Abstract

We characterize the Hopf bifurcations that rule self-pulsing of spatially varying fields in distributed feedback structures with Kerr nonlinear response. Our analysis allows us to distinguish, inside the stop band, between fully unstable regions and those where stable high transmission mediated by localized waves is achievable dynamically. Outside the stop band, the grating reveals a complex behavior where islands of stability are interspersed between regions of self-pulsing and bistability. Numerical integration of the time-dependent coupled-mode equations validates our linear stability analysis and illustrates the dynamics.

© 2007 Optical Society of America

Slaved bistability and self-pulsing in a nonlinear interferometer

F. Marquis, P. Dobiasch, P. Meystre, and E. M. Wright
J. Opt. Soc. Am. B 3(1) 50-59 (1986)

Solitons in Bragg gratings with saturable nonlinearities

Ilya M. Merhasin, Boris A. Malomed, K. Senthilnathan, K. Nakkeeran, P. K. A. Wai, and K. W. Chow
J. Opt. Soc. Am. B 24(7) 1458-1468 (2007)

Self-pulsing and dynamic bistability in cw-pumped Brillouin fiber ring lasers

Carlos Montes, Derradji Bahloul, Isabelle Bongrand, Jean Botineau, Gérard Cheval, Abdellatif Mamhoud, Eric Picholle, and Antonio Picozzi
J. Opt. Soc. Am. B 16(6) 932-951 (1999)

Self-pulsing instabilities in backward parametric wave mixing

M. Conforti, A. Locatelli, C. De Angelis, A. Parini, G. Bellanca, and S. Trillo
J. Opt. Soc. Am. B 22(10) 2178-2184 (2005)

Solitary waves in coupled nonlinear waveguides with Bragg gratings

William C. K. Mak, P. L. Chu, and Boris A. Malomed
J. Opt. Soc. Am. B 15(6) 1685-1692 (1998)