Electromagnetic analysis of arbitrarily shaped pinched carpets

TL;DR

This paper derives electromagnetic tensors for arbitrarily shaped carpets, enabling broadband cloaking by mapping complex regions onto smooth surfaces without singularities in material properties.

Contribution

It introduces a method to compute anisotropic tensors for 2D and 3D carpets of arbitrary shape, facilitating broadband cloaking without permeability singularities.

Findings

No singularities in permeability tensors

Applicable to arbitrary shapes in 2D and 3D

Potential for broadband electromagnetic cloaking

Abstract

We derive the expressions for the anisotropic heterogeneous tensors of permittivity and perme- ability associated with two-dimensional and three-dimensional carpets of an arbitrary shape. In the former case, we map a segment onto smooth curves whereas in the latter case we map a non convex region of the plane onto smooth surfaces. Importantly, these carpets display no singularity of the permeability and permeability tensor components, and this may lead to some broadband cloaking.