Cloaking and Magnifying Using Radial Anisotropy

TL;DR

This paper explores how radially anisotropic structures can be used to achieve cloaking and magnification effects in electrostatics, demonstrating practical cloaking with moderate permittivity contrasts.

Contribution

It introduces a method to use simple radially anisotropic cylinders and spheres for electrostatic cloaking and magnification, with practical permittivity contrasts.

Findings

Cloaking of dielectric inclusions is possible with positive permittivity contrasts.

Magnification of inner cylinder response is achievable with cylindrical shells.

Notable cloaking effects occur even with moderate permittivity contrasts.

Abstract

This paper studies the electrostatic responses of a polarly radially anisotropic cylinder and a spherically radially anisotropic sphere. For both geometries, the permittivity components differ from each other in the radial and tangential directions. We show that choosing the ratio between these components in a certain way, these rather simple structures can be used in cloaking dielectric inclusions with arbitrary permittivity and shape in the quasi-static limit. For an ideal cloak, the contrast between the permittivity components has to tend to infinity. However, only positive permittivity values are required and a notable cloaking effect can already be observed with relatively moderate permittivity contrasts. Furthermore, we show that the polarly anisotropic cylindrical shell has a complementary capability of magnifying the response of an inner cylinder.