Theory of the nanoparticle-induced frequency shifts of whispering-gallery-mode resonances in spheroidal optical resonators

TL;DR

This paper develops analytical models to understand how nanoparticles affect the spectral properties of whispering-gallery modes in spheroidal optical resonators, aiding applications in biosensing and quantum optics.

Contribution

It introduces simple analytical expressions for nanoparticle-induced frequency shifts in spheroidal WGM resonators, valid for moderate shape deviations, enhancing understanding of spectral modifications.

Findings

Analytical formulas match experimental data well.

Spectral effects can be enhanced by optimizing resonator parameters.

Models are applicable for biosensing and cavity QED applications.

Abstract

Nanoparticle-induced modifications of the spectrum of whispering-gallery-modes (WGM) of optical spheroidal resonators are studied theoretically. Combining an ab initio solution of a single resonator problem with a dipole approximation for the particle, we derive simple analytical expressions for frequencies and widths of the particle-modified resonances, which are valid for resonators with moderate deviations from the spherical shape. The derived expressions are used to analyze spectral properties of the resonator-particle system as functions of the particle's position, the size of the resonators and the characteristics of WGMs. The obtained results are shown to agree well with available experimental data. It is also demonstrated that the particle-induced spectral effects can be significantly enhanced by careful selection of resonator's size, refractive index and other experimental parameters. The results presented in the paper can be useful for applications of WGM resonators in biosensing, cavity QED, optomechanics and others.