Carpet cloaking and Laplace transformation

TL;DR

This paper introduces a systematic method for designing 2D isotropic carpet cloaking devices using Laplace transformations, enabling the creation of various cloaks for different bump geometries.

Contribution

The authors develop a novel approach linking Laplace transformations to carpet cloaking design, expanding the diversity of cloaking geometries achievable.

Findings

Multiple cloaking designs corresponding to different Laplace functions

Effective cloaking for various bump geometries

Systematic design methodology demonstrated through examples

Abstract

Recently, researchers have proposed several carpet cloaking designs that are able to hide a real object under a bump in a way that it is perceived as a flat ground plane. Here, we present a method to design two-dimensional isotropic carpet cloaking devices using Laplace transformation. We show that each functional form of a Laplace transformation corresponds to a different carpet cloaking design. Therefore, our approach allows us to systematically design a rich variety of cloaking devices. Our analysis includes several examples containing different bump geometries that illustrate the proposed methodology.