Analytic methods in electron energy-loss and cathodoluminescence spectroscopy of planar and spherical nanostructures: tutorial

In recent years, fast electrons have emerged as ideal probes for exploring the optical properties of nanoscale matter with sub-meV energy resolution and atomic-scale spatial resolution. Considering the remarkable progress in cathodoluminescence (CL) and electron energy-loss spectroscopy (EELS), robust theoretical tools are needed to interpret the plethora of experimental data and provide insight into the properties of matter and its interaction with fast electrons. This tutorial offers a comprehensive overview of analytical methods for simulating CL and EEL spectra of spherical nanoparticles and planar slabs composed of arbitrary isotropic materials. We demonstrate the applicability of these methods to analyze the optical modes sustained in metallic and dielectric nanocavities and explore the underlying physical mechanisms driving the optical response of these systems.