Linear and non-linear theory of short-wave electromagnetic radiation excitation by an electron beam moving along plasma diffraction lattice is constructed. A case is considered when an electromagnetic wave is emitted at an angle to the beam. It is shown that depending on the beam and plasma parameters both vacuum and plasma radiation excitation regimes can be realized. In the first case instability is linked with charge density show wave energy losses for radiation. The plasma regime is characterized by the fact that the effective dielectric permittivity of the system is negative. In this case beam modulation occurs under effect of the fields induced in plasma. Clusters produced in such a way, emit an electromagnetic wave by crossing the lattice. 9 refs.; 12 figs.