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

Three-Dimensional Simulation of Particle-Induced Mode Splitting in Large Toroidal Microresonators

Whispering gallery mode resonators such as silica microtoroids can be used as sensitive biochemical sensors. One sensing modality is mode-splitting, where the binding of individual targets to the resonator breaks the degeneracy between clockwise and counter-clockwise resonant modes. Compared to other sensing modalities, mode-splitting is attractive because the signal shift is theoretically insensitive to the polar coordinate where the target binds. However, this theory relies on several assumptions, and previous experimental and numerical results have shown some discrepancies with analytical theory. More accurate numerical modeling techniques could help to elucidate the underlying physics, but efficient 3D electromagnetic finite-element method simulations of large microtoroid (diameter ~90 µm) and their resonance features have previously been intractable. In addition, applications of mode-splitting often involve bacteria or viruses, which are too large to be accurately described by the existing analytical dipole approximation theory. A numerical simulation approach could accurately explain mode splitting induced by these larger particles. Here, we simulate mode-splitting in a large microtoroid using a beam envelope method with periodic boundary conditions in a wedge-shaped domain. We show that particle sizing is accurate to within 11% for radii a<λ/7, where the dipole approximation is valid. Polarizability calculations need only be based on the background media and need not consider the microtoroid material. This modeling approach can be applied to other sizes and shapes of microresonators in the future.

Effects of the magnetodipole corrections on the spectra of spheroidal whispering gallery mode resonators interacting with a dielectric nanoparticle

Interaction between whispering gallery mode (WGM) resonators and nanoparticles is an area of active interest in fundamental understanding of nanoparticle-induced spectral modifications of the WGM resonances in sensing applications. Existing theories of this phenomenon assume that nanoparticles can be described taking into account only the electrodipole contribution to the field of the nanoparticle. In this paper, we explore theoretically the effects of the magnetodipole contribution to the nanoparticle's field and show that this contribution might become significant even in situations when electrodipole approximation is expected to remain valid.