Unstable strip resonators with misaligned circular mirrors

Abstract

The waveguide approach developed previously by the authors is here applied to unstable strip resonators with unequal sharp-edged circular mirrors that have been tilted with respect to the resonator axis. An equivalent resonator with nontilted mirrors is defined wherein the mirror edges form asymmetrically placed terminations of the open-ended transverse waveguide. The eigenmode losses are found by calculating the waveguide mode reflection coefficients for each pair of edges and inserting these into the previously derived resonance equation. Numerical calculations for the low-loss detached mode are presented for the special case of symmetrical resonators with equally tilted mirrors since results for this configuration, for moderately large Fresnel numbers, have previously been given by Sanderson and Streifer. Our solutions agree with those of Sanderson and Streifer but accommodate also the range of large Fresnel numbers. It is found that misalignment introduces additional ripples into the power loss vs Fresnel number curves. A ray-optical interpretation in terms of edge diffraction is shown to account for this behavior.