Modeling of nonlinear Fabry-Perot resonators by difference-differential equations

The aim of present paper is to propose several dynamical models of nonlinear Fabry-Perot resonators. The models are all described by sets of difference-differential (delay-differential) equations involving multiple time delays, and they are extended versions of the difference-differential equations proposed for the ring-type resonators by one of the present authors. We show in detail how these model equations are derived from the Maxwell-Bloch equations, assuming: 1) fast transversal relaxation, 2) weak nonlinearity, and 3) dispersive limit. We propose a hybrid optical bistable device as an analog system of a model equation.