High-frequency scattering from a wedge with impedance facesilluminated by a line source. II. Surface waves

For pt.I see ibid., vol.37, no.2, p.212-18 (1989). In Part I a rigorous integral representation for the field scattered at a finite distance from the edge of an impedance wedge when it is illuminated by a line source was derived. It was shown that the total field can be expressed as the sum of the geometrical optics (GO) field, the field diffracted by the edge, and terms related to the excitation of surface waves. The double spectral integral representation for the diffracted field was asymptotically evaluated there, in the case in which no surface wave can be supported by the two faces of the wedge. In particular, the high-frequency solution was expressed in the special format of the uniform geometrical theory of diffraction (UTD). Here, field contributions related to the surface wave excitation mechanism are examined. By a convenient asymptotic approximation of the integrals, a high-frequency solution which is uniform with respect to aspects of both incidence and observation is obtained. Moreover, this solution has useful symmetry properties so that it explicitly exhibits reciprocity. Numerical results are presented to show the relevance of the surface wave terms in the evaluation of the field     

Diffraction and Reflection of a Plane Electromagnetic Wave by a Right-Angled Impedance Wedge

The interior of a right-angled impedance wedge is a natural model of a corner reflector and is of interest in the development of wireless propagation models. Using a previously-developed solution for the diffraction of a plane wave by a wedge of arbitrary angle, the geometrical optics field is determined and the diffracted field is computed. If an impedance compatibility condition is not met, the geometrical optics field is discontinuous across a plane specified by the edge of the wedge and the incident field direction. The diffracted field is required to compensate for this and its magnitude is proportional to the discontinuity. The field is computed for a variety of impedances and incident angles. Simple analytical approximations are also provided and their accuracy quantified.      

Scattering by an imperfect right-angled wedge

A solution is obtained for the problem of a plane electromagnetic wave at skew (oblique) incidence on a right-angled wedge one of whose faces is imperfectly conducting. An exact integral expression for the total field is derived, and the geometrical optics and edge diffracted fields are obtained. These are used to produce a uniform solution in the uniform asymptotic theory (UAT) format. Plots of the edge diffracted and total fields are presented to show the effect of the impedance of the wedge face.     

A General Multisegment Artificial Neural Network Architecture for the Efficient Evaluation of Electromagnetic Plane-Wave Wedge Diffraction

A multisegment artificial neural network (ANN) is proposed as an interpolation technique for the evaluation of the electromagnetic field diffracted at the edge of anisotropic impedance wedges under plane wave illumination at oblique incidence. Multisegmentation is needed as the high-frequency wedge diffracted field is characterized by a number of discontinuities at the shadow boundaries of the geometrical optics and surface wave fields. The proposed approach is applied, as a test case, to the problem of an anisotropic impedance right-angled wedge illuminated by a skewly incident plane wave. Some exact analytical solutions valid for specific surface impedance tensors are used to obtain numerical data for the ANN training phase as well as to show the interpolation capabilities of the implemented ANN. Nevertheless, the proposed ANN structure is general and can be trained with data obtained from other available solutions (analytical, perturbative, numerical) valid for more general wedge configurations, eventually leading to a single software tool encompassing all of them and providing accurate approximations of the wedge diffracted field in a relatively short time, comparable to that of a closed form analytical solution.     

Scattering by right angle dielectric wedge

An asymptotic solution of electromagnetic waves scattered by a right-angled dielectric wedge for plane wave incidence is obtained. Scattered far fields are constructed by waves reflected and refracted from dielectric interfaces (geometric-optical fields) and a cylindrical wave diffracted from the edge. The asymptotic edge diffracted field is obtained by adding a correction to the edge diffraction of physical optics approximation, where the correction field in the far-field zone is calculated by solving a dual series equation amenable to simple numerical calculation. The validity of this result is assured by two limits of relative dielectric constantvarepsilonof the wedge. The total asymptotic field calculated agrees with Rawlins' Neumann series solution for smallvarepsilon, and the edge diffraction pattern is shown to approach that of a perfectly conducting wedge for largevarepsilon. Calculated far-field patterns are presented and the accuracy of physical optics approximation is discussed.     

Asymptotic analysis of edge-excited currents on a convex face of aperfectly conducting wedge under overlapping penumbra region conditions

The edge-excited surface currents on a convex face of a perfectly conducting curved wedge are investigated in the asymptotic high-frequency limit for the case where the penumbra regions of the edge and surface diffractions overlap. The edge of the wedge is assumed straight, and the incident electromagnetic wave locally plane and normal to the edge. Both polarizations are considered. The surface field induced by the edge diffraction is synthesized in the spirit of the spectral theory of diffraction (STD): the solution for the edge-diffracted field is interpreted as a spectrum of inhomogeneous plane waves, and the surface field excited by each spectral plane wave is obtained by analytical continuation of the Fock (1965) functions into complex space. The main purpose of this work is to prove the reciprocity of a solution deduced previously for the problem of line source radiation from the wedge in question. As a by-product, useful identities for an incomplete Airy function and an Airy-Fresnel integral are developed     

A uniform GTD formulation for the diffraction by a wedge with impedance faces

A uniform high-frequency solution is presented for the diffraction by a wedge with impedance faces illuminated by a plane wave perpendicularly incident on its edge. Arbitrary uniform isotropic impedance boundary conditions may be imposed on the faces of the wedge, and both the transverse electric (TE) and transverse magnetic (TM) cases are considered. This solution is formulated in terms of a diffraction coefficient which has the same structure as that of the uniform geometrical theory of diffraction (UTD) for a perfectly conducting wedge. Its extension to the present case is achieved by introducing suitable multiplying factors, which have been derived from an asymptotic evaluation of the exact solution given by Maliuzhinets. When the field point is located on the surface near the edge, a more accurate asymptotic evaluation is employed to obtain a high-frequency expression for the diffracted field, which is suitable for several specific applications. The formulation described in this paper may provide a useful, rigorous basis to search for a more numerically efficient but yet accurate approximation.     

Diffraction of a plane skew electromagnetic wave by a wedge with general anisotropic impedance boundary conditions

The three dimensional problem of diffraction of a skew incident plane wave by a wedge with anisotropic impedance boundary conditions is explicitly solved by the probabilistic random walk method. The problem is formulated in terms of two certain components of the electric and magnetic fields which satisfy independent Helmholtz equations but are coupled through the first-order boundary conditions. The solution is represented as a superposition of the geometric waves that are completely determined by elementary methods and of the waves diffracted by the apex of the wedge. The diffracted field is explicitly represented as the mathematical expectation computed over the trajectories of a two-state random motion which runs in a complex space and switches states under the control of stochastic equations determined by the problem's geometry and by the boundary conditions.     

Numerical analysis of the diffraction at an anisotropic impedancewedge

A numerical approach to the electromagnetic scattering of a plane wave impinging at skew incidence on the edge of a wedge with two different anisotropic face impedances is presented. The diffracted field is obtained by applying the finite-difference (FD) method to solve two coupled parabolic equations. The solution obtained is valid in the high-frequency region     

Diffraction by an arbitrary-angled dielectric wedge. I. Physicaloptics approximation

A complete form is presented of the physical optics solution to diffraction by an arbitrary dielectric wedge angle with any relative dielectric constant in cases of both E- and H-polarized plane waves incident on one side of two dielectric interfaces. The solution, which is obtained by performing the physical optics (PO) approximation to the dual integral equation formulated in the spatial frequency domain, is constructed by the geometrical optics terms, including multiple reflection inside the wedge and the edge diffracted field. The diffraction coefficients of the edge diffracted field are represented in a simple form as two finite series of cotangent functions weighted by the Fresnel reflection coefficients. Far-field patterns of the PO solutions for a wedge angle of 45°, relative dielectric constants 2, 10, and 100, and an E-polarized incident angle of 150° are plotted in figures, revealing abrupt discontinuities at dielectric interfaces     

Edge diffraction by right-angled dielectric wedge

Rigorous asymptotic diffracted fields from a right-angled dielectric wedge are obtained for plane wave incidence. A correction field to the physical optics approximation is derived from a dual series equation amenable to simple numerical calculation. The edge-diffracted cylindrical wave pattern is calculated and shown.     

On the GTD scattering by a polygonal cylinder

Using Keller's geometrical theory of diffraction (GTD) the field diffracted by a wedge is infinite at the shadow and reflection boundaries. In general, uniform diffraction coefficients must be used to provide continuous fields at these boundaries. In this communication it is shown that by properly adding the singular contributions from a pair of adjacent edges, Keller's diffraction coefficients yield a continuous far-zone field at the reflection boundaries of a polygonal cylinder illuminated by a plane wave. Furthermore the procedure is justified by noting that the uniform diffraction coefficients reduce to the Keller diffraction coefficients for this case.     

Electromagnetic diffraction of an obliquely incident plane wave bya right-angled anisotropic impedance wedge with a perfectly conductingface

The diffraction of an arbitrarily polarized electromagnetic plane wave obliquely incident on the edge of a right-angled anisotropic impedance wedge with a perfectly conducting face is analyzed. The impedance tensor on the loaded face has its principal anisotropy axes along directions parallel and perpendicular to the edge, exhibiting arbitrary surface impedance values in these directions. The proposed solution procedure applies both to the exterior and the interior right-angled wedges. The rigorous spectral solution for the field components parallel to the edge is determined through the application of the Sommerfeld-Maliuzhinets technique. A uniform asymptotic solution is provided in the framework of the uniform geometrical theory of diffraction (UTD). The diffracted field is expressed in a simple closed form involving ratios of trigonometric functions and the UTD transition function. Samples of numerical results are presented to demonstrate the effectiveness of the asymptotic expressions proposed and to show that they contain as limit cases all previous three-dimensional (3-D) solutions for the right-angled impedance wedge with a perfectly conducting face     

The parabolic equation model for the numerical analysis of thediffraction at an impedance wedge: skew incidence case

A numerical approach to the scattering problem of a plane electromagnetic wave at skew incidence on a wedge with two different arbitrary face impedances is presented. The diffracted field is obtained by applying the finite-difference method to solve two coupled parabolic equations. The present approach is validated by comparison with available asymptotic analytical results for the skew incidence case     

Electric-dipole radiation over a wedge with imperfectly conductivefaces: a first-order physical-optics solution

We solve a three-dimensional (3-D) electromagnetic diffraction problem involving an obtuse wedge with penetrable planar faces and an electric dipole which is parallel to the edge of the wedge. The analytical formulation is based on Stratton-Chu (1941) integrals of the electromagnetic field, which is excited by the dipole source on infinitely extending planes that coincide with the faces of the wedge. Fictitious charges are introduced along the edge to account for the discontinuity of the electromagnetic field on the faces across the edge. We evaluate asymptotically the integral expressions for the electric-field intensity far from the edge to obtain uniformly valid formulas. Our first-order physical-optics solution incorporates single reflection from both faces, the lateral wave, the edge-diffracted space wave, the edge-diffracted lateral wave, and transition terms which ensure that the electromagnetic field is finite and continuous at the single-reflection and lateral-wave boundaries. The numerical results establish the validity of this solution through a reciprocity check and comparisons with other analytical solutions     

Contribution of a single face to the wedge diffracted field

In certain wedge diffraction problems, it is advantageous to know the part of the diffracted field created by the currents induced on a single face of the wedge. The rigorous solution to the corresponding canonical problem is derived. This solution indicates which part of the uniform theory of diffraction (UTD) solution for the wedge-diffracted field should be taken to describe its single-face component.     

A hybrid asymptotic solution for the scattering by a pair ofparallel perfectly conducting wedges

The overlapping transition regions of the double diffraction by a pair of parallel wedge edges are considered for the hybrid case where the gap between the edges is small compared to the distances from the source and the observation point (plane-wave-far-field limit) and the scatterer as a whole is large (or infinite). A closed-form asymptotic solution for the scattered field continuous at all angles of incidence and scattering is constructed for this case. The peculiar feature of this solution is a hybrid representation of the field singly diffracted by the first wedge: a part of it is described by a nonuniform, geometrical theory of diffraction (GTD) expression, while the other part is described in terms of the uniform theory of diffraction (UTD). The rest of the diffracted ray fields are described by nonuniform expressions, with singularities mutually canceling on summation. This solution is applied to the scattering by a perfectly conducting rectangular cylinder with appropriate geometrical parameters, and agreement with moment method calculation is demonstrated     

Characterization of a resistive half plane over a resistive sheet

The diffraction of a resistive half plane over a planar resistive sheet under plane wave illumination is determined via the dual integral equation method (a variation of the Wiener-Hopf method). The solution is obtained by splitting the associated Wiener-Hopf functions via a numerically efficient routine. Based on the derived exact half plane diffraction coefficient, a simplified equivalent model of the structure is developed when the separation of the half-plane and resistive plane is on the order of a tenth of a wavelength or less. The model preserves the geometrical optics field of the original structure for all angles and is based on an approximate image theory of the resistive plane. Good agreement is obtained with the diffracted field exact solution     

Reflections, diffractions, and surface waves for an interiorimpedance wedge of arbitrary angle

The asymptotic-impedance wedge solution for plane-wave illumination at normal incidence is examined for interior wedge diffraction. An efficient method for calculating the diffraction coefficient for arbitrary wedge angle is presented, as previous calculations were very difficult except for three specific wedge angles for the uniform geometrical theory of diffraction (UTD) expansion. The asymptotic solution isolates the incident, singly reflected, multiply reflected, diffracted, surface wave, and associated surface wave transition fields. Multiply reflected fields of any order are considered. The multiply reflected fields from the exact solution arise as ratios of auxiliary Maliuzhinets functions; however, by using properties of the Maliuzhinets functions, this representation can be reduced to products of reflection coefficients which are much more efficient for calculation. A surface-wave transition field is added to the surface wave boundaries. Computations are presented for interior wedge diffractions although the formulation is equally valid for both exterior and interior wedges with uniform but different impedances on each face for both soft and hard polarizations. In addition, the accuracy of the high-frequency asymptotic expansion is examined for small diffraction distances by direct comparison of the exact and asymptotic solutions