Abstract
We study the propagation of electromagnetic radiation through a ring-cavity device containing a dispersive nonlinear medium. Under conditions appropriate for introducing the slowly varying envelope approximation and for adiabatically eliminating the atomic variables, we calculate analytical expressions between the steady-state-output intensity and the input-field amplitude for two models of the nonlinear susceptibility, the two-level atomic medium and the Kerr medium. The stability of these curves is determined, with special attention given to changes in the thresholds by varying the return-trip phase shift, the linear absorption, and the reflection coefficients of the mirrors. We investigate the positive-branch instabilities resulting in a pulsing output intensity and calculate the bifurcation rate for the period-doubling hierarchy and the fractal dimension of our two-dimensional maps for the Kerr medium. The convergence of the bifurcation rate to a constant is slow, and we find, as in the publications of Snapp et al. [ Opt. Commun. 40, 68 ( 1981)] and Carmichael et al. [ Phys. Rev. A 26, 3408 ( 1982)], that this constant is consistent with that found for the class of one-dimensional maps with a quadratic maximum. This universal constant is observed over a large range of fractal dimensions for the chaotic attractor. Discussions of pulse-output bistability, intermittency, and anomalous switching are given.
© 1984 Optical Society of America
Full Article | PDF ArticleMore Like This
S. M. Hammel, C. K. R. T. Jones, and J. V. Moloney
J. Opt. Soc. Am. B 2(4) 552-564 (1985)
D. J. Jones and D. K. Bandy
J. Opt. Soc. Am. B 7(10) 2119-2126 (1990)
G. Reiner, P. Meystre, and E. M. Wright
J. Opt. Soc. Am. B 4(6) 865-874 (1987)