Resonant-state expansion of three-dimensional open optical systems: Light scattering

TL;DR

This paper introduces a rigorous resonant-state expansion method for calculating electromagnetic scattering properties of three-dimensional open optical systems, leveraging spherical basis functions for analytical simplicity.

Contribution

It presents a novel resonant-state expansion approach that simplifies the calculation of scattering matrices and cross-sections for arbitrary 3D optical systems using spherical basis functions.

Findings

Validated method on dielectric sphere example

Achieved accurate scattering matrix calculations

Provided analytical expressions for scattering properties

Abstract

A rigorous method of calculating the electromagnetic field, the scattering matrix, and scattering cross-sections of an arbitrary finite three-dimensional optical system described by its permittivity distribution is presented. The method is based on the expansion of the Green's function into the resonant states of the system. These can be calculated by any means, including the popular finite element and finite-difference time-domain methods. However, using the resonant-state expansion with a spherically-symmetric analytical basis, such as that of a homogeneous sphere, allows to determine a complete set of the resonant states of the system within a given frequency range. Furthermore, it enables to take full advantage of the expansion of the field outside the system into vector spherical harmonics, resulting in simple analytic expressions. We verify and illustrate the developed approach on an example of a dielectric sphere in vacuum, which has an exact analytic solution known as Mie scattering.