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.

Figure 1

(a) Bragg scattering regime for the conventional Kapitza-Dirac effect with one of the two-photon diagrams leading to stationary scattering; (b) Two-color Kapitza-Dirac effect with one of the three-photon diagrams leading to stationary scattering.

Figure 2

Wavelength dependence of the electron deflection. One laser wavelength is fixed at 1064 nm; the other is varied. The peaks are labeled on the plot.

Figure 3

Intensity dependence of the electron deflection. The deflection scales with $E^2$ for $\omega -\omega$ peak, $E^3$ for $\omega -2\omega$ peak, and $E^4$ for $\omega -3\omega$ peak