Weakly singular corners always scatter

TL;DR

This paper proves that scatterers with weakly or strongly singular points always produce a non-zero scattered field, ensuring uniqueness in inverse scattering problems with limited data.

Contribution

It establishes the non-vanishing of scattered fields for scatterers with singular points, advancing shape identification in inverse medium scattering.

Findings

Scattered field cannot vanish for scatterers with singular points

No non-scattering energies exist for certain interfaces

Local uniqueness in inverse shape problems with single far-field pattern

Abstract

Assume that a bounded scatterer is embedded into an infinite homogeneous isotropic background medium in two dimensions. The refractive index function is supposed to be piecewise constant. If the scattering interface contains a weakly or strongly singular point, we prove that the scattered field cannot vanish identically. This particularly leads to the absence of non-scattering energies for piecewise analytic interfaces with a weakly singular point. Local uniqueness is obtained for shape identification problems in inverse medium scattering with a single far-field pattern.