. H. Musslimani, Physica A 249, 141 (1998).
[CrossRef]

M. Tlidi, P. Mandel, and R. Lefever, Phys. Rev. Lett. 81, 979 (1998).
[CrossRef]

K. Staliunas and V. J. Sánchez-Morcillo, Phys. Lett. A 241, 28 (1998).
[CrossRef]

1997 (1)

1996 (4)

S. Trillo and M. Haelterman, Opt. Lett. 21, 1114 (1996).
[CrossRef] [PubMed]

M. Tlidi, R. Lefever, and P. Mandel, Quantum Semiclassic. Opt. 8, 931 (1996).
[CrossRef]

S. Longhi and A. Geraci, Phys. Rev. A 54, 4581 (1996).
[CrossRef] [PubMed]

G. J. de Valcárcel, K. Staliunas, E. Roldán, and V. J. Sánchez-Morcillo, Phys. Rev. A 54, 1609 (1996).
[CrossRef]

1995 (1)

1994 (2)

Bache, M.

P. Lodahl, M. Bache, and M. Saffman, Phys. Rev. A 63, 023815 (2001).
[CrossRef]

Brambilla, M.

G. L. Oppo, M. Brambilla, and L. A. Lugiato, Phys. Rev. A 49, 2028 (1994).
[CrossRef] [PubMed]

de Valcárcel, G. J.

G. J. de Valcárcel, K. Staliunas, E. Roldán, and V. J. Sánchez-Morcillo, Phys. Rev. A 54, 1609 (1996).
[CrossRef]

Dudley, J. M.

Ebrahimzadeh, M.

Etrich, C.

S. Fedorov, D. Michaelis, U. Peschel, C. Etrich, D. V. Skryabin, N. Rosanov, and F. Lederer, Phys. Rev. E 64, 036610 (2001).
[CrossRef]

Fedorov, S.

S. Fedorov, D. Michaelis, U. Peschel, C. Etrich, D. V. Skryabin, N. Rosanov, and F. Lederer, Phys. Rev. E 64, 036610 (2001).
[CrossRef]

Firth, W. J.

D. V. Skryabin and W. J. Firth, Opt. Lett. 24, 1056 (1999).
[CrossRef]

G. L. Oppo, A. J. Scroggie, and W. J. Firth, J. Opt. B 1, 133 (1999).
[CrossRef]

Geraci, A.

S. Longhi and A. Geraci, Phys. Rev. A 54, 4581 (1996).
[CrossRef] [PubMed]

Haelterman, M.

M. Tlidi, M. Haelterman, and P. Mandel, Europhys. Lett. 42, 505 (1998).
[CrossRef]

M. Tlidi and M. Haelterman, Phys. Lett. A 239, 59 (1998).
[CrossRef]

S. Trillo, M. Haelterman, and A. Sheppard, Opt. Lett. 22, 970 (1997).
[CrossRef] [PubMed]

S. Trillo and M. Haelterman, Opt. Lett. 21, 1114 (1996).
[CrossRef] [PubMed]

Hilali, M'F.

M. Tlidi, M’F. Hilali, and P. Mandel, Europhys. Lett. 55, 26 (2001).
[CrossRef]

Le Berre, M.

M. Le Berre, E. Ressayre, and A. Tallet, J. Opt. B 2, 347 (2000).
[CrossRef]

M. Tlidi, P. Mandel, M. Le Berre, E. Ressayre, A. Tallet, and L. Di Menza, Opt. Lett. 25, 487 (2000).
[CrossRef]

M. Le Berre, D. Leduc, S. Patrascu, E. Ressayre, and A. Tallet, Chaos Solitons Fractals 10, 627 (1999).
[CrossRef]

M. Le Berre, E. Ressayre, and A. Tallet, J. Opt. B 1, 153 (1999).
[CrossRef]

Lederer, F.

S. Fedorov, D. Michaelis, U. Peschel, C. Etrich, D. V. Skryabin, N. Rosanov, and F. Lederer, Phys. Rev. E 64, 036610 (2001).
[CrossRef]

Leduc, D.

M. Le Berre, D. Leduc, S. Patrascu, E. Ressayre, and A. Tallet, Chaos Solitons Fractals 10, 627 (1999).
[CrossRef]

Lefever, R.

M. Tlidi, P. Mandel, and R. Lefever, Phys. Rev. Lett. 81, 979 (1998).
[CrossRef]

M. Tlidi, R. Lefever, and P. Mandel, Quantum Semiclassic. Opt. 8, 931 (1996).
[CrossRef]

Lodahl, P.

P. Lodahl, M. Bache, and M. Saffman, Phys. Rev. A 63, 023815 (2001).
[CrossRef]

Longhi, S.

S. Longhi and A. Geraci, Phys. Rev. A 54, 4581 (1996).
[CrossRef] [PubMed]

S. Longhi, Opt. Lett. 20, 1628 (1995).
[CrossRef] [PubMed]

Lugiato, L. A.

G. L. Oppo, M. Brambilla, and L. A. Lugiato, Phys. Rev. A 49, 2028 (1994).
[CrossRef] [PubMed]

Lushnikov, P. M.

P. M. Lushnikov and M. Saffman, Phys. Rev. E 62, 5793 (2000).
[CrossRef]

Mandel, P.

M. Tlidi, M’F. Hilali, and P. Mandel, Europhys. Lett. 55, 26 (2001).
[CrossRef]

M. Tlidi, P. Mandel, M. Le Berre, E. Ressayre, A. Tallet, and L. Di Menza, Opt. Lett. 25, 487 (2000).
[CrossRef]

M. Tlidi and P. Mandel, Phys. Rev. Lett. 83, 4995 (1999).
[CrossRef]

M. Tlidi and P. Mandel, Phys. Rev. A 59, R2575 (1999).
[CrossRef]

M. Tlidi, M. Haelterman, and P. Mandel, Europhys. Lett. 42, 505 (1998).
[CrossRef]

M. Tlidi, P. Mandel, and R. Lefever, Phys. Rev. Lett. 81, 979 (1998).
[CrossRef]

M. Tlidi, R. Lefever, and P. Mandel, Quantum Semiclassic. Opt. 8, 931 (1996).
[CrossRef]

Michaelis, D.

S. Fedorov, D. Michaelis, U. Peschel, C. Etrich, D. V. Skryabin, N. Rosanov, and F. Lederer, Phys. Rev. E 64, 036610 (2001).
[CrossRef]

Musslimani, Z. H.

Z. H. Musslimani, Physica A 249, 141 (1998).
[CrossRef]

Oppo, G. L.

G. L. Oppo, A. J. Scroggie, and W. J. Firth, J. Opt. B 1, 133 (1999).
[CrossRef]

G. L. Oppo, M. Brambilla, and L. A. Lugiato, Phys. Rev. A 49, 2028 (1994).
[CrossRef] [PubMed]

Patrascu, S.

M. Le Berre, D. Leduc, S. Patrascu, E. Ressayre, and A. Tallet, Chaos Solitons Fractals 10, 627 (1999).
[CrossRef]

Peschel, U.

S. Fedorov, D. Michaelis, U. Peschel, C. Etrich, D. V. Skryabin, N. Rosanov, and F. Lederer, Phys. Rev. E 64, 036610 (2001).
[CrossRef]

Reid, D. T.

Ressayre, E.

M. Le Berre, E. Ressayre, and A. Tallet, J. Opt. B 2, 347 (2000).
[CrossRef]

M. Tlidi, P. Mandel, M. Le Berre, E. Ressayre, A. Tallet, and L. Di Menza, Opt. Lett. 25, 487 (2000).
[CrossRef]

M. Le Berre, D. Leduc, S. Patrascu, E. Ressayre, and A. Tallet, Chaos Solitons Fractals 10, 627 (1999).
[CrossRef]

M. Le Berre, E. Ressayre, and A. Tallet, J. Opt. B 1, 153 (1999).
[CrossRef]

Roldán, E.

G. J. de Valcárcel, K. Staliunas, E. Roldán, and V. J. Sánchez-Morcillo, Phys. Rev. A 54, 1609 (1996).
[CrossRef]

Rosanov, N.

S. Fedorov, D. Michaelis, U. Peschel, C. Etrich, D. V. Skryabin, N. Rosanov, and F. Lederer, Phys. Rev. E 64, 036610 (2001).
[CrossRef]

Saffman, M.

P. Lodahl, M. Bache, and M. Saffman, Phys. Rev. A 63, 023815 (2001).
[CrossRef]

P. M. Lushnikov and M. Saffman, Phys. Rev. E 62, 5793 (2000).
[CrossRef]

Sánchez-Morcillo, V. J.

K. Staliunas and V. J. Sánchez-Morcillo, Phys. Lett. A 241, 28 (1998).
[CrossRef]

G. J. de Valcárcel, K. Staliunas, E. Roldán, and V. J. Sánchez-Morcillo, Phys. Rev. A 54, 1609 (1996).
[CrossRef]

Scroggie, A. J.

G. L. Oppo, A. J. Scroggie, and W. J. Firth, J. Opt. B 1, 133 (1999).
[CrossRef]

Sheppard, A.

Sibbett, W.

Skryabin, D. V.

S. Fedorov, D. Michaelis, U. Peschel, C. Etrich, D. V. Skryabin, N. Rosanov, and F. Lederer, Phys. Rev. E 64, 036610 (2001).
[CrossRef]

D. V. Skryabin and W. J. Firth, Opt. Lett. 24, 1056 (1999).
[CrossRef]

D. V. Skryabin, Phys. Rev. E 60, R3508 (1999).
[CrossRef]

Staliunas, K.

K. Staliunas, Phys. Rev. Lett. 81, 81 (1998).
[CrossRef]

K. Staliunas and V. J. Sánchez-Morcillo, Phys. Lett. A 241, 28 (1998).
[CrossRef]

G. J. de Valcárcel, K. Staliunas, E. Roldán, and V. J. Sánchez-Morcillo, Phys. Rev. A 54, 1609 (1996).
[CrossRef]

Tallet, A.

M. Tlidi, P. Mandel, M. Le Berre, E. Ressayre, A. Tallet, and L. Di Menza, Opt. Lett. 25, 487 (2000).
[CrossRef]

M. Le Berre, E. Ressayre, and A. Tallet, J. Opt. B 2, 347 (2000).
[CrossRef]

M. Le Berre, E. Ressayre, and A. Tallet, J. Opt. B 1, 153 (1999).
[CrossRef]

M. Le Berre, D. Leduc, S. Patrascu, E. Ressayre, and A. Tallet, Chaos Solitons Fractals 10, 627 (1999).
[CrossRef]

Tlidi, M.

M. Tlidi, M’F. Hilali, and P. Mandel, Europhys. Lett. 55, 26 (2001).
[CrossRef]

M. Tlidi, P. Mandel, M. Le Berre, E. Ressayre, A. Tallet, and L. Di Menza, Opt. Lett. 25, 487 (2000).
[CrossRef]

M. Tlidi, J. Opt. B 2, 438 (2000).
[CrossRef]

M. Tlidi and P. Mandel, Phys. Rev. Lett. 83, 4995 (1999).
[CrossRef]

M. Tlidi and P. Mandel, Phys. Rev. A 59, R2575 (1999).
[CrossRef]

M. Tlidi, M. Haelterman, and P. Mandel, Europhys. Lett. 42, 505 (1998).
[CrossRef]

M. Tlidi, P. Mandel, and R. Lefever, Phys. Rev. Lett. 81, 979 (1998).
[CrossRef]

M. Tlidi and M. Haelterman, Phys. Lett. A 239, 59 (1998).
[CrossRef]

M. Tlidi, R. Lefever, and P. Mandel, Quantum Semiclassic. Opt. 8, 931 (1996).
[CrossRef]

Trillo, S.

Chaos Solitons Fractals (1)

M. Le Berre, D. Leduc, S. Patrascu, E. Ressayre, and A. Tallet, Chaos Solitons Fractals 10, 627 (1999).
[CrossRef]

Europhys. Lett. (2)

M. Tlidi, M. Haelterman, and P. Mandel, Europhys. Lett. 42, 505 (1998).
[CrossRef]

M. Tlidi, M’F. Hilali, and P. Mandel, Europhys. Lett. 55, 26 (2001).
[CrossRef]

J. Opt. B (4)

M. Tlidi, J. Opt. B 2, 438 (2000).
[CrossRef]

M. Le Berre, E. Ressayre, and A. Tallet, J. Opt. B 1, 153 (1999).
[CrossRef]

M. Le Berre, E. Ressayre, and A. Tallet, J. Opt. B 2, 347 (2000).
[CrossRef]

G. L. Oppo, A. J. Scroggie, and W. J. Firth, J. Opt. B 1, 133 (1999).
[CrossRef]

Opt. Lett. (6)

Phys. Lett. A (2)

K. Staliunas and V. J. Sánchez-Morcillo, Phys. Lett. A 241, 28 (1998).
[CrossRef]

M. Tlidi and M. Haelterman, Phys. Lett. A 239, 59 (1998).
[CrossRef]

Phys. Rev. A (5)

S. Longhi and A. Geraci, Phys. Rev. A 54, 4581 (1996).
[CrossRef] [PubMed]

G. J. de Valcárcel, K. Staliunas, E. Roldán, and V. J. Sánchez-Morcillo, Phys. Rev. A 54, 1609 (1996).
[CrossRef]

P. Lodahl, M. Bache, and M. Saffman, Phys. Rev. A 63, 023815 (2001).
[CrossRef]

M. Tlidi and P. Mandel, Phys. Rev. A 59, R2575 (1999).
[CrossRef]

G. L. Oppo, M. Brambilla, and L. A. Lugiato, Phys. Rev. A 49, 2028 (1994).
[CrossRef] [PubMed]

Phys. Rev. E (3)

P. M. Lushnikov and M. Saffman, Phys. Rev. E 62, 5793 (2000).
[CrossRef]

D. V. Skryabin, Phys. Rev. E 60, R3508 (1999).
[CrossRef]

S. Fedorov, D. Michaelis, U. Peschel, C. Etrich, D. V. Skryabin, N. Rosanov, and F. Lederer, Phys. Rev. E 64, 036610 (2001).
[CrossRef]

Phys. Rev. Lett. (3)

M. Tlidi and P. Mandel, Phys. Rev. Lett. 83, 4995 (1999).
[CrossRef]

K. Staliunas, Phys. Rev. Lett. 81, 81 (1998).
[CrossRef]

M. Tlidi, P. Mandel, and R. Lefever, Phys. Rev. Lett. 81, 979 (1998).
[CrossRef]

Physica A (1)

Z. H. Musslimani, Physica A 249, 141 (1998).
[CrossRef]

Quantum Semiclassic. Opt. (1)

M. Tlidi, R. Lefever, and P. Mandel, Quantum Semiclassic. Opt. 8, 931 (1996).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

3D bifurcation diagram. The maximum amplitude of BCC structures, HPCs, and Lamellae (L) versus the input field amplitude. Solid (dashed) curves represent stable (unstable) solutions. Parameters are δ1=-δ2=-0.5.

Fig. 2
Fig. 2

Bifurcation diagram obtained for the same parameters as in Fig. 1. Full and dashed curves indicate stable and unstable amplitudes of the zero quasi-neutral mode corresponding to the BCC structures and HPCs, respectively.

Fig. 3
Fig. 3

Isosurface corresponding to (a) the HPCs and (b) the BCC structures for the pump field amplitude. They are obtained by numerical simulations of the full model of Eqs. (1) and (2). Parameters are δ1=-δ2=-0.5, β=0.5, and γ=1. (a) S=1.22. (b) S=1.3. Mesh integration is 48×48×48.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

u1t=-1-iδ1u1+u1u2+iL±2τ2u1,
u2t=-γ1+iδ2u2+u12-S+iaL±β2τ2u2,
Et=S21+δ22-1E-21+δ22E3-δ1+L±2τ22E.
Ex,y,τ,t=E0t+l=1NEltexpikl·r+c.c.,

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