  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.
