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Focused beams of electrons, which act as both sources, and sensors ofelectric fields, can be used to characterise the electric response of complexphotonic systems by locally probing the induced optical near fields. Thisfunctionality can be complemented by embracing the recently developed vortexelectron beams (VEBs), made up of electrons with orbital angular momentum,which could, in addition, probe induced magnetic near fields. In this work, werevisit the theoretical description of this technique, dubbed vortex ElectronEnergy-Loss Spectroscopy (v-EELS). We map the fundamental, quantum-mechanicalpicture of the scattering of the VEB electrons to the intuitive classicalmodels, which treat the electron beams as a superposition of linear electricand magnetic currents. We then apply this formalism to characterise the opticalresponse of dielectric nanoantennas with v-EELS. Our calculations reveal thatVEB electrons probe electric or magnetic modes with different efficiency, whichcan be adjusted by changing either beam vorticity or acceleration voltage todetermine the nature of the probed excitations. We also study achirally-arranged nanostructure, which in the interaction with electronvortices produces dichroism in electron energy loss spectra. Our theoreticalwork establishes VEBs as versatile probes that could provide information onoptical excitations otherwise inaccessible with conventional electron beams.

Probing the electromagnetic response of dielectric antennas by vortex electron beams