Spectral theory of a Neumann-Poincar\'e-type operator and analysis of anomalous localized resonance II

TL;DR

This paper investigates the conditions under which cloaking by anomalous localized resonance occurs in radially coated structures, revealing that CALR depends on the eigenvalues of a specific operator and occurs in 2D but not in 3D.

Contribution

It provides a spectral analysis of a Neumann-Poincaré-type operator to determine when CALR occurs in radially symmetric structures in two and three dimensions.

Findings

CALR occurs in 2D when the shell's permittivity is -1.

CALR does not occur in 3D for the structures studied.

The eigenvalue distribution of the Neumann-Poincaré operator determines CALR occurrence.

Abstract

If a body of dielectric material is coated by a plasmonic structure of negative dielectric constant with nonzero loss parameter, then cloaking by anomalous localized resonance (CALR) may occur as the loss parameter tends to zero. The aim of this paper is to investigate this phenomenon in two and three dimensions when the coated structure is radial, and the core, shell and matrix are isotropic materials. In two dimensions, we show that if the real part of the permittivity of the shell is -1 (under the assumption that the permittivity of the background is 1), then CALR takes place. If it is different from -1, then CALR does not occur. In three dimensions, we show that CALR does not occur. The analysis of this paper reveals that occurrence of CALR is determined by the eigenvalue distribution of the Neumann-Poincar\'e-type operator associated with the structure.