Schrödinger electrons interacting with optical gratings: quantum mechanical study of the inverse Smith–Purcell effect

Slow swift electrons with low self-inertia interact differently with matter and light in comparison with their relativistic counterparts: they are easily recoiled, reflected, and also diffracted form optical gratings and nanostructures. As a consequence, they can be also better manipulated into the desired shape. For example, they get bunched quite fast in interaction with acceleration gratings in presence of an external electromagnetic radiation, a phenomenon which can be desirable in development of superradiant coherent light sources. Here, I examine the spatiotemporal behavior of pulsed electron wave packets at low energies interacting with pulsed light and optical gratings, using a quantum-mechanical self-consistent numerical toolbox which is introduced here. It will be shown that electron pulses are accelerated very fast in interaction with the near-field of the grating, demanding that a synchronicity condition is met. To prevent the electrons to be transversely deflected from the grating a symmetric double-grating configuration is necessary. It is found that even in this configuration, diffraction due to the interaction of the electron with the standing-wave light inside the gap between the gratings, is a source of defocusing. Moreover, the longitudinal broadening of the electron pulse directly affects the final shape of the electron wave packet due to the occurrence of multiple electron-photon scatterings. These investigations pave the way towards the design of more efficient electron-driven photon sources and accelerators.