TY - JOUR
T1 - Nearly cloaking the electromagnetic fields
AU - Bao, Gang
AU - Liu, Hongyu
PY - 2014
Y1 - 2014
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
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-84903977908&origin=recordpage
U2 - 10.1137/130939298
DO - 10.1137/130939298
M3 - RGC 21 - Publication in refereed journal
VL - 74
SP - 724
EP - 742
JO - SIAM Journal on Applied Mathematics
JF - SIAM Journal on Applied Mathematics
SN - 0036-1399
IS - 3
ER -