Radiation from a particle in flight through a plate, the parameters of which vary according to an arbitrary periodical law

The radiation from a relativistic charged particle in flight through a layered finite-length medium is investigated. Expressions for the spectral-angular distribution of radiation in forward and backward hemispheres are derived with no limitations on the amplitude and variation profile of the layered medium parameters. It is shown that the periodicity of layered medium strongly influences the radiation from the particle in the wavelength range of the order of layered medium period: the Cherenkov radiation emitted in the forward hemisphere is redirected by the periodical structure of medium in the backward direction. The visual explanation of this effect is given and a possible application is discussed.