# On novel elastic structures inducing plasmonic resonances with finite frequencies and cloaking due to anomalous localized resonances

## TL;DR

This paper develops a general theory of elastic structures that induce plasmonic resonances at finite frequencies, enabling cloaking via anomalous localized resonances, extending previous models and verifying the quasi-static approximation.

## Contribution

It introduces a broad class of elastic structures inducing plasmonic resonances, relaxing previous convexity conditions, and demonstrates cloaking applications in the quasi-static regime.

## Key findings

- New elastic structures induce plasmonic resonances with relaxed conditions.
- Verification of quasi-static approximation for small inclusions.
- Construction of cloaking device using core-shell-matrix structure.

## Abstract

This paper is concerned with the theoretical study of plasmonic resonances for linear elasticity governed by the Lam\'e system in $\mathbb{R}^3$, and their application for cloaking due to anomalous localized resonances. We derive a very general and novel class of elastic structures that can induce plasmonic resonances. It is shown that if either one of the two convexity conditions on the Lam\'e parameters is broken, then we can construct certain plasmon structures that induce resonances. This significantly extends the relevant existing studies in the literature where the violation of both convexity conditions is required. Indeed, the existing plasmonic structures are a particular case of the general structures constructed in our study. Furthermore, we consider the plasmonic resonances within the finite frequency regime, and rigorously verify the quasi-static approximation for diametrically small plasmonic inclusions. Finally, as an application of the newly found structures, we construct a plasmonic device of the core-shell-matrix form that can induce cloaking due to anomalous localized resonance in the quasi-static regime, which also includes the existing study as a special case.