Theoretical study of transient Chrenkov radiation from periodic resonance medium excited at the superluminal velocity

We consider an optical response of one-dimensional string made of dipoles with a periodically varying density excited by a laser pulse moving along the string at the superluminal velocity. We demonstrate that the Cherenkov radiation arising in such system is rather unusual, possessing both transient and resonant character. Our analysis indicates that in addition to the resonance frequency of the medium another Doppler-like frequency appears in the radiation spectrum.