Cherenkov and transition radiation in space--time periodic media

The solution to the problem of determining the radiation emitted by a uniformly moving charged particle in a sinusoidally space-time periodic medium is obtained. The space-time periodicity can be considered as due to a strong pump wave and is expressed as a traveling-wave-type change in the dielectric constant or the plasma density. The solution covers also the limiting case of sinusoidally stratified media. The expression and spectrum of the radiated electromagnetic field are determined for different media: dielectric, isotropic and uniaxial plasma. Depending on the nature of the medium and the velocity of the particle, the radiated field is of the Cerenkov and/or transition type. The Brillouin diagram is used extensively in understanding and determining the nature, extent, and spectrum of the different modes of radiation, and a focusing effect is also studied.