The electro-optic (EO) effect is a powerful diagnostic tool for determining the time profile of ultrashort relativistic electron bunches. When a relativistic bunch passes within a few mm of an electro-optic crystal, its transient electric field is equivalent to a half-cycle THz pulse passing through the crystal. The induced birefringence can be detected with polarized femtosecond laser pulses. A simulation code has been written in order to understand the faithfulness and the limitations of electron bunch shape reconstruction by EO sampling. The THz pulse and the laser pulse are propagated as wave packets through the EO crystal. Alternatively, the response function method is applied. Using experimental data on the material properties of zinc telluride (ZnTe) and gallium phosphide (GaP), the effects of velocity mismatch, pulse shape distortion, and signal broadening are explicitly taken into account. The simulations show that the most severe limitation on the time resolution is given by the transverse-optical (TO) lattice oscillation in the EO crystal. The lowest TO frequency is 5.3 THz in ZnTe and 11 THz in GaP. Only the Fourier components below the TO resonance are usable for the bunch shape reconstruction. This implies that the shortest rms bunch length which can be resolved with moderate distortion amounts to $\sigma \approx 90\mathrm{fs}$ in ZnTe and $\sigma \approx 50\mathrm{fs}$ in GaP. The influence of the crystal thickness on the amplitude and width of the EO signal is studied. The optimum thickness is in the range from 100 to $300\mu \mathrm{m}$ for ZnTe and from 50 to $100\mu \mathrm{m}$ for GaP.

Precise measurements of the temporal profile of ultrashort electron bunches are of high interest for the optimization and operation of ultraviolet and x-ray free-electron lasers. The electro-optic (EO) technique has been applied for a single-shot direct visualization of the time profile of individual electron bunches at FLASH. This paper presents a thorough description of the experimental setup and the results. An absolute calibration of the EO technique has been performed utilizing simultaneous measurements with a transverse-deflecting radio-frequency structure that transforms the longitudinal bunch charge distribution into a transverse streak. EO signals as short as 60 fs (rms) have been observed using a gallium-phosphide (GaP) crystal, which is a new record in the EO detection of single electron bunches and close to the physical limit imposed by the EO material properties. The data are in quantitative agreement with a numerical simulation of the EO detection process.

Recording electric field evolution in single-shot with THz bandwidth is needed in science including spectroscopy, plasmas, biology, chemistry, Free-Electron Lasers, accelerators, and material inspection. However, the potential application range depends on the possibility to achieve sub-picosecond resolution over a long time window, which is a largely open problem for single-shot techniques. To solve this problem, we present a new conceptual approach for the so-called spectral decoding technique, where a chirped laser pulse interacts with a THz signal in a Pockels crystal, and is analyzed using a grating optical spectrum analyzer. By borrowing mathematical concepts from photonic time stretch theory and radio-frequency communication, we deduce a novel dual-output electro-optic sampling system, for which the input THz signal can be numerically retrieved—with unprecedented resolution—using the so-called phase diversity technique. We show numerically and experimentally that this approach enables the recording of THz waveforms in single-shot over much longer durations and/or higher bandwidth than previous spectral decoding techniques. We present and test the proposed DEOS (Diversity Electro-Optic Sampling) design for recording 1.5 THz bandwidth THz pulses, over 20 ps duration, in single-shot. Then we demonstrate the potential of DEOS in accelerator physics by recording, in two successive shots, the shape of 200 fs RMS relativistic electron bunches at European X-FEL, over 10 ps recording windows. The designs presented here can be used directly for accelerator diagnostics, characterization of THz sources, and single-shot Time-Domain Spectroscopy.