Examples of non-scattering inhomogeneities

TL;DR

This paper explores specific materials and geometries that allow non-scattering wave phenomena, including examples with corners, cusps, and anisotropic properties, revealing conditions for invisibility and resonance in wave scattering.

Contribution

It provides explicit examples and theoretical insights into non-scattering inhomogeneities, linking geometry, material properties, and resonance phenomena.

Findings

Certain geometries support non-scattering frequencies.

Non-scattering can occur with inclusions of anisotropic materials.

Material indices must have special boundary structures for all frequencies.

Abstract

We consider the scattering of waves by a penetrable inclusion embedded in some reference medium. We exhibit examples of materials and geometries for which non-scattering frequencies exist, i.e., for which at some frequencies there are incident fields which produce null scattered fields outside of the inhomogeneity. We show in particular that certain domains with corners or even cusps can support non-scattering frequencies. We relate the latter, for some inclusions, to resonance frequencies for Dirichlet or Neumann cavities. We also find situations where incident non-scattering fields solve the Helmholtz equation in a neighborhood of the inhomogeneity and not in the whole space. Finally, in relation with invisibility, we give examples of inclusions of anisotropic materials which are non-scattering for all real frequencies. We prove that corresponding material indices must have a special structure on the boundary.