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

Nanoparticle-induced modifications of the spectrum of whispering-gallery modes (WGMs) 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 the 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 other areas.