Spectral analysis of scattering resonances with application on high-contrast nanospheres

Abstract

In this paper, we provide further spectral analysis of the general asymptotic scattering resonances formula of small 3D dielectrics of arbitrary shape with high contrast, already derived in other works 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, in terms of its radius h in the interval [0, 1]. 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. This formula is further developed and simplified in the case of high contrast nanospheres. Such formulas are useful in imaging applications to identify objects’ properties from frequency measurements. Another application is the study of negative refractive index materials, such as metamaterials, and the anomalous localized resonance phenomenon (ALR) that is associated with cloaking and superlensing.