We analyze the radiation of a charge crossing the
boundary between vacuum and a medium having a “lefthanded” frequency band realized in some modern
metamaterials. We consider both the case of a semiinfinite medium and the case of a circular waveguide and
obtain exact and approximate expressions for the field
components. We develop an algorithm for their
computation. It is shown that two types of radiation can
be generated in vacuum. One of them is an ordinary
transition radiation having a relatively large magnitude.
Another type of radiation, identified in this study, is
referred to as “Cherenkov-transition” radiation.
Conditions for generating this radiation are obtained.
Properties of radiation can be used for diagnostics of
beams. For example, a detector with two energy
thresholds can be designed.