Modes of a thermoelastically disturbed resonator

A theoretical analysis is reported of an optical resonator in the form of a circular cylinder with fixed flat reflecting ends subjected to uniform heating. The modes of such a thermoelastically perturbed resonator are calculated in the first order of the perturbation theory using a small parameter describing the anisotropy of thermooptic perturbations. Explicit expressions are obtained (in terms of the Laguerre polynomials) for the perturbed wave functions, particularly for the distorted TEM₀₀ mode. It is shown that the induced birefringence partly lifts the degeneracy of the eigenfrequency spectrum, which–in the absence of birefringence–is analogous to the spectrum of a hollow resonator in the form of a circular ellipsoid.