Crystals for electro optic detection of femtosecond electron bunches - [e-mail]

The optimum thickness is in the range from 100 to 300 micron for ZnTe and from 50 to 100 micron for GaP.

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Numerical studies on the electro-optic detection of femtosecond electron bunches
S. Casalbuoni,1 H. Schlarb,2 B. Schmidt,2 P. Schmu¨ser,2,3 B. Steffen,2,* and A. Winter3
1 Institute for Synchrotron Radiation, Research Center Karlsruhe, P.O. Box 3640, D-76021 Karlsruhe, Germany
2 Deutsches Elektronen-Synchrotron DESY, Notkestrasse 85, 22607 Hamburg, Germany
3 Institut fu¨r Experimentalphysik, Universita¨t Hamburg, Luruper Chaussee 149, 22607 Hamburg, Germany

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 90 fs in ZnTe and 50 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 micron for ZnTe and from 50 to 100 micron for GaP.

The electro-optic (EO) method has been successfully applied at several accelerators to study the time structure of ultrashort electron bunches [1–3]. The best time resolution has been achieved in a recent experiment [4] at the ultraviolet and soft x-ray free-electron laser FLASH (Free-electron LAser in Hamburg) at an electron energy of 450 MeV and a free-electron laser (FEL) wavelength of 30 nm. The FEL is based on the principle of self amplified spontaneous emission (SASE) which opens the way to powerful lasers in the x-ray regime and requires electron bunches of extremely high local charge density to achieve laser saturation in the 27 m long undulator magnet.
Electron bunches with a charge of 0.5 nC and an rms time duration of 5 ps are generated in a radio frequency photocathode, accelerated to relativistic energies and then longitudinally compressed by 2 orders of magnitude in a two-stage bunch compression scheme. The compressed bunches are characterized by a short leading spike with an rms length of less than 50 fs followed by a tail that is several ps long. Precise measurements of the temporal profile of the compressed electron bunches are essential for
the optimization of the accelerator and a proper understanding of the bunch compression mechanism including subtle effects such as coherent synchrotron radiation and space charge forces. For this purpose an electro-optic detection system [4] has been installed at FLASH with an EO crystal placed inside the electron-beam vacuum chamber at a few millimeter distance from the beam. A major concern are pulse shape distortions in the electrooptic detection process which are known to happen for
ultrashort THz pulses, see, e.g., Ref. [5].
Since quantitative calculations on the EO detection of femtosecond electron bunches were not available to us we have carried out detailed numerical studies on the electro-optic effect in gallium phosphide (GaP) and zinc telluride (ZnTe) with the aim of assessing the faithfulness and the limitations of EO bunch shape reconstruction. In the model calculations we
restrict ourselves to the simple method of electro-optic sampling (EOS), where a narrow laser pulse is scanned in small time steps across the THz pulse. EOS yields the best possible resolution if timing jitter between the laser pulses and the electron bunches is negligible. In practical accelerators time jitter is significant, and one has to resort to single-shot techniques such as spectral, temporal, or spatial decoding [1–4] if one wants to resolve ultrashort electron bunches.