Effect of gain on the electrodynamics of marginally stable resonators

Abstract

We examine the wave equation for an open resonator with flat mirrors in the case in which it is driven by a nonlinear gain term and formulate an integral equation from first principles. The eigenvalues and eigenfunctions of such a resonator equation may be obtained in the limit in which the nonlinear susceptibility is small or has a weak transverse dependence. In particular, we find that for the loaded cavity, the losses and eigenfunctions (modes) may be obtained by solving a linear Fresnel–Kirchhoff integral equation with gain-renormalized eigenvalue and Fresnel number. Relations are presented that may be used to predict for which conditions the effects of gain significantly change the modes from those of an empty resonator.