RAY-OPTICAL ANALYSIS OF CYLINDRICAL UNSTABLE RESONATORS

A study of unstable cylindrical strip resonators is carried out here by utilization solely of the fundamental constructs of ray optics. The analysis combines individual as well as collective treatment of reflected and diffracted rays via the geometrical theory of diffraction and the ray theory of guided modes, respectively. It is found that various propagation parameters and relations so derived resemble closely those appearing in the postulative approach of Horwitz for the asymptotic solution of the resonator integral equation. Subject to stated approximations, the ray-optical results can be reduced completely to those of Horwitz and thereby furnish for the Horwitz solutions a previously lacking deductive and systematic interpretation. Because of the general applicability of ray methods to nonideal mirror shapes and media with local inhomogeneities, it is suggestive that the analysis presented here can be extended to more complicated resonator configurations.