Abstract

We study, in the context of the full wave equation, an approximate cloaking scheme that was previously considered for the Helmholtz equation [R. V. Kohn, D. Onofrei, M. S. Vogelius, and M. I. Weinstein, Comm. Pure Appl. Math., 63 (2010), pp. 973--1016, H.-M. Nguyen and M. S. Vogelius, Arch. Ration. Mech. Anal., 203 (2011), pp. 769--807]. This cloaking scheme consists in a combination of an absorbing layer with an anisotropic layer, obtained by so-called transformation optics. We give optimal bounds for the visibility that tend to zero as a certain regularization parameter approaches 0. Our bounds are based on recent estimates for the Helmholtz equation [from Nguyen and Vogelius], some low frequency improvements of these estimates, and the use of Fourier transformation in time.