Full-wave theory for WGM lasing of fully anisotropic nanoparticles

Abstract

A full-wave theory for the prediction of the complex whispering-gallery-mode (WGM) resonances of fully anisotropic nano/microresonators is presented. The theory is based on the volume integral equation (VIE) method, supported by appropriate perturbation theory which enables analytical closed-form expressions valid for extremely large indices of the involved spherical wavefunctions. These closed-form expressions allow for the instant computation of the eigenbasis required for the solution of the VIE. The theory is applied to the calculation of WGM spectra of uniaxial semiconductor crystals, to gyroelectric magnetic garnets, and to geometrical birefringence enhancement due to large Verdet constants. Combined with a state-of-the-art open-source algorithm for complex roots computation, this theory constitutes a rigorous tool for the interpretation of experimental data obtained from photonic and optomagnonic applications, including WGM lasing of fully anisotropic nanoparticles and magneto-optical coupling.