On Anomalous Localized Resonance for the Elastostatic System

TL;DR

This paper investigates anomalous localized resonance in elastostatic systems with plasmonic structures, revealing conditions under which resonance occurs, including for various source types and core geometries, using variational methods.

Contribution

It introduces a variational approach to analyze ALR in elastostatic systems with general core-shell-matrix structures, extending understanding of resonance conditions.

Findings

Resonance occurs for broad source classes without a core.

Existence of a critical radius for ALR with a nonempty core.

Variational techniques effectively analyze resonance phenomena.

Abstract

We consider the anomalous localized resonance due to a plasmonic structure for the elastostatic system in R^2. The plasmonic structure takes a general core-shell-matrix form with the metamaterial located in the shell. If there is no core, we show that resonance occurs for a very broad class of sources. If the core is nonempty and of an arbitrary shape, we show that there exists a critical radius such that anomalous localized resonance (ALR) occurs. Our argument is based on a variational technique by making use of the primal and dual variational principles for the elastostatic system, along with the construction of suitable test functions.