Quasinormal mode theory and modelling of electron energy loss spectroscopy for plasmonic nanostructures

TL;DR

This paper introduces a simple, accurate quasinormal mode-based method for modeling electron energy loss spectroscopy in plasmonic nanostructures, significantly improving computational efficiency and providing analytical insights.

Contribution

It develops a novel QNM expansion technique for EELS modeling that simplifies calculations and enhances accuracy over traditional full Maxwell simulations.

Findings

QNM method accurately models EELS maps for various nanostructures.

The approach offers orders of magnitude speedup over direct simulations.

The same QNM Green function can be used to compute Purcell factors and local density of states.

Abstract

Understanding light-matter interactions using localized surface plasmons (LSPs) is of fundamental interest in classical and quantum plasmonics and has a wide range of applications. In order to understand the spatial properties of LSPs, electron energy loss spectroscopy (EELS) is a common and powerful method of spatially resolving the extreme localized fields that can be obtained with metal resonators. However, modelling EELS for general shaped resonators presents a major challenge in computational electrodynamics, requiring the full photon Green function as a function of two space points and frequency. Here we present an intuitive and computationally simple method for computing EELS maps of plasmonic resonators using a quasinormal mode (QNM) expansion technique. By separating the contribution of the QNM and the bulk material, we give closed-form analytical formulas for the plasmonic QNM contribution to the EELS maps. We exemplify our technique for a split ring resonator, a gold nanorod, and a nanorod dimer structure. The method is accurate, intuitive, and gives orders of magnitude improvements over direct dipole simulations that numerically solve the full 3D Maxwell equations. We also show how the same QNM Green function can be used to obtain the Purcell factor (and projected local density of optical states) from quantum dipole emitters or two level atoms, and we demonstrate how the spectral features differ in general to the EELS spectrum.