  Semi-transparent mirrors are standard elements in light optics for splitting
light beams or creating two versions of the same image. Such mirrors do not
exist in electron optics, although they could be beneficial in existing
techniques such as electron interferometry and holography and enable novel
electron imaging and spectroscopy techniques. We propose a design for an
electron beam splitter using the concept of quantum interaction-free
measurement (IFM). The design combines an electron resonator with a weak phase
grating. Fast switching gates allow electrons to enter and exit the resonator.
While in the resonator, the phase grating transfers intensity from the direct
beam into one of the weakly diffracted beams at each pass. To make the beam
splitter an efficient two-port splitter, the intensity in all other diffracted
beams is blocked by an aperture. The IFM principle minimizes the loss of total
intensity by this aperture. We use a scattering matrix method to analyze the
performance of the beam splitter, including the effects of inelastic scattering
in the phase grating. This design can be generalized to beam splitters for not
only electrons, but also photons, neutrons, atoms, and other quantum mechanical
systems.
