Phase-matched electron–photon interactions enabled by 3D-printed helical waveguides

The Smith–Purcell effect enables electromagnetic radiation across arbitrary spectral ranges by phase-matching the diffraction orders of an optical grating with the near-field of a moving electron. In this work, we introduce a novel approach using a helically shaped waveguide, where phase-matching is achieved through guided light within a helical optical fiber fabricated via two-photon polymerization using a 3D printer. Our results demonstrate that radiation from these structures precisely satisfies the phase-matching condition and is emitted directionally at specific angles, contrasting with the broad angular distribution characteristic of the traditional Smith–Purcell effect. Helical electron-driven photon sources establish a new paradigm, enabling 3D-printed structures to control electron-beam-induced radiation and, inversely, to facilitate light-induced efficient electron beam shaping and acceleration.