Cylindrical resonator with an internal astigmatic medium

A theoretical analysis is made of a resonator formed by two cylindrical mirrors with mutually orthogonal generators and containing an astigmatic medium. It is shown that elliptic Gaussian beams represent natural oscillation modes of such a cavity resonator. Expressions are obtained for the dimensions of the caustic along characteristic sections of the resonator and these make it possible to solve the problem of synthesis of resonators with the required filling of the active element by the radiation field.