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.
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