Numerical studies on the electro-optic sampling of relativistic electron bunches

Ultraviolet and X ray free electron lasers require sub-picosecond electron bunches of high charge density. Electro-optic sampling (EOS) is a suitable diagnostic tool for resolving the time structure of these ultrashort bunches. The transient electric field of the relativistic bunch induces a polarization anisotropy in a nonlinear crystal which is sampled by femtosecond laser pulses. In this paper, the EOS process is studied in detailed numerical calculations. The THz and the laser pulses are treated as wave packets which are propagated through the zinc telluride resp. gallium phosphide crystals. The effects of signal broadening and distortion are taken into account. The time resolution is severely limited by transverse optical (TO) lattice oscillations (5.3 THz in ZnTe, 11 THz in GaP). The shortest bunch length which can be resolved with moderate distortion is about 200 fs (FWHM) in ZnTe and 100 fs in GaP.