Nonuniform currents on a wedge illuminated by a TE plane wave

Closed-form expressions for nonuniform currents on a perfectly conducting, infinite wedge illuminated by transverse electric (TE) plane wave are presented. These expressions are derived by requiring that they coincide with the current predicted by the asymptotic diffraction method far from the edge and, further, that they agree with the current predicted by the eigenfunction solution at the edge. The angle of incidence is arbitrary and our expressions remain valid even for glancing angles of incidence when either one or both faces of the wedge are in the vicinity of a geometric optic (GO) boundary. Formulas presented here are simple involving the well-known modified Fresnel functions but are not uniform. Exact expressions for nonuniform currents are available for the two special cases of half-plane and infinite plane. For these special cases, our solution reduces to the exact solution. Currents computed using the expressions developed here are compared with currents computed from the eigenfunction solution of the wedge. Good agreement is obtained throughout.     

NONUNIFORM CURRENTS ON A CONDUCTING WEDGE ILLUMINATED BY A TM PLANE WAVE

Closed-form expressions for nonuniform currents induced on a perfectly conductinginfinite wedge illuminated by a TM plane wave are presented.Results computed by using theseexpressions are in good agreement with ones of the eigenfunction solution of the wedge.     

TM平面波照射下无限大导电劈表面的非均匀电流

本文给出了TM平面波照射下无限大导电劈表面非均匀电流的闭合形式表达式。计算结果与用本征函数解计算的准确值吻合较好。     

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     

Diffraction by an arbitrary-angled dielectric wedge. II. Correctionto physical optics solution

For pt.I see ibid., vol.39, no.9, p.1272-81 (1991). The error of the physical optics solution for the E-polarized plane wave incidence in connection with diffraction by an arbitrary-angled dielectric wedge is corrected by calculating the nonuniform current distributed along the dielectric interfaces. Two kinds of series expansions to the nonuniform current are employed. One is an asymptotic expansion as the multipole line source located at the edge of the dielectric wedge, since the correction field seems to be a cylindrical wave emanating from the edge in the far-field region. The other is arbitrary electric and magnetic surface currents expanded by infinite series of the Bessel functions, i.e. the Neumann expansion, of which fractional order is chosen to satisfy the edge condition near the edge of the dielectric wedge in the static limit. Both of the two different expansion coefficients for a wedge angle of 45°, relative dielectric constants 2, 10, and 100, and the E-polarized incident angle of 150° are evaluated by solving the dual series equation numerically after finite truncation     

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.     

Current evaluation on the faces of an impedance wedge illuminatedby an electromagnetic pulse

The scattering of an electromagnetic time-dependent plane wave by the edge of an impedance wedge is analyzed. Suitable expressions are presented for the surface currents which are induced on the two faces of the wedge. Numerical results are shown for different electrical and geometrical configurations and compared with data available in the literature for the case of a perfectly conducting wedge     

Scattering by an infinite wedge with tensor impedance boundaryconditions-a moment method/physical optics solution for thecurrents

Plane wave scattering by an infinite, two-dimensional wedge whose faces are characterized by impedance tensors is discussed. A combination of the moment method (MM) and physical optics (PO) is used to obtain a solution for the equivalent electric currents. The currents near the edge on each face are expanded with a set of basis functions consisting of pulse functions, defined on a meshed region, plus a function spanning the whole face. The currents outside the meshed region are taken to be the sum of physical optics currents, taken to be known, plus the whole-face basis function current. Expressing the equivalent magnetic currents in terms of the electric currents through the impedance tensors, the expansion coefficients for the electric current expansion are determined through an MM solution of the magnetic field integral equation. Sample results for wedges with isotropic and anisotropic face impedances are presented     

On uniform asymptotic Green's functions for the perfectly conducting cylinder tipped wedge

Uniform asymptotic expressions are derived for the Green's functions describing scattering of electric or magnetic type plane waves by a perfectly conducting cylinder tipped wedge (CTW). These expressions are found to agree analytically with heuristic expressions available using the geometrical theory of diffraction (GTD). Numerical comparison of these expressions with results obtained from eigenfunction expansions show good agreement for cylinder diameters >1.5 lambda.     

Closed-form Hankel transforms for circular disk basis modesinvolving Chebyshev polynomials and edge condition

Closed-form expressions for two kinds of Hankel transform integrals, which are encountered in the spectral moment method solution of a circular patch, are obtained. Application of the newly obtained formulas alleviates dramatically the algebraic work for determining the Hankel transforms of the current basis functions involving Chebysbev polynomials and edge condition. Computed moment method results using these expressions are presented     

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     

Electromagnetic scattering by nonplanar junctions of resistivesheets

Approximate uniform asymptotic expressions are provided to determine the field scattered by a penetrable wedge illuminated at normal incidence. The wedge is formed by two resistive sheets or two thin dielectric slabs definable as resistive sheets having identical geometric and electromagnetic characteristics. The solution is limited to wedge angles and source positions where internal reflections cannot occur. It is obtained by using a geometrical optics (GO) approximation for the field internal to the slabs and by performing a uniform asymptotic evaluation of the physical optics (PO) radiation integral in the hypothesis that a resistive sheet condition is valid. Samples of numerical results so obtained are presented and compared with other methods to demonstrate the effectiveness of the proposed technique     

Electromagnetic scattering from a chiral cylinder of arbitrarycross section

A simple moment solution is presented to the problem of electromagnetic scattering from a homogeneous chiral cylinder of arbitrary cross-section. The cylinder is assumed to be illuminated by either a TE or a TM wave. The surface equivalence principle is used to replace the cylinder by equivalent and magnetic-surface currents. These currents radiating in unbounded external medium produce the correct scattered field outside. When radiating in an unbounded chiral medium, they produce the correct total internal field. By enforcing the continuity of the tangential components of the total electric field on the surface of the cylinder, a set of coupled integral equations is obtained for the equivalent surface currents. Unlike a regular dielectric, the chiral scatterer produces both copolarized and cross-polarized scattered fields. Hence, both the electric and magnetic current each have a longitudinal and a circumferential component. These four components of the currents are obtained by using the method of moments (MoM) to solve the coupled set of integral equations. Pulses are used as expansion functions and point matching is used. The Green's dyads are used to develop explicit expressions for the electric field produced by two-dimensional surface currents radiating in an unbounded chiral medium. Some of the advantages and limitations of the method are discussed. The computed results include the internal field and the bistatic and monostatic echo widths. The results for a circular cylinder are in very good agreement with the exact eigenfunction solution     

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     

Diffraction coefficients and field patterns of obtuse angledielectric wedge illuminated by E-polarized plane wave

The diffraction problem is treated for the incidence of an E -polarized plane wave on both interfaces of an obtuse dielectric wedge. Based on the dual integral equation, the total field is obtained by the sum of the physical optics solution and the edge-diffracted correction term. Calculated diffraction coefficients and field patterns are plotted in figures for a wedge angle of 120°, incident angles of 60° and 70°, and relative dielectric constants of 2 and 10. It is shown that the Neumann expansion to the nonuniform currents provides a more accurate correction to the physical optics currents than the multiple expansion as the angle of dielectric wedge increases     

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     

Pulsed field diffraction by a perfectly conducting wedge: aspectral theory of transients analysis

The canonical problem of pulsed field diffraction by a perfectly conducting wedge is analyzed via the spectral theory of transients (STT). In this approach the field is expressed directly in the time domain as a spectral integral of pulsed plane waves. Closed-form expressions are obtained by analytic evaluation of this integral, thereby explaining explicitly in the time domain how spectral contributions add up to construct the field. For impulsive excitation the final results are identical with those obtained previously via time-harmonic spectral integral techniques. Via the STT, the authors also derive new solutions for a finite (i.e., nonimpulsive) incident pulse. Approximate uniform diffraction functions are derived to explain the field structure near the wavefront and in various transition zones. They are the time-domain counterparts of the diffraction coefficients of the geometrical theory of diffraction (GTD) and the uniform theory of diffraction (UTD). An important feature of the STT technique is that it can-be extended to solve the problem of wedge diffraction of pulsed beam fields (i.e., space-time wavepackets)     

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.      

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