Modal approximation for plasmonic resonators in the time domain: the scalar case

TL;DR

This paper develops a modal approximation method for modeling the time-domain electromagnetic response of plasmonic resonators, specifically metallic nanoparticles, using a scalar approach and numerical simulations.

Contribution

It introduces a modal approximation framework based on non-Hermitian eigenmodes for dispersive plasmonic particles, linking frequency domain poles to time domain fields.

Findings

Modal approximation accurately predicts time-domain fields.

Eigenvalues are located near the origin in the complex plane.

Numerical simulations confirm the theoretical results.

Abstract

We study the electromagnetic field scattered by a metallic nanoparticle with dispersive material parameters in a resonant regime. We consider the particle placed in a homogeneous medium in a low-frequency regime. We define modes for the non-Hermitian problem as perturbations of electrostatic modes, and obtain a modal approximation of the scattered field in the frequency domain. The poles of the expansion correspond to the eigenvalues of a singular boundary integral operator and are shown to lie in a bounded region near the origin of the lower-half complex plane. Finally, we show that this modal representation gives a very good approximation of the field in the time domain. We present numerical simulations in two dimensions to corroborate our results.