Resonant state expansion applied to planar open optical systems

TL;DR

This paper applies the resonant state expansion (RSE) perturbation theory to planar optical systems, demonstrating its convergence, error estimation, and accuracy in calculating eigenfrequencies, fields, Green's functions, and transmission spectra.

Contribution

It extends the RSE method to planar optical systems, providing algorithms for error estimation and demonstrating its effectiveness in practical calculations.

Findings

RSE converges with a power law in basis size.

Error estimation and extrapolation improve accuracy.

RSE accurately reproduces transmission spectra of microcavities.

Abstract

The resonant state expansion (RSE), a novel perturbation theory of Brillouin-Wigner type developed in electrodynamics [Muljarov, Langbein, and Zimmermann, Europhys. Lett., 92, 50010(2010)], is applied to planar, effectively one-dimensional optical systems, such as layered dielectric slabs and Bragg reflector microcavities. It is demonstrated that the RSE converges with a power law in the basis size. Algorithms for error estimation and their reduction by extrapolation are presented and evaluated. Complex eigenfrequencies, electro-magnetic fields, and the Green's function of a selection of optical systems are calculated, as well as the observable transmission spectra. In particular we find that for a Bragg-mirror microcavity, which has sharp resonances in the spectrum, the transmission calculated using the resonant state expansion reproduces the result of the transfer/scattering matrix method.