Unified treatment of exact and approximate scalar electromagnetic wave scattering

TL;DR

This paper unifies the analytical understanding of different numerical methods for scalar electromagnetic wave scattering, providing insights and error bounds for each under various scattering conditions.

Contribution

It explicitly relates the Born series, Beam Propagation Method, and Lippmann-Schwinger equation, offering a unified framework and error estimates for strong scattering scenarios.

Findings

Derived explicit relationships between the three methods.

Provided approximate error bounds for different scattering regimes.

Enhanced understanding of numerical method suitability in optical scattering.

Abstract

Under conditions of strong scattering, a dilemma often arises regarding the best numerical method to use. Main competitors are the Born series, the Beam Propagation Method, and direct solution of the Lippmann-Schwinger equation. However, analytical relationships between the three methods have not yet, to our knowledge, been explicitly stated. Here, we bridge this gap in the literature. In addition to overall insight about aspects of optical scattering that are best numerically captured by each method, our approach allows us to derive approximate error bounds to be expected under various scattering conditions.