Coherent electron phase-space manipulation by combined elastic and inelastic light-electron scattering

Photon-Induced Near-field Electron Microscopy (PINEM), Kapitza–Dirac (KD) gratings, and ponderomotive phase plates are examples of techniques in which the wave function of an electron in free space is manipulated using light fields: free electron quantum optics (FEQO). These effects are usually treated in separate theoretical frameworks. In this paper we present a unified, two-pronged framework that can be used to describe and numerically evaluate the performance of a number of FEQO-based electron-optical elements. The first part is a combination of existing analytical treatments of light-electron scattering, based on solving a relativistically corrected Schrödinger equation. The theoretical overview covers both second-order contributions to PINEM and the Kapitza–Dirac effect. The second, novel element of the approach is based on electron wavefront reconstruction by evaluating the quantum mechanical phase along a bundle of classical electron trajectories. The quasi-classical (but fully relativistic) approach lends itself to simulating a wide variety of FEQO devices, including the examples mentioned. We apply both approaches to a few specific experimental configurations: mirror-based first-order PINEM, second-order PINEM in very high laser intensity, and Kapitza–Dirac diffraction. The results show excellent agreement between the analytical results and the quasi-classical simulations. Finally, we propose a setup that combines KD and PINEM to allow for simultaneous coherent energy and transverse momentum shaping of an electron beam, and present simulation results thereof.