Electron energy loss spectroscopy as a probe of two-dimensional photonic crystals

The band structure and density of states of two-dimensional photonic crystals are shown to be directly related to the loss spectra of electrons moving parallel to the direction of translational symmetry. Both broad electron beams and focused beams passing through crystals composed of cylindrical holes in a dielectric host are considered. Energy losses originate in Cherenkov light emission by coupling to radiation modes of the crystal. The angular distribution of transmitted electrons is shown to map quite closely the band structure of the crystal when broad beams are employed, and in particular, Van Hove singularities give rise to peaks in the loss probability. Finally, the degree of convergence towards the infinite crystal results is studied for finite crystals of increasing size.