Stability of optical resonators with an active medium

The problem of the stability of the Gaussian modes of an optical resonator of large mirror apertures filled with a medium having a gain and index profile is considered. Recent results by other investigators are carefully examined in an attempt to clarify a discrepancy between them. It is found that the modes of the resonator are stable if the gain is highest on the resonator axis. When the gain increases with distance from the resonator axis, one can calculate a Gaussian eigenmode,:but this mode is unstable in the sense that any deviation from the exact physical parameters defining the mode will cause its divergence to an infinite spot size.