High-frequency scattering from the edges of impedance discontinuities on a flat plane

A high-frequency solution is presented for the scattering of a plane wave at the edges of surface impedance discontinuities on a fiat ground plane. Arbitrary uniform isotropic boundary conditions and a direction of incidence perpendicular to the edges of the discontinuities are considered for both the transverse electric (TE) and transverse magnetic (TM) cases. An asymptotic approximation of the exact solution given by Maliuzhinets and a spectral extension of the geometrical theory of diffraction (GTD) are used. Uniform expressions for the scattered field received at a point on the surface are given, including surface wave contributions. Numerical results are shown and in some examples they are compared with those obtained from a moment method (MM) solution.     

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     

An asymptotic high-frequency analysis of the radiation by a sourceon a perfectly conducting convex cylinder with an impedance surfacepatch [antennas]

A high-frequency approximation is presented for the fields radiated by a magnetic line or line dipole source which is located on an impedance surface patch that partly covers an electrically large, perfectly conducting convex cylinder. Relatively simple asymptotic approximations are developed for the currents induced on the impedance surface by the line sources, and the radiation patterns are calculated by incorporating these surface currents into the radiation integral. The latter integral exists only over the patch region as it uses a perfectly conducting cylinder Green's function which is expressed in terms of a uniform geometrical diffraction (UTD) solution. Numerical results are presented and shown to compare very well with other independent calculations and measurements     

Hybrid UTD-MM analysis of the scattering by a perfectly conducting semicircular cylinder

A hybrid UTD-MM technique which combines the uniform geometrical theory of diffraction (UTD) and the method of moments (MM) is employed to analyze efficiently the problem of electromagnetic diffraction of transverse electric (TE) and transverse magnetic (TM) waves by a perfectly conducting semicircular cylinder. An analysis of this problem is useful for understanding the coupling between the mechanisms of edge and convex surface diffraction. The accuracy of the numerical results for the far-zone fields based on this solution is established by comparison with an independent formally exact MM solution.     

Pattern distortion of aperture antennas radiating in the presence of conducting platforms

An analytically simple and numerically efficient technique for calculating the pattern distortion of aperture antennas radiating in the presence of conducting platforms located in the near or far field of the antenna is presented. The technique presented, based on uniform geometrical theory of diffraction (UGTD), is also applicable for large aperture antennas (aperture area> 15 lambda^{2}). An excellent agreement between the calculated and measured results obtained for a typical aperture antenna mounted on a conducting platform confirms the validity of the analytical technique developed.     

A uniform GTD solution for the radiation from sources on a convex surface

A compact approximate asymptotic solution is developed for the field radiated by an antenna on a perfectly conducting smooth convex surface. This high-frequency solution employs the ray coordinates of the geometrical theory of diffraction (GTD). In the shadow region the field radiated by the source propagates along Keller's surface diffracted ray path, whereas in the lit region the incident field propagates along the geometrical optics ray path directly from the source to the field point. These ray fields are expressed in terms of Fock functions which reduce to the geometrical optics field in the deep lit region and remain uniformly valid across the shadow boundary transition region into the deep shadow region. Surface ray torsion, which affects the radiated field in both the shadow and transition regions, appears explicitly in the solution as a torsion factor. The radiation patterns of slots and monopoles on cylinders, cones, and spheroids calculated from this solution agree very well with measured patterns and with patterns calculated from exact solutions.     

Diffraction by an arbitrary subreflector: GTD solution

The high-frequency asymptotic solution of diffraction by a conducting subreflector is studied. By using Keller's geometrical theory of diffraction and the newly developed uniform asymptotic theory of diffraction, the scattered field is determined up to an including terms of orderk^{-1/2}relative to the incident field. The key feature of the present work is that the surface of the subreflector is completely arbitrary. In fact, it is only necessary to specify the surface at a set of discrete points over a random net. Our computer program will fit those points by cubic spline functions and calculate the necessary geometrical parameters of the subreflector. In a companion paper by Y. Rahmat-Samii, R. Mittra, and V. Galindo-Israel, the scattered field from the submflector is used to calculate the secondary pattern of an arbitrarily shaped reflector by a series expansion method. Thus, in these two papers, it is hoped that we have developed a "universal" computer program that can analyze most dual-reflector antennas currently conceivable. It should also be added that our method of calculation is extremely numerically efficient. In many cases, it is one order of magnitude faster than the conventional integration method based on physical optics.     

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.     

Simulation and analysis of antennas radiating in a complex environment

An accurate and efficient numerical solution is developed for predicting high-frequency radiation patterns of antennas mounted on curved surfaces. This solution employs the uniform geometrical theory of diffraction (UTD) and has mainly been used to analyze airborne antenna patterns. In this case the aircraft is modeled in its most basic form so that the solution is applicable to general-type aircraft. The fuselage is modeled as a perfectly conducting composite ellipsoid, whereas, the wings, stabilizers, nose, fuel tanks, and engines, etc. are simulated by perfectly conducting fiat plates. The composite-ellipsoid fuselage model is necessary to simulate successfully the wide variety of real world fuselage shapes. Since the antenna is mounted on the fuselage, it has a dominant effect on the resulting radiation pattern, so it must be simulated accurately, especially near the antenna. Various radiation patterns are calculated for military aircraft, private aircraft, and the space shuttle orbiter. The application of this solution to practical airborne antenna problems illustrates its versatility and design capability. The solution accuracy is verified by the comparisons between calculated and measured data.     

A simplified expression of the dyadic Green's function for a conducting half-sheet

Simple analytical expressions of the dyadic Green's function for a conducting half-sheet have been derived. These expressions involve some finite integrals which can be easily calculated by a digital computer and are much simpler than those involving the vector mode function expansion. Input impedances of monopole antennas on and near an edge of a conducting half-sheet and the impedance of a notch antenna have been obtained, and the usefulness of these simplified expressions has been proved. The present results can be applied to check the limits of the applicability of the asymptotic theories, e.g., the geometrical theory of diffraction (GTD) and the uniform asymptotic theory of diffraction (UAT).     

An asymptotic solution for currents in the penumbra region with discontinuity in curvature

An analytical asymptotic result is obtained for evaluating the current distribution on a perfectly conducting surface composed of a flat plate smoothly joined to a parabolic cylinder with the join in the penumbra region. The result presents some improvements over a previous solution of the current distribution obtained by other investigators. The analytical result can be conveniently applied to estimating the backscattering cross section of a cone-sphere.     

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 a discontinuity in curvature including the effect ofthe creeping wave

The existing geometrical theory of diffraction (GTD) solution for the diffraction by a discontinuity in curvature on a perfectly conducting cylindrical surface is uniformly extended in the region where the surface diffraction of the creeping wave launched by the discontinuity is involved     

A uniform GTD analysis of the diffraction of electromagnetic waves by a smooth convex surface

The problem of the diffraction of an arbitrary ray optical electromagnetic field by a smooth perfectly conducting convex surface is investigated. A pure ray optical solution to this problem has been developed by Keller within the framework of his geometrical theory of diffraction (GTD). However, the original GTD solution fails in the transition region adjacent to the shadow boundary where the diffracted field plays a significant role. A uniform GTD solution is developed which remains valid within the shadow boundary transition region, and which reduces to the GTD solution outside this transition region where the latter solution is valid. The construction of this uniform solution is based on an asymptotic solution obtained previously for a simpler canonical problem. The present uniform GTD solution can be conveniently and efficiently applied to many practical problems. Numerical results based on this uniform GTD solution are shown to agree very well with experiments.     

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.     

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     

UTD analysis of a shaped subreflector in a dual offset-reflectorantenna system

The geometrical theory of diffraction (GTD) is known as an efficient high-frequency method for the analysis of electrically large objects such as a reflector antenna. However it is difficult to obtain geometrical parameters in order to apply GTD to an arbitrary shaped reflector, especially a subreflector. The geometrical parameters of an arbitrary shaped subreflector for the uniform theory of diffraction (UTD) analysis are derived based on differential geometry. The radiation patterns of various subreflector types, including hyperboloidal and a shaped subreflector, are evaluated by UTD. The computed result for the hyperboloidal reflector agrees well with that obtained by uniform asymptotic theory (UAT)     

A UTD based asymptotic solution for the surface magnetic field on a source excited circular cylinder with an impedance boundary condition

An asymptotic solution based on the uniform geometrical theory of diffraction (UTD) is proposed for the canonical problem of surface field excitation on a circular cylinder with an impedance boundary condition (IBC). The radius of the cylinder and the length of the geodesic path between source and field points, both of which are located on the surface of the cylinder, are assumed to be large compared to a wavelength. Unlike the UTD based solution pertaining to a perfect electrically conducting (PEC) circular cylinder, some higher order terms and derivatives of Fock type integrals are found to be significantly important and included in the proposed solution. The solution is of practical interest in the prediction of electromagnetic compatibility (EMC) and electromagnetic interference (EMI) between conformal slot antennas on a PEC cylindrical structure with a thin material coating on which boundary conditions can be approximated by an IBC. The cylindrical structure could locally model a portion of the fuselage of an aircraft or a spacecraft, or a missile. Validity and accuracy of the numerical results obtained by this solution are demonstrated in comparison with those of an exact eigenfunction solution.     

Problèmes posés par l’étude des rayons rampants

The electromagnetic scattering by a perfectly conducting smooth surface has been extensively handled through the concept of creeping waves in the past twenty years. However, until now, few information is available when the diffracting body is composed of geometrical combinations of elementary smooth surfaces. The primary goal of the investigation reported here is to describe the scattering of a creeping wave by a surface discontinuity in terms of geometrical theory of diffraction. In this article, special care has been taken when establishing a formulation easy to apply in a practical case. In addition, the paper deals with the important problem of modifying the formulation along directions where the general theory of diffraction representation fails.     

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.