Nonlinear front propagation in optical parametric oscillators

Journal of the Optical Society of America B: Optical Physics

Volumn 17, Issue 6, 2000, Pages 997-1003

  Taki, Majid ^a   Ouarzazi, Najib ^a,b   Ward, Hélène ^a   Glorieux, Pierre ^a  

^a UNIVERSITÉ DES SCIENCES ET TECHNOLOGIES DE LILLE   (France)

^b CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

HYSTERESIS; LIGHT PROPAGATION; WAVE EQUATIONS; WAVEFRONTS;

NONLINEAR FRONT PROPAGATION;

OPTICAL PARAMETRIC OSCILLATORS;

EID: 0034383304     PISSN: 07403224     EISSN: None     Source Type: Journal    
DOI: 10.1364/JOSAB.17.000997     Document Type: Article

References (29)

1. M. Santagiustina, P. Colet, M. San Miguel, and D. Walgraef, "Two-dimensional noise-sustained structures in optical parametric oscillators," Phys. Rev. E 58, 3843-3853 (1998).
2. H. Ward, M. N. Ouarzazi, M. Taki, and P. Glorieux, "Transverse dynamics of optical parametric oscillators in presence of walk-off," Eur. Phys. J. D 8, 275-288 (1998).
3. M. Santagiustina, P. Colet, M. San Miguel, and D. Walgraef, "Walk-off and pattern selection in optical parametric oscillators," Opt. Lett. 23, 1167-1169 (1998); G. Izús, M. Santagiustina, M. San Miguel, and P. Colet, "Pattern formation in presence of walk-off for a type II optical parametric oscillator," J. Opt. Soc. Am. B 16, 1592-1596 (1999).
4. M. Santagiustina, P. Colet, M. San Miguel, and D. Walgraef, "Walk-off and pattern selection in optical parametric oscillators," Opt. Lett. 23, 1167-1169 (1998); G. Izús, M. Santagiustina, M. San Miguel, and P. Colet, "Pattern formation in presence of walk-off for a type II optical parametric oscillator," J. Opt. Soc. Am. B 16, 1592-1596 (1999).
5. J. N. Kutz, T. Erneux, S. Trillo, and M. Haelterman, "Curvature dynamics and stability of topological solitons in the optical parametric oscillator," J. Opt. Soc. Am. B 16, 1936-1941 (1999); S. Trillo, M. Haelterman, and A. Sheppard, "Stable topological spatial solitons in optical parametric oscillators," Opt. Lett. 22, 970-972 (1997).
6. J. N. Kutz, T. Erneux, S. Trillo, and M. Haelterman, "Curvature dynamics and stability of topological solitons in the optical parametric oscillator," J. Opt. Soc. Am. B 16, 1936-1941 (1999); S. Trillo, M. Haelterman, and A. Sheppard, "Stable topological spatial solitons in optical parametric oscillators," Opt. Lett. 22, 970-972 (1997).
7. 4 crystals," J. Appl. Phys. 77, 4941-4947 (1995).
8. 4 crystals," J. Appl. Phys. 77, 4941-4947 (1995).
9. G. L. Oppo, M. Brambilla, and L. A. Lugiato, "Formation and evolution of roll patterns in optical parametric oscillators," Phys. Rev. A 49, 2028-2032 (1994); K. Staliunas, "Optical vortices during three-wave nonlinear coupling," Opt. Commun. 58, 82-86 (1992); G. J. de Varcacel, K. Staliunas, E. Roldan, and V. J. Sanchez-Morcillo, "Transverse patterns in degenerate optical parametric oscillators and degenerate four-wave mixing, " Phys. Rev. A 54, 1609-1624 (1996).
10. G. L. Oppo, M. Brambilla, and L. A. Lugiato, "Formation and evolution of roll patterns in optical parametric oscillators," Phys. Rev. A 49, 2028-2032 (1994); K. Staliunas, "Optical vortices during three-wave nonlinear coupling," Opt. Commun. 58, 82-86 (1992); G. J. de Varcacel, K. Staliunas, E. Roldan, and V. J. Sanchez-Morcillo, "Transverse patterns in degenerate optical parametric oscillators and degenerate four-wave mixing, " Phys. Rev. A 54, 1609-1624 (1996).
11. G. L. Oppo, M. Brambilla, and L. A. Lugiato, "Formation and evolution of roll patterns in optical parametric oscillators," Phys. Rev. A 49, 2028-2032 (1994); K. Staliunas, "Optical vortices during three-wave nonlinear coupling," Opt. Commun. 58, 82-86 (1992); G. J. de Varcacel, K. Staliunas, E. Roldan, and V. J. Sanchez-Morcillo, "Transverse patterns in degenerate optical parametric oscillators and degenerate four-wave mixing, " Phys. Rev. A 54, 1609-1624 (1996).
12. S. Longhi, "Spatial-temporal instabilities and threshold conditions in broad-area optical parametric oscillators," Opt. Commun. 158, 90-94 (1998); "Traveling waves states and secondary instabilities in optical parametric oscillators," Phys. Scr. 56, 611-618 (1997).
13. S. Longhi, "Spatial-temporal instabilities and threshold conditions in broad-area optical parametric oscillators," Opt. Commun. 158, 90-94 (1998); "Traveling waves states and secondary instabilities in optical parametric oscillators," Phys. Scr. 56, 611-618 (1997).
14. A. Newell and J. Moloney, Nonlinear Optics (AddisonWesley, Redwood City, Calif., 1992), Chaps. 5 and 6.
15. P. Coullet, L. Gil, and F. Rocca, "Optical vortices," Opt. Commun. 73, 403-408 (1989).
16. A. Bers, Basic Plasma Physics I, A. A. Galeev and R. N. Sudan, eds. (North-Holland, Amsterdam, 1983).
17. P. A. Monkewitz, P. Huerre, and J. M. Chomaz, "Global linear stability analysis of weakly nonparallel shear flows," J. Fluid Mech. 251, 1-20 (1993).
18. H. W. Müller and M. Tveitereid, "Absolute and convective nature of Eckhaus and zigzag instability," Phys. Rev. Lett. 74, 1582-1585 (1995); K. L. Babcock, G. Ahlers, and D. S. Cannell, "Noise amplification in open Taylor-Couette flow," Phys. Rev. B 50, 3670-3692 (1994).
19. H. W. Müller and M. Tveitereid, "Absolute and convective nature of Eckhaus and zigzag instability," Phys. Rev. Lett. 74, 1582-1585 (1995); K. L. Babcock, G. Ahlers, and D. S. Cannell, "Noise amplification in open Taylor-Couette flow," Phys. Rev. B 50, 3670-3692 (1994).
20. W. van Saarloos and P. C. Hohenberg, "Fronts, pulses, sources and sinks in generalized complex Ginzburg-Landau equations," Physica D 14, 303-367 (1992).
21. A. Couairon and J. M. Chomaz, "Global instability in nonlinear systems," Phys. Rev. Lett. 77, 4015-4018 (1996); "Absolute and convective instabilities, front velocities and global modes in nonlinear systems," Physica D 108, 236-276 (1997).
22. A. Couairon and J. M. Chomaz, "Global instability in nonlinear systems," Phys. Rev. Lett. 77, 4015-4018 (1996); "Absolute and convective instabilities, front velocities and global modes in nonlinear systems," Physica D 108, 236-276 (1997).
23. W. van Saarloos, "Front propagation into unstable states: marginal stability as a dynamical mechanism for velocity selection," Phys. Rev. A 37, 211-229 (1988); W. van Saarloos, "Front propagation into unstable states: II. Linear versus nonlinear marginal stability and rate of convergence," Phys. Rev. A 39, 6367-6390 (1989).
24. W. van Saarloos, "Front propagation into unstable states: marginal stability as a dynamical mechanism for velocity selection," Phys. Rev. A 37, 211-229 (1988); W. van Saarloos, "Front propagation into unstable states: II. Linear versus nonlinear marginal stability and rate of convergence," Phys. Rev. A 39, 6367-6390 (1989).
25. M. Taki, M. San Miguel, and M. Santagiustina, "Order parameter description of walk-off effect on pattern selection in degenerate optical parametric oscillators," Phys. Rev. E 61, 2133-2136 (2000).
26. S. Longhi, "Spatial solitary waves in nondegenerate optical parametric oscillators near an inverted bifurcation," Opt. Commun. 149, 335-340 (1998).
27. J. A. Powell and M. Tabor, "Non-generic connections corresponding to front solutions," J. Phys. A 25, 3773-3796 (1992); J. A. Powell, A. C. Newell, and C. K. R. T. Jones, "Competition between generic and nongeneric fronts in envelope equations," Phys. Rev. A 44, 3636-3652 (1991); C. K. R. T. Jones, T. M. Kapitula, and J. A. Powell, "Nearly real fronts in a quintic amplitude equation," Proc. R. Soc. Edinburgh Sect. A 116, 193-206 (1990).
28. J. A. Powell and M. Tabor, "Non-generic connections corresponding to front solutions," J. Phys. A 25, 3773-3796 (1992); J. A. Powell, A. C. Newell, and C. K. R. T. Jones, "Competition between generic and nongeneric fronts in envelope equations," Phys. Rev. A 44, 3636-3652 (1991); C. K. R. T. Jones, T. M. Kapitula, and J. A. Powell, "Nearly real fronts in a quintic amplitude equation," Proc. R. Soc. Edinburgh Sect. A 116, 193-206 (1990).
29. J. A. Powell and M. Tabor, "Non-generic connections corresponding to front solutions," J. Phys. A 25, 3773-3796 (1992); J. A. Powell, A. C. Newell, and C. K. R. T. Jones, "Competition between generic and nongeneric fronts in envelope equations," Phys. Rev. A 44, 3636-3652 (1991); C. K. R. T. Jones, T. M. Kapitula, and J. A. Powell, "Nearly real fronts in a quintic amplitude equation," Proc. R. Soc. Edinburgh Sect. A 116, 193-206 (1990).