Cloaking due to anomalous localized resonance in plasmonic structures of confocal ellipses

TL;DR

This paper extends the understanding of cloaking via anomalous localized resonance (CALR) from concentric disks to confocal ellipses, providing mathematical proofs and critical elliptic radii using spectral analysis of boundary operators.

Contribution

It proves CALR occurs in confocal elliptical structures and computes the critical elliptic radii, expanding prior results from circular geometries.

Findings

CALR occurs in confocal elliptical structures.

Critical elliptic radii are explicitly computed.

Spectral analysis of boundary operators underpins the proofs.

Abstract

If a core of dielectric material is coated by a plasmonic structure of negative dielectric material with non-zero loss parameter, then anomalous localized resonance may occur as the loss parameter tends to zero and the source outside the structure can be cloaked. It has been proved that the cloaking due to anomalous localized resonance (CALR) takes place for structures of concentric disks and the critical radius inside which the sources are cloaked has been computed. In this paper, it is proved that CALR takes place for structures of confocal ellipses and the critical elliptic radii are computed. The method of this paper uses the spectral analysis of the Neumann-Poincar\'e type operator associated with two interfaces (the boundaries of the core and the shell).