Decomposition of scattered electromagnetic fields into vector spherical wave functions on surfaces with general shapes

TL;DR

This paper introduces a shape-independent orthogonal decomposition method for scattered electromagnetic fields into vector spherical wave functions, enhancing numerical stability and applicability to arbitrary surfaces.

Contribution

It presents a novel orthogonal decomposition approach that works on any enclosing surface, improving flexibility and stability over traditional spherical surface methods.

Findings

Method works on arbitrary surfaces

Demonstrated with finite-element simulations

Shows improved numerical stability

Abstract

Decomposing the field scattered by an object into vector spherical harmonics (VSH) is the prime task when discussing its optical properties on more analytical grounds. Thus far, it was frequently required in the decomposition that the scattered field is available on a spherical surface enclosing the scatterer; being with that adapted to the spatial dependency of the VSHs but being rather incompatible with many numerical solvers. To mitigate this problem, we propose an orthogonal expression for the decomposition that holds for any surface that encloses the scatterer, independently of its shape. We also show that the orthogonal relations remain unchanged when the radiative VSH used for the expansion of the scattered field are substituted by the VSH used for the expansion of the illumination as test functions. This is a key factor for the numerical stability of our decomposition. As example, we use a finite-element based solver to compute the multipole response of a nanorod illuminated by a plane wave and study its convergence properties.