Resonant-state expansion of dispersive open optical systems

TL;DR

This paper develops a resonant-state expansion method for open optical systems with frequency-dependent permittivity, enabling precise calculation of optical modes in dispersive materials by transforming Maxwell's equations into a linear eigenvalue problem.

Contribution

It introduces a generalized RSE for dispersive open optical systems with permittivity described by simple poles, extending previous non-dispersive methods.

Findings

Validated the dispersive RSE using an analytically solvable sphere model.

Accurately computed mode changes when switching between gold and silica.

Demonstrated the method's precision against exact solutions.

Abstract

A resonant-state expansion (RSE) for open optical systems with a general frequency dispersion of the relative permittivity, described by a finite number of simple poles, is presented. As in the non-dispersive case, the RSE of dispersive systems converts Maxwell's wave equation into a linear matrix eigenvalue problem in the basis of unperturbed resonant states, in this way numerically exactly determining all relevant eigenmodes of the optical system. This dispersive RSE is verified by application to the analytically solvable system of a sphere in vacuum, with a dispersion of the dielectric constant described by the Drude and Drude-Lorentz models. We calculate the change of the optical modes when converting the sphere material from gold to non-dispersive silica and back to gold, and evaluate the accuracy using the exact solutions.