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

## TL;DR

Researchers developed a new way to control electron-photon interactions using 3D-printed helical waveguides, enabling directional radiation and new applications in electron beam shaping.

## Contribution

A novel helical waveguide design fabricated via 3D printing enables phase-matched electron-photon interactions with directional radiation emission.

## Key findings

- Radiation from helical waveguides satisfies phase-matching conditions and is emitted at specific angles.
- The helical structure allows for directional emission, unlike the broad angular distribution in traditional Smith–Purcell effects.
- This approach enables new paradigms for controlling electron-beam-induced radiation and shaping electron beams with light.

## Abstract

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.