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Journal of the Optical Society of America B

Steady-state and pulse behavior of light transmitted through dispersive nonlinear media in a ring cavity

Joseph W. Haus, C. M. Bowden, Chi C. Sung

Published Oct 1, 1984• 4 citations

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. A26, 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.

DOI: 10.1364/josab.1.000742

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