Exactness of the first Born approximation in electromagnetic scattering

TL;DR

This paper establishes conditions under which the first Born approximation provides an exact solution for electromagnetic scattering in anisotropic media and demonstrates broadband invisibility under these conditions.

Contribution

It introduces a specific condition on permittivity and permeability tensors ensuring the first Born approximation's exactness and omnidirectional invisibility for certain wave numbers.

Findings

First Born approximation is exact under specific tensor conditions.

Medium exhibits broadband invisibility for wave numbers up to half of alpha.

Conditions apply to anisotropic, stationary linear media in three dimensions.

Abstract

For the scattering of plane electromagnetic waves by a general possibly anisotropic stationary linear medium in three dimensions, we give a condition on the permittivity and permeability tensors of the medium under which the first Born approximation yields the exact expression for the scattered wave whenever the incident wavenumber $k$ does not exceed a pre-assigned value $\alpha$. We also show that under this condition the medium is omnidirectionally invisible for $k\leq \alpha/2$, i.e., it displays broadband invisibility regardless of the polarization of the incident wave.