Diffraction Losses of a Dielectric Open Resonator

This paper was stimulated by the experimental studies of solid-state lasers initiated by N. G. Basov and carried out at the Laboratory of Luminescence of the P. N. Lebedev Physical Institute under the direction of M. D. Galanin and A. M. Leontovich in the 1960-ies. Here, the classical parabolic equation method is extended in order to calculate complex eigenfrequencies of optical oscillations in a dielectric-filled open resonator. Accurate estimates confirm a high quality factor of ruby lasers. The developed approach can be used to find complex eigenfrequencies of other dielectric optical objects in laser systems of current interest.