  A quantum mechanical scattering theory for relativistic, highly focused
electron beams near nanoscopic platelets is presented, revealing a new
excitation mechanism due to the electron wave scattering from the platelet
edges. Radiative electromagnetic excitations within the light cone are shown to
arise, allowed by the breakdown of momentum conservation along the beam axis in
the inelastic scattering process. Calculated for metallic (silver and gold) and
insulating (SiO2 and MgO) nanoplatelets, new radiative features are revealed
above the main surface plasmon-polariton peak, and dramatic enhancements in the
electron energy loss probability at gaps of the 'classical' spectra, are found.
The corresponding radiation should be detectable in the vacuum far-field zone,
with e-beams exploited as sensitive 'tip-detectors' of electronically excited
nanostructures.
