Analytical Approximations of Whispering gallery Modes in Anisotropic Ellipsoidal Resonators

TL;DR

This paper develops analytical approximations for whispering gallery modes in anisotropic ellipsoidal resonators, facilitating easier analysis of their eigenmodes and eigenfrequencies through numerical and qualitative methods.

Contribution

It introduces manageable analytical formulas for anisotropic resonator modes based on numerical evolutions and superposition analysis, advancing understanding of their eigenproperties.

Findings

Analytical approximations closely match numerical results.

Superposition of spherical modes explains anisotropic mode behavior.

Eigenfrequencies derived for various anisotropic ellipsoids.

Abstract

Numerical evolutions of whispering gallery modes of both isotropic and anisotropic spheroidal resonators are presented and used to build analytical approximations of these modes. Such approximations are carried out mainly to have the possibility to have a manageable analytic formulas for the eigenmodes and eigenfrequencies of anisotropic resonators. A qualitative analysis of ellipsoidal anisotropic modes in term of superposition of spherical modes is also presented.