On the GTD scattering by a polygonal cylinder

Using Keller's geometrical theory of diffraction (GTD) the field diffracted by a wedge is infinite at the shadow and reflection boundaries. In general, uniform diffraction coefficients must be used to provide continuous fields at these boundaries. In this communication it is shown that by properly adding the singular contributions from a pair of adjacent edges, Keller's diffraction coefficients yield a continuous far-zone field at the reflection boundaries of a polygonal cylinder illuminated by a plane wave. Furthermore the procedure is justified by noting that the uniform diffraction coefficients reduce to the Keller diffraction coefficients for this case.     

A uniform GTD treatment of surface diffraction by impedance andcoated cylinders

In the context of the uniform geometrical theory of diffraction (UTD), computation of the scattered fields near the shadow boundary of a smooth convex surface requires values for the Pekeris-integral function p*(ξ,q). While in a small number of cases such as the case of perfect conductivity (q=0 and q→∞), tabulated values of the function are available; in the general case, these values must be obtained by some numerical method. A procedure for approximating p*(ξ,q) by residue-series means is introduced. In contrast with traditional residue-series representations, the new procedure requires only a limited knowledge of pole locations even in the shadow boundary transition region and thereby extends the regime of practical applicability of residue-series methods beyond the deep shadow. It is demonstrated that the new procedure can be combined with an earlier residue-series representation derived by Hussar and Albus (1991), and with geometrical optics, to provide a computationally efficient procedure for computing fields scattered by an impedance or coated cylinder     

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.     

Analysis of the electromagnetic scattering by perfectly conducting convex polygonal cylinders

An effective method for the analysis of the scattering by a perfectly conducting convex polygonal cross-section cylinder is presented. The effectiveness stems from the generalization of the Neumann series, factorising the right edge behavior of the electromagnetic field, thus leading to a quickly convergent method. The induced currents, the radar cross section (RCS) and the induced field ratio have been evaluated.     

High frequency scattering from polygonal impedance cylinders andstrips

An analysis is presented for the high-frequency diffraction by convex polygonal cylinders with arbitrary side impedances. The authors extend their solution for the multiply diffracted fields associated with a double wedge (see ibid., vol.36, no.5, p.664-678, 1988). The analysis thus utilizes the extended spectral ray method (ESRM) that is applicable to nonray optical regions. Diffraction coefficients yielding a uniform total field are given for up to and including all fourth-order mechanisms. An important aspect of this analysis is the rigorous and uniform incorporation of the surface-wave effects in the resulting diffraction coefficients. A general polygon computer code was written that includes up to a third-order mechanisms. Based on this code, backscatter and bistatic patterns are given for impedance cylinders with triangular and square cross sections. The results are found to be in remarkable agreement with corresponding moment method data. As a matter of completeness, uniform diffraction coefficients are presented for a strip (which is a special case of a cylinder) that can have unequal face impedances     

Radiation and scattering from large polygonal cylinders, transverse electric fields

The computation of radiation and scattering of electromagnetic fields by electrically large convex conducting cylinders, using the geometrical theory of diffraction (GTD) is considered. A general computer program has been developed for the transverse electric case. Illustrative computations are made for examples of radiation from a line source of magnetic current in the vicinity of a polygonal cylinder, scattering of plane waves, radiation from slots, and radiation from electric dipoles. Also given are examples of computations for conducting strips, grazing incidence on polygonal cylinders, and scattering from small cylinders. The computational accuracy is checked by comparing the results to corresponding ones computed by a moment solution to theH-field integral equation.     

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.     

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     

Applying GTD to calculate the RCS of polygonal plates

A difficulty that may be encountered in applying the geometrical theory of diffraction (GTD) to calculate the radar cross section (RDC) of polygonal plates is discussed. The simple example of a square plate is considered and it is shown that when the same specular direction is reached through two different pattern cuts, a different value of the total scattered field is obtained. This difference may be quite noticeable for impedance plates. Its physical explanation suggests a suitable alternative approach to overcome this difficulty     

Modified GTD for generating complex resonances for flat strips and disks

The complex resonance frequencies of a scatterer are important elements in target classification and identification. In the singularity expansion method (SEM), the resonances are defined by a homogeneous integral equation whose numerical solution is feasible in the low, but not in the high, frequency range. At high frequencies, the geometrical theory of diffraction (GTD) provides an attractive numerical alternative and, furthermore, incorporates an interpretation of the resonance generation process in terms of multiple wavefront (ray) traversals. Except for extremely simple scatterer configurations, the (damped) complex resonances are known to occupy an entire half of the complex frequency plane. Dominant and higher order creeping wave GTD applied to cylinders and spheres does indeed yield resonances arranged along a sequence of "layers" in that entire half-plane, but multiple edge diffracted GTD applied to flat strips and disks furnishes only a single (dominant) layer. By drawing analogies with higher order creeping waves on a smooth object, the conventional edge diffracted GTD field is here augmented by higher order ray fields undergoing higher order "slope diffraction." Each of these higher order ray fields can be made to satisfy its own resonance equation, which is now found to provide the missing layers, with remarkably accurate values for the resonances when compared, where available, with those calculated numerically by the moment and T-matrix methods. The success of higher order ray diffraction in predicting the complex resonance structure suggests that this mechanism may play a corrective role also in other edge dominated scattering phenomena.     

A hybrid method for the solution of scattering from inhomogeneousdielectric cylinders of arbitrary shape

A hybrid moment method/edge-element method (MM/EEM) is presented. The formulation is quite general; however, the method is applied to two-dimensional scattering problems. Such a hybrid formulation unites the advantages of finite and integral-equation methods and is able to handle unbounded problems in which complex inhomogeneities are present. The edge-element method is easily coupled to the moment method, and it doesn't introduce spurious modes. The equivalence principle is used to divide the original problem into two separate problems: an unbounded homogeneous one in which the moment method is used and a bounded inhomogeneous one in which the edge-element method is used. Several examples involving two-dimensional scattering with TE and TM plane wave excitation are presented. The RCS is computed and compared to results obtained by other numerical techniques     

Integral equation solution for analyzing scattering fromone-dimensional periodic coated strips

A set of integral equations based on the surface/surface formulation are developed for analyzing electromagnetic scattering by one-dimensional periodic structures. To compare the accuracy, efficiency, and robustness of the formulation, the electric field integral equation (EFIE), magnetic field integral equation (MFIE), and combined field integral equation (CFIE) are developed for analyzing the same structure for different excitations. Due to the periodicity of the structure, the integral equations are formulated in the spectral domain using the Fourier transform of the integrodifferential operators. The generalized-biconjugate-gradient-fast Fourier transform method with subdomain basis functions is used to solve the matrix equation     

Time domain version of the uniform GTD

The uniform geometrical theory of diffraction (UTD) solutions can be inversely transformed analytically to obtain a time-domain version of the UTD. The time-domain solutions are valid in the early time period where an observation time t is close to the time after the arrival of the first diffracted wavefront. Comparisons with GTD (geometrical theory of diffraction) and also with available rigorous results (J.B. Keller and A. Blank, 1951) reveal that the UTD solutions are accurate for substantial early time periods while the GTD (Keller and Blank) results are valid for very early time periods     

A partitioning technique for the finite element solution ofelectromagnetic scattering from electrically large dielectric cylinders

A finite element partitioning scheme has been developed to reduce the computational costs of modeling electrically large geometries. In the partitioning scheme, the cylinder is divided into many sections. The finite element method is applied to each section independent of the other sections, and then the solutions in each section are coupled through the use of the tangential field continuity conditions between adjacent sections. Since the coupling matrix is significantly smaller than the original finite element matrix, it is expected that both the CPU time and memory costs can be significantly reduced. The partitioning scheme is coupled to the bymoment method to account for the boundary truncation. Numerical results are presented to demonstrate the efficiency and accuracy of the method     

Electromagnetic scattering from a 2-D chiral strip simulated by circular cylinders for uniform and nonuniform chirality distribution

A semi-analytical solution is presented to the problem of electromagnetic scattering from an incident plane wave on a rectangular strip. The strip is simulated by parallel circular cylinders, illuminated by either a TE/sub z/ or a TM/sub z/ incident plane wave. The solution is based on the application of the boundary conditions on the surface of each cylinder in terms of the local coordinate system of each individual cylinder. This technique is used to predict the radar cross-section of strips composed of dielectric, conducting, and chiral material with uniform or nonuniform chiral admittance distribution.     

A method for computing scattering by large arrays of narrow strips

The electromagnetic scattering characteristics of an array of narrow, conducting strips can he developed readily by extending the work of Butler and Wilton who show that Chebyshev polynomials augmented with the edge condition can be used to solve the narrow-strip/narrow-slot integral equations. The strips reside in a homogeneous medium of infinite extent and are considered narrow relative to wavelength in the medium at the frequency of excitation. The unknown current distributions on the strips are represented as linear combinations of certain basis functions that are exact solutions to the approximate equation for an isolated narrow strip subject to a special excitation. The resulting power-series treatment allows easy calculation of the coupling terms among the strips in the array in a simple matrix equation by which the unknown coefficients in the current distribution expansions may be readily computed. With these coefficients, one can obtain the distribution of current on each strip and the total scattered field. The method is particularly well suited for handling large arrays with more strips than could be accommodated by the usual moment method. Numerical data-currents and scattered fields-are presented for various cases of interest.     

Low-frequency scattering by rectangular cylinders

An integral equation formulation is used to investigate potential problems associated with low-frequency scattering by both dielectric and perfectly conducting cylinders of rectangular cross section. Induced dipoles and scattering cross sections are obtained for 1) waves withbar{E}orbar{H}parallel to the axis, and 2) directions of propagation perpendicular and parallel to the broad side of the rectangle.     

A new solution for TE plane-wave scattering from a symmetricdouble-strip grating composed of equal strips

The paper presents a new rigorous solution for the problem of TE plane-wave scattering from a periodic planar symmetric double-strip grating, i.e., the grating which has two equal strips per unit cell. The grating is placed at a dielectric interface and is assumed to be perfectly conductive and infinite in length and width. The formulation is based on a multimode equivalent network representation and the relevant integral equation defined on two separate intervals is rigorously solved by reducing to two simpler equations with known solutions. From this a new simple analytic expression is obtained for the coupling matrix elements which involves no integration. Some computations based on this new expression are carried out and the results are compared to those obtained by the Riemann-Hilbert method and also to some of the previously obtained single-strip results in the limiting case     

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.     

Transient scattering by resistive cylinders

The two-dimensional scattering of an electromagnetic pulse normally incident on a collection of infinitely long cylinders of arbitrary shape is considered. ForE-polarization an electric field integral equation is derived that is applicable to solid cylinders and/or thin sheets, resistive and/or perfectly conducting. The contribution of the self-cell at later times is carefully analyzed. The expression obtained represents a generalization of previously known results. For an incident Gaussian pulse, numerical results are presented for surface currents and far-fields, for perfectly conducting and resistive circular cylinders and strips. A fast Fourier transform (FFT) algorithm is implemented to obtain the backscattering radar cross section, which is in good agreement with results obtained from either exact continuous wave (CW) solutions or the method of moments.