Whispering gallery modes in axisymmetric resonators

Using quasiclassical approach rather precise analytical approximations for the eigenfrequencies of whispering gallery modes in convex axisymmetric bodies may be found. We use the eikonal method to analyze the limits of precision of this approach using as a practical example spheroidal dielectric cavity. The series obtained for the calculation of eigenfrequency is compared with the known series for dielectric sphere and numerical calculations.