On anomalous localized resonance and plasmonic cloaking beyond the quasistatic limit

TL;DR

This paper develops mathematical models for core-shell plasmonic structures that achieve anomalous localized resonance and cloaking at finite frequencies beyond the quasistatic limit, with novel spectral analysis of related operators.

Contribution

It introduces a new mathematical construction of plasmonic structures capable of cloaking at finite frequencies and derives the first complete spectrum of the Neumann-Poincaré operator in this context.

Findings

Successful construction of plasmonic structures for cloaking beyond quasistatic limit

Derivation of the complete spectrum of the Neumann-Poincaré operator at finite frequencies

Spectral results are of significant mathematical interest

Abstract

In this paper, we give the mathematical construction of novel core-shell plasmonic structures that can induce anomalous localized resonance and invisibility cloaking at certain finite frequencies beyond the quasistatic limit. The crucial ingredient in our study is that the plasmon constant and the loss parameter are constructed in a delicate way that are correlated and depend on the source and the size of the plasmonic structure. As a significant byproduct of this study, we also derive the complete spectrum of the Neumann-Poinc\'are operator associated to the Helmholtz equation with finite frequencies in the radial geometry. The spectral result is the first one in its type and is of significant mathematical interest for its own sake.