Diffraction loss of stable optical resonators with internal limiting apertures

In many stable laser resonators, the diffraction loss is principally or entirely due to internal occluding elements with two or more limiting apertures, rather than to any mirror size limitations. Such resonators, with any number of arbitrarily located circular or rectangular limiting apertures, can be decomposed into a set of equivalent empty symmetric cavities with finite size mirrors. When the end mirrors are convex, with radii of curvature greater than the distance to the nearest aperture, the equivalent symmetric cavities are stable, and their diffraction losses are given by graphs published by Fox and Li [6]-[8] and reproduced here for the reader's convenience. The method is illustrated by examples with circular and rectangular limiting apertures.