Investigation of transition radiation from a regular-roughness interface

Transition radiation at the interface between two media having regular inhomogeneities is considered in the framework of perturbation theory, assuming that the dielectric constants of the two media differ insignificantly from each other. The advantage of this approach is that no limitations exist on the characteristic size of the inhomogeneities. The general case of a surface with two-dimensional roughness is considered. Attention is paid to radiation characteristics that are general for periodic structures, independently of their particular features. The physical picture of the radiation from a rough interface is determined by both longitudinal and transverse effects. The case of normal incidence of an electron on a planar interface having either single or multiple rectangular lugs (diffraction grating) is analyzed in detail. For the single lug infinite in one dimension, simple expressions for transition radiation intensity are obtained, for both relativistic and nonrelativistic electrons. They demonstrate that corrections to the plane-surface intensity become significant at small radiation angles. In this case. the radiation is also completely unpolarized, i.e., the spectral energy density of the perpendicular component has the same order of magnitude as that of the parallel component. Consideration of these issues is important since rough surfaces, as compared to planar surfaces, give a number of additional results that may be used for the analysis of surface irregularities.