How to calculate the pole expansion of the optical scattering matrix from the resonant states

TL;DR

This paper introduces a new method to accurately compute the optical scattering matrix of open resonators using resonant states, eliminating the need for fitting procedures and enabling efficient analysis of complex geometries.

Contribution

The authors develop a pole expansion approach that directly relates the scattering matrix to resonant states, improving accuracy and computational efficiency over traditional methods.

Findings

Accurate pole expansion of scattering matrix from resonant states.

Application to complex nanoantenna systems demonstrating absorption and circular dichroism.

Elimination of frequency discretization in Maxwell's equation solvers.

Abstract

We present a formulation for the pole expansion of the scattering matrix of open optical resonators, in which the pole contributions are expressed solely in terms of the resonant states, their wavenumbers, and their electromagnetic fields. Particularly, our approach provides an accurate description of the optical scattering matrix without the requirement of a fit for the pole contributions or the restriction to geometries or systems with low Ohmic losses. Hence, it is possible to derive the analytic dependence of the scattering matrix on the wavenumber with low computational effort, which allows for avoiding the artificial frequency discretization of conventional frequency-domain solvers of Maxwell's equations and for finding the optical far- and near-field response based on the physically meaningfull resonant states. This is demonstrated for three test systems, including a chiral arrangement of nanoantennas, for which we calculate the absorption and the circular dichroism.