Smith-Purcell radiation from electrons moving parallel to a grating at oblique incidence to the rulings

Smith-Purcell radiation is produced when a charged particle moves parallel and close to a diffraction grating. We extend previous descriptions of the phenomenon by considering a particle moving parallel to the grating surface at an arbitrary angle with respect to the grating rulings. The problem of calculating the emitted radiation intensity is shown to be linked to a special grating problem involving evanescent incident waves and conical diffraction. Conservation relations are derived by applying techniques from electromagnetic grating theory, and Smith-Purcell spectra are calculated for some specific cases of practical interest.