Quantum modulation of an electron beam in the field of opposite electromagnetic waves

The quantum modulation of an electron beam in the field of opposite electromagnetic waves, at a frequency equal to the difference of the wave frequencies, and its harmonics, is obtained. The depth of the modulation becomes of order one at relatively small intensities of the laser fields (including a real spreading of the beam). In the case of equal frequencies of the waves (when the Kapitza-Dirac effect occurs particles form a beam. An experiment for obtaining a modulated beam of particles at the frequencies of the laser radiation, and its harmonics, as well as for bunching of particles in the field of a standing wave is suggested.