Perturbations of the scattering resonances of an open cavity by small particles. Part II: The transverse electric polarization case

TL;DR

This paper analyzes how small particles affect the scattering resonances of open dielectric cavities under transverse electric polarization, providing a rigorous small-volume formula and exploring plasmonic effects and exceptional resonances.

Contribution

It extends previous work by rigorously deriving resonance shifts for TE polarization using pole-pencil decompositions, including plasmonic and exceptional resonance cases.

Findings

Strong frequency shift enhancement with plasmonic particles

Derived small-volume resonance shift formula for TE polarization

Analyzed perturbations near exceptional resonances

Abstract

This paper is concerned with the scattering resonances of open cavities. It is a follow-up of "Perturbation of the scattering resonances of an open cavity by small particles. Part I" where the transverse magnetic polarization was assumed. In that case, using the method of matched asymptotic expansions, the leading-order term in the shifts of scattering resonances due to the presence of small particles of arbitrary shapes was derived and the effect of radiation on the perturbations of open cavity modes was characterized. The derivations were formal. In this paper, we consider the transverse electric polarization and prove a small-volume formula for the shifts in the scattering resonances of a radiating dielectric cavity perturbed by small particles. We show a strong enhancement in the frequency shift in the case of plasmonic particles. We also consider exceptional scattering resonances and perform small-volume asymptotic analysis near them. Our method in this paper relies on pole-pencil decompositions of volume integral operators.