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

An analytic solution for a uniaxial spherical resonator is presented using the method of Debye potentials. This serves as a starting point for the calculation of whispering gallery modes (WGMs) in such a resonator. Suitable approximations for the radial functions are discussed in order to best characterize WGMs. The characteristic equation and its asymptotic expansion for the anisotropic case is also discussed, and an analytic formula with a precision of the order O[v-1] is also given. Our careful treatment of both boundary conditions and asymptotic expansions makes the present work a particularly suitable platform for a quantum theory of whispering gallery resonators. [ABSTRACT FROM AUTHOR]