Numerical investigations of cavity mode instabilities induced by a Gaussian gain medium

The variational equations of Firth [W.J. Firth, Opt. Commun. 22 (1977) 226] are used to study instabilities of the Gaussian mode of a resonator containing a Gaussian gain medium. A series of symmetric two-mirror resonators were chosen for study. When the Rayleigh range of the bare cavity Gaussian mode becomes much greater than the cavity length, and the effective gain spot size drops below that of the bare cavity mode, regions of gain in which the cavity does not have a bound, stable modes appear. This is similar to the results obtained by Firth [W.J. Firth, Opt. Commun. 27 (1978) 267] with a confocal cavity. The results are compared to diffraction calculations for the one of the resonators. The comparison points out some intriguing areas of agreement, and suggest that it may be possible to observe the effects in a real system.