An analysis for resonance characteristics of whispering gallery modes on an elliptic dielectric disk

We analyze the resonance characteristics of whispering gallery modes on an elliptic dielectric disk resonator. We assume that the elliptic disk is decomposed into a slab waveguide having the same thickness as the elliptic disk and an elliptic rod having the same cross section as the disk. On a basis of an effective dielectric constant method, an effective permittivity of the rod resonator is derived from the propagation constant of the slab waveguide. Approximated resonance frequencies of the elliptic disk are given by an eigenvalue equation of the elliptic rod resonator with the effective permittivity. We have also performed experiments to confirm the validity and usefulness of our analysis. As a result of our study, it has been found that the present analysis is very simple and useful even if the elliptic disk has a high permittivity.