Whispering gallery modes at the rim of an axisymmetric optical resonator: analytical versus numerical description and comparison with experiment.

Optical whispering gallery modes (WGMs) of mm-sized axisymmetric resonators are well localized at the equator. Employing this distinctive feature, we obtain simple analytical relations for the frequencies and eigenfunctions of WGMs which include the major radius of the resonator and the curvature radius of the rim. Being compared with results of finite-element simulations, these relations show a high accuracy and practicability. High-precision free-spectral-range measurements with a millimeter-sized disc resonator made of MgF(2) allow us to identify the WGMs and confirm the applicability of our analytical description.