ITD Double-Edge Diffraction for Complex Source Beam Illumination

Alberto Toccafondi,Stefano Mihai Canta,Danilo Erricolo

doi:10.1109/tap.2013.2244553

Abstract

A new high-frequency incremental theory of diffraction (ITD) formulation for the double diffraction by metallic wedges when illuminated by complex source points (CSP) is provided. The main motivation is the extension of the class of problems that can be studied using asymptotic (i.e., ray-based and incremental) methods by providing a double diffraction description for CSP, which are considered because they are efficient to analyze electrically large structures. The new formulation provides an accurate asymptotic description of the interaction between two edges in an arbitrary configuration, including slope diffraction contributions. Advantages of the ITD formulation for CSP illumination include avoiding the typical ray-caustic impairments of the GTD/UTD ray techniques and not requiring ray tracing in complex space. Numerical results are presented and compared to a Method-of-Moments analysis to demonstrate the accuracy of the solution.

Highlights

E FFICIENT techniques to represent the illuminating field are often employed in the accurate prediction of the far field radiated or scattered by large structures, such as large reflector antennas
The incremental double-diffracted field is represented as the reaction between the incremental field diffracted by one of the wedges and the filamentary current sources associated with the diffraction by the other wedge
As in the case of real sources illuminating the wedges [25], [26], it is best to retain in the spectral formulation the product of both the even and the odd parts of each cotangent term associated with the spectral Green’s Function of a single wedge [36]

Summary

Introduction

E FFICIENT techniques to represent the illuminating field are often employed in the accurate prediction of the far field radiated or scattered by large structures, such as large reflector antennas. The total double-diffracted field representation requires a two-fold numerical integration in the space domain on each edge of the complex structures This formulation provides an accurate asymptotic description of the interaction between two edges, which is valid both for skewed separate wedges and for edges joined by a common PEC face. It explicitly satisfies reciprocity and includes a double incremental slope diffraction augmentation, which provides the correct dominant high-frequency incremental contribution at grazing aspect of incidence and observation. All the derivations in this article are carried out for time-harmonic fields at the angular frequency ω; the time convention exp(jωt) is assumed and suppressed throughout

Incremental Double Diffraction

Incremental formulation

Even and odd spectral contributions

Perfectly conducting disc

Conclusions