Solution of the problem of electromagnetic wave diffraction by complex dielectric bodies by means of the pattern equation method

An efficient method is proposed for solving the problem of electromagnetic wave diffraction by dielectric bodies of complex shapes. Scattering patterns are decomposed in vector spherical harmonics to reduce the problem to a system of algebraic equations. It is shown that the method exhibits a high convergence rate that depends on the complexity of a scatterer’s boundaries only slightly. Examples of simulation of the characteristics of wave scattering by various complex bodies are considered. The correctness of the obtained data is verified through checking the fulfillment of the optical theorem.     

Use of the pattern equation method for solution of problems of scattering of electromagnetic waves by bodies covered with a dielectric

The pattern equation method is generalized to problems of scattering of electromagnetic waves by 3D perfectly conducting bodies covered with a dielectric. The method is implemented in an algorithm for bodies of a rather arbitrary shape. In the case of a sphere, explicit analytic expressions for the coefficients involved in the scattering pattern are obtained from the general system of equations for these coefficients. The expressions obtained coincide with the corresponding formulas in the theory of Mie series. Scattering patterns are calculated for various bodies of revolution. The calculation results for bodies with a coating are compared to similar characteristics obtained via simulation of a dielectric coating with the suitable impedance.     

阻抗球涂覆均匀等离子体电磁散射的解析解

均匀无源各向异性等离子体介质中的电磁场是第一、第二类各向异性等离子体球矢量波函数的线性叠加,在阻抗球表面满足阻抗边界条件、等离子体与自由空间表面满足电磁场切向连续的边界条件,可得出各向异性等离子体涂覆阻抗球在平面波入射情况下,均匀等离子体介质中电磁场用各向异性等离子体球矢量波函数表示的系数满足的矩阵方程,进而得出散射场由球矢量波函数展开的展开系数和雷达散射截面.数值计算的结果表明:当阻抗球的半径趋于0时,其结果和均匀各向异性等离子体球对平面波的电磁散射结果相同.最后还给出了一些数值计算的结果.     

Singular points and singular lines in problems of diffraction by bodies with an anisotropic impedance

The effect (earlier discovered) of penetration of an electromagnetic-field power flux into a wall exhibiting perfect mixed anisotropic conductivity is considered in more detail. It is shown that the power transmitted into the screen through the nodes of conductivity lines and through resonance-length closed contours can be regarded as the limit value of the power absorbed in a wall characterized by an anisotropic impedance when the absorbing impedance approaches the values corresponding to the case of perfect mixed conductivity.     

Analysis of electromagnetic scattering from an anisotropic cylinderusing the FD-MEI method

The electromagnetic scattering from an anisotropic cylinder is analysed using the FD-MEI method. Some numerical results, which are in good agreement with the exact solutions when available, are given     

Solution to the problem of scattering of electromagnetic waves by layered inhomogeneous bodies

The pattern-equation method is generalized for solution of the problem of scattering by layered inhomogeneous bodies. The algorithm of the method and calculated scattering patterns for bodies of various geometries are presented. The convergence rate of the numerical algorithm is demonstrated for bodies of various dimensions, and the method is compared to other numerical techniques of solution of the considered problem.     

VIRTUAL-RAY METHOD AND ITS APPLICATION IN THE PLANE WAVE SCATTERING BY AN IMPEDANCE WEDGE

The virtual-ray method for treating HF electromagnetic scattering problems is derived from the plane wave of free space, and using this the plane wave scattering by an impedance wedge is studied. In the solution process a novel concept of generalized circle is introduced so that the complete amplitude function is obtained. And a reasonable physical interpretation for the term W2, which was neglected previously, is given. The calculated results agree well with those of the analytical solution obtained by G.D. Maliuzhinets(1958).     

Diffraction of a plane skew electromagnetic wave by a wedge with general anisotropic impedance boundary conditions

The three dimensional problem of diffraction of a skew incident plane wave by a wedge with anisotropic impedance boundary conditions is explicitly solved by the probabilistic random walk method. The problem is formulated in terms of two certain components of the electric and magnetic fields which satisfy independent Helmholtz equations but are coupled through the first-order boundary conditions. The solution is represented as a superposition of the geometric waves that are completely determined by elementary methods and of the waves diffracted by the apex of the wedge. The diffracted field is explicitly represented as the mathematical expectation computed over the trajectories of a two-state random motion which runs in a complex space and switches states under the control of stochastic equations determined by the problem's geometry and by the boundary conditions.     

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     

Calculation of electromagnetic waves scattering by non-homogeneous surface impedance using moment method

In this paper, using the method of moments to calculate the current density and mono-static and bi-static radar cross section of an unlimited strip by a non-homogeneous impedance. Here, incident wave is a plane wave. To authenticate the method, using the iterative method to solve the integral equations is engaged. Simulation results show that the surface with non-homogeneous impedance has reduced or increase in potential for bi- and mono-static radar cross section in certain azimuth.     

Integral equation based analysis of scattering from 3-D inhomogeneous anisotropic bodies

This paper presents an integral equation based scheme to analyze scattering from inhomogeneous bodies with anisotropic electromagnetic properties. Both the permittivity and permeability are assumed to be generalized tensors. Requisite integral equations are derived using volume equivalence theorem with the electric and magnetic flux densities being the unknown quantities. Matrix equations are derived by discretizing these unknowns using three dimensional Rao-Wilton-Glisson basis functions. Reduction of the integral equation to a corresponding matrix equation is considerably more involved due to the presence of anisotropy and the use of vector basis function; methods for evaluation of the integrals involved in the construction of this matrix is elucidated in detail. The method of moments technique is augmented with the fast multipole method and a compression scheme. The latter two enable large scale analysis. Finally, several numerical results are presented and compared against analytical solutions to validate the proposed scheme. An appendix provides analytical derivations for the formulae that are used to validate numerical method, and the necessary formulae that extends the approach presented herein to the analysis of scattering bianisotropic bodies.     

High-frequency scattering by an isorefractive wedge with theparabolic equation method

The parabolic equation (PE) method is applied to the problem of the high-frequency scattering from a diaphanous wedge, that is, a wedge made of a material which is isorefractive with respect to the surrounding medium, illuminated by a plane wave or by a line current parallel to the edge. The proposed approach is able to handle any wedge aperture and incidence angle and presents some novelties that allows overcoming the problems arising in the numerical solution of the parabolic equation applied to penetrable wedges     

Solution of combined-field integral equation using multilevel fastmultipole algorithm for scattering by homogeneous bodies

We present an accurate method of moments (MoM) solution of the combined field integral equation (CFIE) using the multilevel fast multipole algorithm (MLFMA) for scattering by large, three-dimensional (3-D), arbitrarily shaped, homogeneous objects. We first investigate several different MoM formulations of the CFIE and propose a new formulation, which is both accurate and free of interior resonances. We then employ the MLFMA to significantly reduce the memory requirement and computational complexity of the MoM solution. Numerical results are presented to demonstrate the accuracy and capability of the proposed method. The method can be extended in a straightforward manner to scatterers composed of different homogeneous dielectric and conducting objects     

A recursive single-source surface integral equation analysis for wave scattering by heterogeneous dielectric bodies

The problem of electromagnetic wave scattering by heterogeneous dielectric bodies is formulated in a recursive manner by organizing their homogeneous subregions into hierarchical multiply-nested structures. The inner details of each multiply-nested body are completely accounted for by an equivalent surface representation that yields the electric and magnetic fields tangent to the body only in terms of a single unknown electric surface current density distributed on its outer surface. In this manner, the problem of wave scattering by heterogeneous dielectric bodies is reduced to a scattering problem over their outermost surfaces in terms of only a single unknown current density. For a large number N of different homogeneous dielectric subregions within such a heterogeneous body, the proposed method has a computational complexity of O(N/sup 1.5/) and storage requirements that increase in proportion to O(N). Furthermore, the equivalent surface representation derived for a particular subregion is invariant under rotation and translation and may, therefore, be applied to identical subregions without repeating the computation. The fields at any interior points are calculated by a fast backward recursion.     

Diffraction of electromagnetic plane wave by an infinite slit in a screen with surface impedance

Diffraction of an electromagnetic plane wave by an infinite slit in a screen with surface impedance is solved analytically as a boundary value problem under the assumption that the plane of incidence is normal to the slit in a screen of zero thickness surrounded by a homogeneous medium. The field expressions and the transmission coefficient are derived asymptotically, and their numerical solutions are presented for a special case of perfect conducting screen.     

Combining an extrapolation technique with the method of moments forsolving large scattering problems involving bodies of revolution

The purpose of this work is to combine an extrapolation technique with the method of moments (MoM) to solve scattering problems involving large bodies. It has been shown in a previous work that the current induced on the smooth parts of large scatterers may be represented as a series of complex exponential functions with a few terms. Based on this concept, a hybrid set of basis functions is constructed using entire domain functions of complex exponential type on the smooth portion of the scatterer, complemented by subdomain basis functions near edges and discontinuities. An extrapolation procedure is developed in which the scattering problem is first solved for a portion of the scatterer using the conventional MoM. Next, a set of entire-domain basis functions, whose behaviour could be extrapolated with an increase in the size of the scatterer, is extracted from this original solution. The procedure outlined has the very desirable feature that the total number of basis functions remains unchanged even as the scatterer size is increased, allowing for large scatterers to be handled with a relatively small number of unknowns. The extrapolation technique is applied to scattering problems from bodies of revolution (BORs), and numerical results for an open cylinder and a barrel-shaped BOR are presented     

A tetrahedral modeling method for electromagnetic scattering by arbitrarily shaped inhomogeneous dielectric bodies

A method for calculating the electromagnetic scattering from and internal field distribution of arbitrarily shaped, inhomogeneous, dielectric bodies is presented. A volume integral equation is formulated and solved by using the method of moments. Tetrahedral volume elements are used to model a scattering body in which the electrical parameters are assumed constant in each tetrahedron. Special basis functions are defined within the tetrahedral volume elements to insure that the normal electric field satisfies the correct jump condition at interfaces between different dielectric media. An approximate Galerkin testing procedure is used, with special care taken to correctly treat the derivatives in the scalar potential term. Calculated internal field distributions and scattering cross sections of dielectric spheres and rods are compared to and found in agreement with other calculations. The accuracy of the fields calculated by using the tetrahedral cell method is found to be comparable to that of cubical cell methods presently used for modeling arbitrarily shaped bodies, while the modeling flexibility is considerably greater.     

Solution of the vector wave equation for general dielectricwaveguides by the Galerkin method

Numerical guided mode solutions for vector waves of general dielectric waveguides are obtained by expanding the unknown field vectors in a double series consisting only of sine functions. The authors formulate solutions by series expansion for the electric and magnetic vector wave equations that yield different matrix equations but identical eigenvalues. The general results are applied to a simple step-index fiber with a large core-cladding index difference and to a fiber core in proximity to a semiinfinite dielectric half space     

求解多尺度目标电磁散射的积分方程快速算法

多层快速卡特森展开算法(Multilevel Accelerated Cartesian Expansion Algorithm, MLACEA)可用于加速电小尺寸结构积分方程矩量法,且矩阵与矢量乘积运算计算复杂度为O（N）量级; MLACEA和多层快速多级子算法(Multilevel Fast Multipole Algorithm, MLFMA)均基于八叉树分组结构,便于实现它们的混合快速算法MLACEA-MLFMA. 该混合算法可大幅度降低模拟含精细结构的电大尺寸目标宽带电磁散射问题的计算复杂度. 还详细阐述了求解电场积分方程的MLACEA算法及其与MLFMA算法的混合快速算法MLACEA-MLFMA算法;并通过计算实例对比分析了MLFMA算法与MLACEA-MLFMA混合算法的计算效率.     

A method of moments solution for electromagnetic scattering by inhomogeneous dielectric bodies of revolution

A method of calculating the electromagnetic scattering from and internal field distribution of inhomogeneous dielectric bodies of revolution (BOR) is presented. The method uses a typical mode-by-mode solution scheme. The electric flux density is chosen as the unknown quantity, which, together with the special construction of basis and testing functions, enables considerable reduction of the number of unknowns. A key element in this technique is expressing of the azimuthal field components of basis functions in terms of transverse components. A Galerkin testing procedure is used, with special attention put on the efficiency of calculating scalar potential term. Results of calculation for a few classes of dielectric bodies are given and compared with calculations done by other authors.