Smith–Purcell Radiation in Dielectric and the Anomalous Doppler Effect

The features of Smith–Purcell radiation in a dielectric from a grating consisting of metal strips deposited on the surface of the dielectric is considered. Smith–Purcell radiation is able to propagate in the dielectric at an angle smaller than the angle of the Cherenkov cone. This can be considered as a manifestation of the so-called anomalous Doppler effect. An experiment aimed at detecting the anomalous Doppler effect in the gigahertz range on a relativistic electron beam is proposed and substantiated.