Relativistic electron energy-loss spectroscopy in cylindrical waveguides and holes

TL;DR

This paper develops an analytical framework for simulating electron energy-loss spectroscopy (EELS) in cylindrical systems like wires and holes, including new solutions for perpendicular electron trajectories, validated by numerical methods.

Contribution

It introduces closed-form analytical solutions for EELS in cylindrical geometries with perpendicular electron trajectories, expanding existing theory and enabling better analysis of nanostructures.

Findings

Analytical solutions for EELS in cylindrical geometries with perpendicular electron trajectories.

Validation of analytical results through numerical simulations.

Application potential in designing free-electron--photonic hybrid systems.

Abstract

Swift electrons passing near or through metallic structures have proven to be an excellent tool for studying plasmons and other types of confined optical modes involving collective charge oscillations in the materials hybridized with electromagnetic fields. In this work, we provide a general analytical framework for the simulation of electron energy-loss spectroscopy (EELS) in infinite systems with cylindrical symmetry, such as wires, holes, and optical fibers. While EELS theory is well developed for electrons moving parallel to the direction of translational symmetry, we introduce closed-form analytical solutions for perpendicular electron trajectories. These analytical results are corroborated by comparison to numerical simulations based on a frequency-domain boundary-element method and a discontinuous-Galerkin time-domain finite-element method. Numerical methods further allow us to study termination effects in finite-sized cylindrical objects such as nanorods. The present study of the interaction between free electrons and cylindrically symmetric photonics systems can find application in the analysis of EELS spectra and the design of free-electron--photonic hybrid systems.