Geometrical theory of whispering-gallery modes

Using a quasi-classical approach, rather precise analytical approximations for the eigenfrequencies of whispering-gallery modes (WGMs) in convex axisymmetric bodies may be found. We use the eikonal method to analyze the limits of precision of quasi-classical approximation using, as a practical example, a spheroidal dielectric cavity. The series obtained for the calculation of eigenfrequencies is compared with the known series for a dielectric sphere, and with numerical calculations. We show how geometrical interpretation allows expansion of the method on arbitrarily-shaped axisymmetric bodies.