Equivalence Relations among Spherical Mirror Optical Resonators

The frequencies, field patterns, and losses of the resonant modes of spherical mirror optical resonators can be obtained to good accuracy as the solutions of the integral equations of Fresnel diffraction theory. By a simple transformation of the variables and parameters of the integral equations, we have found certain families of resonators which have the same diffraction loss at each mirror, and whose field patterns are scaled versions of each other. In the case of the infinite strip resonator, this reduces from five to three the number of parameters necessary to specify the losses and mode patterns.