Edge effects of truncated periodic surfaces of thin wire elements

The effects of truncating a periodic structure of thin wire elements is examined. The structure is assumed to be infinite in extent along a single axis, enabling the analysis to be simplified via Floquet's currents on the infinite axis for plane wave incidence. The analysis of an infinite linear array of elements is thereby reduced to that of a single element. Scattered fields are presented for several truncated planar geometries and are compared to three approximate solutions that use unperturbed two-dimensionally infinite Floquet currents, diffraction from a strip, and a physical optics solution for a strip, respectively     

Effects of surface waves on the currents of truncated periodic arrays

The behavior of surface waves in truncated periodic arrays is examined through analysis of the currents. The surface waves to be studied are guided by the perfectly conducting elements of the array itself and are to be distinguished from the dielectric slab-guided surface waves encountered elsewhere in the literature. The conditions under which surface waves may arise are given. The surface wave currents are extracted from the method of moments solution for the finite by an infinite array using a least squares algorithm. Surface wave excitation and reflection coefficients are then be determined from the data and compared with the semi-infinite array solution.     

The effects of the truncation and curvature of periodic surfaces: astrip grating

Equations are outlined for surfaces which are finite and curved in two dimensions (only locally periodic), as well as infinitely periodic in one dimension but truncated and curved in the second dimension. By removing the periodicity, a truncated strip-grating results and the scattered fields as well as an associated reflection coefficient are calculated. These numerically rigorous calculations are compared against two approximate solutions. The comparison is intended as a check of the approximate solutions toward their application, in particular, in the analysis of surfaces which are finite and curved in two dimensions. In general, the edge currents always differed from the currents induced on an infinite grating, while the interior strip currents on a finite grating (depending on the excitation wavelength) may or may not differ from those of an infinite grating. It is concluded that if a more accurate calculation of the spectral response is to be found, the interior currents must be better approximated     

Analysis of finite arrays-a new approach

A novel method for the analysis of finite arrays is presented. The method is based on a global array concept where the array problem (for single-mode elements) is reduced to a solution of a single Fredholm integral equation of the second kind. This formulation offers several types of solutions (not all explored yet) with illuminating results. The approximate solution of this integral equation, for example, yields finite array characteristics in terms of equivalent infinite array scattering parameters and mutual admittances. The method is general, i.e., applicable to any element-type and periodic array geometry. Presently, the method applies to single-mode elements (one unknown per element), however, it can be extended to a multimode analysis     

Electromagnetic scattering from a coaxial dielectric circularcylinder loading a semicircular gap in a ground plane

An exact dual series solution of a plane wave incident on a coaxial dielectric circular cylinder imbedded in a semicircular gap of a ground plane is presented. Both TM and TE cases are considered here. The scattered field is represented in terms of an infinite series of cylindrical waves with unknown coefficients. By applying the boundary conditions and employing the partial orthogonality of the trigonometric functions the scattering coefficients are obtained. The resulting infinite series is then truncated to a finite number of terms to produce numerical results. For the sake of comparison with the published data some special cases are introduced first. The comparisons showed excellent agreement in all cases     

High-frequency Green's function for a semi-infinite array ofelectric dipoles on a grounded slab .I. formulation

A uniform, high-frequency solution is presented for the electromagnetic field radiated at finite distance by a semi-infinite array of elementary electric dipoles placed on an infinite grounded dielectric slab. This solution is useful for the efficient analysis of printed arrays. The field is represented in terms of a series encompassing propagating and evanescent truncated Floquet waves together with their corresponding diffracted rays, which arise from the edge of the array. The high-frequency formulation also includes surface and leaky wave contributions excited at the array edge. The diffracted waves contain discontinuities which compensate the disappearance of surface, leaky and truncated Floquet waves at their pertinent shadow boundaries     

Efficiency as a measure of size of a phased-array antenna

This communication addresses the problem of estimating the minimum size a phased-array antenna must have in order that analyses based on simple infinite-array models yield meaningful results. The measure of array size proposed herein is an efficiency parameter defined for an infinite array with truncated excitations. Numerical results are presented for arrays of slots and dipoles, showing the rate of convergence of the efficiency parameter for various spacings and scan angles. The conclusions deduced from this analysis as to the minimum array size are in substantial agreement with exact computations dealing with finite arrays published in the literature.     

A truncated Floquet wave diffraction method for the full waveanalysis of large phased arrays. I. Basic principles and 2-D cases

This two-part sequence deals with the formulation of an efficient method for the full wave analysis of large phased array antennas. This is based on the method of moments (MoM) solution of a fringe integral equation (IE) in which the unknown function is the difference between the exact solution of the finite array and that of the associated infinite array. The unknown currents can be interpreted as produced by the field diffracted at the array edge, which is excited by the Floquet waves (FWs) pertinent to the infinite configuration. Following this physical interpretation, the unknown in the IE is efficiently represented by a very small number of basis functions with domain on the entire array aperture. In order to illustrate the basic concepts, the first part of this sequence deals with the two-dimensional example of a linearly phased slit array. It is shown that the dominant phenomenon fur describing the current perturbation with respect to the infinite array is accurately represented in most cases by only three diffracted-ray-shaped unknown functions. This also permits a simple interpretation of the element-by-element current oscillation, which was described by other authors     

Electromagnetic scattering by two parallel dielectric ellipticcylinders

The transverse magnetic (TM) multiple scattering by two parallel homogeneous dielectric elliptic cylinders is investigated. The solution is an exact one and based on the separation of variables technique in conjunction with the addition theorem for Mathieu functions. It is expressed in terms of a system of simultaneous linear equations of infinite order which is then truncated for numerical computations. Representative numerical results with emphasis on the multiple scattering effects on the backscattering echo width are then generated, for some selected parameters, and presented. It is found that the multiple interactions between the two cylinders affect the echo width significantly     

Finite phased array of microstrip patch antennas: the infinitearray approach

An efficient method of analysis of large infinite arrays based on a convolution technique that allows one to obtain the finite array characteristics from the infinite array results is presented. The edge effects are taken into account by convoluting the infinite array results with the proper current amplitude window on the array. The method is based on the use of Poisson's sum formula in the case of finite arrays applied here to microstrip antennas. It is an approximate technique that can be assimilated into a perturbation method     

Frequency- and time-domain Green's functions for a phasedsemi-infinite periodic line array of dipoles

We extend a previous prototype study of Felsen and Capolino (see ibid. vol.48, p.921-931, June 2000) of frequency-domain (FD) and time-domain (TD) Green's functions for an infinite periodic phased line array of dipoles to account for the effects of truncation, as modeled by a semi-infinite array. These canonical problems are to be used eventually for the systematic analysis and synthesis of actual rectangular TD plane phased arrays. In the presentation, we rely on the analytic results and phenomenologies pertaining to the infinite array, which are reviewed. Major emphasis is then placed on the modifications introduced by the truncation. Finite Poisson summation is used to convert the individual dipole radiations into collective truncated wavefields, the FD and TD Floquet waves (FW). In the TD, exact closed-form solutions are obtained, and are examined asymptotically to extract FD and TD periodicity-matched conical truncated FW fields (both propagating and nonpropagating), corresponding tip-diffracted periodicity-matched spherical waves, and uniform transition functions connecting both across the FD and TD-FW truncation boundaries. These new effects can again be incorporated in a FW-modulated geometrical theory of diffraction. A numerical example of radiation from a finite phased TD dipole array with band-limited excitation demonstrates the accuracy and efficiency of the FW-(diffracted field) asymptotic algorithm when compared with an element-by-element summation reference solution     

Fringe integral equation method for a truncated grounded dielectricslab

The problem of scattering by a semi-infinite grounded dielectric slab illuminated by an arbitrary incident TM_z polarized electric field is studied by solving a new set of “fringe” integral equations (F-IEs), whose functional unknowns are physically associated to the wave diffraction processes occurring at the truncation. The F-IEs are obtained by subtracting from the surface/surface integral equations pertinent to the truncated slab, an auxiliary set of equations obtained for the canonical problem of an infinite grounded slab illuminated by the same source. The F-IEs are solved by the method of moments by using a set of subdomain basis functions close to the truncation and semi-infinite domain basis functions far from it. These latter functions are properly shaped to reproduce the asymptotic behavior of the diffracted waves, which is obtained by physical inspection. The present solution is applied to the case of an electric line source located at the air-dielectric interface of the slab. Numerical results are compared with those calculated by a physical optics approach and by an alternative solution, in which the integral equation is constructed from the field continuity through an aperture orthogonal to the slab. The applications of the solution to an array of line currents are also presented and discussed     

Impedance boundary conditions for finite planar and curved frequency selective surfaces

We consider the time-harmonic electromagnetic scattering problem from a finite planar or curved, infinitesimally thin, frequency selective surface (FSS), the periodic unit cells of which are constituted, exclusively, by electric conductors and free-space. In order to avoid the meshing of these cells, the problem is solved by employing an integral equation formulation in conjunction with approximate impedance boundary conditions (IBC) prescribed on the sheet that models the FSS. The impedance in the IBC is derived from the exact reflection coefficient calculated, for the fundamental Floquet mode, on the infinite planar FSS illuminated by a plane-wave at a given incidence. When the FSS is curved, and/or the direction of the incident wave is unknown, higher order IBCs are proposed that are valid in a large angular range and can be implemented in a standard method of moments formulation. Also, a simple technique is presented that allows to reproduce the radiating Floquet modes in the scattered field even though those are not accounted for in these IBCs. Their numerical efficiencies are evaluated for a curved strip grating translationally invariant along one direction. Finally, we present an alternative approach where the impedance is approximated by its truncated Fourier series, that considerably enhances the accuracy of the results at the cost, however, of a denser mesh of the sheet.     

The design of large waveguide arrays of shunt slots

It is shown that the method of moments (MM) solution can determine the active admittance of each slot in a finite array and that the infinite array model is quite accurate for the design of large waveguide arrays of shunt slots. Active admittances computed by an infinite array model agree favorably with that of slots in sufficiently large finite arrays. Measured results verify the MM solution, thereby validating the infinite array model accuracy     

Electromagnetic scattering from an arbitrary, inhomogeneous 2-Dobject-a finite and infinite element solution

The application of finite elements to the open region associated with scattering problems necessarily requires the truncation of the solution region. This work investigates the use of infinite elements to extend the solution region beyond that of the finite elements which can be truncated by a noncircular boundary. A finite/infinite element formulated is developed in two dimensions and tested on dielectric, magnetic, and conducting scatterers with known analytic solutions     

Analysis of electromagnetic scattering from linear periodic arraysof perfectly conducting bodies using a cylindrical-current model

A novel solution is presented for the problem of three-dimensional scattering of a time-harmonic plane wave from a infinite periodic linear array of finite-size perfectly conducting bodies. A set of fictitious sources comprising periodic and properly modulated cylindrical electric current sheets of cross polarization is used to simulate the scattered field. The complex amplitudes of these fictitious sources are adjusted to render the tangential component of the electric field zero at a selected set of points on the surface of one of the scatterers. The suggested solution procedure is simple to implement and is applicable to linear periodic arrays composed of disjoint bodies of smooth, but otherwise arbitrary, shape. The accuracy of the method is demonstrated. It is shown that in the limiting case of widely spaced spherical scatterers the numerical solution agrees well with an approximate analytic solution     

Scattering Coefficients for Wall Impedance Changes in Waveguides

The Wiener-Hopf tectilque is used to obtain an exact solution to a two-dimensional scattering problem. In the problem solved, an incident TE/sub 10/ mode, traveling from z= -/spl infin/ in the positive z direction, is confined by infinite bounding planes; these planes have infinite conductivity for z<0 and an impedance Z/sub 1/, for z>0. The scattering from the junction at z=0 gives rise to reflection and transmission coefficients that are exactly determined. An approximate solution for the reflection coefficients is also given when the TE/sub 10/ mode is incident from the opposite direction. Finally, a table is presented which lists some transmission and reflection coefficients for rectangular and circular waveguides with discontinuities in the wall impedances.     

Scattering by an infinite array of multiple parallel strips

The transverse electric (TE) and transverse magnetic (TM) electromagnetic scattering solutions for an infinite array of multiple parallel strips are considered. The solution is found using the perturbational form of the modified residue calculus technique (MRCT). In particular, the solution is found from the canonical problem of an infinite periodic array of semi-infinite parallel plates. Numerical results are presented and discussed. In addition, numerical results are given for a polarizer application.     

用特征散射方向图预估电大平面阵的散射

利用平面照射波在无限大周期阵列上感应电流的周期特性，对无限阵列格林函数加窗的方法得到了有限阵列的格林函数，从而将电大有限阵列的分析缩减到单个的阵元上。进而由矩量法得到单个阵元上的电流分布和散射场，并定义为单元的特征散射方向图。仿照阵列综合理论，整个阵列的散射归结为特征散射方向图和阵因子的乘积，极大的简化了电大有限阵列的散射分析，并通过算例验证了该方法的有效性。     

On the application of numerical methods to Hallen's equation

The so-called Hallen integral equation for the current on a finite linear antenna center-driven by a delta-function generator takes two forms depending on the choice of kernel. The two kernels are usually referred to as the exact and the approximate or reduced kernel. With the approximate kernel, the integral equation has no solution. Nevertheless, the same numerical method is often applied to both forms of the integral equation. In this paper, the behavior of the numerical solutions thus obtained is investigated, and the similarities and differences between the two numerical solutions are discussed. The numerical method is Galerkin's method with pulse functions. We first apply this method to the two corresponding forms of the integral equation for the current on a linear antenna of infinite length. In this case, the method yields an infinite Toeplitz system of algebraic equations in which the width of the pulse basis functions enters as a parameter. The infinite system is solved exactly for nonzero pulse width; the exact solution is then developed asymptotically for the case where the pulse width is small. When the asymptotic expressions for the case of the infinite antenna are used as a guide for the behavior of the solutions of the finite antenna, the latter problem is greatly facilitated. For the approximate kernel, the main results of this paper carry over to a certain numerical method applied to the corresponding equation of the Pocklington type