Theory of bistability and self pulsing in a ring resonator with saturable photorefractive gain and loss

Abstract

We present a theory for a ring resonator with saturable photorefractive two-beam coupling gain and loss to address the experimental results of reversible and irreversible bistability and self pulsing. Refractive index gratings in the photorefractive crystals couple energy from a gain pump beam into a resonator beam, and from the resonator beam into a loss pump beam. The spatiotemporal dependence of the optical fields and the index gratings are described by Maxwell's equations and the Kukhtarev model, respectively. Steady-state solutions of the equations demonstrate both reversible and irreversible bistability. We next derive conditions for the stability of the resonator's off state from a small-signal analysis of the spatio-temporal evolution equations. A stable off state is necessary for bistability, an unstable off state for self pulsing. Numerical simulation of the evolution equations qualitatively reproduces the experimental self pulsing and gives physical insight into the grating dynamics.