Scattering matrix of arbitrarily shaped objects: Combining Finite Elements and Vector Partial Waves

TL;DR

This paper introduces a hybrid computational method combining Finite Element analysis with Vector Partial Wave formulation to accurately determine the electromagnetic scattering properties of arbitrarily shaped objects, validated on spheres and ellipsoids.

Contribution

It presents a novel approach that integrates Finite Element calculations with Vector Partial Waves to compute the T-matrix of complex scatterers, including explicit recurrence relations and open-source code.

Findings

Accurately determines scattering matrices for spheres and ellipsoids.

Provides explicit recurrence relations for vector partial waves.

Offers an open-source implementation for reproducibility.

Abstract

We demonstrate the interest of combining Finite Element calculations with the Vector Partial Wave formulation (used in T-matrix and Mie theory) in order to characterize the electromagnetic scattering properties of isolated individual scatterers. This method consists of individually feeding the finite element problem with incident Vector Partial Waves in order to numerically determine the T-matrix elements of the scatterer. For a sphere and an ellipsoid, we demonstrate that this method determines the scattering matrix to high accuracy. Recurrence relations for a fast determination of the vector partial waves are given explicitly, and an open-source code allowing the retrieval of the presented numerical results is provided.