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 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.     

High-frequency scattering from a wedge with impedance facesilluminated by a line source. I. Diffraction

The canonical problem of evaluating the scattered field at a finite distance from the edge of an impedance wedge which is illuminated by a line source is considered. The presentation of the results is divided into two parts. In this first part, reciprocity and superposition of plane wave spectra are applied to the left far-field response of the wedge to a plane wave, to obtain exact expression for the diffracted field and the surface wave contributions. In addition, a high-frequency solution is given for the diffracted field contribution. Its expression, derived via a rigorous asymptotic procedure, has the same structure as that of the uniform geometrical theory of diffraction (UTD) solution for the field diffracted by a perfectly conducting wedge. This solution for the diffracted field explicitly exhibits reciprocity with respect to the direction of incidence and scattering     

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     

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 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.     

Electromagnetic diffraction of an obliquely incident plane wavefield by a wedge with impedance faces

A uniform asymptotic solution is presented for the electromagnetic diffraction by a wedge with impedance faces and with included angles equal to 0 (half-plane), π/2 (right-angled wedge), π (two-part plane) and 3π/2 (right-angled wedge). The incident field is a plane wave of arbitrary polarization, obliquely incident to the axis of the wedge. The formal solution, which is expressed in terms of an integral, was obtained by the generalized reflection method. A careful study of the singularities of the integrand is made before the asymptotic evaluation of the integral is carried out. The asymptotic evaluation of the integral is performed taking into account the presence of the surface wave poles in addition to the geometrical optics poles near the saddle points. This results in a uniform solution which is continuous acros the shadow boundaries of the geometrical optics fields as well as the surface wave fields     

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     

Wave diffraction by a right-angled interface between resistive half and whole planes

The interaction phenomenon of electromagnetic plane waves by a right angled interface between whole and half screens with different resistivities is studied. The construction, under examination, is considered in order to model various corner discontinuities between transmissive surfaces for indoor wireless communications. First of all, the initial waves, which occur in the absence of the diffracting edge, are determined. Then the scattered geometrical optics fields are obtained by subtracting the initial waves from the total geometrical optics fields. The diffracted field is constructed directly from the scattered geometrical optics wave by a new method. The resultant field expressions are examined numerically.     

Closed-form expressions for uniform currents on a wedge illuminatedby TM plane wave

Closed-form expressions for nonuniform currents on a perfectly conducting, infinite wedge illuminated by a transverse magnetic plane wave are presented. The expressions are derived by requiring that they agree with the current predicted by the eigenfunction solution close to the edge and J.B. Keller's geometrical theory of diffraction (1962) far from the edge. The angle of incidence is arbitrary and the expressions remain uniformly valid even for glancing angles of incidence when the geometrical optics boundaries are in the vicinity of the wedge faces. The formulas presented are simple, involving Fresnel functions with complex arguments. These functions can be expressed in terms of complimentary error functions which may be computed using standard subroutine packages. Exact expressions for nonuniform currents are available for the two special cases of half-planes and infinite planes. Closed-form expressions for the axial electric field, and hence all the field components in the vicinity of the wedge axes, are also obtained. Currents computed using expressions obtained are compared with currents computed from the eigenfunction solution of the wedge, with good agreement throughout     

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.     

Two-dimensional Green's function for a wedge with impedance faces

The solution for the two-dimensional (2-D) Green's function for a wedge with impedance faces is presented. The important feature of this Green's function is that there are no restrictions on the locations for the source and observation points-they can be anywhere. Its development proceeds along two separate lines: one for when the source or observation point is far from the wedge vertex and another one for when it is close. Much of the effort that has been expended in these formulations has been in obtaining forms for the Green's function which are efficient to evaluate numerically. This involved deforming the various contours of integration so that they are rapidly convergent and separating the contributions from the numerous singularities that occur in the integrands and evaluating them in closed form. The formulations that are employed here allow for the individual field components such as the diffracted, geometrical optics, and surface wave components to be identified and studied individually so that a physical understanding for the various scattering mechanisms for the impedance wedge can be appreciated     

GTD analysis of a hyperboloidal subreflector with conical flange attachment

A geometrical theory of diffraction (GTD) analysis of the principal plane far-field radiation patterns of a hyperboloidal subreflector with a conical flange attachment (HWF) fed by a primary feed located at its focus is presented. While using the uniform geometrical theory of diffraction (UGTD) for evaluating the nonaxial fields, the method of equivalent currents is used in the axial region. In this paper, both the diffraction by the wedge formed between the hyperboloid and the conical flange and the diffraction by the edge of the flange are considered. While considering the diffraction by the edge due to the diffracted ray from the wedge in theH-plane, the slope diffraction technique has been used. The computed diffracted farfields of a typical HWF illuminated by a high performance primary feed shows good agreement with the available measured data and with the results based on the method of physical optics (PO). The sharp cutoff and the low spillover characteristics of the HWF are highlighted by comparing its radiation pattern with that of a hyperboloid without a flange. Further, the effects of the different parameters of the HWF on its radiation pattern are also studied and plotted, so that these results can be utilized in the design of the HWF for a specific requirement.     

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.     

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.     

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     

Time-domain three-dimensional diffraction by the isorefractivewedge

The extension of the Biot-Tolstoy (1957) exact time domain solution to the electromagnetic isovelocity or isorefractive wedge is described. The TM field generated by a Hertzian electric dipole can be represented by a vector potential parallel to the apex of the wedge and a scalar potential necessitated by the three dimensionality of the magnetic field. The derivation of the former is exactly that of the pressure in the corresponding acoustic situation, and a more efficient version of the lengthy details is presented herein. A Lorentz gauge determines the scalar potential from the vector potential, and the diffracted field contains impulsive and “switch-on” terms that cannot be evaluated in closed form. The ratio of arrival times, at a given point, of the geometrical optics and diffracted fields provides a convenient parameter, in addition to the usual metric-related variable, for graphically displaying this scalar potential     

阻抗劈散射的MM-PO混合算法研究

本文系统地研究了各向异性阻抗劈绕射的矩量法-物理光学(MM-PO)混合算法.首先研究了任意各向异性阻抗面的物理光学模型,推导出表面物理光学等效电磁流计算式.其次,提出了一种有效的含Hankel函数的弱振荡被积函数无穷积分处理方法.最后,将作者已公开发表的修正绕射电流基函数用于各向异性阻抗劈散射场研究,数值结果和已知的一致性绕射理论结果高度吻合.     

Ray-optical prediction of radio-wave propagation characteristics intunnel environments. 1. Theory

A tunnel is modeled as congregates of walls, with the wall being approximated by a uniform impedance surface. The aim is to get a solution for a canonical problem of a wedge with uniform impedance surface. The diffraction by a right-angle wedge with different impedance boundary conditions at its two surfaces is first considered. A functional transformation is used to simplify the boundary conditions. The eigenfunction solutions for the transformed functions are replaced by integral representations, which are then evaluated asymptotically by the modified Pauli-Clemmow method of steepest descent. The asymptotic solution is interpreted ray optically to obtain the diffraction coefficient for the uniform geometrical theory of diffraction (UTD). The obtained diffraction coefficients are related directly to the Keller diffraction coefficients in the uniform version. The total field is continuous across the shadow of the geometrical optics fields     

The geometric optics contribution to the scattering from a large dense dielectric sphere

An analysis is presented for calculating the backscattered fields of an electromagnetic plane wave by lossless dielectric spheres of arbitrary density. This method involves the Watson transformation which serves to split the exact Mie solution, given as an infinite series, into the geometrical optics fields and the diffracted fields. The former comes from the illuminated region of the sphere and may be obtained from the geometrical optics method. The latter comes from the shadow region and consists of two different types of surface waves. One is a "creeping wave" analogous to that of perfectly conducting spheres. The other is a wave which enters the sphere and emerges as a surface wave in the shadow region. This wave is unique to dielectric spheres and is the stronger of the two surface waves. In the widely used geometric optics methods it is assumed that the optics fields are the dominant contributors even though stationary rays which are not in the direction of backscatter must be added in to give a degree of agreement with the exact Mie series results. In this paper we derive the optics fields and show that they differ in some respects from those obtained by the geometric optics method. They are smaller than heretofore assumed and contribute negligibly to the backscatter in this particular range ofka(4-20). Using our rigorous approach we can show the diffracted fields to be the major contributors to the total backscatter. Numerical results for the backscattering cross sections using diffracted and optics fields, and optics fields alone will be presented for relative index of refraction of 1.6. The agreement between our results (diffracted and optics) and exact results from the Mie series is excellent. A subsequent paper will be concerned with the diffracted fields.