Spatial bandlimitedness of scattered electromagnetic fields

TL;DR

This paper demonstrates that for transverse electric polarization, scattered electromagnetic fields from a 2D dielectric object are spatially bandlimited, with implications for inverse problems, using a simpler approach than previous functional analysis methods.

Contribution

The paper provides a straightforward analytical and numerical proof that scattered fields are spatially bandlimited, independent of dielectric properties, and derives bounds relevant for inverse problems.

Findings

Scattered fields are spatially bandlimited for TE polarization.

An upper bound on useful incidence angles is derived.

Results depend only on geometry, not dielectric properties.

Abstract

In this tutorial paper, we consider the problem of electromagnetic scattering by a bounded two-dimensional dielectric object, and discuss certain interesting properties of the scattered field. Using the electric field integral equation, along with the techniques of Fourier theory and the properties of Bessel functions, we show analytically and numerically, that in the case of transverse electric polarization, the scattered fields are spatially bandlimited. Further, we derive an upper bound on the number of incidence angles that are useful as constraints in an inverse problem setting (determining permittivity given measurements of the scattered field). We also show that the above results are independent of the dielectric properties of the scattering object and depend only on geometry. Though these results have previously been derived in the literature using the framework of functional analysis, our approach is conceptually far easier. Implications of these results on the inverse problem are also discussed.