Abstract

Modes of resonators formed by paraxial elements of infinite extent and single internal aperture are shown to be the solutions of two coupled symmetric integral equations involving four parameters: two Fresnel numbers N1 and N2 and two geometrical factors A1 and A2. The modes become the eigenfunctions of an Hermitian operator when N1 = ±N2, A1 = ∓A2; analytical solutions can then be written as generalized prolate spheroidal functions. The same solutions are derived for a resonator in which one mirror is replaced by an infinite phase conjugate mirror. Real nonsymmetric eigenvalue problems are associated with the condition N1A1 = −N2A2; such configurations can generate pairs of modes with same power losses but different oscillation frequencies. Extension to cavities with two internal apertures yields a system of four coupled integral equations with eight independent parameters; again the modes can be the solutions of Hermitian or real nonsymmetric eigenvalue problems under special conditions.

© 1983 Optical Society of America

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