1210.2447 (Gang Bao et al.)

Nearly Cloaking the Full Maxwell Equations    [PDF]

Gang Bao, Hongyu Liu

In this paper, we consider approximate cloaking for time-harmonic Maxwell's equations via the approach of transformation-optics. The study is reduced to the boundary effect estimate due to an inhomogeneous electromagnetic inclusion with an asymptotically small support but an arbitrary content enclosed by a thin high-conducting layer. We derive very sharp estimate in terms of the asymptotic parameter, and moreover, the estimate is independent of the material tensors of the small EM inclusion. The result can be immediately applied to show that the `blow-up-a-small-region' construction via the transformation optics approach yields a near-cloak for the electromagnetic waves. Moreover, by incorporating the conducting layer developed in the present paper right between the cloaked region and the cloaking region, one can nearly cloak arbitrary EM contents. We work with general geometry of the cloaking device, and the mathematical argument follows the general strategy developed in [29] for nearly cloaking the Helmholtz equation that governs scalar waves.

View original: http://arxiv.org/abs/1210.2447