Perturbation of the scattering resonances of an open cavity by small particles. Part I: The transverse magnetic polarization case

TL;DR

This paper develops a mathematical framework to analyze how small particles perturb the scattering resonances of open cavities, accounting for radiation effects and applicable to arbitrary shapes, with applications in imaging and plasmonics.

Contribution

It introduces a small-volume expansion for resonance shifts in open cavities perturbed by small particles, including radiation effects and arbitrary shapes, with practical imaging applications.

Findings

Frequency shifts are significantly enhanced for plasmonic particles.

The derived formula accurately predicts resonance shifts near cavity boundaries.

Numerical examples demonstrate the method's applicability to real-world problems.

Abstract

This paper aims at providing a small-volume expansion framework for the scattering resonances of an open cavity perturbed by small particles. The induced shift of the scattering frequencies by the small particles is derived without neglecting the radiation effect. The formula holds for arbitrary-shaped particles. It shows a strong enhancement in the frequency shift in the case of plasmonic particles. The formula is used to image small particles located near the boundary of an open resonator which admits whispering-gallery modes. Numerical examples of interest for applications are presented.