Electromagnetic field of a moving charge in the presence of a left-handed medium

We analyze the electromagnetic field of a moving point charge in the presence of a ``left-handed'' medium (LHM). First, the case of uniform motion of the charge in infinite LHM was considered. Using complex function theory methods, we decomposed the total field into a ``quasi-Coulomb'' field, a wave field (Cherenkov radiation) and a ``plasma trace.'' In addition, an effective numerical algorithm was developed for the total field computation, and typical plots were presented. It was shown that the wave field in LHM lags behind the charge more so than it does in ordinary medium. Furthermore, we investigated a charge intersecting the interface between vacuumlike medium and LHM. Asymptotic expressions for the field components were obtained and algorithms for their computation were developed. The spatial radiation can be separated into three distinct components, corresponding to ordinary transition radiation with a relatively large magnitude, Cherenkov radiation and reversed Cherenkov-transition radiation (RCTR). Rigorous conditions for generating RCTR were obtained: RCTR in the vacuum area was found to be the double threshold effect in both frequency and charge velocity domain. The RCTR decay in vacuum due to the losses in LHM was studied. Areas of the RCTR significance were determined and were found to be sufficiently large for observation. Possible applications to the beam diagnostics and the characterization of metamaterials were suggested.