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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: George I. Stegeman
  • Vol. 22, Iss. 10 — Oct. 1, 2005
  • pp: 2178–2184

Self-pulsing instabilities in backward parametric wave mixing

M. Conforti, A. Locatelli, C. De Angelis, A. Parini, G. Bellanca, and S. Trillo  »View Author Affiliations

JOSA B, Vol. 22, Issue 10, pp. 2178-2184 (2005)

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We investigate temporal stability of stationary solutions for backward degenerate parametric mixing. We show that self-oscillating solutions can be obtained from properly chosen continuous-wave counterpropagating inputs at fundamental and second-harmonic frequencies under general phase-mismatched conditions. The temporal oscillation period near the bifurcation points is predicted by linear stability analysis and verified by numerical simulation of the governing equations.

© 2005 Optical Society of America

OCIS Codes
(190.1450) Nonlinear optics : Bistability
(190.3100) Nonlinear optics : Instabilities and chaos
(190.4410) Nonlinear optics : Nonlinear optics, parametric processes
(230.4320) Optical devices : Nonlinear optical devices
(230.4910) Optical devices : Oscillators

ToC Category:
Nonlinear Optics

M. Conforti, A. Locatelli, C. De Angelis, A. Parini, G. Bellanca, and S. Trillo, "Self-pulsing instabilities in backward parametric wave mixing," J. Opt. Soc. Am. B 22, 2178-2184 (2005)

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  1. S. E. Harris, "Proposed backward wave oscillation in the infrared," Appl. Phys. Lett. 9, 114-116 (1966).
  2. P. St. J. Russell, "Theoretical study of parametric frequency and wavefront conversion in nonlinear holograms," IEEE J. Quantum Electron. 27, 830-835 (1991).
  3. J. U. Kang, Y. J. Ding, W. K. Burns, and J. S. Melinger, "Backward second-harmonic generation in periodically poled bulk LiNbO3," Opt. Lett. 22, 862-864 (1997).
  4. X. Gu, M. Makarov, Y. J. Ding, J. B. Khurgin, and W. P. Risk, "Backward second-harmonic generation and third-harmonic generation in a periodically poled KTP waveguide," Opt. Lett. 24, 127-129 (1999).
  5. X. Mu, I. B. Zotova, Y. J. Ding, and W. P. Risk, "Backward second-harmonic generation in submicron-period ion-exchanged KTiOPO4 waveguide," Opt. Commun. 181, 153-159 (2000).
  6. C. Conti, S. Trillo, and G. Assanto, "Energy localization in photonic crystals of a purely nonlinear origin," Phys. Rev. Lett. 85, 2502-2505 (2000).
  7. M. Matsumoto and K. Tanaka, "Quasi-phase-matched second-harmonic generation by backward propagating interaction," IEEE J. Quantum Electron. 31, 700-705 (1995).
  8. P. M. Lushnikov, P. Lodhal, and M. Saffman, "Transverse modulational instability of counterpropagating quasi-phase-matching beams in a quadratically nonlinear medium," Opt. Lett. 23, 1650-1652 (1998).
  9. G. D'Alessandro, P. St. J. Russell, and A. A. Wheeler, "Nonlinear dynamics of a backward quasi-phase-matched second-harmonic generator," Phys. Rev. A 55, 3211-3218 (1997).
  10. C. Conti, G. Assanto, and S. Trillo, "Cavityless oscillator through backward quasi-phase-matched second-harmonic generation," Opt. Lett. 24, 1139-1141 (1999).
  11. K. J. McNeil, P. D. Drummond, and D. F. Walls, "Self pulsing in second-harmonic generation," Opt. Commun. 27, 292-294 (1978).
  12. L. A. Lugiato and R. Lefevre, "Spatial dissipative structures in passive optical systems," Phys. Rev. Lett. 58, 2209-2211 (1987).
  13. L. A. Lugiato, C. Oldano, C. Fabre, E. Giacobino, and R. J. Horowicz, "Bistability, self-pulsing and chaos in optical parametric oscillators," Nuovo Cimento D 10, 959-977 (1988).
  14. S. Trillo and M. Haelterman, "Pulse train generation through modulational instability in intracavity second-harmonic generation," Opt. Lett. 21, 1114-1116 (1996).
  15. H. G. Winful, J. H. Marburger, and E. Garmire, "Theory of bistability in non-linear distributed feedback structures," Appl. Phys. Lett. 35, 379-381 (1979).
  16. H. G. Winful and G. D. Cooperman, "Self-pulsing and chaos in distributed feedback bistable optical devices," Appl. Phys. Lett. 40, 298-300 (1982).
  17. A. Mecozzi, S. Trillo, and S. Wabnitz, "Spatial instabilities, all-optical limiting and thresholding in nonlinear distributed-feedback devices," Opt. Lett. 12, 1008-1010 (1987).
  18. C. M. de Sterke, "Stability analysis of nonlinear periodic media," Phys. Rev. A 45, 8252-8258 (1992).
  19. Y. Silberberg and I. Bar-Joseph, "Instabilities, self-oscillation and chaos in a simple nonlinear optical interaction," Phys. Rev. Lett. 48, 1541-1544 (1982).
  20. C. Richy, K. I. Petsas, E. Giacobino, C. Fabre, and L. Lugiato, "Observation of bistability and delayed bifurcation in a triply resonant optical parametric oscillator," J. Opt. Soc. Am. B 12, 456-461 (1995).
  21. M. Bache, P. Lodhal, A. V. Mamaev, M. Marcus, and M. Saffman, "Observation of self-pulsing in singly resonant optical second-harmonic generation with competing nonlinearities," Phys. Rev. A 65, 033811 (2002). [CrossRef]
  22. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer-Verlag, 1983).
  23. G. Cappellini, S. Trillo, S. Wabnitz, and R. Chisari, "Two wave mixing in a quadratic nonlinear medium: bifurcations, spatial instabilities, and chaos," Opt. Lett. 17, 637-639 (1992).
  24. A. V. Buryak, I. Towers, and S. Trillo, "Multistability, homoclinic clamping, and chaos in nonlinear quadratic distributed feedback systems," Phys. Lett. A 267, 319-325 (2000).

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