Diffraction loss of stable optical resonators with internal limiting apertures

It is pointed out that in many stable laser resonators, the diffraction loss derives principally or even entirely from internal occluding elements with two or more limiting apertures rather than from any mirror size limitations. Resonators of this type, 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. It is shown that when the end mirrors are convex, with radii of curvature greater than the distance to the nearest aperture, the equivalent symmetric cavities are stable. Their diffraction losses are given by the graphs published by Fox and Li (1963), Li (1965), and Kogelnik and Li (1966). Circular and rectangular limiting apertures are discussed as examples of the method.