Uniform high-frequency description of singly, doubly, and vertex diffracted rays for a plane angular sector

F Capolino,S Maci

doi:10.1163/156939396x00658

Abstract

A high-frequency analysis of the scattered field at a plane angular sector is presented, for the scalar case in which hard boundary conditions are imposed on the two faces. In this formulation, the ordinary UTD field is augmented by uniform vertex diffraction contributions that provide the compensation of the UTD ray field when the first order diffraction points disappear from the tip. Furthermore, an expression of the doubly diffracted rays from the two edges is derived, that provides a uniform description of the total field at the ordinary double diffraction transition regions, including their possible overlapping. Moreover, a new transition function is introduced, which uniformly describes the transition field between doubly diffracted and vertex rays, that occurs when the double diffraction points merge in the tip. In spite of the complication of the physical mechanism, the final solution is simple and easy to implement.

Highlights

Within the framework of the Geometrical Theory of Diffraction (GTD) [1] and its uniform extension (UTD) [2], an important canonical problem is that of a corner at the interconnection of two straight edges, joined by a plane angular sector
There, the scalar problem of the plane angular sector with soft boundary conditions (BCs) was treated; the double diffraction contributions were neglected, since they are of higher asymptotic order with respect to the tip contribution
When the observation point crosses the first order SBCs ({3i = (3:), the first order diffraction point on the i -th edge disappears from the tip and a discontinuity occurs in the dominant asymptotic contribution

Summary

INTRODUCTION

Within the framework of the Geometrical Theory of Diffraction (GTD) [1] and its uniform extension (UTD) [2], an important canonical problem is that of a corner at the interconnection of two straight edges, joined by a plane angular sector. The asymptotic treatment of the hard plane angular sector up to k-1 asymptotic order is more elaborate than the corresponding soft problem In this case the doubly diffracted rays have the same k-1 asymptotic order of the vertex ray, so that they should be necessarily included in a rigorous analysis. 3, a double integral describing the near field of the plane angular sector is derived by spectral synthesis This integral is asymptotically evaluated in Sect. 4. The asymptotic solution has been derived in such a way that the first and the second order GTD ray field structure is recognizable far from the transition regions. The asymptotic solution has been derived in such a way that the first and the second order GTD ray field structure is recognizable far from the transition regions This provides physical insight into the diffraction mechanism and gives simplicity to the solution.

PLANE-WAVE FAR-FIELD SOLUTION

SPECTRAL SYNTHESIS

HIGH-FREQUENCY SOLUTION

Total Ray Field

NUMERICAL EXAMPLES

CONCLUDING REMARKS