Resonant-state expansion for a simple dispersive medium

TL;DR

This paper extends the resonant-state expansion (RSE) method to dispersive media with Ohm's law dispersion, enabling accurate analysis of materials like doped semiconductors and optical glass without increasing computational complexity.

Contribution

It introduces a way to apply RSE to dispersive media with a single pole at zero frequency, maintaining linearity and simplicity of the eigenvalue problem.

Findings

Successfully applied RSE to doped silicon and BK7 glass.

Demonstrated RSE's effectiveness in transitioning between dispersive and non-dispersive media.

Validated results with analytically solvable models.

Abstract

The resonant-state expansion (RSE), a rigorous perturbative method developed in electrodynamics for non-dispersive optical systems is applied to media with an Ohm's law dispersion, in which the frequency dependent part of the permittivity scales inversely with the frequency, corresponding to a frequency-independent conductivity. This dispersion has only a single pole at zero frequency, which is already present in the non-dispersive RSE, allowing to maintain not only the linearity of the eigenvalue problem of the RSE but also its size. Media which can be described by this dispersion over the relevant frequency range, such as optical glass or doped semiconductors, can be treated in the RSE without additional complexity. Results are presented using analytically solvable homogeneous spheres, for doped silicon and BK7 glass, both for a perturbation of the system going from non-dispersive to dispersive media and the reverse, from dispersive to non-dispersive media.