Smith–Purcell radiation driven by the field of a standing laser wave

Smith–Purcell radiation is well known as a source of quasi-monochromatic electromagnetic radiation that occurs when fast electrons move above a diffraction grating. In this paper, we calculated the Smith–Purcell radiation generation from a flat surface along which there is a field of a standing laser wave. A periodically changing laser field induces a periodic inhomogeneity in the distribution of electrons in the near-surface layer. This periodicity, being an analogue of a diffraction grating, leads to the possibility of generating Smith–Purcell radiation. It is shown that the properties of Smith–Purcell radiation from such an unusual “light” grating are also unusual: the dispersion relation, unlike the standard for Smith–Purcell radiation, does not contain diffraction orders, so that all radiation is concentrated in one peak. The calculated effect makes it possible to control the radiation frequency or angle by changing the laser frequency and may be of interest for the development of new compact radiation sources with tunable characteristics and for non-invasive diagnostics of relativistic electron beams.