Cloaking via Change of Variables for the Helmholtz Equation in the Whole Space

This paper is devoted to the study of a cloaking device that is composed of a standard near cloak based on a regularization of the transformation optics, i.e., a change of variables that blows up a small ball to the cloaked region, and a fixed lossy layer for the Helmholtz equation in the whole space of dimension 2 or 3 with the outgoing condition at infinity. We establish a degree of near invisibility, which is independent of the content inside the cloaked region, for this device. We also show that the lossy layer is necessary to ensure the validity of the degree of near invisibility when no constraint on physical properties inside the cloaked region is imposed. (c) 2010 Wiley Periodicals, Inc.