多层各向异性等离子体球电磁散射的解析解

给出s层各向异性等离子体球电磁场球矢量波函数解析表达式,应用电磁场在(s-1)层球壳边界上切向电磁场连续以及辐射条件,导出了平面波入射情况下,s层等离子体球电磁场的展开系数。将数值计算结果分别与矩量法-共扼梯度-傅里叶变换(MOM-CG-FFT)计算结果和均匀等离子体球的结果进行了比较,符合得较好。该文研究结果预期可应用于新型天线的研制和卫星通信等领域。     

Electromagnetic scattering by an inhomogeneous plasma anisotropic sphere of multilayers

Electromagnetic scattering by an inhomogeneous plasma anisotropic sphere is formulated and obtained, where the inhomogeneous plasma anisotropic sphere is divided into (s-1) homogeneous anisotropic spherical layers. The electromagnetic fields in the inner spherical multilayers and outer free space of the inhomogeneous plasma anisotropic spherical structure can be expanded in terms of the spherical vector wave functions in plasma anisotropic medium and in isotropic medium, respectively. By applying the continuous boundary conditions of electromagnetic fields on the spherical interfaces of the (s-1)-layered homogeneous anisotropic plasma medium, the unknown expansion coefficients of fields in the multilayered plasma spherical structure are obtained, and then the electromagnetic field distributions are calculated. Numerical results for the very general inhomogeneous plasma dielectric material sphere are given and the data in a special case are obtained using the present method and the method of moments accelerated with the conjugate-gradient fast-Fourier-transform approach and compared to each other to verify the correctness and applicability of the present analysis.     

导体球涂覆各向异性铁氧体介质电磁散射的解析解

该文用球矢量波函数对各向异性铁氧体介质涂覆导体球的电磁散射解析解开展研究。各向异性铁氧体介质中电磁场的球矢量波函数解可表示成第一、二、三、四类球矢量波函数之和。根据球Bessel函数的性质,可以得出导体球涂覆各向异性铁氧体介质的球矢量波函数解析解。应用铁氧体与自由空间分界面上电磁场切向连续和在导体球面上切向电场等于零的边界条件以及球矢量波函数切向正交性质,可分别得出铁氧体介质中电磁场和散射场的展开系数。给出了平面波入射情况下的数值计算结果。该文的结果可应用于有关微波器件、天线以及目标特征的分析和计算。     

手征涂覆球对高斯波束的散射

在广义米理论的基础上,通过把入射高斯波束、散射场和内部场用适当的球矢量波函数展开,给出了一种求解手征涂覆球对高斯波束散射的解析方法。待定的展开系数可由从边界条件得到的线性方程组求出。对于波束的区域近似模型,给出了微分散射截面的数值结果。结果表明：与介质涂覆的情况相比,手征涂覆对微分散射截面和散色场的极化特性都产生了较大的影响。     

离轴球形粒子对高斯波束的散射

本文根据广义米氏理论，将入射高斯波束用矢量球谐函数展开，研究离轴球形粒子的电磁（光）散射。获得波束因子／ｇ表达式和它的局域近似结果，以及散射系数ａｎ和ｂｎ的计算公式。讨论了波束宽度和粒子离轴位置对散射系数、消光系数、散射强度角分布，以及对粒子的内场和表面场分布的影响     

A diagonalized multilevel fast multipole method with spherical harmonics expansion of the k-space Integrals

Diagonalization of the fast multipole method (FMM) for the Helmholtz equation is usually achieved by expanding the multipole representation in propagating plane waves. The resulting k-space integral over the Ewald sphere is numerically evaluated. Storing the k-space quadrature samples of the method of moments (MoM) basis functions constitutes a large portion of the overall memory requirements of the resulting algorithm for solving the integral equations of scattering and radiation problems. In this paper, it is proposed to expand the k-space representation of the basis functions by spherical harmonics in order to reduce the sampling redundancy introduced by numerical quadrature rules. Aggregations, plane wave translations, and disaggregations in the realized multilevel fast multipole method (MLFMM) are carried out using the k-space samples of a numerical quadrature rule. However, the incoming plane waves on the finest MLFMM level are expanded in spherical harmonics again. Thus, due to the orthonormality of spherical harmonics, the testing integrals for the individual testing functions are simplified into series over products of spherical harmonics expansion coefficients. Overall, the resulting MLFMM can save a considerable amount of memory without compromising accuracy and numerical speed.     

Electromagnetic dyadic Green's function in cylindricallymultilayered media

A spectral-domain dyadic Green's function for electromagnetic fields in cylindrically multilayered media with circular cross section is derived in terms of matrices of the cylindrical vector wave functions. Some useful concepts, such as the effective plane wave reflection and transmission coefficients, are extended in the present spectral domain eigenfunction expansion. The coupling coefficient matrices of the scattering dyadic Green's functions are given by applying the principle of scattering superposition. The general solution has been applied to the case of axial symmetry (n=0, n is eigenvalue parameter in φ direction) where the scattering coefficients are decoupled between TM and TE waves. Two specific geometries, i.e., two- and three-layered media that are frequently employed to model the practical problems are considered in detail, and the coupling coefficient matrices of their dyadic Green's functions are given, respectively     

Scattering from a chirally coated DB elliptic cylinder

An exact analytic solution to the problem of scattering of a plane electromagnetic wave from a chirally coated elliptic cylinder defined by a DB boundary has been obtained, by expanding the different electromagnetic fields associated with the problem in terms of suitable elliptic vector wave functions and a set of expansion coefficients. The incident field expansion coefficients are known, but the expansion coefficients associated with the fields scattered outside the coated cylinder and the fields transmitted inside the coating are unknown. These unknown coefficients are obtained by imposing appropriate boundary conditions at the two boundaries. Results have been presented as normalized bistatic and backscattering widths for a variety of admittances, permeabilities, and permittivities of the chiral materials used for the coating, to show their effects on scattering from the chirally coated cylinder.     

Analysis of energy coupling into spheroidal ferritic implants forhyperthermia applications

The coupling of energy of RF power into lossy tissues using a needle-shaped ferromagnetic implant excited by an externally applied current loop is analyzed theoretically. The ferritic implant is assumed to be of prolate spheroidal shape, while the tissue medium is modeled as a lossy sphere. The electromagnetic fields inside the ferritic implant, the surrounding lossy tissue, and the free space are appropriately expressed in terms of spherical and spheroidal wave functions. Application of the boundary conditions results in an infinite system of equations for the unknown field expansion coefficients. This system is truncated and solved and the electromagnetic field is computed numerically. Absorbed power density inside the implant and the surrounding medium is computed, and the efficiency of the method in producing in-depth energy deposition is examined     

在轴零阶贝塞尔波束对手征介质球的散射特性分析

贝塞尔波束自产生以来,凭借其无衍射、自修复特性已经获得了越来越多学者的关注。基于广义洛伦兹米理论, 将在轴贝塞尔波束与手征介质球相互作用的入射场及散射场展开为球矢量波函数的表达式。结合球矢量波函数的正交完备性及电磁场的连续性边界条件,推导出了在轴零阶贝塞尔波束对手征介质球电磁散射的解析解。数值模拟了散射强度随散射角的分布,将在轴贝塞尔波束退化为平面波照射手征介质球的散射结果与文献比较,吻合得较好。分析了波束及介质球参数、介质球偏离波束中心位置对散射强度的影响。该理论为手征材料和手征涂覆目标在微波工程及目标隐身中的应用提供了很好的理论应用价值。     

Electromagnetic wave scattering by a system of two spheroids ofarbitrary orientation

An exact solution to the problem of the scattering of a plane electromagnetic wave by two perfectly conducting arbitrarily oriented prolate spheroids is obtained by expanding the incident and scattered electric fields in terms of an appropriate set of vector spheroidal eigenfunctions. The incident wave is considered to be a monochromatic, uniform plane electromagnetic wave of arbitrary polarization and angle of incidence. To impose the boundary conditions, the field scattered by one spheroid is expressed in terms of its spheroidal coordinates, using rotational-translational addition theorems for vector spheroidal wave functions. The column matrix of the scattered field expansion coefficients is equal to the product of a square matrix which is independent of the direction and polarization of the incident wave, and the column matrix of the known incident-field expansion coefficients. The unknown scattered-field expansion coefficients are obtained by solving the associated set of simultaneous linear equations. Numerical results for the bistatic and backscattering cross sections for prolate spheroids with various axial ratios and orientations are presented     

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.     

Scattering by a conducting spheroidal object with dielectriccoating at axial incidence

An analytic solution of a plane electromagnetic wave scattering by coated prolate spheroidal bodies is obtained, for axial incidence, by expanding the incident and scattered fields in terms of prolate spheroidal vector wave functions. The unknown expansion coefficients are determined by an infinite system of equations derived using appropriate boundary conditions. To solve for the unknown coefficients, the system of equations is truncated by retaining only the first N equations in N unknowns, where N depends on the size of the body and the desired accuracy. Numerical results for the scattering cross section are presented to show the effect of different coatings on the magnitude of the scattered field     

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     

常阻抗地平面上方垂直电偶极源电磁场的精确和有效解

地平面上方偶极源的电磁场可以分解成直达波场、镜像波场和Somm erfeld型积分三部分之和。应用圆柱波函数的球面波展开式和超几何函数理论,常阻抗地平面上方垂直电偶极源电磁场中的Somm erfeld型积分被表达成圆柱波函数(表面波模)与快速、绝对收敛的球面波函数集展开式之和;其级数展开式的系数是以表面阻抗为宗量的勒让德函数。该展开式数学物理意义明显,并且便于计算,它是此类Somm erfeld半空间问题的精确、有效解答。     

Diffraction of guided waves by the end face of a dielectric slab waveguide terminated with a finite conductive strip

The diffraction of guided waves by the end face of a dielectric slab waveguide short circuited with a finite conductive strip is analyzed. An integral equation technique is employed to formulate the corresponding boundary problem. The unknown term in this integral equations is the electric field E(x) on the terminal plane of the waveguide. The homogeneous term is determined from the incident guided wave. A method of moments technique is employed to compute approximately the electric field E(x) by using Laguerre functions as describing and testing functions. The reflection coefficients of the guided waves are computed by using the approximate expression of the E(x) field. Numerical results are given for several guide and conductor plate dimensions.     

介质覆盖导电球上缝隙天线的辐射

给出了用位函数方法推导介质覆盖导电球上缝隙天线辐射场严格解的过程.基于球Hankel函数加法定理,将基本磁流源激励的场展开为以球心为原点的球面波的叠加.利用球矢量波函数的定义及性质,提取出场的径向分量,将初级场分解为相对于径向的TE波和TM波,避免了复杂的矢量微分运算.在此基础上依据散射叠加原理,构造出各区域中场的一般表示形式,其中待定系数直接由球面分层介质中波的反射和透射规律给出.作为实际应用的例子,给出了介质覆盖导电球上均匀环缝问题的计算结果,并对结果进行了分析.     

Scattering from a sphere of small radius embedded into a dielectricone

In this paper, the scattering of a plane electromagnetic wave from a metallic or dielectric sphere of electrically small radius, embedded into a dielectric one, is considered. The classical method of separation of variables is used, combined with translational addition theorems for spherical vector wave functions. Analytical expressions are obtained for the scattered field and the various scattering cross-sections, in the case of an inner sphere with electrically small radius. Numerical results are given for various values of the parameters and for metallic and dielectric inner sphere. Some remarks are made about the possibility of detection or identification of inhomogeneities or nonsymmetries     

计算索末菲尔德型积分的新方法——球面波级数展开法

利用广义阻抗边界条件模拟和简化地球表面对电磁场的影响。应用圆柱波函数的球面波展开表达式,地平面上方水平电偶极子电磁场中的索末菲尔德型积分可表达成快速、绝对收敛的球面波展开式,利用积分路径的变换和超几何函数理论,展开式中的展开系数可表达成以大地表面复阻抗为宗量的第二类勒让德函数。该展开式数学物理意义明显,并且十分便于数值计算,该文给出的方法是求解下索末菲尔德半空间问题的精确、有效解析方法。     

Radiation pattern computation of a spherical lens using Mie series

The radiation pattern of a sphericai layered dielectric lens is computed using eigenfunction expansions. The method is an adaptation of the well-known classical solution for plane wave scattering from a layered sphere but uses the less well-known vector addition theorem for spherical wave functions to represent the off-center sources. The usefulness of this formulation is that the solution is analytical and "exact," and is an efficient tool for investigating spherical lens radiation properties. The method is illustrated for a typical Luneburg lens.