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Full and Partial Cloaking in Electromagnetic Scattering

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Abstract

In this paper, we consider two regularized transformation-optics cloaking schemes for electromagnetic (EM) waves. Both schemes are based on the blowup construction with the generating sets being, respectively, a generic curve and a planar subset. We derive sharp asymptotic estimates in assessing the cloaking performances of the two constructions in terms of the regularization parameters and the geometries of the cloaking devices. The first construction yields an approximate full-cloak, whereas the second construction yields an approximate partial-cloak. Moreover, by incorporating properly chosen conducting layers, both cloaking constructions are capable of nearly cloaking arbitrary EM contents. This work complements the existing results in Ammari et al. (SIAM J Appl Math 73:2055–2076, 2013), Bao and Liu (SIAM J Appl Math 74:724–742, 2014), Bao et al. (J Math Pure Appl (9) 101:716–733, 2014) on approximate EM cloaks with the generating set being a singular point, and it also extends Deng et al. (On regularized full- and partial-cloaks in acoustic scat- tering. Preprint, ar**v:1502.01174, 2015), Li et al. (Commun Math Phys, 335:671–712, 2015) on regularized full and partial cloaks for acoustic waves governed by the Helmholtz system to the more challenging EM case governed by the full Maxwell system.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Central South University, Changsha, Hunan, People’s Republic of China

    Youjun Deng

  2. Department of Mathematics, Hong Kong Baptist University, Kowloon, Hong Kong SAR

    Hongyu Liu

  3. Department of Mathematics, University of Washington, Seattle, WA, 98195, USA

    Gunther Uhlmann

  4. Institute for Advanced Study, Hong Kong University of Science and Technology, Hong Kong, Hong Kong SAR

    Gunther Uhlmann

Authors
  1. Youjun Deng
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  2. Hongyu Liu
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  3. Gunther Uhlmann
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Correspondence to Gunther Uhlmann.

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Communicated by F. Lin

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Deng, Y., Liu, H. & Uhlmann, G. Full and Partial Cloaking in Electromagnetic Scattering. Arch Rational Mech Anal 223, 265–299 (2017). https://doi.org/10.1007/s00205-016-1035-6

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