Radio-Wave-Propagation Modeling in the Presence of Multiple Knife Edges by the Bidirectional Parabolic-Equation Method

Fast full-wave computation of fields is the main reason for a radio system planner to apply the parabolic-equation method (PEM) for radio-coverage prediction. In this paper, the capability of PEM for the determination of backward electromagnetic-field scattering by single and multiple knife edges is investigated. For the wave equation, a suitable solution is considered. Contrary to the available formulations for the PEM, the proposed method includes a backward-propagating term. For both the forward and backward terms, the split-step algorithm is employed. Similar to the terrain-masking method, the effect of edges is exerted by the Fresnel-Kirchhof approximation into the forward-propagating wave. For the backward field, a similar algorithm is derived. Then, an iterative marching algorithm is developed for modeling radio wave propagation over multiple knife edges. Numerical results are compared with those of Uniform Theory of Diffraction (UTD) and finite-difference time-domain methods for the single-knife-edge problem. In addition, the effect of the backward-propagating field on radio wave propagation is investigated. The effect of edge locations and heights on the backward scattered field and number of computational iterations is studied. It is seen that, for the single knife edge, the backward scattered field depends on the height and location of the edge. The intensity of the backscattered field is a monotonic increasing function of the edge height. In addition, by increasing the edge height, the beam width of the backward scattered field increases. In ranges far from the knife edge in front of it, the field spreads, and its amplitude decreases. For multiple knife edges, it is seen that, in addition to the single backward scattered field, radio-wave-propagation modeling requires multiple forward-backward terms between successive edges. The geometry of the problem determines the required number of terms for sufficient accuracy     

A physical optics version of the geometrical theory of diffraction

The authors derive a diffraction coefficient which is suitable for calculating the filed diffracted by the vertices of perfectly conducting objects. This diffraction coefficient is used to calculate the field scattered by the corner of a metallic sheet. Two diffraction coefficients, one for edges and one for vertices, are derived by solving the appropriate canonical problems using the physical optics (PO) approximation. The diffraction coefficients are calculated by first using the PO approximation which consists of calculating the total field on the surface of an object from the incident field according to the laws of geometrical optics, and then calculating the scattered field by employing this total surface field in a vector diffraction integral. The validity of the diffraction coefficients has been investigated by comparing their predictions with experimental measurements of the scattered field from a single corner of a rectangular metal sheet, and good agreement was found     

Diffraction by a wide double wedge with rounded edges

The multiple diffraction by two conducting wedges with rounded edges is investigated, using an expression for the scattered field of a plane wave incident on a single wedge with rounded edge derived by Ross and Hamid, as well as the technique proposed by Karp and Keller for the diffraction by a slit in an infinite screen. Numerical results for the diffraction pattern, transmission coefficient and the effect of rounding are also presented. It is shown that small rounding of the two edges decreases the transmission coefficient for large separation distances between the wedges.     

TM scattering by a wedge with concaved edge

The TM scattering problem by a perfectly conducting wedge with concaved edge is formulated for a line source excitation using the mode-matching technique. The scattered and guided fields are represented in terms of an infinite series of radial waveguide modes with unknown coefficients. By applying the appropriate boundary conditions, the coefficients of scattered field are obtained. For small ka, the diffraction coefficient of concaved edge is derived from the scattered field     

Diffraction by a planar junction between a perfectly conducting anda periodically loaded impedance surface

By using a perturbative method, an integral representation for the field scattered by a planar junction between a perfectly conducting and a periodically loaded impedance surface is determined, when the junction is illuminated by a plane wave perpendicularly incident on its edge. Both a uniform, asymptotic expression and a series representation are presented for the first-order perturbative correction to the field scattered by the junction. The series representation is expressed in terms of Bessel functions of integer order and is suitable for field calculations at small distances from the edge. Several numerical results are presented to demonstrate the applicability of the proposed technique     

Radiation by a corner reflector with dielectric loaded edges

The first part, of this paper deals with the electromagnetic scattering by a cylindrical dielectric shell with an azimuthal permittivity profile and an internal E-polarized line source or an externally incident plane wave. The integral equation for the resulting scattered electric field is solved approximately by the method of moments and the results for the echo width and polar radiation pattern are displayed graphically for typical geometrical dimensions, frequency and permittivity profiles.

The second part of this paper deals with the cylindrical dielectric shell terminating a conducting strip with one edge coinciding with the axis of the cylinder. The results for the scattered field due to a line source excitation are presented and extended to the case of two such strips whose unloaded edges intersect to form a corner reflector antenna. The resulting radiation pattern is shown to improve for specific dimensions and complex permittivity profiles of the dielectric caps.     

TE-scattering and reception by a parallel-plate waveguide array

TE-wave scattering and reception by a parallel plate waveguide array is Investigated. A Fourier-transform technique is used to express the scattered field in the spectral domain. The boundary conditions are enforced on the conducting surface and the array apertures to obtain simultaneous equations for the transmitted field inside the waveguide. The simultaneous equations are solved to obtain the transmitted field in a series representation whose first term is the Kirchoff solution. The behavior of the far-zone scattered field and the transmission coefficient are studied in terms of the scattering angle, array size, and frequency     

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     

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.     

Scattering from apertures in infinite ground planes using FDTD

A scattered field version of FDTD for scattering from an aperture in an infinite ground plane is presented. In this formulation the fields reflected from the infinite ground plane are computed analytically, not as FDTD scattered fields. This is necessary to eliminate scattering from the edges of the ground plane, where it is terminated at the FDTD outer boundary. Also, the fields scattered by the ground plane are usually of much higher amplitude than the desired aperture-scattered fields. In this formulation these fields need not be absorbed by the FDTD outer boundary. This provides more accurate calculation of low amplitude scattering from the aperture. The formulation can include materials in the aperture and on both sides of the infinite ground plane. For example, scattering from an aperture antenna with a dielectric cover backed by an aperture filled with lossy dielectric can be computed with this formulation     

A model for edge scattering from dichroic surfaces

This paper discusses experimental and theoretical results for edge scattering from dichroic (frequency selective) surfaces. Measurements presented for half planes show the nature of the scattering from the edge for both reflection and transmission frequencies. An impedance boundary condition approach is used to calculate the diffraction from dichroic edges. In the analysis the dichroic surface is replaced with an equivalent surface impedance and the total scattered field calculated. Measurements support the theory demonstrating the usefulness of the approach. The method is also useful for calculating diffraction from dielectric edges.     

Surface Wave Radiation from a Thick, Semi-Infinite Plane with a Reactive Surface

The idealized surface wave radiator considered here is a thick, semi-infinite plane with a reactive surface. The scattered field is found when symmetrical and unsymmetrical surface waves are radiated at the termination of the plane. Since there are semi-infinite boundary conditions, the Wiener-Hopf technique is used for finding equations describing the scattered field. These equations contain a series of unknown constants which require numerical solution. Field patterns are plotted for different plane thicknesses and surface reactances with even excitation. The scattering of a plane wave by a thick, reactive plane is also discussed briefly.     

Electromagnetic plane wave scattering by a system of two parallel conducting prolate spheroids

By means of modal series expansions of electromagnetic fields in terms of prolate spheroidal vector wave functions, as exact solution is obtained for the scattering by two perfectly conducting prolate spheroids in parallel configuration, the excitation being a monochromatic plane electromagnetic wave of arbitrary polarization and angle of incidence. Using the spheroidal translational addition theorems recently presented by the authors which are necessary for the two-body (or multibody) scattering solution, an efficient computational algorithm of the translational coefficients is given in terms of spherical translational coefficients. The field solution gives the column vector of the series coefficients of the scattered field in terms of the column vector of the series coefficients of the incident field by means of a matrix transformation in which the system matrix depends only on the scatterer ensemble. This eliminates the need for repeatedly solving a new set of simultaneous equations in order to obtain the scattered field for a new direction of incidence. Numerical results in the form of curves for the bistatic and monostatic radar cross sections are given for a variety of prolate spheroid pairs having resonant or near resonant lengths.     

A pseudospectral method for time-domain computation ofelectromagnetic scattering by bodies of revolution

We present a multidomain pseudospectral method for the accurate and efficient time-domain computation of scattering by body-of-revolution (BOR) perfectly electrically conducting objects. In the BOR formulation of the Maxwell equations, the azimuthal dependence of the fields is accounted for analytically through a Fourier series. The numerical scheme in the (r,z) plane is developed in general curvilinear coordinates and the method of characteristics is applied for patching field values in the individual subdomains to obtain the global solution. A modified matched-layer method is used for terminating the computational domain and special attention is given to proper treatment of the coordinate singularity in the scattered field formulation and correct time-domain boundary conditions along edges. Numerical results for monochromatic plane wave scattering by smooth and nonsmooth axis-symmetric objects, including spheres, cone-spheres, and finite cylinders, is compared with results from the literature, illustrating the accuracy and computational efficiency associated with the use of properly constructed spectral methods. To emphasize the versatility of the presented framework, we compute plane wave scattering by a missile and find satisfactory agreement with method-of-moment (MoM) computations     

Radiation from multiple circumferential slots on a conductingcircular cylinder

Electromagnetic wave radiation from multiple circumferential slots on a conducting circular cylinder is theoretically investigated. The Fourier transform/series technique is used to represent the continuous and discrete modes of the scattered field. The mode matching is utilized to constitute a set of simultaneous equations for the discrete modal coefficients. The residue calculus is applied to transform the scattered field integral representations into fast-converging series forms, thereby facilitating the numerical computations. Numerical computations illustrate the behavior of radiation in terms of the slot geometry, the incident mode, and the operating frequency     

Study of curved and planar frequency-selective surfaces withnonplanar illumination

A locally planar technique (LPT) is investigated for determining the forward scattered field from a generally shaped inductive frequency-selective surface (FSS) with nonplanar illumination. The results of an experimental study are presented to assess the LPT accuracy. The effects of a nonplanar incident field are determined by comparing the LPT numerical results with a series of experiments with the feed source placed at varying distances from the planar FSS. The limitations of the LPT model due to surface curvature are investigated in an experimental study of the scattered fields from a set of hyperbolic cylinders of different curvatures. From these comparisons, guidelines for applying the locally planar technique are developed     

TE scattering from a slit in a thick conducting screen: revisited

TE plane-wave scattering from a slit in a thick conducting screen is reexamined. The boundary conditions are enforced to obtain simultaneous equations for the transmitted field inside the thick conducting screen. The simultaneous equations are solved to represent the transmitted and scattered fields in series forms. An approximate series solution for transmission is obtained in closed form which is valid for the high-frequency scattering regime     

Scattering by thin dielectric strips

A plane wave incident on a thin dielectric strip with infinite length is considered, letting the incident electric field vector be parallel with the edges of the strip. The field is expanded in the dielectric region as the sum of three plane waves (the forced wave and two surface waves). Thex-axis andy-axis propagation constants are known for each wave, and Galerkin's method is employed to determine the amplitudes of these waves. Finally, the far-zone scattered field is determined by considering the polarization currents radiating in free space. Numerical data are presented to illustrate the scattering properties of lossless and lossy dielectric strips as a function of the angle of incidence and the width of the strip. The calculations show excellent agreement with an earlier moment method using pulse bases and point matching.     

High-frequency scattering by a conducting circular cylinder coatedwith a lossy dielectric of nonuniform thickness

A closed-form expression for the field produced by a plane wave incident on an infinitely long conducting cylinder, coated with a lossy dielectric of nonuniform thickness, is obtained using perturbation theory. This approximate series solution is later evaluated asymptotically for electrically large cylinder sizes. The scattered fields are interpreted using geometric optics and creeping waves. The fields are calculated using the exact series, the approximate perturbation series, and the high-frequency asymptotic solutions, and compared for different angles of incidence     

A UGO/EUTD solution for the scattering and diffraction from cubicpolynomial strips

A combined uniform geometrical optics (UGO) and extended uniform geometrical theory of diffraction (EUTD) solution is developed for scattering and diffraction by perfectly conducting cubic polynomial strips. The new solution overcomes the difficulties of the classic GO/UTD solution near caustics and composite shadow boundaries. The approach for constructing the UGO/EUTD solution is based on a spatial domain physical optics (PO) radiation integral representation for the scattered field, which is then reduced using a uniform asymptotic procedure. New uniform reflection, zero-curvature diffraction, and edge diffraction coefficients are derived and involve the ordinary and incomplete Airy integrals as canonical functions. The UGO/EUTD solution is very efficient and provides useful physical insight into the various scattering and diffraction processes. It is also universal in nature and can be used to effectively describe the scattered fields from flat, strictly concave or convex, and concave-convex boundaries containing edges. Its accuracy is confirmed via comparison with some reference moment method (MM) results