# Applying the resonant-state expansion to realistic materials with frequency dispersion

## TL;DR

This paper extends the resonant-state expansion method to realistic dispersive materials like metals and semiconductors, enabling detailed analysis of their resonant states, surface modes, and lasing phenomena.

## Contribution

It applies the dispersive resonant-state expansion to complex materials using a generalized Drude-Lorentz model, revealing new insights into surface plasmon polaritons and lasing states.

## Key findings

- Resonant states are accurately calculated for dispersive materials.
- Surface plasmon polariton modes evolve with nanoparticle size.
- Lasing resonant states are characterized near the band gap.

## Abstract

The dispersive resonant-state expansion, developed for an accurate calculation of the resonant states in open optical systems with frequency dispersion, is applied here to realistic materials, such as metallic nanoparticles and semiconductor microspheres. The material permittivity is determined by fitting the measured indices of refraction and absorption with a generalized Drude-Lorentz model containing a number of poles in the complex frequency plane. Each Drude or Lorentz pole generates an infinite series of resonant states. Furthermore, for small nanoparticles, each of these poles produces a distinct surface plasmon polariton mode. The evolution of these multiple surface modes with increasing radius traces the transition from the electrostatic limit to significant retardation and radiation. Treating the optical phonon range in a semiconductor microsphere, a reststrahlen band separating the resonant states is found. Considering a small energy range around the semiconductor band gap, the transition from absorption to gain is described by inverting the Lorentz pole weight, which results in the formation of lasing resonant states. Interestingly, the series of resonant states converging towards the absorption pole from the lower frequency side reshapes for a gain pole into a clockwise loop approaching the pole from the higher frequency side, being separated from a series spanning from low to high frequencies and containing the lasing modes.