NEARLY CLOAKING THE FULL MAXWELL EQUATIONS

The approximate cloaking is investigated for time-harmonic Maxwell's equations via the approach of transformation optics. The problem is reduced to certain boundary effect estimates due to an inho- mogeneous electromagnetic inclusion with an asymptotically small sup- port but an arbitrary content enclosed by a thin high-conducting layer. Sharp estimates are established in terms of the asymptotic parameter, which are independent of the material tensors of the small electromag- netic inclusion. The result implies that the 'blow-up-a-small-region' con- struction via the transformation optics approach yields a near-cloak for the electromagnetic waves. A novelty lies in the fact that the geometry of the cloaking construction of this work can be very general. Moreover, by incorporating the conducting layer developed in the present paper right between the cloaked region and the cloaking region, arbitrary electro- magnetic contents can be nearly cloaked. Our mathematical technique extends the general one developed in (30) for nearly cloaking scalar op- tics. In order to investigate the approximate electromagnetic cloaking for general geometries with arbitrary cloaked contents, new techniques and analysis tools must be developed for this more challenging vector optics case.