Nonparaxial eigenmodes of stable resonators

A method to determine the nonparaxial eigenmodes of stable resonators is pr esented. The method is based on the perturbation theory of Lax et al. for c alculating nonparaxial components of the electric field. A matrix formalism which uses a mode expansion into paraxial Hermite-Gaussian modes is applie d to describe the nonparaxial propagation and the phase shift at a paraboli c and a spherical mirror. Expressions for these matrices are derived analyt ically. Multiplying all matrices corresponding to a round trip, a matrix fo r the resonator is obtained, Eigenmodes of the resonator are numerically fo und by solving the eigenvalue problem, In the special case of paraxial prop agation and parabolic mirror profiles, the standard Hermite-Gaussian modes result analytically, Nonparaxial modes of a given resonator are compared fo r different mirror profiles. It is found that, in the nonparaxial domain, s pherical mirrors do not change the mode profile and the frequencies of the transverse modes, in contrast to parabolic mirrors which aberrate the beam profile and cause frequency shifts.