A study is made of the resonant or normal modes of optic and quasioptic interferometer cavities with plane-parallel end reflectors. The solution of the integral equation governing the relation between the normal modes and the geometry of the cavity is found by means of a series expansion of orthogonal functions. The terms of the series for the normal modes can be interpreted as Fraunhofer diffraction patterns characteristic of the geometry of the end reflectors. Various geometries, such as the infinite-strip, rectangular, and circular end reflector cavities, are considered and the results plotted and interpreted.
LEONARD BERGSTEIN and HARRY SCHACHTER, "Resonant Modes of Optic Interferometer Cavities. I. Plane-Parallel End Reflectors," J. Opt. Soc. Am. 54, 887-903 (1964)