On isotropic cloaking and interior transmission eigenvalue problems

TL;DR

This paper introduces a new isotropic cloaking scheme for acoustic waves using interior transmission eigenvalue problems, demonstrating near-invisibility under specific conditions through theoretical and numerical analysis.

Contribution

It proposes a cloaking method with a three-layer structure involving isotropic media and links interior transmission eigenvalues to cloaking effectiveness.

Findings

Existence of infinite incident waves for near-invisibility

Cloaking achieved with a regular, isotropic medium structure

Theoretical and numerical validation of the cloaking scheme

Abstract

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 \cite{CCH}. 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.