  When a charged particle moves nearby a spatially inhomogeneous condensed
medium or inside it, different types of radiation may arise: Diffraction
radiation (DR), Smith-Purcell radiation (SPR), Transition radiation (TR),
Cherenkov radiation (CR) etc. Along with transverse waves of radiation, the
charged particle may also generate longitudinal oscillations. We show that all
these phenomena may be described via quite simple and universal approach, where
the source of the field is the polarization current density induced inside the
medium by external field of the particle, that is direct proof of the physical
equivalence of all these radiation processes. Exact solution for one of the
basic radiation problems is found with this method: emission of a particle
passing through a cylindrical channel in a screen of arbitrary width and
permittivity $\epsilon (\omega) = \epsilon^{\prime} + i \epsilon^{\prime
\prime}$. Depending on geometry, the formula for radiated energy obtained
describes different types of polarization radiation: DR, TR and CR. The
particular case of radiation produced by the particle crossing axially the
sharp boundary between vacuum and a plasma cylinder of finite radius is also
considered. The problem of SPR generated when the particle moves nearby a set
of thin rectangular strips (grating) is solved for the arbitrary value of the
grating's permittivity. An exact solution of Maxwell's equations for the fields
of polarization current density suitable at the arbitrary distances (including
the so-called pre-wave zone) is presented. This solution is shown to describe
transverse fields of polarization radiation and the longitudinal fields
connected with the zeros of permittivity.
