Finiteness Results for Non-Scattering Herglotz Waves: The case of inhomogeneities obtained by very general perturbations of disks

TL;DR

This paper proves that for broad classes of star-shaped inhomogeneities, only finitely many wave numbers produce non-scattering Herglotz incident waves, advancing understanding of wave scattering in complex media.

Contribution

It establishes finiteness results for non-scattering phenomena in inhomogeneous media with general perturbations of disks, extending previous theoretical frameworks.

Findings

Finitely many wave numbers lead to non-scattering in broad classes of inhomogeneities.

Results apply to very general star-shaped domains.

Advances the theoretical understanding of wave scattering in complex media.

Abstract

We study non-scattering phenomena associated with the time-harmonic Helmholtz equation in two dimensions. For very general classes of star-shaped domains, we show that there are at most finitely many wave numbers such that Herglotz incident waves with a fixed density function are non-scattering.