  We demonstrate the ability to create electron beams with high-contrast,
nanometer-scale density modulations as a first step toward developing full
control of the phase fronts of an x-ray free-electron laser. The nanopatterned
electron beams are produced by diffracting electrons through thin
single-crystal silicon membranes that are lithographically patterned to
different thicknesses. For transform-limited x-ray production the desired
pattern is a series of regularly spaced lines (i.e. a grating) that generate
uniformly spaced nanobunches of electrons, however nearly any pattern can be
etched in the silicon, such as frequency-chirps or multiple patterns of
different colors or line spacings. When these patterns are transferred from the
spatial to the temporal dimension by accelerator electromagnetic optics they
will control the phase fronts of coherent x-rays, giving unprecedented
deterministic control over the phase of ultrashort x-ray pulses. In short, this
method allows the time-structure for a fully coherent x-ray beam to be
generated from a pattern written on a semiconductor wafer by lithography.
