The Vavilov-Cherenkov effect produced by an electromagnetic pulse

In this paper the Vavilov-Cherenkov radiation produced by an electromagneti c pulse propagating, unchanged in shape, inside a medium is analysed. The e lectromagnetic pulse induces a polarization charge which moves inside the m edium with the group velocity. This polarization charge induces time-depend ent elemental dipoles in the material medium. If the group velocity is grea ter than the phase velocity of light in such a medium there is a coherent s uperposition of the radiation emitted by each elemental dipole that gives r ise to Vavilov-Cherenkov radiation. Two methods to obtain the energy spectrum are developed.