We study the role of polarization in modulational instabilities in a synchronously pumped ring resonator that is filled with an isotropic nonlinear dispersive medium. To describe nonlinear propagation of the polarized field through the ring, we introduce two coupled driven and damped nonlinear Schrödinger equations. These equations, which result from averaging propagation and boundary conditions over each circulation through the ring, permit a simple stability analysis. This analysis predicts polarization multistability in the steady state as well as the emergence of stable pulse trains whose polarization state is either parallel or orthogonal to a linearly polarized synchronous pump beam. The analytical predictions are confirmed and extended by numerical simulations of polarized wave propagation in the cavity.
© 1994 Optical Society of America
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