Structured free-space optical fields for transverse and longitudinal control of electron matter waves

Abstract

Controlling free-electron momentum states is of significant interest in electron microscopy, enabling momentum- and energy-resolved probing and manipulation of physical systems. Interactions between free electrons and light have emerged as a powerful technique to achieve this. Here, we numerically demonstrate both longitudinal and transverse phase control of a slow-electron wavepacket by extending the Kapitza–Dirac effect to spatially structured pulsed laser beams. This extension facilitates both inelastic and elastic stimulated Compton scattering. The interaction reveals distinct electron transverse momentum orders, each exhibiting a comb-like electron energy spectrum. By adjusting light parameters such as wavelength, field intensity, pulse duration, spatial mode order, and their combinations, it becomes possible to coherently control the population of these electron energy–momentum states, separated by a few meV and multiple photon momentum orders. This free-space electron–light interaction could enable precise energy and momentum control of electron beams in electron microscopes. Additionally, it has the potential to selectively probe various material excitations, including plasmons, excitons, and phonons, as well as to perform Talbot–Lau matter-wave interferometry using transversely shaped electron beams.

Keywords

• matter wave optics
• nonlinear optics
• optics
• electron microscopy