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A self-consistent perturbation method is developed for the determination of the normal modes and eigenvalues of optic cavities of small Fresnel numbers. The method permits direct determination of the field distribution and eigenvalue (i.e., the diffraction loss and resonant frequency) of a normal mode of any given order to within any desired accuracy without simultaneously solving for the other modes, and can be applied to cavities having end reflectors of arbitrary shape and curvature. The method is applied to solve the integral equation governing the relation between the normal modes and the geometry of the cavity for the particular case of infinite-strip parabolic cavities.
Bergstein et al. (1965) studied this question.