Four-Photon Kapitza-Dirac Effect as Electron Spin Filter

We theoretically demonstrate the feasibility of producing electron beam splitter using Kapitza-Dirac diffraction on bichromatic standing waves which are created by the fundamental frequency and the third harmonic. The relativistic electron in Bragg regime absorbs three photons with frequency of w and emits a photon with frequency of 3w, four-photon Kapitza-Dirac effect. In this four-photon Kapitza-Dirac effect distinct spin effects arise in different polarizations of the third harmonic laser beam. It is shown that the shape of Rabi oscillation between initial and scattered states is changed and finds two unequal peaks. In circular polarization for fundamental and third harmonic, despite Rabi oscillation, the spin down electron in 0.56 fs intervals maintains its momentum and spin. Also we present an electron spin filter with combination of a linearly polarized fundamental laser beam and a third harmonic with circular polarization that scatters the electron beam according to its spin state.