Full and Partial Cloaking in Electromagnetic Scattering

TL;DR

This paper analyzes two regularized transformation-optics cloaking schemes for electromagnetic waves, deriving asymptotic estimates and demonstrating nearly cloaking capabilities for arbitrary EM contents, extending previous acoustic cloaking results to the Maxwell system.

Contribution

It introduces two new regularized EM cloaking schemes based on different generating sets and provides sharp asymptotic estimates for their performance.

Findings

First scheme achieves approximate full cloaking.

Second scheme achieves approximate partial cloaking.

Both schemes can nearly cloak arbitrary EM contents.

Abstract

In this paper, we consider two regularized transformation-optics cloaking schemes for electromagnetic (EM) waves. Both schemes are based on the blowup construction with the generating sets being, respectively, a generic curve and a planar subset. We derive sharp asymptotic estimates in assessing the cloaking performances of the two constructions in terms of the regularization parameters and the geometries of the cloaking devices. The first construction yields an approximate full-cloak, whereas the second construction yields an approximate partial-cloak. Moreover, by incorporating properly chosen conducting layers, both cloaking constructions are capable of nearly cloaking arbitrary EM contents. This work complements the existing results in [5--7] on approximate EM cloaks with the generating set being a singular point, and it also extends [9,25] on regularized full and partial cloaks for acoustic waves governed by the Helmholtz system to the more challenging EM case governed by the full Maxwell system.