Brillouin-Wigner perturbation theory in open electromagnetic systems

TL;DR

This paper develops a Brillouin-Wigner perturbation theory tailored for open electromagnetic systems with complex resonant states, enabling spectral representation and mode calculation through a linear eigenvalue problem.

Contribution

It introduces a modified normalization for resonant states and applies the theory to solvable dielectric and microsphere examples.

Findings

Spectral representation of Green's function achieved

Perturbed modes obtained via linear eigenvalue problem

Method validated on dielectric slab and microsphere

Abstract

A Brillouin-Wigner perturbation theory is developed for open electromagnetic systems which are characterised by discrete resonant states with complex eigenenergies. Since these states are exponentially growing at large distances, a modified normalisation is introduced that allows a simple spectral representation of the Green's function. The perturbed modes are found by solving a linear eigenvalue problem in matrix form. The method is illustrated on exactly solvable one- and three-dimensional examples being, respectively, a dielectric slab and a microsphere.