Ab initio computational analysis of spectral properties of dielectric spheroidal resonators interacting with a subwavelength nanoparticle.

An efficient numerical method for determining the spectral characteristics and spatial distribution of the field of a spheroidal whispering-gallery-mode (WGM) resonator interacting with a dielectric nanoparticle is presented. The developed approach is based on a combination of T-matrix formalism applied to a single resonator with a dipole approximation for the field of the nanoparticle. The method is illustrated by computation of the scattered field of the resonator-particle system illuminated by an incident field in the form of a single WGM mode of TE or TM polarization mimicking the excitation of the resonances by a tapered fiber. Our calculations show that even a very small (less than 0.1%) deviation of the resonator's shape from an ideal sphere renders spherical approximation invalid. They also confirm that analytical resonant approximation for spheroidal resonators developed previously gives a reasonable qualitative description of the spectral characteristics of the resonator-particle system. It was found, however, that corrections to the resonant approximation are significant enough for realistic nominally spherical resonators to be taken into account for accurate analysis of the experimental data.