Accurate Simulation of Ideal Circular and Elliptic Cylindrical Invisibility Cloaks

TL;DR

This paper develops a rigorous method for simulating ideal circular and elliptic cylindrical invisibility cloaks by deriving appropriate boundary conditions that handle singularities at the cloaking boundary, ensuring perfect concealment.

Contribution

It introduces a novel set of cloaking boundary conditions based on pole conditions of singular transformations, improving the accuracy of electromagnetic simulations for ideal cloaks.

Findings

Cloaking boundary conditions (CBCs) ensure perfect concealment.

The governing equations can be decoupled inside the cloaked region.

Total fields in the cloaked region vanish with the proposed CBCs.

Abstract

The coordinate transformation offers a remarkable way to design cloaks that can steer electromagnetic fields so as to prevent waves from penetrating into the {\em cloaked region} (denoted by $\Omega_0$, where the objects inside are invisible to observers outside). The ideal circular and elliptic cylindrical cloaked regions are blown up from a point and a line segment, respectively, so the transformed material parameters and the corresponding coefficients of the resulted equations are highly singular at the cloaking boundary $\partial \Omega_0$. The electric field or magnetic field is not continuous across $\partial\Omega_0.$ The imposition of appropriate {\em cloaking boundary conditions} (CBCs) to achieve perfect concealment is a crucial but challenging issue. Based upon the principle that finite electromagnetic fields in the original space must be finite in the transformed space as well, we obtain CBCs that intrinsically relate to the essential "pole" conditions of a singular transformation. We also find that for the elliptic cylindrical cloak, the CBCs should be imposed differently for the cosine-elliptic and sine-elliptic components of the decomposed fields. With these at our disposal, we can rigorously show that the governing equation in $\Omega_0$ can be decoupled from the exterior region $\Omega_0^c$, and the total fields in the cloaked region vanish. We emphasize that our proposal of CBCs is different from any existing ones.