Fast self-pulsing through nonlinear incoherent feedback

We consider a double-pass ring cavity with nonlinear incoherent optical feedback and analyze its response when it is driven by a continuous laser beam. This particular cavity is equivalent, in the temporal domain, to a simple spatial-pattern-generating system made from a Kerr slice and a feedback mirror. After formulating the evolution equations, we investigate the behavior of small-amplitude solutions and obtain an expression for the round-trip gains. We then explore the important effect of dispersion in the nonlinear medium. Finally, we show that stable modes are possible by solving numerically the full nonlinear equations.