Polarization shaping of focused Smith–Purcell radiation with phase gradient metasurface

Abstract The manipulation of Smith–Purcell radiation wavefronts has garnered extensive attention due to its significant potential for the development of electronic radiation sources and nanoscale light sources. While extensive research has focused on line focusing, achieving point focusing in Smith–Purcell radiation remains an unmet challenge. In this work, we propose a method to shape the polarization and phase of the point focused field of Smith–Purcell radiation using rotationally periodic grating and phase gradient metasurfaces. By precisely arranging the spatial distribution of the unit cells, the Smith–Purcell radiation energy can be concentrated into a diffraction-limited focal point, and the number and positions of the focal points can be flexibly controlled. Moreover, the polarization state of the focal point can be tailored via multi-layer metasurface configurations. Our work provides the demonstration of point focusing of Smith–Purcell radiation and introduces a novel way for multidimensional control, offering a new pathway toward multifunctional and high-efficiency free-electron radiation devices.