On isotropic cloaking and interior transmission eigenvalue problems

Xia Ji, Hongyu Liu*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

12 Citations (Scopus)


This paper is concerned with the invisibility cloaking in acoustic wave scattering from a new perspective. We are especially interested in achieving the invisibility cloaking by completely regular and isotropic mediums. It is shown that an interior transmission eigenvalue problem arises in our study, which is the one considered theoretically in Cakoni et al. (Transmission eigenvalues for inhomogeneous media containing obstacles, Inverse Problems and Imaging, 6 (2012), 373-398). Based on such an observation, 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 if a certain non-transparency condition is satisfied, then 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 Herglotz approximation of the associated interior transmission eigenfunctions. We provide both theoretical and numerical justifications.

Original languageEnglish
Pages (from-to)253-280
Number of pages28
JournalEuropean Journal of Applied Mathematics
Issue number2
Early online date22 May 2017
Publication statusPublished - Apr 2018

Scopus Subject Areas

  • Applied Mathematics

User-Defined Keywords

  • Acoustic wave scattering
  • interior transmission eigenvalues
  • invisibility cloaking
  • isotropic and regular


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