Analysis of the electro-optic measurement of an electron beam with new refractive indices

Abstract

Electro-optic sampling (EOS) is a promising method of measuring the electron bunch length and arrival time nondestructively. When an electric field is applied to the EO crystal, the EO crystal shows birefringence which is described by an ellipsoid of refractive indices. The ellipsoid can be expressed with the principal axes associated with the crystallographic axes. If a linearly polarized laser is passing through the EO crystal with external electric field, the polarization of the laser is modulated elliptically or even circularly. The polarization modulation of the laser probe beam should be expressed in terms of the relative phase shift between the decomposed vectors of the laser. Conventional analysis assumes that the polarization direction of the laser probe beam is to set to be at an angle of 45 degrees with the principal axes. Only the principal refractive indices have been used until now with this assumption. However, if the position of the electron beam is changed in experiments, the electric field applied to the EO crystal is also changed. Thus, the directions of the principal axes of the isotropic crystal are also changed. The principal axes do not make an angle of 45 degrees anymore with the fixed polarization vector of the laser probe beam in this situation. New refractive indices are needed to explain the experimental result with such deviation properly. In our work, new refractive indices are derived and simulation studies are carried out with the pulse propagation method, which utilizes the Fourier transform to investigate the evolution of the electromagnetic pulse inside the EO crystal. Experimental results are in good agreement with the prediction from the simulation with newly derived refractive indices.