Characterization of an acoustic spherical cloak. (10th February 2015) - Dassios, George; S Fokas, Athanassios
Abstract: We analyze the following particular cloaking problem: the cloaked region consists of a sphere of a homogeneous medium which is identical with the medium occupying the exterior background space; this sphere is surrounded by a cloaking medium occupying a spherical shell and consisting of material with parameters depending only on the radial variable r . For this very special case, we show that the problem of determining the three functions characterizing the cloaking medium, namely, the radial mass density, the tangential mass density, and the compressibility, reduces to solving a well defined inverse problem for the Schrödinger equation. In particular, a concrete procedure is introduced for determining two of the above three functions in terms of the radial mass density via the solution of a Riemann–Hilbert problem.