Spatiotemporal dynamics of a unidirectional ring oscillator with photorefractive gain

In a cavity with photorefractive gain the resonator field is fed by a pump beam through two-wave mixing inside a photorefractive crystal. In this paper we develop a simplified model for such a system which takes into account the transverse dependence of the pump and the resonator fields. We then study the onset of spatiotemporal structures both analytically and numerically.