Extending the applicability of the T-matrix method to light scattering by flat particles on a substrate via truncation of Sommerfeld integrals

TL;DR

This paper improves the T-matrix method for light scattering by flat particles on substrates by proposing an empirical formula for optimal Sommerfeld integral truncation, enhancing accuracy in simulations.

Contribution

It introduces an empirical formula for selecting the maximal in-plane wavenumber in the T-matrix method, improving scattering simulation accuracy for particles on substrates.

Findings

The empirical formula effectively guides the truncation of Sommerfeld integrals.

Simulations with the new method match well with discrete-sources method results.

Proper truncation enhances the accuracy of light scattering predictions.

Abstract

The simulation of light scattering by particles on a substrate with the $T$-matrix method relies on the expansion of the scattered field in spherical waves, followed by a plane wave expansion to allow the evaluation of the reflection from the substrate. In practice, the plane wave expansion (i.e., the Sommerfeld integrals) needs to be truncated at a maximal in-plane wavenumber $\kappa_\mathrm{max}$. An appropriate selection of $\kappa_\mathrm{max}$ is essential: counter-intuitively, the overall accuracy can degrade significantly if the integrals are truncated with a too large value. In this paper, we propose an empirical formula for the selection of $\kappa_\mathrm{max}$ and discuss its application using a number of example simulations with dielectric and metallic oblate spheroids on dielectric and metallic substrates. The computed differential scattering cross sections are compared to results obtained from the discrete-sources method.