Coordinate transformation makes perfect invisibility cloak with arbitrary shape

TL;DR

This paper demonstrates that coordinate transformations can be used to design perfectly invisible cloaks of arbitrary shape, analyzing wave behavior at boundaries and revealing conditions for reflectionless cloaking.

Contribution

It provides a general analytical framework for arbitrary-shaped cloaks using coordinate transformations, clarifying boundary behaviors and differences between line and point transformed cloaks.

Findings

Cloaks are perfectly invisible to external waves.

No reflection occurs at cloak boundaries despite material mismatches.

Inner boundary conditions differ between line and point transformed cloaks.

Abstract

By investigating wave properties at cloak boundaries, invisibility cloaks with arbitrary shape constructed by general coordinate transformations are confirmed to be perfectly invisible to the external incident wave. The differences between line transformed cloaks and point transformed cloaks are discussed. The fields in the cloak medium are found analytically to be related to the fields in the original space via coordinate transformation functions. At the exterior boundary of the cloak, it is shown that no reflection is excited even though the permittivity and permeability do not always have a perfect matched layer form. While at the inner boundary, no reflection is excited either, and in particular no field can penetrate into the cloaked region. However, for the inner boundary of any line transformed cloak, the permittivity and permeability in a specific tangential direction are always required to be infinitely large. Furthermore, the field discontinuity at the inner boundary always exists; the surface current is induced to make this discontinuity self-consistent. For a point transformed cloak, it does not experience such problems. The tangential fields at the inner boundary are all zero, implying no field discontinuity exists