Spectral properties of Neumann-Poincare operator and anomalous localized resonance in elasticity beyond quasi-static limit

TL;DR

This paper investigates the spectral properties of the Neumann-Poincaré operator in elastic systems beyond the quasi-static limit, demonstrating how these properties enable anomalous localized resonance and cloaking effects at finite frequencies.

Contribution

It derives the spectral system of the Neumann-Poincaré operator in the finite frequency regime and constructs elastic configurations that induce polariton resonances beyond the quasi-static limit.

Findings

Spectral system of the Neumann-Poincaré operator derived for finite frequencies.

Elastic configurations inducing polariton resonances beyond quasi-static limit.

Cloaking achieved with core-shell-matrix structures when source is inside a critical radius.

Abstract

This paper is concerned with the polariton resonances and their application for cloaking due to anomalous localized resonance (CALR) for the elastic system within the finite frequency regime beyond the quasi-static approximation. We first derive the complete spectral system of the Neumann-Poincar\'e operator associated with the elastic system within the finite frequency regime. Based on the obtained spectral results, we construct a broad class of elastic configurations that can induce polariton resonances beyond the quasi-static limit. As an application, the invisibility cloaking effect is achieved through constructing a class of core-shell-matrix metamaterial structures provided the source is located inside a critical radius. Moreover, if the source is located outside the critical radius, it is proved that there is no resonance.