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     

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。     

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.     

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     

Uniform physical theory of diffraction equivalent edge currents fortruncated wedge strips

New uniform closed-form expressions for physical theory of diffraction equivalent edge currents are derived for truncated incremental wedge strips. In contrast to previously reported expressions, the new expressions are well behaved for all directions of incidence and observation and take a finite value for zero strip length. This means that the expressions are well suited for implementation in general computer codes. The new expressions are expressed as the difference between two terms. The first term is obtained by integrating the exact fringe wave current on a wedge along an untruncated incremental strip extending from the leading edge of the structure under consideration. The second term is calculated from an integration of the asymptotic fringe wave (FW) current along another untruncated incremental strip extending from the trailing edge of the structure. The new expressions are tested numerically on a triangular cylinder and the results are compared with those obtained using the method of moments and the previously reported expressions     

Elimination of infinities in equivalent edge currents, part I: Fringe current components

New expressions are derived for the fringe current components of the equivalent edge currents. They are obtained by asymptotic endpoint evaluation of the fringe current radiation integral over the "ray coordinate" measured along the diffracted ray grazing the surface of the local wedge. The resulting expressions, unlike the previous ones, are finite for all aspects of illumination and observation, except for the special case where the direction of observation is the continuation of a glancing incident ray propagating "inwards" with respect to the wedge surface (the Ufimtsev singularity).     

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.     

Incremental length diffraction coefficients for an impedance wedge

An incremental length diffraction coefficient (ILDC) formulation is presented for the canonical problem of a locally tangent wedge with surface impedance boundary conditions on its faces. The resulting expressions are deduced in a rigorous fashion from a Sommerfeld spectral integral representation of the exact solution for the canonical wedge problem. The ILDC solution is cast into a convenient matrix form which is very simply related to the familiar geometrical theory of diffraction (GTD) expressions for the field on the Keller cone. The scattered field is decomposed into physical optics, surface wave, and fringe contributions. Most of the analysis is concerned with the fringe components; however, the particular features of the various contributions are discussed in detail     

Numerical calculation of diffraction coefficients of genericconducting and dielectric wedges using FDTD

Classical theories such as the uniform geometrical theory of diffraction (UTD) utilize analytical expressions for diffraction coefficient for canonical problems such as the infinite perfectly conducting wedge. We present a numerical approach to this problem using the finite-difference time-domain (FDTD) method. We present results for the diffraction coefficient of the two-dimensional (2-D) infinite perfect electrical conductor (PEC) wedge, the 2-D infinite lossless dielectric wedge, and the 2-D infinite lossy dielectric wedge for incident TM and TE polarization and a 90° wedge angle. We compare our FDTD results in the far-field region for the infinite PEC wedge to the well-known analytical solutions obtained using the UTD. There is very good agreement between the FDTD and UTD results. The power of this approach using FDTD goes well beyond the simple problems dealt with in this paper. It can, in principle, be extended to calculate the diffraction coefficients for a variety of shape and material discontinuities, even in three dimensions     

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 diffraction of an inhomogeneous plane wave by an impedancewedge in a lossy medium

The diffraction of an inhomogeneous plane wave by an impedance wedge embedded in a lossy medium is analyzed. The rigorous integral representation for the field is asymptotically evaluated in the context of the uniform geometrical theory of diffraction (UTD) so that the asymptotic expressions obtained can be employed in a ray analysis of the scattering from more complex edge geometries located in a dissipative medium. Surface wave excitations at the edge and their propagation along the wedge faces are discussed with particular emphasis on the effects of losses     

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     

Green's function for the harmonic potential of the three-dimensional wedge transmission problem

The point-source static potential in a wedge geometry consisting of two homogeneous media is solved via the Kontorovich-Lebedev and Fourier transforms. Inverse transforms enable the solution of Laplace's equation to be expressed in terms of image contributions plus residue sums (Fourier series) of toroidal functions. As in previous wave equation solutions for isovelocity wedges, explicit expressions for the poles that are the site of the residues are exploited when the wedge angle is a rational multiple of /spl pi/.     

Equivalent edge currents for arbitrary aspects of observation

Explicit expressions for equivalent edge currents are derived for an arbitrary local wedge angle and arbitrary directions of illumination and observation. Thereby the method of equivalent currents (MEC) is completed as a practically applicable theory of the electromagnetic high-frequency diffraction by edges. The derivation is based on an asymptotic relationship between the surface radiation integral of the physical theory of diffraction (PTD) and the line radiation integral of MEC, and the resulting expressions are deduced from the exact solutions of the canonical wedge problem.     

一致性绕射理论的等效边缘电磁流在多边形板双站散射中的应用

介绍一致性绕射理论等效边缘电磁流（ＵＴＤＥＥＣ）的公式。该公式是基于Ｍｉｃｈａｅｌｉ的半平面等效边缘电磁流（ＥＥＣ）表达式，用平截的劈增量条计算等效边缘电磁流。这样可以消除以往计算中的虚假奇异点，对任意入射和观察方向均有良好的性态。本文用此方法计算了方板和梯形板的双站散射，并与高阶等效边缘电磁流的结果比较，具有良好的精度。     

Reply to 'Comment on 'Comparison of excess 1/f noise spectra in trimmed and untrimmed thick film resistors'

An iterative surface current density replacement technique is used to formulate the electromagnetic scattering from any perfectly conducting body defined as the intersection of two bodies for which expressions for the scattering are known. The application of the iterative surface current density replacement technique to the truncated wedge results in a secondary edge diffraction coefficient which is accurate for closely spaced edges, and is identical to the secondary diffraction coefficient of the geometrical theory of diffraction when the edges are separated by a distance which is large compared with the wavelength of the field. Results are presented which show the accuracy of this secondary edge diffraction coefficient when applied to the perfectly conducting truncated wedge and narrow strip.     

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     

Diffraction by a wedge with variable-impedance faces

The scattering from a wedge with nonuniform impedance faces illuminated by a plane wave, perpendicularly incident on its edge, is analyzed. The solution technique is in the framework of perturbative methods; it applies to surface impedances of the wedge faces having the form of a constant plus a small amplitude perturbation which exhibits an exponential dependence on the distance from the edge in a plane transverse to the edge. This is of remarkable importance for applications as it allows the modeling of the actual behavior of the equivalent surface impedance in the special case of wedges coated with dielectric slabs. Uniform asymptotic expressions for the fields are obtained in the context of the uniform geometrical theory of diffraction (UTD)     

Multiple microstrip lines on a multilayered cylindrical dielectricsubstrate on perfectly conducting wedge

The quasi-TEM characteristics of a class of cylindrical microstrip lines are rigorously determined. The class of microstrip lines considered consists of multiple infinitesimally thin strips on a multilayered dielectric substrate on a perfectly conducting wedge. Expressions for the potential distribution inside and outside the dielectric substrate, charge distribution on the strips, and capacitance matrix of the microstrip lines are derived. The problems of a microstrip line on a cylindrically capped wedge and on a cylindrical dielectric substrate on perfectly conducting core are also considered as special cases. Sample numerical results based on the derived expressions are given and discussed