Showing papers in "Electromagnetics in 1985"

Homogenization Techniques as Applied in the Electromagnetic Theory of Gratings

Abstract: Homogenization theory deals with asymptotic methods in periodic structures. In this paper we apply these methods to the study of a dielectric or conducting grating when the spacing of the grating, supposed to be periodic with respect to x, tends to zero. We prove, from a mathematical point of view, that it is in effect possible to replace the groove region by a stratified layer whose optical index is x-independant. Our results, obtained in a rigorous way, confirm and strengthen those foreseen by colleagues of the University of Sydney.

Error Minimization and Covergence in Numerical Methods

Abstract: Operators that occur in the solution to boundary value problems in electromagnetic theory are reviewed in Hilbert space. Various types of convergence are discussed. The Method of Moments is reviewed and the special cases of Galerkin's Method, the Raleigh-Ritz Method, and the Method of Least Squares are included. Error minimisation and convergence in the various cases are emphasised. A classic electromagnetic example is discussed and operator characteristics in the quasistatic limit are noted.

Iterative Schemes Based on the Minimization of the Error in Field Problems

Abstract: The computation of electromagnetic fields In complex structures Is discussed. To handle the functional equation (e.g. integral equation) that results computationally from the analysis and at the same time have a measure for the accuracy attained, we introduce the global (i.e. Integrated over the domain of structure) root-mean-square error in the equality sign of the functional equation that has to be satisfied by the exact solution. This error criterion also enables us to develop an Iterative technique to solve the problem. In It, variational techniques are employed that enforce a monotonic decrease of the error in each iteration, and thus lead to an iterative improvement of the solution of the problem. Starting with an arbitrary Initial guess and a set of arbitrarily chosen varlational functions, some iteration schemes are derived. Suitable choices for the varlational functions are discussed. Some numerical results pertaining to a number of representative field problems illustrate the rate of co...

Application of the Fast Fourier Transform and the Conjugate Gradient Method for Efficient Solution of Electromagnetic Scattering from Both Electrically Large and Small Conducting Bodies

Abstract: This paper presents a combination of the conjugate gradient method with the fast Fourier Transform technique. With this combination, the computational time required to solve large scatterer problems is much less than the time required by the ordinary conjugage gradient method and the method of moments. Also, the advantages of the conjugate gradient method over the conventional matrix methods is also outlined. In this novel approach, since the spatial derivatives are replaced by simple multiplications in the transformed domain, some of the computational difficulties present in the ordinary conjugate gradient method and the method of moments do not exist here. Therefore, both electrically large and small structures can be handled easily. Finally, since the method is iterative, it is possible to know with what accuracy is the problem solved. Computational results are presented for electromagnetic scattering from square plates (very large and small). Also, the method of conjugate gradient can be appl...

Scattering from Passive Arrays in Plane Stratified Regions

Abstract: A spectral formulation of the scattering problem relative to planar passive arrays in a stratified medium is presented. The solution is obtained in terms of generalized scattering matrix by means of the Galerkin version of the Moment Method technique. Further, an original approach to solve the multiple grid problem which allows to treat efficiently also cases of closely spaced arrays is presented. Comparisons with experimental results relative to crossed dipole arrays are presented.

Iterative Approaches to the Solution of Electromagnetic Boundary Value Problems

Abstract: The objective of this paper is to present the development of the conjugate gradient method (CGM). and other related iterative techniques, by viewing the iterative problem as that of reducing the norm of the error in the satisfaction of the boundary conditions in a systematic manner. It is demonstrated that the choice of the direction vectors, as dictated by CGM. is not optimal and that alternate choices for these vectors, that have the potential of accelerating the convergence over that achieved by the CGM technique, are theoretically possible. It is also shown that the approximate inverse of the operator, which can be constructed by using the spectral iterative technique, can some-times be employed with advantage, to generate these direction vectors. The important problem of multiple incident fields is addressed and the difficulties associated with the CGM method for multiple right-hand side problem is linked lo the machine round-off errors that are responsible for the loss of orthogonality gene...

A Unified Formulation for the Analysis of General Frequency Selective Surfaces

Abstract: In this paper we solve the problem of the scattering of an arbitrary field from a general Frequency Selective Surface (FSS). The keypoint of our approach is a functional equation in the spectral domain, which is solved numerically by the Calrkin Method of Moments. Two approaches are possible, according to whether one assumes as unknown the induced current on the metalilc patches or the, electric field in the complcnentpry aperatures. The former Is convenient when the patches have a simple shape (e.g. strips, rings,discs), the latter in the case of a perforatec screen (e.g. round or rectangular apertures). The formulation Is then extended to treat the case where the patches are not metallic, but constituted by an anysotropic imoodance surfacf. The computer program AHPA is based on this formulation and car. perform a spectral charecterization of multiple grid FSS, with metallic patches described as a collection of scrips. Sample results relative to tripoles and square loops are presented and discussed.

Scattering from General Periodic Screens

Abstract: This paper is intended as a short review of techniques for the analysis of planar periodic structures. Emphasis is directed toward the study of arbitrary surface geometries and the development of a framework suitable for combining surfaces with dielectric layers in the design of a screen. An outline of several essential properties of periodic surfaces is initially presented. A more detailed presentation of a technique with an iterative solution is then given with results directed toward structures with loss both in metal and dielectric.

A Note on the Integral Equations for the Scattering of a Plane Wave by an Electromagnetically Permeable Body

Abstract: The integral equations governing the scattering of a plane wave by an electrically and magnetically permeable obdy are investigated by two alternative methods. In the first method, the homogeneous wave equations for Ē are integrated with the aid of the free-space dyadic Green's function that yields directly an integral equation for Ē. In the second method the equivalent polarized currents are introduced as previously done by Harrington that yields two coupled integral equations for Ē and . By eliminating between these two equations one obtains the same integral equation for Ē as derived by the first method.

Scattering Analysis of Dichroic Subreflectors

Abstract: This paper presents an efficient technique developed to analyse dual reflector antenna systems operating with double curved dichroic subreflectors. The analysis is based on the Physical Optics integration of proper equivalent currents computed on the subreflector surface. The possibility of determining the optimum position of the dichroic subreflector in the antenna system, taking conveniently into account its finite thickness, is also discussed and evidenced through a meaningful example of design analysis. The same example gives to the reader an idea about the high performance achievable by dichroic antennas.

Iterative Solution of Some Direct and Inverse Problems in Electromagnetics and Acoustics

Abstract: Five radiation and scattering problems in electromagnetics and acoustics are successively investigated to illustrate the interest and drawbacks of iterative solutions with respect to conventional direct ones, if they exist All these solutions are based upon integral formulations of the fields The iterative ones are in general developed from two conjugate-gradient algorithms whose main properties are recalled herein from the viewpoint of linear operator equations in Hilbert space The first two problems concern radiation by rotational thick antennas and by large wire-structures Methods of moments are applied as usual and the linear systems deduced from are directly or iteratively solved; conditioning is confirmed to be the main reason of either choice The next two concern scattering by inhomogeneous cylindrical targets: fluid ones illuminated by a compressional plane-wave in acoustics, and lossy dielectric ones illuminated by a wave whose field is parallel with the target cross-section In elec

Design of Single-Layer Frequency Selective Surfaces for Multiband Reflector Antennas

Abstract: Future communication satellites will require single reflector antennas to operate at three or more frequency bands simultaneously. Frequency-selective surfaces are spatial filters which when incorporated as either flat or curved subreflectors into a reflector antenna allows it to operate at a number of different frequency bands. Multiple-layer frequency selective surfaces are currently being proposed for this application. In this paper two single-layer frequency selective surfaces are presented which offer potentially better crosspolar performance than multiple-layers together with reduced mechanical complexity. The surfaces are based on square loop elements and their transmission responses and crosspolar performances when measured in 45° plane dlplexers are discussed. Peak crosspolar levels of better than 30 dB are obtained. In addition models based on an equivalent circuit analysis are presented for the arrays. The calculated transmission responses are compared with experimental measurements fo...

On Stabilization of the Bandwidth of a Dichroic Surface by Use of Dielectric Slabs

Abstract: Dichroic surfaces, also called Frequency Selectric Surfaces (FSS), are typically made of periodic surfaces of either dipole or slot like elements. In either case, a significant change of bandwidth is generally experienced as a function of Incidence angle and polarization. In this paper it is shown that using dielectric slabs with the surface can greatly reduce this bandwidth variation. The dielectric slabs must have the proper dielectric constant (usually less than 2) and proper thickness (approximately a quarter wavelength, measured In the slab). An example of such a dichroic surface is given. This surface is reflective in the range 27.5 to 30.0 GHz and transparent in the range 17.7 to 20.2 GHz. The surface operates for arbitrary polarization and incidence angles from 0° (normal) to 75°. It is comprised of two dipole like periodic structures sandwiched between three dielectric slabs.

Theoretical and Experimental Scattering by Hyperbolic Loaded Dishes

Abstract: Experiments are presented on electromagnetic scattering by hyperbolic reflectors peripherally loaded by epoxid resin melted to graphite powder, made in the X-bande range in an anechoic electromagnetic room. The results are compared with the theoretical prediction carried out using both the Uniform Theory of Diffraction (UTD) extended to surface impedances and Physical Optics (PO). The effectiveness of the behaviour of a lossy material layer as a surface impedance as well as the effectiveness of such loading technique applied to the subreflector in order to control the radiation diagram, have been verified. The good agreement between experimental and computed data confirms the conclusions obtained theoretically.

The Discrete Convolution Method for Electromagnetic Problems

Abstract: A discrete convolution method for electromagnetic problems is described. It is particularly well-suited to periodic structures such as linear and planar arrays, although some non-periodic structures may also be treated. The method may be applied to any structure for which a Moment Method formulation is available. The matrix equation becomes a discrete convolution equation which is treated by Discrete Fourier Transform methods using Fast Fourier Transform algorithms. An iterative procedure which converges rapidly is utilized. The number of complex multiplication and divisions is equal to kINlogN where N is the number of unknowns or expansion function, I is the number of iterations and k is a factor which depends on the type of problem treated. Typical results are presented for linear and planar arrays. Good agreement is obtained with direct methods such as Gaussian elimination.

An Anisotropic Lens for Launching TEM Waves on a Conducting Circular Conical System

Abstract: A differential impedance and transit-time matching approach is used in the design of an aniostropic lens for launching TEM waves from a small source, through the lens, and onto a conducting circular conical system. This approach leads to a system or ordinary differential equations which may be solved exactly to obtain the lens parameters. An approximate solution, which would be applicable to a design procedure, is also given.