Modified Edge Representation (MER) Consisting of Keller’s Diffraction Coefficients With Weighted Fringe Waves and Its Localization for Evaluation of Corner Diffraction

Abstract

Equivalent edge currents (EECs) for high-frequency diffraction analysis are intermediate concepts between ray theory and wave optics [physical optics (PO)]. The methods of EEC present some ambiguity in the definition of currents at general edge points, which do not satisfy the diffraction law. Modified edge representation (MER) is a unique concept for a complete definition of EEC with simple and classical Keller-type knife-edge diffraction coefficients. Although singularities in the definition of EEC exist, the line integration of MER EEC results uniform and accurate fields everywhere including geometrical boundaries except for the case of grazing incidence, where reflection and incidence shadow boundaries (RSB and ISB) are close to each other. In this paper, fringe wave (FW) part of MER EEC is modified by introducing the weighting in terms of Fresnel zone number (FZN) distance from the reflection point to improve the accuracy at and near shadow boundaries even in grazing incidence. Next, the corner diffraction, a contribution coming from edge point which does not satisfy the diffraction law, is extracted in MER by introducing another weighting function using the FZN distance from scattering centers on edge. Its remarkable accuracy fully validates MER EECs at general edge points. The dipole wave scattering from flat square and triangular plates are discussed with numerical examples. Index Terms-Corner diffraction, equivalent edge current (EEC), Fresnel zone, geometrical theory of diffraction (GTD), modified edge representation (MER), uniform theory of diffraction (UTD).

Accuracy Check of GTD MER with Weighted Fringe Wave Using Fresnel Zone Number for Grazing Incidence and Slope Wave Diffraction

“…A concept of MER, which extends the definition of EEC for diffraction points to those for general edge points, is detailed in [7,8] for PO and FW components, respectively. Classical Keller's diffraction coefficients in [6] were used in GTD MER [11,12].…”

“…Numerical verification and validation of GTD MER were conducted with Wipl-D [11][12][13]16], and the advantages of GTD MER over UTD in terms of corner diffraction were discussed. A dipole along the x-axis is considered at (0, 0, 2.5k) on a circular disk plate of the radius r a ¼ 2:5k.…”

“…The GTD diffraction coefficient D GTD can be written in terms of PO D PO À Á and FW D FW ð Þ as follows [11]:…”

“…GTD MER contrasts with the uniform geometrical theory of diffraction (UTD) [9,10] in two ways: the classical Keller-type diffraction coefficients with singularities are used that dispense with the Fresnel function; and corner diffraction is implemented without any extra techniques as demonstrated in [11] for dipole wave diffraction from rectangular and triangular plates. The important and inherent advantage of GTD MER for slope wave diffraction was also observed there.…”

“…The important and inherent advantage of GTD MER for slope wave diffraction was also observed there. On the other hand, the degradation of accuracy of GTD MER at and near the shadow boundaries (SBs) for the grazing incidence was also reported as the unique and sole difficulty of GTD MER in [11][12][13], where the correction was also proposed as new MER; the FW is suppressed with the weighting by using the Fresnel zone number (FZN). The accuracy checks of new MER in detail, however, have not been conducted, mainly due to the lack of a rigorous solution for an electrically large object.…”