Longitudinal Polarization Influence Of Gaussian Beamon Electron Spin In The Kapitza-Dirac Effect

The Kapitza-Dirac effect was first proposed in 1933.In previous studies of the Kapitza-Dirac effect,the paraxial approximation was taken into account and Gaussian beam was treated as plane wave.In fact,Gaussian beam is longitudinally polarized due to focus.Longitudinal polarization may influence the electron spin in the study of Gaussian standing wave.Based on this point,this paper studies the influence of longitudinal polarization of Gaussian beam on electron spin in Kapitza-Dirac effect.The longitudinal polarization of Gaussian beam is considered in this paper.Gaussian beam is divided into transverse polarization and longitudinal polarization which are mutually perpendicular and mutually independent.Based on the Dirac equation in relativity theory,the second order time evolution operator of electron in standing wave is obtained by combining the interaction between electron and Gaussian beam and the time-dependent perturbation theory.Then change the second order time evolution operator into the form of matrix.By simulating matrix elements and linear fitting,the function of matrix elements with(?)and longitudinal wave vector as variables is obtained.The results show that the longitudinal polarization of Gaussian beam has an effect on the electron spin of at least(?)2.The discriminant of the effect of longitudinal polarization of Gaussian beam on electron spin can be ignored when the wavelength and divergence angle of Gaussian beam or the beam waist radius are known.