Longitudinal and transverse modulation of electron wave function with light, and its application to electron microscopy

Conventional electron microscopy operates with flat electron wave fronts. Employing attenuative or electrostatic phase plates allows transversally modulating the wave front, enhancing cross-sections of particular scattering channels. Utilization of light from coherent ultrafast sources allows modulating electrons phase both transversally and longitudinally. This results in a plethora of phenomena, as well as conceptually new techniques such as non-local electron holography of light fields and generation of ultrafast electron vortex beams, which we present in this contribution.