Classical theory of resonant transition radiation in multilayer structures

A rigorous classical electromagnetic theory of the transition radiation in finite and infinite multilayer structures is presented. It makes the standard results of thin-film optics, such as the matrix formalism, accountable; it allows thus an exact treatment of the propagation of the waves induced by the electron. This method is applied to the particular case of the periodic structures to treat the resonant transition radiation (RTR). It is noted that the present theory gives, in the hard x-ray domain, results previously published. The reason for this approach is to make the numerical calculations rigorous and easy. The numerical results of our theory are compared to experimental RTR data obtained recently by Yamada et al. [Phys. Rev. A 59, 3673 (1999)] with a nickel-carbon multilayer structure.