Department of Mathematics
Electromagnetic interior transmission eigenvalue problem for inhomogeneous media containing obstacles and its applications to
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.
electromagnetic scattering, invisibility cloaking, interior transmission eigenvalues
Source Publication Title
IMA Journal of Applied Mathematics
Oxford University Press
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.
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.
Link to Publisher's Edition
Li, X., Li, J., Liu, H., & Wang, Y. (2017). Electromagnetic interior transmission eigenvalue problem for inhomogeneous media containing obstacles and its applications to. IMA Journal of Applied Mathematics, 82 (5), 1013-1042. https://doi.org/10.1093/imamat/hxx022