A Rigorous Analysis of Plane-transformed Invisibility Cloaks

TL;DR

This paper provides a quantitative analysis of plane-transformed invisibility cloaks, demonstrating their inherent visibility, conditions for perfect invisibility, and proposing a practical, non-singular cloak design with potential ground-plane cloaking applications.

Contribution

It offers a rigorous electromagnetic analysis of elliptical cylindrical cloaks, introduces a non-singular conical cloak design, and explores ground-plane cloaking capabilities.

Findings

Ideal elliptical cylindrical cloak is inherently visible.

Perfect invisibility achieved with a PEC lining along the major axis.

Proposed conical cloak has spatially invariant, non-singular parameters.

Abstract

The electromagnetic characteristics of plane-transformed invisibility cloaks are quantitatively studied in this paper. We take elliptical cylindrical cloak as the example, and use an elliptical cylindrical wave expansion method to obtain the scattered field. It is demonstrated that an ideal elliptical cylindrical cloak is inherently visible. Noticeable field scattering and penetration will be induced when the cloak is exposed directly to an electromagnetic wave. However, as long as the cloak consists of a perfect electric conducting lining at the interior surface, perfect invisibility can still be achieved along the direction parallel to the major axis of the cloak for transverse magnetic illumination. Another plane-transformed cloak with a conical geometry is also proposed. The advantage of this cloak is that all the permittivity and permeability elements are spatially invariant while none of them is singular. Hence, it is easily realizable with artificially structured metamaterials. Finally, we show that this kind of cloak can also be used to cloak objects on a flat ground plane.