S and Q Matrices Reloaded: applications to open, inhomogeneous, and complex cavities

TL;DR

This paper introduces a flexible numerical algorithm for calculating resonances in open dielectric cavities with arbitrary geometries and media, utilizing scattering matrices to analyze eigenmodes and electromagnetic fields.

Contribution

The paper presents a general scattering-based numerical method for computing resonances in complex, inhomogeneous open dielectric cavities, adaptable to various geometries and media.

Findings

Effective computation of cavity resonances using S- and Q-matrices

Ability to extract near- and far-field electromagnetic data

Demonstration of method's flexibility on a selected system

Abstract

We present a versatile numerical algorithm for computing resonances of open dielectric cavities. The emphasis is on the generality of the system's configuration, i.e. the geometry of the (main) cavity (and possible inclusions) and the internal and external dielectric media (homogeneous and inhomogeneous). The method is based on a scattering formalism to obtain the position and width of the (quasi)-eigenmodes. The core of the method lies in the scattering S-matrix and its associated delay Q-matrix which contain all the relevant information of the corresponding scattering experiment. For instance, the electromagnetic near- and far-fields are readily extracted. The flexibility of the propagation method is displayed for a selected system.