Simulating electron energy-loss spectroscopy and cathodoluminescence for particles in arbitrary host medium using the discrete dipole approximation

Electron energy-loss spectroscopy (EELS) and cathodoluminescence (CL) are widely used experimental techniques for characterization of nanoparticles. The discrete dipole approximation (DDA) is a numerically exact method for simulating interaction of electromagnetic waves with particles of arbitrary shape and internal structure. In this work we extend the DDA to simulate EELS and CL for particles embedded into arbitrary (even absorbing) unbounded host medium. The latter includes the case of the dense medium, supporting the Cherenkov radiation of the electron, which has never been considered in EELS simulations before. We build a rigorous theoretical framework based on the volume-integral equation, final expressions from which are implemented in the open-source software package ADDA. This implementation agrees with both the Lorenz-Mie theory and the boundary-element method for spheres in vacuum and moderately dense host medium. And it successfully reproduces the published experiments for particles encapsulated in finite substrates. The latter is shown for both moderately dense and Cherenkov cases - a gold nanorod in $\text{SiO}_{\text{2}}$ and a silver sphere in $\text{SiN}_{\text{x}}$ respectively.