Equivalence Relations among Spherical Mirror Optical Resonators

The resonant frequencies, field patterns, and losses of the modes of spherical mirror optical resonators can lie obtained to good accuracy as the solutions of the integral equations of Fresnel diffraction theory. 1 The equations are particularly applicable when the separation between the two mirrors forming the resonator is large compared with the dimensions of the mirrors, rnfortunately, the equations are usually not soluble analytically, and require numerical (machine) computation. There are many parameters involved: the dimensions and curvatures of the mirrors and their separation. 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. II. TIIE TRANSFORMATION'