We develop a theory for surface electromagnetic waves at the boundary
of a layer-periodical structure and a vacuum. The excitation of these
waves by a charged particle, moving in vacuum and specularly reflected
by the boundary, is investigated. The radiation field in vacuum is ob
tained. This field consists of fields of electromagnetic waves of a di
fferent physical nature: the surface cylindrical wave and the volume s
pherical wave, whose powers are of the same order as the power of the
transition radiation.