Quantitative spectral analysis of electromagnetic scattering. I: $ L^2$ and Hilbert-Schmidt norm bounds

TL;DR

This paper provides quantitative spectral analysis of the Born equation in electromagnetic scattering, establishing norm bounds for the Green operator to aid in error estimation of the Born approximation.

Contribution

It introduces new norm bounds for the Green operator related to the Born equation, enhancing numerical error estimation in light scattering analysis.

Findings

Established L^2 and Hilbert-Schmidt norm bounds for the Green operator.

Provided numerical tools for error estimates of the Born approximation.

Enhanced understanding of electromagnetic scattering spectral properties.

Abstract

We perform quantitative spectral analysis on the Born equation, an integral equation for electromagnetic scattering that descends from the Maxwell equations. We establish norm bounds for the Green operator associated with the Born equation, thereby providing numerical tools for error estimates of the Born approximation to light scattering problems.