Resonant state expansion applied to two-dimensional open optical systems

TL;DR

This paper applies the resonant state expansion (RSE) method to two-dimensional open optical systems, demonstrating its accuracy and convergence in calculating complex eigenfrequencies for various perturbations.

Contribution

It extends the RSE method to 2D open optical systems, including the Green's function with a complex frequency plane cut, and validates it with multiple perturbations.

Findings

RSE accurately computes eigenfrequencies for perturbed systems.

The method converges reliably across different perturbations.

Resonant states match analytical solutions for thin-wire perturbations.

Abstract

The resonant state expansion (RSE), a rigorous perturbative method in electrodynamics, is applied to two-dimensional open optical systems. The analytically solvable homogeneous dielectric cylinder is used as unperturbed system, and its Green's function is shown to contain a cut in the complex frequency plane, which is included in the RSE basis. The complex eigenfrequencies of modes are calculated using the RSE for a selection of perturbations which mix unperturbed modes of different orbital momentum, such as half-cylinder, thin-film and thin-wire perturbation, demonstrating the accuracy and convergency of the method. The resonant states for the thin-wire perturbation are shown to reproduce an approximative analytical solution.