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

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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.

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Notes

  1. In this paper, the notation \(D \Subset \Omega \) means \({\bar{D}} \subset \Omega \) for two subsets D and \(\Omega \) of \(\mathbb {R}^3\).

  2. Here, \(\nu \) and \(\nu '\) denote the outward unit normal vector on \(\partial \Omega \) and \(\partial \Omega '\).

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  1. Department of Mathematics, EPFL SB CAMA, Station 8, 1015, Lausanne, Switzerland

    Hoai-Minh Nguyen

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Nguyen, HM. The invisibility via anomalous localized resonance of a source for electromagnetic waves. Res Math Sci 6, 32 (2019). https://doi.org/10.1007/s40687-019-0194-0

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