Vavilov–Cherenkov Radiation in an Inclined Dielectric Plate and Violation of Azimuthal Symmetry

Abstract: For over half a century, Vavilov–Cherenkov radiation (VCR) has been used for detecting elementary particles. Lately, some authors have proposed using the coherent VCR emitted by a short particle bunch for measuring its length. Towards this, they envisage using dielectric targets of conical (or more complex) shapes whereby the radiation is transported to a vacuum with minimum losses for multiple reflections. Unfortunately, analytical methods for deriving the VCR spectral and angular characteristics are restricted to targets with simplest geometries even for noncoherent radiation. In this paper, the characteristics of Vavilov–Cherenkov radiation emitted by an inclined dielectric plate are analytically derived using the imaging and polarization-current approaches. Our calculations adequately reproduce the results of a recent experiment. We demonstrate that not only the bunch length, but also its transverse profile can be probed using its VCR.