Self pulsing in a ring resonator with saturable photorefractive gain and loss

A ring resonator with photorefractive gain and loss is an active nonlinear system that exhibits self pulsing of the resonator intensity1. The novel feature of this resonator over single crystal resonators2,3 is the addition of a second crystal in our case to couple light out of the resonator providing a saturable loss4. The nonlinearity of a single crystal resonator is manifested in the saturation of the small signal gain. The nonlinearity of the two crystal system is enriched by the interplay between the two crystal time constants and the small signal gain and loss, as well as the addition of the second saturation point The dynamic behavior of the system can be described as a competitive interaction between gain and loss; if the gain wins, the resonator turns on, and if the loss wins the resonator remains off. Self pulsing occurs when the winner is alternately the gain and then the loss, and then the gain again, and so forth. The relative time constants, coupling strengths, and saturation points of the two crystals dictate the details of the competitive interaction. In this communication we include the loss crystal in a theory for photorefractive resonators to address the experimental observations of self pulsing.