On the theory of polarization radiation in media with sharp boundaries

Abstract

Polarization radiation arising when a charged particle moves uniformly in vacuum nearby the media possessing a finite permittivity ε(ω) = ε ′ + iε ′′ 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 vacuum 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 radiation, transition radiation and diffraction radiation. In particular, when the channel radius approaches zero and external radius of the screen tends to infinity the expression found for radiated energy completely coincides with the one derived by Pafomov for transition radiation generated 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 infinitely 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 possible multiple reflections of radiation inside the screen. Solution is also found for a problem of polarization 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.

Conical effect in diffraction radiation

“…The method consists in calculation of the radiation field due to polarization currents induced by the moving charge in target and following consideration of the processes of refraction on a surface of the target. By the way, polarization currents method allows also describing the radiation processes for optical [16,17] and terahertz ranges [18,19]. Generally speaking, the radiation can be refracted and reflected from the upper and forward sides.…”

Effect of Vavilov–Cherenkov radiation cone transformation upon entry of a relativistic electron into a substance layer

“…It also takes into account radiation re-reflection at the interface. Noteworthy is the alternative polarization current method [14], which can also be used to solve the formulated problem.…”

Polarization radiation of vortex electrons with large orbital angular momentum

“…Although many macroscopic manifestations of PR were known since 1930-50's (ChR, TR, DR, SPR), the microscopic quantum theory of PR explicitly demonstrating their common physical origin was developed only in the 1970-80's by Amusia with co-workers (see e.g., [3,24] and the references therein; qualitative explanations of the microscopic nature of, say, ChR were of course given before). The macroscopic approaches, in which such a unified nature of various radiation processes was explicitly demonstrated, have been developed only in recent years [2,4,25,26].…”

“…According to the polarization currents approach developed in Ref. [4], the radiation field in the wave zone is found as…”

“…is a quantity proportional to the polarization current [4]. We introduced here the "on-shell" wave vector in the medium k = e k ω/c, where…”