Spectral Analysis of Scattering Resonances with Application on High Contrast Nanospheres

TL;DR

This paper analyzes the spectral properties of scattering resonances in high contrast nanospheres, providing new formulas for resonance frequencies applicable to imaging and characterization of nanoscale objects.

Contribution

It offers a detailed spectral analysis of scattering resonances for high contrast nanospheres and derives an exact resonance formula for spherical scatterers with arbitrary size and dielectric contrast.

Findings

Derived a full expansion breakdown for high contrast nanospheres

Established an exact resonance formula for spherical scatterers

Simplified formulas for high contrast nanospheres in imaging applications

Abstract

In this paper we provide further spectral analysis of the general asymptotic scattering resonances formula of small high contrast 3D dielectrics of arbitrary shape, initially derived to a first order approximation. To investigate the components of a full expansion of such resonances, a breakdown is presented for the case of high contrast nanospheres. We also derive, for radially symmetric fields, an exact resonance formula for a spherical scatterer in terms of its radius, not necessarily small, and dielectric susceptibility coefficient, not necessarily high. Formula that is useful in imaging applications to identify objects' properties from frequency measurements. The latter formula is further developed and simplified in the case of high contrast nanospheres.