# Geometry of the problem

**Figure 1.** Geometry of the problem. The electron moves parallel to the rough surface at the plane *xy* which is illuminated by an external laser field.

**Abstract**

Absorption of a photon by an electron moving parallel to a rough surface is studied. In the weak scattering regime we have evaluated the absorption probability of absorption of a single photon of energy ω. It is shown that the absorption probability with diffusional contribution becomes large by a *l*_{in}/*l* 1 factor compared to the analogous result with the single scattering contribution. The maximum of probability takes place for the infrared wavelengths and strongly depends on the particle energy. We also discuss the case of two-dimensional periodical surface profile and indicate optimal conditions for maximal absorption probability. The results can be used in electron energy gain spectroscopy and in laser-driven acceleration.