On the theory of polarization radiation generated in the media with sharp boundaries

Polarization radiation arising when a charged particle moves uniformly in vacuum nearby the media possessing a finite permittivity $\epsilon (\omega) = \epsilon^{\prime} + i \epsilon^{\prime \prime}$ and sharp boundaries is considered. The method is developed in which polarization radiation is represented as a field of the current density induced in matter by the field of the moving charge. Solution is found for a problem of radiation arising when the particle moves along the axis of the cylindrical channel inside a thin screen of a finite radius and a finite permittivity. Depending on parameters of the problem, the solution obtained describes different types of polarization radiation: Cherenkov, transition, and diffraction radiations. In particular, when the channel radius approaches zero and external radius of the screen tends to infinity the expression found for radiated energy coincides with Pafomov solution for transition radiation in a slab. In another special case of ideal conductivity, the result obtained coincides with the one for diffraction radiation generated by the particle in the round hole in the thin screen. Solution is found for a problem of radiation generated when the charge moves nearby a rectangular screen possessing a finite permittivity. The expression derived describes diffraction and Cherenkov mechanisms of radiation and takes into account the multiple reflections of radiation inside the screen. Solution is also found for a problem of radiation generated when the particle moves nearby a thin grating consisting of a finite number of rectangular strips possessing a finite permittivity and separated with vacuum gaps (Smith-Purcell radiation). In the special case of an ideally conducting grating, the formula derived for radiated energy coincides with the one of the well-known surface current model.