A rigorous analysis of high order electromagnetic invisibility cloaks

TL;DR

This paper rigorously proves that high order electromagnetic invisibility cloaks, created via transformation media from anisotropic materials, are perfectly undetectable in scattering experiments and can cloak both passive and active objects, including within crystals.

Contribution

It provides a rigorous mathematical proof that high order transformation media cloaks are perfectly invisible for all incident waves and can cloak objects inside general anisotropic media, extending prior results.

Findings

Scattered wave is identically zero for any incident plane wave.

Scattering matrix is the identity for finite energy wave packets.

Cloaks can hide passive and active objects, decoupling them from the exterior.

Abstract

There is currently a great deal of interest in the invisibility cloaks recently proposed by Pendry et al. that are based in the transformation approach. They obtained their results using first order transformations. In recent papers Hendi et al. and Cai et al. considered invisibility cloaks with high order transformations. In this paper we study high order electromagnetic invisibility cloaks in transformation media obtained by high order transformations from general anisotropic media. We consider the case where there is a finite number of spherical cloaks located in different points in space. We prove that for any incident plane wave, at any frequency, the scattered wave is identically zero. We also consider the scattering of finite energy wave packets. We prove that the scattering matrix is the identity, i.e., that for any incoming wave packet the outgoing wave packet is the same as the incoming one. This proves that the invisibility cloaks can not be detected in any scattering experiment with electromagnetic waves in high order transformation media, and in particular in the first order transformation media of Pendry et al. We also prove that the high order invisibility cloaks, as well as the first order ones, cloak passive and active devices. The cloaked objects completely decouple from the exterior. Actually, the cloaking outside is independent of what is inside the cloaked objects. The electromagnetic waves inside the cloaked objects can not leave the concealed regions and viceversa, the electromagnetic waves outside the cloaked objects can not go inside the concealed regions. As we prove our results for media that are obtained by transformation from general anisotropic materials, we prove that it is possible to cloak objects inside general crystals.