Stability of optical laser resonators with mirrors of gaussian reflectivity profiles,which contain an active medium

The stability of laser resonators which contain a medium with a gain profile is investigated. Such resonators are unstable when the resonator mirrors are large (infinite aperture approximation), and the gain is lowest on the optical axis and increases with radial distance. It is shown that such resonators have well-defined regions of stability if the mirrors have gaussian reflectivity tapers.