Vavilov-Cherenkov radiation in passive and active media with complex resonant dispersion.

Some of the problems with the theory of moving charge radiation in media with frequency dispersion are analyzed. First, some general properties of the integrals for field components are described. The results are applied to the cases of passive and active media. In one instance, the field of a charge moving in passive media with an arbitrary number of resonances is considered. Components of the field have been presented as a sum of the "quasi-Coulomb" field, the wave field, and the "plasma trace." In another example, the case of an active medium with two resonant frequencies is considered. It has been demonstrated that radiation is amplified even with a purely real refractive index if the following conditions are fulfilled: the "lower" resonance is active, the "upper" one is passive, and the charge movement velocity lies within a certain range. Efficient algorithms for the computation of fields in the cases of passive and active media have been developed.