A theoretical analysis of resonator modes in the presence of homogeneous media

A method of analyzing the modes of laser resonators containing homogeneous media is presented and established. This analysis is based on a derivation, which begins with Maxwell's equations and displays the required assumptions, of a pair of integral equations involving the tangential fields on the resonator mirrors. This pair of equations, which must be solved simultaneously, is specialized to apply to paraxial resonators with perfectly conducting mirrors. The result of the specialization is a pair of integral, eigenvalue equations for the current distributions induced on the resonator mirrors.