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     

On scattering of waves by the infinite grating of elliptic cylinders

The functional equation derived previously for the scattering by a grating of relatively arbitrary elements is applied to elliptic cylinders. This specifies the problem in terms of an infinite set of linear algebraic equations involving the scattering coefficients of an isolated elliptic cylinder and certain combinations of Schlömilch series. General approximations are obtained by series expansions, and by truncating the sets of equations; we consider both polarizations (EorHparallel to the elements), arbitrary angle of incidence, and arbitrary spacing. Explicit results are given for ellipses that are small compared to the wavelength.     

Electromagnetic scattering by a multilayer elliptic cylinder undertransverse-magnetic illumination: series solution in terms of Mathieufunctions

An exact solution to the electromagnetic scattering by a dielectric multilayer infinite cylinder of elliptic cross section is proposed. The interfaces between different media, which are assumed to be lossless and nonmagnetic, are confocal elliptic cylinders. Starting from the series expansions in terms of Mathieu functions, an efficient recursive procedure for the computation of fields and radar cross sections per unit length under a transverse-magnetic illumination is developed. The mathematical formulation is detailed and some numerical results are provided     

二维各向异性椭圆柱的电磁散射

分析了二维无限长均匀各向异性椭圆柱体的电磁散射特性。基于平面波谱的积分方程以及马丢函数的级数展开式,以横电型(TE)平面波为例,导出了均匀各向异性椭圆柱内场及其单位长度的雷达散射截面(RCS)的表达式。计算了部分数值并讨论了电尺寸、介电材料等影响雷达散射截面的因素。当椭圆柱体退化到各向异性圆柱时,数值与已有文献的结果吻合较好。     

Recursive T-matrix methods for scattering from multiple dielectricand metallic objects

We present an efficient, stable, recursive T-matrix algorithm to calculate the scattered field from a heterogeneous collection of spatially separated objects. The algorithm is based on the use of higher order multipole expansions than those typically employed in recursive T-matrix techniques. The use of these expansions introduces instability in the recursions developed by Chew (1990) and by Wang and Chew (1990), specifically in the case of near-field computations. By modifying the original recursive algorithm to avoid these instabilities, we arrive at a flexible and efficient forward solver appropriate for a variety of scattering calculations. The algorithm can be applied when the objects are dielectric, metallic, or a mixture of both. We verify this method for cases where the scatterers are electrically small (fraction of a wavelength) or relatively large (12λ). While developed for near-field calculation, this approach is applicable for far-field problems as well. Finally, we demonstrate that the computational complexity of this approach compares favorably with comparable recursive algorithms     

Solution of electromagnetic scattering problems using time domaintechniques

New method are developed to calculate the electromagnetic diffraction or scattering characteristics of objects of arbitrary material and shape. The methods extend the efforts of previous researchers in the use of finite-difference and pulse response techniques. Examples are given of the scattering from infinite conducting and nonconducting cylinders, open channel, sphere, cone, cone sphere, coated disk, open boxes, and open and closed finite cylinders with axially incident waves     

Effective Solution of 3-D Scattering Problems via Series Expansions: Applicability and a New Hybrid Scheme

Accurate and reliable evaluation of the electromagnetic field scattered by dielectric objects is a canonical problem in the electromagnetic community. In the framework of integral equation formulations, iterative techniques, and in particular conjugate gradient (CG) schemes, are widely used. However, when the number of parameters grows, CG techniques may become too demanding from a computational point of view. In this paper, we show that many forward scattering problems can be conveniently solved by means of very simple series expansions, which allow a lower computational complexity and memory storage with respect to other iterative schemes. In particular, we consider three different series expansions, namely: 1) the traditional Born series; 2) the contrast source-extended Born series, which is recently introduced by rewriting the traditional source-type integral equations; and 3) a new series, which is a hybridization of the previous ones. Theoretical conditions for the applicability of the series expansions are discussed, and practical tools to foresee that a problem can be solved by means of these simple iterative schemes are provided. Numerical examples are reported for the sake of comparison and to assess performance     

On the superresolution identification of observables fromswept-frequency scattering data

A superresolution signal processing algorithm is used for the identification of wavefronts from the fields scattered from several canonical targets. Particular wave objects that are examined are single and multiple edge diffraction, scattering from flat and curved surfaces, cone diffraction, and creeping waves. The scattering data are computed numerically via the method of moments (MoM) and are processed using a modified matrix-pencil algorithm. General properties of superresolution processing of such data-independent of the particular algorithm used-are assessed through an examination of the Cramer-Rao (C-R) bounds for basic scattering scenarios     

手征材料涂覆导体目标电磁散射特性的PO分析

从Maxwell方程出发 ,推导出平面波照射下手征介质涂覆导体目标表面等效电磁流的一般表达式 ,并基于切平面近似 ,给出了计算手征介质涂覆导体目标电磁散射的物理光学 (PO)解。在此基础上 ,计算了T形结构及锥柱结构的散射特性 ,分析了手征材料参数对电磁散射的影响 ,得到了一些有益的结果。为电大尺寸手征介质涂覆导体目标电磁散射特性的快速估计提供了一种有效的手段     

Electromagnetic scattering from finite circular and elliptic cones

A formulation based on the physical theory of diffraction (PTD) is presented for finite conical surfaces with circular and elliptic cross sections. The base-rim discontinuity is represented by equivalent currents, including second-order terms extended for elliptic boundaries. Tip-rim interactions are examined as a function of the tip-rim distance, cone angle, and illumination angle for circular cones; and their implication for elliptic cones is noted. The diffraction contribution from tip-rim interactions is shown to be dependent on the cone angle and the illumination angle but to be relatively insensitive to the tip-rim distance. The Fock Ansatz is used to enlarge the validity of the PTD formulation to cases where nonspecular effects arising from surface curvature and shadow boundaries are significant. The formulation is applied to cones with varying ellipticity for axial and oblique illumination. Correlation is made with published results for circular cones and with experimental data for an elliptic cone.     

Electromagnetic scattering by a conducting strip with a multilayerelliptic dielectric coating

The scattering of an electromagnetic plane wave by a conducting strip coated with a multilayer elliptic dielectric is considered. The solution of this problem is carried out by using an expansion of the electromagnetic field in terms of Mathieus functions and by implementing an efficient procedure for the “treatment” of the boundary conditions. This procedure could be a useful tool for checking the accuracy of numerical techniques widely used in electromagnetic compatibility, as it allows the solution of one of the few canonically solvable scattering problems involving perfectly conducting objects with sharp edges and inhomogeneous dielectrics. Many numerical results concerning the scattering cross section per unit length are provided and, where possible, they are compared with already available results. We consider only perpendicular incidence, although oblique generalization is conceptually easy     

Scattering from a coated perfect electromagnetic conducting elliptic cylinder

An exact analytic solution is presented to the problem of scattering from a coated perfect electromagnetic conducting (PEMC) elliptic cylinder, when it is illuminated by a plane wave as well as a line source. The problem is formulated by expanding the various fields in terms of appropriate angular and radial Mathieu functions and a set of expansion coefficients. The expansion coefficients associated with the incident fields are known, but those associated with the scattered fields and the fields within the coating are unknown. Imposing boundary conditions at the surface of the PEMC elliptic cylinder and the surface of the coating, enables the determination of the unknown expansion coefficients. Results are presented in the form of normalized scattering widths for elliptic cylinders of various sizes, PEMC admittances, and different coatings, to show the effects of these on scattering.     

Extension of on-surface radiation condition theory to scattering bytwo-dimensional homogeneous dielectric objects

A recent analytical formulation by G.A. Kriegsmann et al. (see ibid., vol.AP-35, p.153-61, Feb. 1987) of electromagnetic wave scattering by perfectly conducting two-dimensional objects using the on-surface radiation boundary condition approach is extended to the case of two-dimensional homogeneous convex dielectric objects. It is shown that a substantial simplification in the analysis can be obtained by applying the outgoing radiation boundary condition on the surface of the object. The analysis procedure decouples the fields in the two regions to yield explicitly a differential equation relationship between the external incident field excitation and the corresponding field distribution in the interior of the dielectric object. The interior fields can be obtained by solving the differential equation using either an analytical approach or a suitable numerical method. Two-dimensional scattering examples along with validations are reported, showing the near-surface field distributions for a homogeneous circular dielectric cylinder and an elliptic dielectric cylinder, with with transverse magnetic plane-wave excitation     

椭圆锥带线的严格解

本文研究椭圆锥带线的特性阻抗等基本参数.假定中心导体带是无限薄理想导体,传输的主模是TEM模,通过坐标变换和共形映射,椭圆锥带线变为平面周期性结构,然后用椭圆积分变换处理变换后的有限宽带线问题,得到了椭圆锥带线的严格解.     

Two Limiting Values of the Capacitance of Symmetrical Rectangular Coaxial Strip Transmission Line, Jul. 1981

This paper determines the first two terms in two different expansions for the total capacitance of rectangular coaxial strip transmission line which are of interest in an improved approximation for the characteristic impedance of rectangular coaxial line. For this purpose, expansions which express the total capacitance of the rectangular coaxial strip transmission line exactly and explicitly in terms of it's dimensions are introduced. As a by-product, it is shown how these expansions may be terminated after a few terms to obtain approximations of sufficient accuracy for most purposes. In the Appendix, certain results from the theory of elliptic functions, that are required in this paper but are not presented in the literature on this problem, are reviewed and in some cases extended.     

The physical optics radar cross section of an elliptic cone

The physical optics approximation is used to evaluate the backseattering radar cross section of a semi-infinite metallic elliptic cone. The resulting formula can be directly interpreted as a generalization Of the well-known formula for the baekscattering cross section of a circular cone. In addition the bistatic radar cross section of the elliptic cone is calculated.     

分形粗糙表面涂覆目标太赫兹散射特性

该文采用物理光学法方法研究了具有分形粗糙表面的涂覆目标太赫兹散射特性。基于分形粗糙面建立表面粗糙目标模型,根据菲涅尔反射系数得出表面电流分布进而得到涂覆粗糙目标的雷达散射截面。对比分析了具有粗糙表面和光滑目标的散射结果,详细讨论了不同频率、不同涂层厚度的表面粗糙钝锥目标模型的太赫兹散射特性,计算结果表明在太赫兹波段目标表面的粗糙度对散射有显著的影响。      

Ray Optical Electromagnetic Far-Field Scattering Computations Using Planar Near-Field Scanning Techniques

For accurate scattering computations in the far-field of flat finite objects, field based ray optical methods cannot be used directly, since the finiteness of the objects is not considered in the formulations. In this paper, planar near-field scanning techniques are used to overcome this problem. In particular, scattered ray optical fields are first computed in a scanning plane in the near-field region of the involved objects and are transformed into the far-field afterwards using field expansions in terms of spectrum density functions of outgoing waves. Since evanescent waves are avoided in the scanning plane, sampling rates less than lambda₀/2 can be used for restricted angle range around the normal direction to the scanning plane. Reduced accuracy at grazing directions of observation is overcome by combining solutions provided by several scanning planes. The proposed approach is applied in the postprocessing stage of the recently developed hybrid method combining the uniform geometrical theory of diffraction with the finite element boundary integral technique and with the multilevel fast multipole method.     

A new sectioning procedure for calculating scattering andabsorption by elongated dielectric objects

The iterative extended boundary condition method (IEBCM) has recently been developed to calculate scattering and absorption by elongated dielectric objects. The authors present a new sectioning procedure to improve the computational efficiency of the IEBCM. In this technique, the total geometry of the object is divided into overlapping sections, each of which includes only 3-5 spherical expansions to describe the internal fields. The total number of expansions required to describe the internal fields in the overall object may be as large as 15. Results illustrating the improvement in the computational efficiency of the IEBCM, as well as the dependence of the minimum number of expansions that should be included in each section on the dielectric properties of the scatter and on the frequency, are presented. It is shown that the sectioning procedure is particularly useful at frequencies below (ka<3) and above the resonance frequency of the object (4<ka<7)     

Ramp response radar imagery spectral content

The physical optics (PO) approximation is examined in the time domain to illustrate certain relationships between an area function interpretation of the physical optics scattering estimate and the span of interrogating frequencies required to produce an image of the object. The consequences of extending the normal physical optics integration limit to encompass the entire object are demonstrated using conducting spheres, disks, cone spheres, and hemispherical objects. Low frequency interrogating signals are stressed for imaging purposes with an interpretation of when such signals must be supplemented by higher frequencies.