Abstract

We analyze a simple model of dispersive optical bistability in a ring cavity filled with a Kerr medium in the presence of two and three (carrier and one sideband pair) different frequencies. The steady-state characteristics are shown and the condition for selective switching is studied. We show the phenomenon of the so-called competition for resonance between different frequencies. The characteristic phenomenon of locking of the output intensities is presented. The model of two frequencies may also be used to describe bistability in the presence of two different polarizations. For three frequencies our discussion is based on the rigorous propagation equations, which admit a real Hamiltonian description and are completely integrable. We also discuss a general numerical approach, based on a relaxation method, for finding steady-state solutions and checking their stability. The relaxation dynamics is physically related to a finite response time of the medium. The effect of this finite response time on the stability of the steady states and on the dynamics is also discussed.

© 1991 Optical Society of America