Radiation of Charge Moving along Face of Inverted Prism

TL;DR

This paper analyzes Cherenkov radiation emitted by a charge moving along a face of an inverted dielectric prism, introducing a new aperture method suitable for plane-faced objects, and computes radiation patterns in the far-field.

Contribution

It develops a new version of the aperture method using plane wave expansion, tailored for objects with plane interfaces, and applies it to analyze Cherenkov radiation in a dielectric prism.

Findings

Derived single-integral expressions for Fourier transforms of the radiation field.

Computed angular radiation diagrams for the inverted prism configuration.

Provided physical insights into Cherenkov radiation behavior in complex dielectric geometries.

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.