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/spl deg/ 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 diffraction coefficients of generic conducting and dielectric wedges using FDTD

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. >

Improved numerical diffraction coefficients with application to frequency-selective surfaces

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.

Numerical determination of diffraction, slope-, and multiple-diffraction coefficients of impedance wedges by the method of parabolic equation: Space waves

Numerical diffraction coefficients are presented for vertex-diffracted edge waves induced on an infinitely-thin, perfectly conducting, semi-infinite plane angular sector. The current density on the surface of the plane angular sector is modeled using the physical theory of diffraction (PTD). The vertex-diffracted currents are defined as the difference between the exact and the PTD currents. The difference current is then modeled as a wave traveling away from the corner with unknown amplitude and phase factors. The unknown coefficients for the vertex-diffracted currents are calculated by using a least squares fit approximation. The vertex-diffracted currents are successfully modeled even for narrow angular sectors. The vertex-diffracted currents provide a substantial improvement to the accuracy of RCS patterns in off-specular directions.

/pdf/vertex-diffracted-edge-waves-on-a-perfectly-conducting-plane-14xcw62i4y.pdf

Vertex Diffracted Edge Waves on a Perfectly Conducting Plane Angular Sector

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 for surface waves

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 diffraction coefficients in the shadow transition region

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Numerical diffraction coefficients in the shadow transition region