  Spectroscopies utilizing free electron beams as probes offer detailed
information on the reciprocal-space excitations of 2D materials such as
graphene and transition metal dichalcogenide monolayers. Yet, despite the
attention paid to such quantum materials, less consideration has been given to
the electron-beam characterization of 2D periodic nanostructures such as
photonic crystals, metasurfaces, and plasmon arrays, which can exhibit the same
lattice and excitation symmetries as their atomic analogs albeit at drastically
different length, momentum, and energy scales. Due to their lack of covalent
bonding and influence of retarded electromagnetic interactions, important
physical distinctions arise that complicate interpretation of scattering
signals. Here we present a fully-retarded theoretical framework for describing
the inelastic scattering of wide field electron beams from 2D materials and
apply it to investigate the complementarity in sample excitation information
gained in the measurement of a honeycomb plasmon array versus angle-resolved
optical spectroscopy in comparison to single monolayer graphene.
