Errors in the ``Universal and sufficient'' heuristic criteria of estimating validity limits of geometric optics and of the geometric theory of diffraction

TLDR: In this article, the validity of the heuristic criteria (HC) of geometric optics and of the geometric theory of diffraction (GTD), suggested in (2-7, 13, 14) and based on identifying the physical volume occupied by the ray with the Fresnel volume (FV) introduced in these papers (i.e., the envelope of the first Fresnel zone), are analyzed.

Abstract: The heuristic criteria (HC) of validity of geometric optics (GO) and of the geometric theory of diffraction (GTD), suggested in (2-7, 13, 14) and based on identifying the physical volume occupied by the ray with the Fresnel volume (FV) introduced in these papers (i.e., the envelope of the first Fresnel zone), are analyzed. Numerous examples of HC invalidity are given, as well as the reasons. In particular, HC provide an incorrect answer for all GO problems with caustics, since in these problems there always exists a ray, whose FV is nonlocal and covers the FV of other rays. The HC are shown to be unsuitable for multiple ray GTD problems, as well as for the simplest problems of diffraction of a cylindrical wave by a half-plane and of a plane wave by a curved half-plane.