Smith-Purcell radiation from metallic and dielectric photonic crystals

Smith-Purcell (SP) radiation from a charge running near a periodically grooved solid-state surface has a long history of investigation. It is a kind of Cerenkov radiation, in which an evanescent photon emitted by the running charge turns to an observable one by the umklapp scattering by the periodic array of grooves; an evanescent photon originally present in the phase space outside the light line gets into the light cone when an umklapp shift of its momentum component takes place. This paper treats a theoretical study of the SP spectrum from a photonic crystal, which is used in place of a grating as a source of the umklapp light scattering. We use as a model photonic crystal a periodic array of dielectric and metallic spheres. We are interested in (a) the difference of the SP spectrum between dielectric and metallic photonic crystals, (b) the effect of the umklapp scattering in the direction normal to the trajectory of charge and (c) the dependence of the spectrum with the charge velocity.