A detection system based on electro-optical(EO) sampling is designed for the established high-power, wide-band and wave-tunable FEL-THz source at Huazhong University of Science and Technology (HUST). The phase mismatch and dispersion propagation of the femtosecond laser pulse in the crystal are the main reasons that cause the distortion of the EO signal. We theoretically calculate and analyze the mixing process of the probe pulse and THz pulse in the crystal. Calculating the coherence length to find the suitable center wavelength probe for different detected crystals (ZnTe, Gap, GaAs). In addition, our simulation results show that the broadband laser can eliminate the effect caused by phase mismatch between the THz phase velocity and the group velocity of the laser in different crystals (ZnTe, Gap, GaAs). Moreover, the experiment results of 3-mm-thick ZnTe with sampling laser of 100nm bandwidth agree the simulation results well. The research is meaningful for optimizing the EO sampling system in the future.
 

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