COHERENT EVOLUTION-EQUATIONS FOR LASER RESONATORS

An analytical formulation is presented for the derivation of exact dif ferential equations describing the evolution of the complex cavity fie lds in laser resonators. The starting point is an integral equation, f or example, of Fox-Li type, from which a differential equation is deri ved following a rigorous procedure that guarantees preservation of the resonator modal structure. The form of such evolution equations for g iven resonator and field definitions is not unique, but all expression s derived by this method are equivalent in the sense that they carry t he same dynamical information as the original integral equation. The e xample of two longitudinally coupled Fabry-Perot lasers separated by a gap is studied in detail. Agreement with previous heuristic models is found in the weak interaction limit, but in the case of semiconductor lasers, which have comparatively transmissive facets, the corrections are significant. In a second application, the evolution equation of a distributed feedback laser is derived. [S1050-2947(98)00809-9].