On spectral properties of Neuman-Poincare operator and plasmonic resonances in 3D elastostatics

TL;DR

This paper analyzes the spectral properties of the Neumann-Poincaré operator in 3D elastostatics, deriving its spectrum for spherical geometries and applying it to characterize plasmonic resonances and cloaking in elastostatic systems.

Contribution

It extends the spectral analysis of the Neumann-Poincaré operator from 2D to 3D elastostatics and applies this to plasmonic resonance and cloaking in complex core-shell structures.

Findings

Spectral properties of the Neumann-Poincaré operator in 3D elastostatics are fully characterized.

The spectral analysis enables precise description of anomalous localized resonance.

Application to core-shell plasmonic structures reveals conditions for cloaking.

Abstract

We consider plasmon resonances and cloaking for the elastostatic system in $\mathbb{R}^3$ via the spectral theory of Neumann-Poincar\'e operator. We first derive the full spectral properties of the Neumann-Poincar\'e operator for the 3D elastostatic system in the spherical geometry. The spectral result is of significant interest for its own sake, and serves as a highly nontrivial extension of the corresponding 2D study in [8]. The derivation of the spectral result in 3D involves much more complicated and subtle calculations and arguments than that for the 2D case. Then we consider a 3D plasmonic structure in elastostatics which takes a general core-shell-matrix form with the metamaterial located in the shell. Using the obtained spectral result, we provide an accurate characterisation of the anomalous localised resonance and cloaking associated to such a plasmonic structure.