  We propose a scheme for constructing a phase plate for use in an ultrafast
Zernike-type phase contrast electron microscope, based on the interaction of
the electron beam with a strongly focused, high-power femtosecond laser pulse
and a pulsed electron beam. Analytical expressions for the phase shift using
the time-averaged ponderomotive potential and a paraxial approximation for the
focused laser beam are presented, as well as more rigorous quasiclassical
simulations based on the quantum phase integral along classical, relativistic
electron trajectories in an accurate, non-paraxial description of the laser
beam. The results are shown to agree well unless the laser beam is focused to a
waist size below a wavelength. For realistic (off-the-shelf) laser parameters
the optimum phase shift of $-\pi/2$ is shown to be achievable. When combined
with RF-cavity based electron chopping and compression techniques to produce
electron pulses, a femtosecond regime pulsed phase contrast microscope can be
constructed. The feasibility and robustness of the scheme are further
investigated using the simulations, leading to motivated choices for design
parameters such as wavelength, focus size and polarization.
