Comparison of geometric optics and «aperture» methods for calculation of the electromagnetic radiation caused by charged particles flying by dielectric objects

Calculation of the electromagnetic field exited by a charged particle flying close to dielectric object is one of the important problems of charged particle radiation theory. In some cases, geometric optics area is preferable for calculations. In the article, two methods of solution of such problem with dielectric prism possessing large size (in comparison with the wavelength under consideration) are considered. One of them is based on geometric optics method, another one is based on asymptotics of aperture integrals. It is shown that, in geometric optics area, the first method has a series of advantages. For example, ray tube cross-section expression obtained within geometric optics method allows one to find caustics or to show their abscence, which is demonstrated in the article for three objects of various shapes.