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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 9, Iss. 2 — Feb. 1, 1992
  • pp: 251–260

Transverse instability in a nonlinear waveguide. II. Saturation and steady state

B. D. Robert and J. E. Sipe  »View Author Affiliations

JOSA B, Vol. 9, Issue 2, pp. 251-260 (1992)

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We consider a laser that is incident normally upon a planar waveguide with a Kerr nonlinearity. In a previous paper [J. Opt. Soc. Am. 8, 786 (1991)] we demonstrated that the waveguide fields can participate in a transverse instability of the incident beam. We examine the evolution of this instability, show that the system evolves to a steady-state pattern, and develop a general instability criterion.

© 1992 Optical Society of America

B. D. Robert and J. E. Sipe, "Transverse instability in a nonlinear waveguide. II. Saturation and steady state," J. Opt. Soc. Am. B 9, 251-260 (1992)

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  1. See, e.g., feature on transverse effects in nonlinear-optical systems, N. B. Abraham and W. J. Firth, eds., J. Opt. Soc. Am. B 7, 947–1157, 1259–1373 (1990).
  2. E.g., K. Dworschak, J. E. Sipe, and H. M. van Driel, "Solid–melt patterns induced on silicon by a continuous laser beam at nonnormal incidence," J. Opt. Soc. Am. B 7, 981–989 (1990); J. V. Moloney, H. Adachihara, R. Indik, C. Lizarraga, R. Northcutt, D. W. McLaughlin, and A. C. Newell. "Modulation-induced optical pattern formation in a passive optical-feedback system," J. Opt. Soc. Am. B 7, 1039–1044 (1990).
  3. E.g., F. Hollinger, Chr. Jung, and H. Weber, "Simple mathematical model describing multitransversal solid-state lasers," J. Opt. Soc. Am. B 7, 1013–1018 (1990).
  4. E.g., M. Dagenais and H. G. Winful, "Low transverse optical bistability near bound excitons in cadmium sulfide," Appl. Phys. Lett. 44, 574–576 (1984); Chr. Tamm and C. O. Weiss, "Bistability and optical switching of spatial patterns in a laser," J. Opt. Soc. Am. B 7, 1034–1038 (1990).
  5. B. D. Robert and J. E. Sipe, "Transverse instability in a nonlinear waveguide. I. Linear analysis," J. Opt. Soc. Am. B 8, 786–796 (1991). We take this opportunity to correct an error in that paper: In all equations from Eq. (3.4) onward any occurrences of ω, the detuning between the waveguide field and the incident beam, should be replaced by ω/vg, where vg = 1/(dk/dω) is the group velocity of the waveguide mode. This holds for both the real and the imaginary parts of ω.
  6. H. Goldstein, Classical Mechanics (Addison-Wesley, New York, 1981).
  7. J. H. Marburger and J. F. Lam, "Nonlinear theory of degenerate four-wave mixing," Appl. Phys. Lett. 34, 389–391 (1979).
  8. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).
  9. E. Hairer, S. P. Nørsett, and G. Wanner, Solving Ordinary Differential Equations I (Springer-Verlag, Berlin, 1987).
  10. K. Dekker and J. G. Verwer, Stability of Runge–Kutte Methods for Nonstiff Nonlinear Equations (North-Holland, Amsterdam, 1984).
  11. C. M. de Sterke, K. R. Jackson, and B. D. Robert, "Nonlinear coupled-mode equations on a finite interval: a numerical procedure," J. Opt. Soc. Am. B 8, 403–412, (1991).
  12. R. A. Fisher, ed., Optical Phase Conjugation (Academic, New York, 1983); B. T. Zel'dovich, N. F. Pipiletsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, New York, 1983).
  13. C. M. de Sterke and J. E. Sipe, "Switching behavior of finite periodic nonlinear media," Phys. Rev. A 42, 2858–2869 (1990).
  14. T. J. Karr, J. R. Morris, D. H. Chambers, J. A. Viecelli, and P. G. Cramer, "Perturbation growth by thermal blooming in turbulence," J. Opt. Soc. Am. B 7, 1103–1124 (1990); M. D. Fiet and J. A. Fleck, Jr., "Beam nonparaxiality, filament formation, and beam breakup in the self-focusing of optical beams," J. Opt. Soc. Am. B 5, 633–640 (1988).
  15. A. L. Gaeta, R. W. Boyd, J. R. Ackerhalt, and P. W. Milonni, "Instabilities and chaos in the polarization of counterpropagating light fields," Phys. Rev. Lett. 58, 2432–2435 (1987).
  16. W. J. Firth and C. Paré, "Transverse modulation instabilities for counterpropagating beams in Kerr media," Opt. Lett. 13, 1096–1098 (1988).
  17. Y. Silberberg and I. Bar Joseph, "Instabilities, self-oscillation, and chaos in a simple nonlinear interaction," Phys. Rev. Lett. 48, 1541–1543 (1982); I. Bar-Joseph and Y. Silberberg, "The mechanism of instabilities in an optical cavity," Opt. Commun. 48, 53–56 (1983).
  18. C. T. Law and A. E. Kaplan, "Dispersion-related multimode instabilities and self-sustained oscillations in nonlinear counterpropagating waves," Opt. Lett. 14, 734–736 (1989).

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