| Free-electron laser(FEL) is a new light source based on linear accelerator. It is the most promising fourth- generation synchrotron radiation source, with characteristics of high power, ultra-short temporal pulses and good coherence, and will greatly accelerate the development of many research field.The ultra-short electron bunch, down to sub-picosecond, is needed to obtain ultra- high power and ultra-short laser pulse. In order to maintain the high performance of facility, it is necessary to develop a method to measure the length of electron bunches on- line efficiently. However, the time resolution of conventional techniques is hardly up to sub-picosecond.Electro-optic sampling is becoming a new essential method to measure the sub-picosecond length bunches for its advantages of simplicity, high-resolution and single-shot. In this dissertation, theoretical simulation and experimental design of the electro-optic sampling method were researched.In theoretical simulation, the distribution characteristics of the Coulomb field were firstly researched. The response function of electro-optic crystal was derived and the response curves were made. Then, we simulated the whole process of electro-optical encoding and analyzed the influences of several experimental factors on measurement signal. The results showed that the Coulomb field in crystal was attenuated rapidly with the length of electron bunch decrease. The relation curve between phase retardation and crystal thickness was nonlinear and the curve existed a "turning point" when the bunch length was in the order of sub-picosecond. On our experimental conditions, the electro-optic signal broadening was less than 2.8% and the shape has no observed distortion. The time resolution was expected up to 263 fs(RMS) at best. The signal strength can be greatly influenced by the orientation of Coulomb field and the rotation angle of half-wave plate.In the experimental design aspect, a complete system of spectral decoding electro-optic sampling, based on Shanghai Deep Ultraviolet Free Electron Laser(SDUV-FEL), was designed and built. In order to meet measurement requirement of different bunch length in range of 1 picosecond to 10 picosecond, an adjustable grating stretcher system was designed and built. The measured value of broadening coefficient is consistent with the theoretical value within error range. We designed a new coarse synchronization scheme between laser and electron bunch that was nondestructive to electron beam in the whole process. A special vacuum chamber and internal optical components, used for synchronization and measurement, were design and had been processed. Finally, we deduced the theoretical value of the spectrometer calibration factor and found that it was approximately linear related with the distance between two diffraction surfaces of grating pair. |