Detection of Cherenkov radiation: the inverse problem to generation of nondiffracting beams

Nondiffracting beams have been in the center of interest for the last decade. These beams, however, can be realized in practice only approximately. The simplest scheme for generating such a beam is to use a sufficiently narrow annular source placed in the back focal plane of a lens. Behind the lens, the beam is pseudo-nondiffracting in some length. The inverse problem is detection of Cherenkov radiation. The trace of a charged particle travelling through a dielectric medium faster than light emits this radiation at a certain angle. Generated conical wave front creates in the back focal plane of a lens a diffraction pattern in the form of a ring. A theoretical analysis of both problems is given in the paper