Diffraction of a skew incident plane electromagnetic wave by a wedge with axially anisotropic impedance faces

Abstract

[1] This paper presents, as an extension of the authors' recent work, an exact solution to diffraction of a skew incident plane electromagnetic wave by a wedge with axially anisotropic impedance faces. Applying the Sommerfeld-Malyuzhinets technique to the boundary-value problem yields a coupled system of difference equations for the spectra; on elimination, a functional difference (FD) equation of higher order for one spectrum arises; after simplification in terms of a generalized Malyuzhinets function and accounting for the Meixner's edge condition as well as the poles and residues of the spectrum in the basic strip of the complex plane, the FD equation is converted, via the so-called S integrals, to an integral equivalent; for points on the imaginary axis which belong to the basic strip the integral equivalent becomes a Fredholm equation of the second kind with a nonsingular, wave number-free and exponentially decreasing kernel; solving this integral equation by the quadrature method the spectrum can be determined by integral extrapolation and by analytical continuation; a first-order uniform asymptotic solution follows from evaluating the Sommerfeld integrals with the saddle-point method.Comparison with available exact solutions in several special cases shows that this approach leads to a fast and accurate solution of the problem under study.

Diffraction of a skew incident plane electromagnetic wave by an impedance wedge

“…The present work supports a conjecture uttered at the end of [18] that seemingly ''such an approach, based on the direct reduction of the coupled Malyuzhinets system to a second-order difference equation and then to a Fredholm integral equation of the second kind, can be applied, with corresponding technical modification, to other problems encountered in diffraction theory.'' The approach presented in this paper can be immediately applied to solving rigorously diffraction of a skew incident electromagnetic wave by a wedge whose faces are characterized by axial impedance tensors [64]. Departing from the exact solution given above, we are studying now the electromagnetic field excited by an electric dipole in a wedge-shaped region whose boundaries are described by scalar surface impedances.…”

“…Together with (64), we arrive at a matrix equation of dimension N + 2 for the N discrete values of the auxiliary function L 1 ½tðx n Þ, n = 1,2, . .…”

Diffraction by a Wedge or by a Cone With Impedance-Type Boundary Conditions and Second-Order Functional Difference Equations

“…At the end of this paper it is worth mentioning that the presented approach can equivally be applied to skew incidence on wedges [17,18] and diffraction of electromagnetic waves by either a right-circular impedance cone [19] or a conical surface of circular cross-section [20].…”

High‐frequency asymptotic solutions benchmarking skew incidence diffraction by anisotropic impedance half and full planes

“…tional equation for a linear combination of the angular spectra of the field components parallel to the edge. Lyalinov and Zhu [2005] reduced the solution of the second-order functional equation to the numerical evaluation of an equivalent Fredholm integral equation of the second kind. A simple approach to solve the second-order difference functional equation was presented in [Senior et al, 2001;Senior and Topsakal, 2002], where the original problem is reduced to an inhomogeneous nonsingular integral equation that can be solved by using only a few terms in a Taylor series expansion of the unknown.…”