Radiation of Charge Moving along Face of Inverted Prism

Abstract

Cherenkov radiation (CR) generated by a charge moving along one of the faces of a dielectric prism is analyzed. Unlike our previous papers, here we suppose that the charge moves from the the prism ``nose'' to its base. For CR analysis, we use the technique described in our previous papers and called the ``aperture method''. However, here we develop a new version of this technique which is suitable for objects with plane faces: it utilizes field expansion only over plane waves inside the object. This approach is especially convenient for objects having two or more plane interfaces on which the waves are reflected and/or refracted. Using this technique, we obtain the electromagnetic field distribution over the aperture and then apply Stratton-Chu formulas (aperture integrals). Further, the main attention is paid to the calculation of the radiation field in the Fraunhofer (far-field) area. It is notable that we obtain expressions for corresponding Fourier transforms in the form of single integrals. Using them, the series of typical angular diagrams are computed and physical conclusions are made.