Numerical diffraction coefficients for surface waves

The numerical uniform theory of diffraction (UTD) is extended to include surface waves. A method for extracting surface wave diffraction coefficients from moment method data is given and Prony's method is applied to the problem of determining surface wave propagation constants. The method is validated through comparison with the exact solution of the problem of surface wave diffraction by a truncated dielectric slab recessed in a conducting surface. Examples are given for scattering from dielectric slabs and frequency-selective surfaces and for radiation from a conformal microstrip antenna with a truncated substrate. The accuracy obtained is demonstrated by comparison with moment method calculations     

Numerical diffraction coefficients in the shadow transition region

Numerical techniques for the evaluation of diffraction coefficients are extended to shadow transition regions and examined in detail for perfectly conducting and lossy dielectric semi-infinite slabs with a line source in the near-field and polarization along the slab edge. One approach is based on a direct computation of the radiation from a finite two-dimensional slab illuminated from a near-field source, with the current filtered by appropriate windows. For the perfectly conducting half-plane this approach yields diffraction coefficients in the transition region that are in good agreement with uniform theory of diffraction (UTD) analytic values. Alternatively, geometric theory of diffraction (GTD) coefficients are computed once and for all for a far-field source and these are used formally within a UTD or uniform asymptotic theory (UAT) framework. The direct, the UTD, and the UAT approaches are in satisfactory agreement with each other, and predictions for the radiation from finite slabs based on the computed diffraction coefficients are in satisfactory agreement with those of the method of moments (MM)     

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     

Numerical calculation of the diffraction coefficients for anarbitrary shaped perfectly conducting cone

A method for numerical calculation of the diffraction coefficients for electromagnetic diffraction by arbitrarily shaped perfectly conducting cones is proposed. The approach makes an extensive use of the analytic formulas of Smyshlyaev [1993] in combination with further developments, including a use of the potential theory adapted to the Laplace-Beltrami operator on a subdomain of unit sphere. This reduces the problem to a Fredholm integral equation on the closed curve of the unit sphere (defining the cone's geometry) which can be solved numerically. This strategy permits us to implement a numerical code for calculation of the diffraction coefficients for cones of rather general cross sections. Results of sample calculations for the circular and elliptic cones are given     

Incremental diffraction coefficients for the extended physicaltheory of diffraction

The extended physical theory of diffraction (EPTD), which is an extension of Ufimtsev's (1962) theory to aperture integration, is formulated in terms of incremental diffraction coefficients (IDC). Closed-form expressions for these coefficients are derived. The utility of the derived IDC is exemplified in a calculation of the cross-polar pattern of a parabolic reflector     

Recursive computation of discrete Legendre polynomial coefficients

Discrete Legendre polynomials play an important role in image processing, signal processing, and control. This paper presents two new recursive methods to compute Legendre polynomials' coefficients. One method computes the coefficients of the (m + 1)th order term using the coefficient of themth order term of the same degree plynomial. The other method computes thenth order coefficient of a higher degree polynomial using themth order coefficient of a lower degree polynomial.     

Modified diffraction coefficients for focusing reflectors

A modification to the halfplane diffraction coefficients is given for a plane wave incident on a curved screen. The result is used to calculate the near field of a parabolic reflector under plane-wave illumination. Comparison with the physical-optics method shows excellent agreement.     

Incremental diffraction coefficients for planar surfaces

Exact expressions for incremental diffraction coefficients at arbitrary angles of incidence and scattering are derived directly in terms of the corresponding two-dimensional, cylindrical diffraction coefficients. The derivation is limited to perfectly conducting scatterers that consist of planar surfaces, such as the wedge, the slit in an infinite plane, the strip, parallel or skewed planes, polygonal cylinders, or any combination thereof; and requires a known expression (whether exact or approximate) for the two-dimensional diffraction coefficients produced by the current on each different plane. Specifically, if one can supply an expression for the conventional diffraction coefficients of a two-dimensional planar scatterer, one can immediately find the incremental diffraction coefficients through direct substitution. No integration, differentiation, or specific knowledge of the current is required. Special attention is given to defining ambiguously all real angles and their analytic continuation into imaginary values required by the incremental diffraction coefficients     

Numerical evaluation of dyadic diffraction coefficients andbistatic radar cross sections for a perfectly conducting semi-infiniteelliptic cone

In this paper, the scattering of electromagnetic waves by a perfectly conducting semi-infinite elliptic cone is treated. The exact solution of this boundary value problem in problem-adapted spheroconal coordinates in the form of a spherical multipole expansion is of poor convergence if both the source point and the field point are far away from the cone's tip. Therefore, an appropriate sequence transformation of these series expansions (we apply the Shanks transformation) is necessary to numerically determine the dyadic diffraction coefficients and bistatic radar cross sections (RCS) for an arbitrary elliptic cone. Our far-field data for an elliptic cone, a circular cone, and a plane angular sector are compared with some other results obtained with the aid of quite different methods     

Application of eliminating zero-order diffraction light in wavefront reconstruction of inverse diffraction computation

With the development of computer and CCD tech-niques ,a technique of capturing the complex amplitudeof object light accordingto anintensity holographrecor-ded by a CCD detector array has been becoming an in-teresting area[1-4].In reference [5] the frequen…     

On the computation of discrete Legendre polynomial coefficients

A new and fast method to find the discrete Legendre polynomial (DLP) coefficients is presented. The method is based on forming a simple matrix using addition only and then multiplying two elements of the matrix to compute the DLP coefficients.     

Corner diffraction coefficients for the quarter plane

The current near a right-angled corner on a perfectly conducting flat scatterer illuminated by a plane wave is expressed as a sum of three currents. The first is the physical optics current, which describes the surface effect. The second is the fringe wave current, which is found from the half-plane solution and accounts for the distortion of the current caused by the edges. The third is the corner current, which is found from the numerical solution to the electric-field integral equation applied to the square plate, and accounts for the distortion of the current caused by the corner. It is found that the corner current for the right-angled corner, illuminated from a forward direction, consists mainly of two edge waves propagating along the edges forming the corner. Analytical expressions for these edge wave currents are constructed from the numerical results. A corner diffracted field is calculated by evaluating the asymptotic corner contributions to the radiation integral over the sum of the three currents. It is found that the corner contribution from the edge wave currents in some cases is of the same size as the corner contributions from the physical optics current and the fringe wave current     

Incremental length diffraction coefficients for arbitrarycylindrical scatterers

Convenient expressions are derived for incremental length diffraction coefficients (ILDCs) in terms of the far fields of arbitrary cylindrical canonical scatterers composed of linear electromagnetic material. The derivation of these general expressions for ILDCs is based on a surface-current equivalence theorem that states that the electromagnetic fields outside cylindrical sources can be generated to any degree of accuracy by localized electric and magnetic surface currents that lie in a single plane within the source region. This equivalence theorem is proven with the help of cylindrical wave expansions and the Kottler-Franz formulas. It combines with a general even and odd decomposition of cylindrical electromagnetic fields to allow the use of previous formulas for planar surface current ILDCs in the derivation of the general expressions for ILDCs in terms of cylindrical far fields     

Uniform diffraction coefficients for an impedance wedge

Uniform diffraction coefficients for an astigmatic electromagnetic wave normally incident on a wedge having curved faces with given surface impedances are derived from the earlier work of Maliuzhinets. These coefficients are to be used with standard formulas in the geometrical theory of diffraction to predict diffraction effects from structures having impedance surfaces terminating in an edge.     

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     

Fringe wave diffraction coefficients for higher order discontinuities

We consider the diffraction of waves by objects with higher order discontinuities. The geometric theory of diffraction (gtd) diffracted field for this type of discontinuities have strong divergence near normal incidence. We substract from this diffracted field, the field radiated by the Luneberg-Kline currents to get the fringe diffracted field; and show that this field is finite. The formulae can be used to improve the accuracy of physical theory of diffraction (ptd) for smooth objects without edges. Explicit formulas are given for the discontinuity up to order 5. We present a numerical application for the discontinuity in the curvature. All computations are done by using Maple symbolic computation system.     

Improved numerical diffraction coefficients with application tofrequency-selective surfaces

A method for numerically determining diffraction coefficients for arbitrary scattering centers is described. In this method finite bodies possessing scattering centers of the type of interest are first analyzed via the moment method. The various contributions to the total scattered fields are then isolated by solving low-order simultaneous equations obtained by writing expressions for the fields in terms of unknown diffraction coefficients. The method yields numerical diffraction coefficients in angular sectors where previous methods fail (e.g., near grazing angles), and can be applied in the context of measured as well as simulated scattering data. Finite frequency-selective surfaces are shown to be amenable to analysis with ray-optics techniques, and several two-dimensional examples are given with comparisons to far- and near-field moment method results     

Numerical evaluation of one-dimensional diffraction integrals

An efficient technique is described for performing one-dimensional (1-D) integrals of oscillatory complex functions, such as might arise in the numerical solution of diffraction problems. The upper integration limit may be infinite, provided that the phase of the integrand varies rapidly beyond some point. The integration is done in segments chosen so that both the phase and amplitude may be approximated as cubic polynomials on each segment, with a small cubic term for phase, and continued to infinity from the last segment. Three methods are given for integrating at each step: 1) an asymptotic-series method; 2) an “almost-quadratic-phase” method; and 3) an “almost-linear-phase” method. Criteria are given for choosing among the methods. An example calculation verifies the method in the special case of wave diffraction over two knife edges     

Numerical determination of diffraction, slope-, andmultiple-diffraction coefficients of impedance wedges by the method ofparabolic equation: Space waves

By generalizing the results of Malyuzhinets (1959), Ufimtsev (1965), and Popov (1969), the method of the parabolic equation (PE) can be applied to study the space wave diffraction of a line source by an impedance wedge. The respective diffraction as well as the slope-diffraction coefficients are numerically determined. Contrary to conventional methods, which usually first solve the scattering by a finite body containing the desired diffraction center and then extract the corresponding diffraction coefficient, the PE studies a semi-infinite scattering body and the diffracted field directly. A comparison of PE results with exact ones, as far as available, and uniform geometrical theory of diffraction (UTD) results confirm the accuracy of this method. In addition, a straightforward application of the PE for calculating multiple wedge diffraction eliminates the discontinuities which are typical of the “mechanical” application of the UTD to the same problem. A possible way for combining the PE and the UTD is pointed out. The latter should be of special interest to dealing with wave propagation problems