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.
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