Double diffraction at a pair of coplanar skew edges

Abstract

Abstract-A high-frequency solution is presented for the scattering in the near zone by a pair of coplanar skew edges when they are illuminated by a source at a finite distance. The solution is obtained by using a spherical-wave spectral representation of the first-order diffracted field from each edge. The final closedform asymptotic solution includes terms up to the second order. It is shown that this second-order contribution is of the same order as the first one in overlapping transition regions. Moreover, the solution is cast in a convenient form, which is also directly applicable to treat the case when the two edges share a common face for both soft and hard boundary conditions. By choosing appropriate reference systems, the formulation for the scalar case is directly used to construct the solution of the more general electromagnetic problem for an arbitrarily polarized incident field. Numerical results are presented and discussed.

Shielding effect of a thick screen with corrugations

“…The contribution is obtained from the formulation presented in [6], [7] that is relevant to a line source illumination, by introducing a suitable modification in the spreading factor and in the distance parameters. This leads to (8) where the diffraction dyad is defined as (9) In (9), denotes the DD coefficient for soft BC that applies to TM pol, while and denote the DD diffraction coefficients for the hard and the artificially soft cases, respectively; these latter apply to the TE pol for smooth and corrugated screen, respectively.…”

High-frequency analysis of an array of line sources on a truncated ground plane

“…in which (6) and . The term , which is the Fourier transform of a Hankel function, is associated to the geometrical optics (GO) field from the line source and its image, while the contribution represents the diffracted field.…”

“…This yields (24) where is the same as that defined in (15) and (25) Next, the integral on the SDP is evaluated by the Van der Waerden method, by adding and subtracting an appropriate spectral function . A convenient expression of is (26) in which , where is the spectrum of the half-plane Green's function with hard boundary conditions, which is defined in (6), and (27) is the spectrum for the same half-plane with soft boundary conditions. This function is constructed in such a way as to have the same residues of in the region , and , which is shadowed in Fig.…”

“…Equation (20) is the transition function of UTD [1], and is the transition function introduced in [6] and [7];…”

“…In Section III, the asymptotic evaluation of this integral is carried out, leading to a uniform solution in terms of FW's and their pertinent singly and doubly diffracted rays. These latter are expressed in terms of the multiple-argument transition function derived in [6] and [7] for the double diffraction at a couple of wedges and used in [8] for describing the diffraction at a vertex of a plane angular sector. In the present case, this transition function is extended to complex values of its argument.…”