Numerical studies on the electro-optic detection of femtosecond electron bunches

Abstract

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 m for ZnTe and from 50 to 100 m for GaP.

Extending electro-optic detection to ultrashort electron beams

“…It has been the focus of most ongoing research to obtain thinner and thinner crystals to measure shorter bunches. This leads to reduced signal and does not resolve the ultimate issue, namely the resonance [12,15]. Fortunately, the picture described above is not complete in its treatment of the mixing process that occurs between the self-fields and the optical probe.…”

“…Additionally, certain frequencies can be suppressed by the slippage between the phase/group velocities of the self-fields and the optical probe. These effects are often discussed in terms of the so-called electro-optic response function, Gð!Þ, that approximates the ratio of the reconstructed spectrum to the actual spectrum [15,17]. An example of such a response function plotted for various thicknesses of ZnTe is given in Brunken et al [17].…”

“…The earliest detection method was the balanced photodiode detection scheme [2,15,17]. When the charged particle beam is present, a birefringence is induced within the crystal.…”

“…In the case of the former, the particle beam's longitudinal profile can be deduced from its self-fields due to the fact that for sufficiently relativistic beams the temporal structure of the selffields matches the temporal structure of the beam [14]. The technique is commonly described as being analogous to an electro-optic modulator based on Pockels effect [15]. The electric field of interest induces a time-varying birefringence within an electro-optic crystal that is being probed optically.…”

Electro-optical measurement of sub-ps structures in low charge electron bunches

“…For a more comprehensive description of EO detection techniques, theory, and the simulations see also Refs. [4,22].…”