  We investigate - both experimentally and theoretically - the inelastic
interaction between fast electrons and the electromagnetic field scattered by
metallic apertures and nanostructures on dielectric membranes using photon
induced near-field electron microscopy. The experiments - performed in a high
brightness ultrafast transmission electron microscope - on gold apertures on
silicon nitride membranes reveal strong modulations of the electron-light
coupling strength. We demonstrates that this effect results from the combined
action of the electric field scattered by the aperture edges and the reflection
and transmission of the incident wave by the dielectric membrane. Moreover,
when a nanostructure is added inside the metallic aperture, the new scattered
field interferes with the previous contributions, thus imprinting the optical
response of the nanostructure in additional modulations of the electron-light
coupling strength. Using systematic electrodynamics simulations based on the
Green dyadic method, we quantitatively analyze these different contributions to
the electron-light coupling and propose further applications.
