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Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Vol. 17, Iss. 6 — Jun. 1, 2000
  • pp: 997–1003

Nonlinear front propagation in optical parametric oscillators

Majid Taki, Najib Ouarzazi, Hélène Ward, and Pierre Glorieux  »View Author Affiliations


JOSA B, Vol. 17, Issue 6, pp. 997-1003 (2000)
http://dx.doi.org/10.1364/JOSAB.17.000997


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Abstract

Transverse nonlinear front (or domain wall) propagation in degenerate optical parametric oscillators, for positive detunings and in the presence of walk-off, is investigated. A quintic Ginzburg–Landau equation including diffraction and walk-off is derived close to subcritical bifurcation. A new threshold is found below the linear one, where nonlinear front propagation dominates the dynamics. The velocity and the wave number of these fronts are determined. Nonlinear absolute and convective instabilities are shown to strongly alter the hysteresis cycle, which completely vanishes when the walk-off exceeds some critical value.

© 2000 Optical Society of America

OCIS Codes
(190.0190) Nonlinear optics : Nonlinear optics
(190.4420) Nonlinear optics : Nonlinear optics, transverse effects in
(190.4970) Nonlinear optics : Parametric oscillators and amplifiers
(190.5530) Nonlinear optics : Pulse propagation and temporal solitons

Citation
Majid Taki, Najib Ouarzazi, Hélène Ward, and Pierre Glorieux, "Nonlinear front propagation in optical parametric oscillators," J. Opt. Soc. Am. B 17, 997-1003 (2000)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-17-6-997


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References

  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). [CrossRef]
  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 3, 275–288 (1998). [CrossRef]
  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). [CrossRef]
  4. 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). [CrossRef] [PubMed]
  5. T. Nishikawa and N. Uesugi, “Walk-off and pump energy dependence of transverse beam profiles on traveling wave parametric generation,” Opt. Commun. 140, 277–280 (1997); “Effects of walk-off and group velocity difference on the optical parametric generation in KTiOPO4 crystals,” J. Appl. Phys. 77, 4941–4947 (1995). [CrossRef]
  6. 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 PLRAAN 54, 1609–1624 (1996). [CrossRef] [PubMed]
  7. S. Longhi, “Spatial-temporal instabilities and threshold conditions in broad-area optical parametric oscillators,” Opt. Commun. 153, 90–94 (1998); “Traveling waves states and secondary instabilities in optical parametric oscillators,” Phys. Scr. 56, 611–618 (1997). [CrossRef]
  8. A. Newell and J. Moloney, Nonlinear Optics (Addison-Wesley, Redwood City, Calif., 1992), Chaps. 5 and 6.
  9. P. Coullet, L. Gil, and F. Rocca, “Optical vortices,” Opt. Commun. 73, 403–408 (1989). [CrossRef]
  10. A. Bers, Basic Plasma Physics I, A. A. Galeev and R. N. Sudan, eds. (North-Holland, Amsterdam, 1983).
  11. 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). [CrossRef]
  12. 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. E 50, 3670–3692 (1994). [CrossRef]
  13. W. van Saarloos and P. C. Hohenberg, “Fronts, pulses, sources and sinks in generalized complex Ginzburg–Landau equations,” Physica D 14, 303–367 (1992). [CrossRef]
  14. 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). [CrossRef] [PubMed]
  15. 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). [CrossRef] [PubMed]
  16. 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). [CrossRef]
  17. S. Longhi, “Spatial solitary waves in nondegenerate optical parametric oscillators near an inverted bifurcation,” Opt. Commun. 149, 335–340 (1998). [CrossRef]
  18. 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 PEAMDU 116, 193–206 (1990). [CrossRef] [PubMed]

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