Active steering of cathodoluminescence through a generalized Smith–Purcell effect

Optical metasurfaces can shape the near fields of energetic electrons, enabling Smith–Purcell (SP) emission. We introduce a generalized SP effect relying on finite periodic arrays whose elements possess individually tunable polarizabilities, allowing us to explore higher-order SP radiation. By controlling the amplitude and phase of each of the elements, we show through rigorous theory the ability to create an SP steering device. In particular, we explore the active tuning capabilities of doped graphene, and thermally driven phase-change materials, which we compare with standard passive plasmonic structures made of gold and silver. Our results establish programmable electron-driven light sources and spectroscopic probes spanning the terahertz-to-visible range, advancing tunable metasurfaces for next-generation electron-photon technologies.