Optical Resonator Modes—Rectangular Reflectors of Spherical Curvature*

A combined analytic and numerical technique for solving the integral equation for optical-resonator modes based on the work of Schmidt is introduced. The method involves a kernel expansion which converts the integral equation to a matrix equation. Numerical diagonalization of the matrix then yields all modes simultaneously.The potentialities of the method in treating resonator configurations such as those with tilted or irregular mirrors, which are intractable by present analytic or semi-analytic theories, are discussed. Numerical results of mode patterns, including both magnitude and phase, losses, and resonance conditions are presented for a resonator formed by two spherical mirrors of differing curvature and rectangular cross section. These results are for a moderately large Fresnel number and include “high-loss” geometries.

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