Smith-Purcell radiation is emitted by an electron moving near a periodically inhomogeneous target. The main features of Smith-Purcell radiation is monochromaticity and relation between the wavelength of radiation and the observation angle. As during generation there is no direct scattering the electrons on the atoms of material, this type of radiation can serve as a tool for non-invasive beam diagnostics. Here, we report on the recent progress in theoretical investigation of Smith-Purcell radiation from two-periodical arrays consisting of small particles. Such targets are referred as metasurfaces or photonic crystals as well. Second period in direction perpendicular to the electron trajectory opens new possibilities for the diagnostics of relativistic electron beam, including simultaneous measuring the two emittances for the electron beams with asymmetric cross-section.
This work was supported by the Russian Science Foundation, grant № 19-72-00178.