Inelastic electron-light scattering at dielectric thin films

In a recently developed methodology termed photon induced near-field electron microscopy (PINEM), the inelastic scattering of electrons off illuminated nanostructures provides direct experimental access to the structure of optical near-field modes and their population. Whereas the inelastic scattering probability can be quantitatively linked to the near field distribution, analytical results for simple light scattering geometries are scarce. Here we derive a fully analytical expression for the coupling strength between free electrons and optical near-fields in planar geometries representing dielectric thin films. Contributions to the overall coupling from the electric field above, below and within the sample are analyzed in detail. By carefully choosing the relative angles between electron beam, light and thin film and by accounting for a broad spectrum of photon energies, we demonstrate that one can imprint optical material properties like the reflectivity onto the electron energy distribution.