Radiation of a charge passing from vacuum into the left-handed medium

We analyse the problem with a charge intersecting the interface between ordinary medium and “left-handed” one. Both the case of semi-infinite media and the case of a cylindrical waveguide are considered. We describe exact and asymptotic approaches for investigation of the electromagnetic field. We note features of spatial radiation due to unusual properties of “left-handed” medium. In particular, the effect of “reversed Cherenkov-transition radiation” (RCTR) is demonstrated both analytically and numerically.