On quasi-static cloaking due to anomalous localized resonance in $\mathbb{R}^3$

TL;DR

This paper investigates cloaking via anomalous localized resonance in three dimensions, extending previous 2D results, and identifies conditions under which CALR occurs or does not occur in 3D plasmonic configurations.

Contribution

It extends the study of CALR to three dimensions and provides new constructions that ensure CALR, including cases with arbitrary core shapes and dielectric distributions.

Findings

CALR does not occur for certain 3D plasmonic configurations.

Two constructions guarantee the occurrence of CALR in 3D.

CALR can occur with arbitrary core shapes and dielectric distributions.

Abstract

This work concerns the cloaking due to anomalous localized resonance (CALR) in the quasi-static regime. We extend the related two-dimensional studies in [2,10] to the three-dimensional setting. CALR is shown not to take place for the plasmonic configuration considered in [2,10] in the three-dimensional case. We give two different constructions which ensure the occurrence of CALR. There may be no core or an arbitrary shape core for the cloaking device. If there is a core, then the dielectric distribution inside it could be arbitrary.