Transition radiation of a charged particle crossing the waveguide filled with a dispersive dielectric medium perpendicularly to the waveguide axis

The theory of charged particle transition radiation is developed for the case when the particle crosses the waveguide, which is filled with a piecewise-homogeneous dielectric, perpendicularly to the waveguide axis. The cases where the charged particle is flying between two dispersive plates and between two thin impedance films are considered.