Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Electromagnetic interior transmission eigenvalue problem for inhomogeneous media containing obstacles and its applications to

Language

English

Abstract

This article is concerned with the invisibility cloaking in electromagnetic wave scattering from a new perspective. We are especially interested in achieving the invisibility cloaking by completely regular and isotropic mediums. Our study is based on an interior transmission eigenvalue problem. We propose a cloaking scheme that takes a three-layer structure including a cloaked region, a lossy layer and a cloaking shell. The target medium in the cloaked region can be arbitrary but regular, whereas the mediums in the lossy layer and the cloaking shell are both regular and isotropic. We establish that there exists an infinite set of incident waves such that the cloaking device is nearly invisible under the corresponding wave interrogation. The set of waves is generated from the Maxwell–Herglotz approximation of the associated interior transmission eigenfunctions. We provide the mathematical design of the cloaking device and sharply quantify the cloaking performance.

Keywords

electromagnetic scattering, invisibility cloaking, interior transmission eigenvalues

Publication Date

10-2017

Source Publication Title

IMA Journal of Applied Mathematics

Volume

82

Issue

5

Start Page

1013

End Page

1042

Publisher

Oxford University Press

Peer Reviewed

1

Copyright

This is a pre-copyedited, author-produced PDF of an article accepted for publication in IMA Journal of Applied Mathematics following peer review. The version of record Xiaofei Li, Jingzhi Li, Hongyu Liu, Yuliang Wang; Electromagnetic interior transmission eigenvalue problem for inhomogeneous media containing obstacles and its applications to near cloaking, IMA Journal of Applied Mathematics, Volume 82, Issue 5, 1 October 2017, Pages 1013–1042, https://doi.org/10.1093/imamat/hxx022 is available online at: http://dx.doi.org/10.1093/imamat/hxx022.

Funder

China Postdoctoral Science Foundation (No. 2017M612490) to X.L.; NSF of China (No. 11571161) and the Shenzhen Sci-Tech (No. JCYJ20160530184212170) to J.L.; Startup fund and the FRG grants from Hong Kong Baptist University, and the Hong Kong RGC grant (No. 12302415) to H.L.; Hong Kong RGC (No. 12328516) and the NSF of China (No. 11601459) to Y.W.

DOI

10.1093/imamat/hxx022

Link to Publisher's Edition

http://dx.doi.org/10.1093/imamat/hxx022

ISSN (print)

02724960

ISSN (electronic)

14643634

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