Kapitza-Dirac diffraction without standing waves: diffraction without a grating?

We discuss electron diffraction from two counterpropagating light waves with two different frequencies. We show that, even though these waves do not form a standing wave, electron diffraction similar to the conventional Kapitza-Dirac effect, i.e., scattering on a standing wave, is still possible. The nonlinear response of the electron to the laser fields creates a stationary diffraction grating from which the same electron scatters.