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The invisibility via anomalous localized resonance of a source for electromagnetic waves

The invisibility via anomalous localized resonance of a source for electromagnetic waves We investigate the invisibility via anomalous localized resonance of a general source in anisotropic media for electromagnetic waves. To this end, we first introduce the concept of doubly complementary media in the electromagnetic setting. These are media consisting of negative-index metamaterials in a shell and positive-index materials in its complement for which the shell is complementary to a part of the core and a part of the exterior of the core–shell structure. We then provide criteria for establishing the invisibility of a source in these media. We show that (i) a source is invisible if the power is blown up; (ii) a source is invisible if it is sufficiently close to the plasmonic shell structure, and it is visible if it is far from this plasmonic structure; (iii) if the plasmonic structure is complementary to an annulus of constant isotropic medium, there is a critical length that characterizes the cloaking phenomena, as first observed in the two-dimensional acoustic quasistatic setting by Milton and Nicorovici. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Research in the Mathematical Sciences Springer Journals

The invisibility via anomalous localized resonance of a source for electromagnetic waves

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Publisher
Springer Journals
Copyright
Copyright © 2019 by Springer Nature Switzerland AG
Subject
Mathematics; Mathematics, general; Applications of Mathematics; Computational Mathematics and Numerical Analysis
eISSN
2197-9847
DOI
10.1007/s40687-019-0194-0
Publisher site
See Article on Publisher Site

Abstract

We investigate the invisibility via anomalous localized resonance of a general source in anisotropic media for electromagnetic waves. To this end, we first introduce the concept of doubly complementary media in the electromagnetic setting. These are media consisting of negative-index metamaterials in a shell and positive-index materials in its complement for which the shell is complementary to a part of the core and a part of the exterior of the core–shell structure. We then provide criteria for establishing the invisibility of a source in these media. We show that (i) a source is invisible if the power is blown up; (ii) a source is invisible if it is sufficiently close to the plasmonic shell structure, and it is visible if it is far from this plasmonic structure; (iii) if the plasmonic structure is complementary to an annulus of constant isotropic medium, there is a critical length that characterizes the cloaking phenomena, as first observed in the two-dimensional acoustic quasistatic setting by Milton and Nicorovici.

Journal

Research in the Mathematical SciencesSpringer Journals

Published: Sep 20, 2019

References