  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.
