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A hybrid method based on the combination of generalized forward backward method (GFBM) and Green's function for the grounded dielectric slab together with the acceleration of the combination via a discrete Fourier transform (DFT) based algorithm is developed for the efficient and accurate analysis of electromagnetic radiation/scattering from electrically large, irregularly contoured two-dimensional arrays consisting of finite number of probe-fed microstrip patches. In this method, unknown current coefficients corresponding to a single patch are first solved by a conventional Galerkin type hybrid method of moments (MoM)/Green's function technique that uses the grounded dielectric slab's Green's function. Because the current distribution on the microstrip patch can be expanded using an arbitrary number of subsectional basis functions, the patch can have any shape. The solution for the array currents is then found through GFBM, where it sweeps the current computation element by element. The computational complexity of this method, which is originally O ([N.sup.2.sub.tot]) ([N.sub.tot] being the total number of unknowns) for each iteration, is reduced to O([N.sub.tot]) using a DFT based acceleration algorithm making use of the fact that array elements are identical and the array is periodic. Numerical results in the form of array current distribution are given for various sized arrays of probe-fed microstrip patches with elliptical and/or circular boundaries, and are compared with the conventional MoM results to illustrate the efficiency and accuracy of the method. Index Terms--Discrete Fourier transform (DFT), finite arrays, generalized forward backward method (GFBM), method of moments (MoM).

A time-domain version of the uniform geometrical theory of diffraction (TD-UTD) is developed to describe, in closed form, the transient electromagnetic scattering from a smooth convex surface excited by a general time impulsive astigmatic ray field. This TD-UTD impulse response is obtained by employing an analytic time transform (ATT) for the inversion in time of an available and accurate corresponding frequency domain UTD (FD-UTD) solution. The ATT is employed because it overcomes the difficulties that occur when inverting FD-UTD fields associated with rays that traverse line or smooth caustics. Furthermore, the TD-UTD response to a general pulsed astigmatic wave excitation may be found by a convolution of the general excitation with the TD-UTD impulse response which can be performed in closed form. Some numerical examples illustrating the utility of this TD-UTD are presented. Index Terms--Analytic time transform, electromagnetic (EM) scattering, time domain (TD), uniform geometrical theory of diffraction (UTD).

A closed-form analytic solution based on a time-domain (TD) physical optics (PO) approximation is developed for the scattering from a finite second-order surface when illuminated by a transient impulsive plane wave. This TD-PO solution can be applied via a convolution to derive the early time transient fields scattered from the same scatterer that is illuminated by a realistic astigmatic finite-energy pulse. The closed form TD-PO solution is obtained by inverting the corresponding frequency-domain PO solution into TD. This solution can be expressed in terms of reflection and diffraction components of the scattering mechanisms as in other conventional high-frequency asymptotic solutions. Numerical examples are presented to demonstrate its physical phenomenon of the scattering mechanisms. Index Terms--Electromagnetic scattering, time-domain physical optics, transient analysis.

In this paper a discrete time (DT) representation of Maxwell's equations is employed to describe the time domain (TD) Maxwell's equations in terms of matrix equations analogous to time harmonic Maxwell's equations, which allows one to conveniently develop many TD solutions based on their frequency domain (FD) formulations. It was then employed to develop a TD version of the uniform geometrical theory of diffraction (UTD) (referred as DT-UTD) for the efficient electromagnetic transient analysis of scattering from perfectly conducting curved wedges. This DT-UTD retains the advantages of its corresponding FD UTD solution in several aspects including the form, ray physical picture and definitions of ray parameters. Furthermore, the transformation of the FD-UTD to the DT-UTD formulation can be easily achieved via a simple interpretation of notation. Numerical examples are presented to validate and illustrate the utilizations of this DT-UTD. Index Terms--Discrete time, Hilbert transform, time domain uniform geometrical theory of diffraction (TD-UTD), transient electromagnetics.

Forward-backward method (FBM) was successfully developed for the analysis of electromagnetic radiation/scattering from one-dimensional (1-D) phased array in an efficiency appealing fashion. The FBM applications to treat 2-D array problems are developed in this paper. Acceleration algorithm, performing better than the novel spectrum acceleration algorithm used for 1-D FBM computation, is also developed for this 2-D FBM so the unique advantages of high efficiency and O([N.sup.tot]) computational complexity as in the 1-D problems can be retained where ([N.sup.tot]) is the total number of array element. Numerical examples are presented to demonstrate its validity. Index Terms--Discrete Fourier transform (DFT), forward-backward method (FBM), moment method, novel acceleration algorithm, phased array.

A closed-form analytical solution is developed for predicting the early-time transient electromagnetic fields which are generated by a perfectly conducting parabolic reflector antenna when it is illuminated by a transient step spherical wave due to an elemental Huygen's source located at the focus. This closed-form time-domain solution, which is valid both near and far from the reflector (and anywhere in the forward region) can be used via the convolution theorem to efficiently obtain the early-time transient fields generated by the same parabolic reflector antenna when it is illuminated by a realistic finite-energy pulse which emanates as a spherical wave from the focus. The transient solution is developed here by analytically inverting, in closed form, the corresponding frequency-domain solution in terms of a radiation integral that employs an asymptotic high-frequency geometrical optics (GO)-based approximation for the fields in the aperture. Numerical results are presented for the transient fields both near and far from the reflector. The fields on boresight exhibit an impulse-like behavior similar to that of the impulse radiating antenna (IRA) introduced by Baum et al. Index Terms - Reflector antennas, transient analysis.

A relatively fast and simple method utilizing Gaussian beams (GBs) is developed which requires only a few seconds on a workstation to compute the near/far fields of electrically large reflector antennas when they are illuminated by a feed with a known radiation pattern. This GB technique is fast, because it completely avoids any numerical integration on the large reflector surface which is required in the conventional physical optics (PO) analysis of such antennas and which could take several hours on a workstation. Specifically, the known feed radiation field is represented by a set of relatively few, rotationally symmetric GBs that are launched radially out from the feed plane and with almost identical interbeam angular spacing. These GBs strike the reflector surface from where they are reflected, and also diffracted by the reflector edge; the expressions for the fields reflected and diffracted by the reflector illuminated with a general astigmatic incident GB from an arbitrary direction (but not close to grazing on the reflector) have been developed in [1] and utilized in this work. Numerical results are presented to illustrate the versatility, accuracy, and efficiency of this GB method when it is used for analyzing general offset parabolic reflectors with a single feed or an array feed, as well as for analyzing nonparabolic reflectors such as those described by ellipsoidal and even general shaped surfaces. Index Terms--Gaussian beams, reflector antennas.

The forward-backward method with a novel spectral acceleration algorithm (FB/NSA) has been shown to be an extremely efficient iterative method of moments (MoM) for the computation of scattering from one-dimensional (1-D) perfect electric conducting (PEC) and impedance rough surfaces [1]. The NSA algorithm is employed to rapidly compute interactions between widely separated points in the conventional FB method and is based on a spectral domain representation of source currents and the associated Green's function. For fixed surface roughness statistics, the computational cost and memory storage of the FB/NSA method are O([N.sub.tot]) as the surface size increases, where [N.sub.tot] is the total number of unknowns to be solved. This makes studies of scattering from large surfaces, required in low grazing-angle scattering problems, tractable. In this paper, the FB/NSA method is extended to analyze scattering from two-dimensional (2-D) rough surfaces. The NSA algorithm for this case involves a double spectral integral representation of source currents and the 3-D free-space scalar Green's function. The coupling between two spectral variables makes the problem more challenging, and the efficiency improvements obtained for 2-D surfaces are appreciable but not as dramatic as those for 1-D surfaces. However, the computational efficiency of the FB/NSA method for 2-D rough surfaces remains O([N.sub.tot]) as one of the surface dimensions increases. Comparisons of numerical results between the conventional FB method and the FB/NSA method for large-scale PEC rough surfaces show that the latter yields identical results to the former with a reduction of CPU time and only a slight increase in memory storage. In addition, the numerical results of FB/NSA method are in good agreement with experimental data obtained from the University of Washington, Seattle, WA. Index Terms--Forward-backward method, novel spectral acceleration algorithm, tough surfaces.

F-BM/NSA [3] with computational complexity of O(N) is very efficient in method of moment (MoM) modeling of large-scale scattering problems from rough surfaces. The previous formulation for PEC surfaces is here extended to treat impedance surfaces. Similarly, numerical experiment shows F-BM/NSA is far more efficient than the competitive BMIA/CAG [4] in the order of magnitude. Index Terms--Forward-backward method, method of moment (MoM), rough surfaces, scattering.

Poisson sum formulas have been previously presented and utilized in the literature [1]-[8] for converting a finite element-by-element array field summation into an alternative representation that exhibits improved convergence properties with a view toward more efficiently analyzing wave radiation/scattering from electrically large finite periodic arrays. However, different authors [1]-[6] appear to use two different versions of the Poisson sum formula; one of these explicitly shows the end-point discontinuity effects due to array truncation, whereas the other contains such effects only implicitly. It is shown here, via the sifting property of the Dirac delta function, that first of all, these two versions of the Poisson sum formula are equivalent. Second, the version containing implicit end point contributions has often been applied in an incomplete fashion in the literature to solve finite-array problems; it is also demonstrated here that the latter can lead to some errors in finite-array field computations. Index Terms - Array antennas, Poisson sum formula.