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Many calculations in strong-field quantum field theory are carried out by using a simple field geometry, often neglecting the spatial field envelope. In this paper, we simulate the electron-diffraction quantum dynamics of the Kapitza-Dirac effect in a Gaussian beam standing light wave. The two-dimensional simulation is computed in a relativistic framework, by solving the Dirac equation with the fast Fourier-transform split operator method. Except the numerical propagation method, our results are obtained without applying approximations and demonstrate that a spin flip in the Kapitza-Dirac effect is possible. We further discuss properties such as the validity of a plane-wave approach for the theoretical description, the influence of the longitudinal polarization component due to laser beam focusing, and higher-order diffraction peaks in Kapitza-Dirac scattering.
Ge et al. (Mon,) studied this question.