TY - JOUR

T1 - Nearly Cloaking the Electromagnetic Fields

AU - Bao, Gang

AU - Liu, Hongyu

N1 - Funding information:
Department of Mathematics, Zhejiang University, Hangzhou 310027, China and Department of Mathematics, Michigan State University, East Lansing, MI 48824 (bao@math.msu.edu). This author’s work was supported in part by the NSF grants DMS-0908325, DMS-0968360, DMS-1211292, the ONR grant N00014-12-1-0319, a Key Project of the Major Research Plan of NSFC (91130004), and a special research grant from Zhejiang University
Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong (hongyu.liuip@gmail.com). This author’s work was supported by the NSF grant DMS-1207784.
Publisher copyright:
© 2014, Society for Industrial and Applied Mathematics

PY - 2014/6/3

Y1 - 2014/6/3

N2 - 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 inhomogeneous electromagnetic inclusion with an asymptotically small support 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 electromagnetic inclusion. The result implies that the “blow-up-a-small-region” construction 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 electromagnetic contents can be nearly cloaked. Our mathematical technique extends the general one developed in [H. Y. Liu and H. Sun, J. Math. Pures Appl., 99 (2013), pp. 17--42] for nearly cloaking scalar optics. In order to investigate the approximate electromagnetic cloaking for general geometries with arbitrary cloaked contents in the present study, new techniques and analysis tools are developed for this more challenging vector optics case.

AB - 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 inhomogeneous electromagnetic inclusion with an asymptotically small support 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 electromagnetic inclusion. The result implies that the “blow-up-a-small-region” construction 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 electromagnetic contents can be nearly cloaked. Our mathematical technique extends the general one developed in [H. Y. Liu and H. Sun, J. Math. Pures Appl., 99 (2013), pp. 17--42] for nearly cloaking scalar optics. In order to investigate the approximate electromagnetic cloaking for general geometries with arbitrary cloaked contents in the present study, new techniques and analysis tools are developed for this more challenging vector optics case.

KW - Asymptotic estimates

KW - Invisibility cloaking

KW - Layer potential technique

KW - Maxwell's equations

KW - Transformation optics

UR - http://www.scopus.com/inward/record.url?scp=84903977908&partnerID=8YFLogxK

U2 - 10.1137/130939298

DO - 10.1137/130939298

M3 - Article

AN - SCOPUS:84903977908

SN - 0036-1399

VL - 74

SP - 724

EP - 742

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

IS - 3

ER -