Instability of optical tetrahedral dissipative crystals

Europhysics Letters

Volumn 55, Issue 1, 2001, Pages 26-32

  Tlidi, M ^a   Hilali, M'F ^a   Mandel, P ^a  

^a UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035385009     PISSN: 02955075     EISSN: None     Source Type: Journal    
DOI: 10.1209/epl/i2001-00376-7     Document Type: Article

References (39)

1. NICOLIS G. and PRIGOGINE I., Self-Organization in Nonequilibrium Systems (Wiley Press, New York) 1977; CROSS M. C. and HOHENBERG P. C., Rev. Mod. Phys., 65 (1993) 851;
2. NICOLIS G. and PRIGOGINE I., Self-Organization in Nonequilibrium Systems (Wiley Press, New York) 1977; CROSS M. C. and HOHENBERG P. C., Rev. Mod. Phys., 65 (1993) 851;
3. PISMEN L. M., Vortices in Nonlinear Fields (Oxford University Press) 1998.
4. LUGIATO L. A., Chaos, Solitons Fractals, 4 (1994) 1264; ROSANOV N. N., Progress in Optics, Vol. 35 (North-Holland, Amsterdam) 1996; MANDEL P., Theoretical Problems in Cavity Nonlinear Optics (Cambridge University Press) 1997; DE VALCÁRCEL E.. ROLDÁN E. and VILASECA R. (Editors), Quantum Semiclass. Opt., 10 (1998) 775; J. Opt. B Quantum Semiclass. Opt., 1 (1999) 1; VASNETSOV M. and STALIUNAS K., Optical Vortices (Nova Science, New York) 1999; LANGE W. and ACKEMANN T. (Editors), J. Opt. B Quantum Semiclass. Opt., 2 (2000) 347.
5. LUGIATO L. A., Chaos, Solitons Fractals, 4 (1994) 1264; ROSANOV N. N., Progress in Optics, Vol. 35 (North-Holland, Amsterdam) 1996; MANDEL P., Theoretical Problems in Cavity Nonlinear Optics (Cambridge University Press) 1997; DE VALCÁRCEL E.. ROLDÁN E. and VILASECA R. (Editors), Quantum Semiclass. Opt., 10 (1998) 775; J. Opt. B Quantum Semiclass. Opt., 1 (1999) 1; VASNETSOV M. and STALIUNAS K., Optical Vortices (Nova Science, New York) 1999; LANGE W. and ACKEMANN T. (Editors), J. Opt. B Quantum Semiclass. Opt., 2 (2000) 347.
6. LUGIATO L. A., Chaos, Solitons Fractals, 4 (1994) 1264; ROSANOV N. N., Progress in Optics, Vol. 35 (North-Holland, Amsterdam) 1996; MANDEL P., Theoretical Problems in Cavity Nonlinear Optics (Cambridge University Press) 1997; DE VALCÁRCEL E.. ROLDÁN E. and VILASECA R. (Editors), Quantum Semiclass. Opt., 10 (1998) 775; J. Opt. B Quantum Semiclass. Opt., 1 (1999) 1; VASNETSOV M. and STALIUNAS K., Optical Vortices (Nova Science, New York) 1999; LANGE W. and ACKEMANN T. (Editors), J. Opt. B Quantum Semiclass. Opt., 2 (2000) 347.
7. LUGIATO L. A., Chaos, Solitons Fractals, 4 (1994) 1264; ROSANOV N. N., Progress in Optics, Vol. 35 (North-Holland, Amsterdam) 1996; MANDEL P., Theoretical Problems in Cavity Nonlinear Optics (Cambridge University Press) 1997; DE VALCÁRCEL E.. ROLDÁN E. and VILASECA R. (Editors), Quantum Semiclass. Opt., 10 (1998) 775; J. Opt. B Quantum Semiclass. Opt., 1 (1999) 1; VASNETSOV M. and STALIUNAS K., Optical Vortices (Nova Science, New York) 1999; LANGE W. and ACKEMANN T. (Editors), J. Opt. B Quantum Semiclass. Opt., 2 (2000) 347.
8. LUGIATO L. A., Chaos, Solitons Fractals, 4 (1994) 1264; ROSANOV N. N., Progress in Optics, Vol. 35 (North-Holland, Amsterdam) 1996; MANDEL P., Theoretical Problems in Cavity Nonlinear Optics (Cambridge University Press) 1997; DE VALCÁRCEL E.. ROLDÁN E. and VILASECA R. (Editors), Quantum Semiclass. Opt., 10 (1998) 775; J. Opt. B Quantum Semiclass. Opt., 1 (1999) 1; VASNETSOV M. and STALIUNAS K., Optical Vortices (Nova Science, New York) 1999; LANGE W. and ACKEMANN T. (Editors), J. Opt. B Quantum Semiclass. Opt., 2 (2000) 347.
9. LUGIATO L. A., Chaos, Solitons Fractals, 4 (1994) 1264; ROSANOV N. N., Progress in Optics, Vol. 35 (North-Holland, Amsterdam) 1996; MANDEL P., Theoretical Problems in Cavity Nonlinear Optics (Cambridge University Press) 1997; DE VALCÁRCEL E.. ROLDÁN E. and VILASECA R. (Editors), Quantum Semiclass. Opt., 10 (1998) 775; J. Opt. B Quantum Semiclass. Opt., 1 (1999) 1; VASNETSOV M. and STALIUNAS K., Optical Vortices (Nova Science, New York) 1999; LANGE W. and ACKEMANN T. (Editors), J. Opt. B Quantum Semiclass. Opt., 2 (2000) 347.
10. LUGIATO L. A., Chaos, Solitons Fractals, 4 (1994) 1264; ROSANOV N. N., Progress in Optics, Vol. 35 (North-Holland, Amsterdam) 1996; MANDEL P., Theoretical Problems in Cavity Nonlinear Optics (Cambridge University Press) 1997; DE VALCÁRCEL E.. ROLDÁN E. and VILASECA R. (Editors), Quantum Semiclass. Opt., 10 (1998) 775; J. Opt. B Quantum Semiclass. Opt., 1 (1999) 1; VASNETSOV M. and STALIUNAS K., Optical Vortices (Nova Science, New York) 1999; LANGE W. and ACKEMANN T. (Editors), J. Opt. B Quantum Semiclass. Opt., 2 (2000) 347.
11. TURING A. M., Philos. Trans. R. Soc. B, 327 (1952) 37; PRIGOGINE I. and LEFEVER R., J. Chem. Phys., 48 (1968) 1695.
12. TURING A. M., Philos. Trans. R. Soc. B, 327 (1952) 37; PRIGOGINE I. and LEFEVER R., J. Chem. Phys., 48 (1968) 1695.
13. LUGIATO L. A. and LEFEVER R., Phys. Rev. Lett., 58 (1987) 2209; GRYNBERG G., Opt. Commun., 66 (1988) 321.
14. LUGIATO L. A. and LEFEVER R., Phys. Rev. Lett., 58 (1987) 2209; GRYNBERG G., Opt. Commun., 66 (1988) 321.
15. m are also found (with fractional n), if u = ρ exp[φ], the phase φ will, in general, contain such contributions, as in the Kuramoto-Sivashinsky equation: KURAMOTO Y. and TSUZUKI T., Prog. Theor. Phys., 54 (1975) 687; SIVASHINSKY G. I., Acta Astronaut., 4, (1977) 1177. Such a Sivashinsky-Kuramoto equation was first derived in nonlinear optics by LEFEVER R., LUGIATO L. A., KAIGE W., ABRAHAM N. B. and MANDEL P., Phys. Lett. A, 135 (1989) 254.
16. m are also found (with fractional n), if u = ρ exp[φ], the phase φ will, in general, contain such contributions, as in the Kuramoto-Sivashinsky equation: KURAMOTO Y. and TSUZUKI T., Prog. Theor. Phys., 54 (1975) 687; SIVASHINSKY G. I., Acta Astronaut., 4, (1977) 1177. Such a Sivashinsky-Kuramoto equation was first derived in nonlinear optics by LEFEVER R., LUGIATO L. A., KAIGE W., ABRAHAM N. B. and MANDEL P., Phys. Lett. A, 135 (1989) 254.
17. m are also found (with fractional n), if u = ρ exp[φ], the phase φ will, in general, contain such contributions, as in the Kuramoto-Sivashinsky equation: KURAMOTO Y. and TSUZUKI T., Prog. Theor. Phys., 54 (1975) 687; SIVASHINSKY G. I., Acta Astronaut., 4, (1977) 1177. Such a Sivashinsky-Kuramoto equation was first derived in nonlinear optics by LEFEVER R., LUGIATO L. A., KAIGE W., ABRAHAM N. B. and MANDEL P., Phys. Lett. A, 135 (1989) 254.
18. ALEXANDER S. and MCTAGUE J., Phys. Rev. Lett., 41 (1978) 702.
19. WALGRAEF D., DEWEL G. and BORCKMANS P., Phys. Rev. A, 21 (1980) 397; CASTETS V., DULOS E., BOISSONADE J. and DE KEPPER P., Phys. Rev. Lett., 64 (1990) 2953.
20. WALGRAEF D., DEWEL G. and BORCKMANS P., Phys. Rev. A, 21 (1980) 397; CASTETS V., DULOS E., BOISSONADE J. and DE KEPPER P., Phys. Rev. Lett., 64 (1990) 2953.
21. PISMEN L. M., Phys. Rev. E, 50 (1994) 4896.
22. TLIDI M., HAELTERMAN M. and MANDEL P., Europhys. Lett., 42 (1998) 505.
23. TLIDI M., HAELTERMAN M. and MANDEL P., Quantum Semiclass. Opt., 10 (1998) 869.
24. STALIUNAS K., Phys. Rev. Lett., 81 (1998) 81.
25. TLIDI M. and MANDEL P., Phys. Rev. Lett., 83 (1999) 4995; TLIDI M., J. Opt. B Quantum Semiclass. Opt., 2 (2000) 438.
26. TLIDI M. and MANDEL P., Phys. Rev. Lett., 83 (1999) 4995; TLIDI M., J. Opt. B Quantum Semiclass. Opt., 2 (2000) 438.
27. LUSHNIKOV P. M. and SAFFMAN M., Phys. Rev. E, 62 (2000) 5793.
28. HAELTERMAN M., TRILLO S. and WABNITZ S., Opt. Commun., 93 (1992) 343; COEN S. and HAELTERMAN M., Opt. Lett., 24 (1999) 80.
29. HAELTERMAN M., TRILLO S. and WABNITZ S., Opt. Commun., 93 (1992) 343; COEN S. and HAELTERMAN M., Opt. Lett., 24 (1999) 80.
30. SCROGGIE A. J., FIRTH W. J., MCDONALD G. S., TLIDI M., LEFEVER R. and LUGIATO L. A., Chaos, Solitons and Fractals, 4 (1994) 1323.
31. ROBERTS A. J., SIAM J. Math. Anal., 20 (1989) 1447; DEWEL G., MÉTENS S., M'F HILALI, BORCKMANS P. and PRICE C. B., Phys. Rev. Lett., 74 (1995) 4647.
32. ROBERTS A. J., SIAM J. Math. Anal., 20 (1989) 1447; DEWEL G., MÉTENS S., M'F HILALI, BORCKMANS P. and PRICE C. B., Phys. Rev. Lett., 74 (1995) 4647.
33. OPPO G. L., BRAMBILLA M. and LUGIATO L. A., Phys. Rev. A, 49 (1994) 2028.
34. TRILLO S. and HAELTERMAN M., Opt. Lett., 21 (1996) 1114; TLIDI M. and HAELTERMAN M., Phys. Lett. A, 239 (1998) 59.
35. TRILLO S. and HAELTERMAN M., Opt. Lett., 21 (1996) 1114; TLIDI M. and HAELTERMAN M., Phys. Lett. A, 239 (1998) 59.
36. LONGHI S. and GERACI A., Phys. Rev. A, 54 (1996) 5481.
37. DE VALCÁRCEL G. J., STALIUNAS K., E. ROLDÁN and SÁNCHEZ-MORCILLO V. J., Phys. Rev. A, 54 (1996) 1609.
38. MUSSLIMANI Z. H., Physica A, 249 (1998) 141.
39. YARIV A. and YEH P., Optical Waves in Crystals (J. Wiley, New York) 1984.