Modified Spherical Wave Functions With Anisotropy Ratio: Application to the Analysis of Scattering by Multilayered Anisotropic Shells

We describe a novel and rigorous vector eigenfunction expansion of electric-type Green's dyadics for radially multi- layered uniaxial anisotropic media in terms of the modified spherical vector wave functions, which can take into account the effects of anisotropy ratio systematically. In each layer, the material constitutions e and epsiv macrmu macr are tensors and distribution of sources is arbitrary. Both the unbounded and scattering dyadic Green's functions (DGFs) for rotationally uniaxial anisotropic media are derived in spherical coordinates (r, thetas, phi). The coefficients of scattering DGFs, based on the coupling recursive algorithm satisfied by the coefficient matrix, are derived and expressed in a compact form. With these DGFs obtained, the electromagnetic fields in each layer are straightforward once the current source is known. A specific model is proposed for the scattering and absorption characteristics of multilayered uniaxial anisotropic spheres, and some novel performance regarding anisotropy effects is revealed.     

Symbolic derivation and numeric computation of dyadic Green'sfunctions using Mathematica

This paper presents a mathematical-software functional package that is capable of performing symbolic derivation and numeric computation of dyadic Green's functions for certain multilayered structures: a planar stratified multilayered medium, a spherical multilayered medium, a cylindrical multilayered medium, and a conducting rectangular waveguide with a multilayered dielectric load. The algorithms of this software package are based on the eigenfunction-expansion method. Using Mathematica^TM, two packages were written to fulfill the aforementioned objectives. Upon completion of the software development, dyadic Green's functions for three-layered media were generated. A comparison of these outputs with published results showed good agreement. This demonstrated the applicability of the symbolic package. For the numeric package, the Green's dyadics for a particular three-layered spherical isotropic multilayered medium were generated as an illustration. These packages have been successfully implemented, and future derivation of dyadic Green's functions for these media may be performed     

A general expression of dyadic Green's functions in radiallymultilayered chiral media

A general expression of spectral-domain dyadic Green's function (DGF) is presented for defining the electromagnetic radiation fields in spherically arbitrary multilayered and chiral media. Without any loss of the generality, each of the radial multilayers could be the chiral layer with different permittivity, permeability, and chirality admittance, while both distribution and location of current sources are assumed to be arbitrary. The DGF is composed of the unbounded DGF and the scattering DGF, based on the method of scattering superposition. The scattering DGF in each layer is constructed in terms of the modified and normalized spherical vector wave functions. The coefficients of the scattering DGFs are derived and expressed in terms of the equivalent reflection and transmission coefficients, by applying boundary conditions satisfied by the coefficient matrices     

Unbounded and scattered field representations of the Dyadic Green'sfunctions for planar stratified bianisotropic media

This paper presents a rigorous formulation of the spectral-domain dyadic Green's functions for planar stratified bianisotropic media. The media may consist of any number of layers bounded by optional impedance/admittance walls. Both electric and magnetic dyadic Green's functions for arbitrary field and source locations are derived simultaneously. Based on the principle of scattering superposition, these dyadics are decomposed into unbounded and scattered parts. The scattered dyadic Green's functions are determined without cumbersome operations using the concepts of effective reflection and transmission of outward-bounded and inward-bounded waves. The scattering coefficient matrices are expressed in compact and convenient forms involving global reflection and transmission matrices. Corresponding to the impedance/admittance boundary walls, the global reflection matrices are related directly to the wall impedance/admittance dyadics. For illustration, the general expressions of dyadic Green's functions are applied to the configuration of a grounded bianisotropic slab embedded in isotropic halfspace     

球形分层媒质中并矢格林函数的求解 I:并矢格林函数的推导

首先,在球坐标系下,通过德拜位函数得到均匀各向同性介质中矢量波动方程的解。然后,分析了内、外向波的单界面和多层界面的反射和透射,得到了相应的反射系数和透射系数以及广义反射系数和透射系数。接着,推导了啄源在球形分层介质中的不同位置产生的德拜位。最后,根据得到的德拜位,用球坐标系下的矢量波函数表达出场点在不同位置时的电并矢格林函数和磁并矢格林函数。     

Analysis of radiowave propagation in a four-layered anisotropicforest environment

Propagation of electromagnetic waves in forest environments is examined in which both the transmitting and receiving points are located in the trunk layer of a four-layered anisotropic forest model. This propagation model considers the forest as a horizontally stratified, anisotropic media of canopy and trunk, bounded by ground below and air above. The electromagnetic fields are obtained using dyadic Green's functions in their eigenfunction expansion forms for an anisotropic four-layered geometry. Analytical results are found for the fields, which consist primarily of three wave modes: a direct wave, multiply reflected waves, and lateral waves. These field constituents are compared, and their domains of preponderance are calculated; it is found that the lateral wave plays a major role in communication at large distances. Radio losses for typical forest are calculated to illustrate numerical application of the forest model     

Electromagnetic dyadic Green's functions for multilayeredspheroidal structures. I: formulation

Dyadic Green's functions (DGFs) and their scattering coefficients are formulated in this paper for defining the electromagnetic fields in multilayered spheroidal structures. The principle of scattering superposition is applied, in a similar form of the DGF in an unbounded medium under spheroidal coordinates, the scattering DGFs due to multiple spheroidal interfaces are expanded in terms of the spheroidal vector wave functions. For the lack of general orthogonality of the spheroidal radial and angular functions, the Green's dyadics are expressed in a different way where the coordinate unit vectors are also combined in the construction, as compared with the conventional form of vector wave eigenfunction expansion. The matrix equation systems satisfied by the coupled scattering (i.e., reflection and transmission) coefficients of the DGFs are obtained so that these coefficients can be solved uniquely. The DGFs can be employed to investigate effects of spheroidal radomes used to protect the airborne or satellite antenna systems and of handy phone radiation near the spheroid-shaped human head, and so forth. Numerical calculations about the applications of the formulated multilayered DGFs are presented in part II of this paper     

含源多层弱起伏介质中的电磁场

本文在Born近似下提出了求解含源多层随机介质的电磁场的并矢格林函数方法。激发源可以在N层随机介质中的任意一层。在背景介质的任一层均为各向同性慢变分层的假定下,利用W.K.B近似及电型和磁型并矢格林函数,导出了N层介质中任意一层中的平均场和起伏场,并用反射系数、透射系数、阻抗、电导和波数比等物理量表示。     

A numerical formulation of dyadic Green's functions for planarbianisotropic media with application to printed transmission lines

An integral equation (IE) method with numerical solution is presented to determine the complete Green's dyadic for planar bianisotropic media. This method follows directly from the linearity of Maxwell's equations upon applying the volume equivalence principle for general linear media. The Green's function components are determined by the solution of two coupled one-dimensional IE's, with the regular part determined numerically and the depolarizing dyad contribution determined analytically. This method is appropriate for generating Green's functions for the computation of guided-wave propagation characteristics of conducting transmission lines and dielectric waveguides. The formulation is relatively simple, with the kernels of the IE's to be solved involving only linear combinations of Green's functions for an isotropic half-space. This method is verified by examining various results for microstrip transmission lines with electrically and magnetically anisotropic substrates, nonreciprocal ferrite superstrates, and chiral substrates. New results are presented for microstrip embedded in chiroferrite media     

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     

分层介质电,磁流场,位谱域并矢格林函数的统一形式

利用谱域导抗法推导分层介质的电磁流场位并矢格林函数积发量的统一的表达式。在谱域中通过坐标旋转，得到了两组独立的等效传输线，这样问题转化为求２解等效传输线的电流与电压，因而对于这类问题用一个统一的传输线公式即可得到各种情况的解，从而使推导变得非常简便。推导中考虑到单轴各向异性介质的情况，各向同性介质可以作为它的特例。     

任意分层手征介质球域中并矢格林函数理论和应用

本文首先应用散射迭加法，给出了含源任意分层手征介质球域中的并矢格林函数，以手征介质球壳为例，分析了位于球中心处点偶极天线的辐射特性，以及归一化辐射阻抗随球壳厚度的变化规律，在平板近似条件下，研究了手征导纳对手征介质球壳传输特性的影响，并且讨论了手征介质球壳内、外表面与空气之间阻抗匹配时，点偶极天线远区辐射场的极化特性。结果表明，通过改变球壳的归一化厚度，可以调节辐射场的极化状态。     

Dyadic Green's functions inside/outside a dielectric elliptical cylinder: theory and application

Dyadic Green's functions in two regions separated by an infinitely long elliptical dielectric cylinder are formulated in this paper. As an application, the plane electromagnetic wave scattering by an isotropic elliptical dielectric cylinder is revisited by applying these dyadic Green's functions and the scattering-to-radiation transform. First, the dyadic Green's functions are formulated and expanded in terms of elliptical vector wave functions. The general equations are derived from the boundary conditions and expressed in matrix form. Then the scattering and transmission coefficients coupled to each other are solved from the matrix equations. To verify the theory developed and its applicability, we revisit the plane electromagnetic wave scattering (of TE- and TM-polarizations) by an infinitely long elliptical cylinder, and consider it as a special case of electromagnetic radiation using the dyadic Green's function technique. The derived equations and computed numerical results are then compared with published results and a good agreement in each case is found. Special cases where the elliptical cylinder degenerates to a circular cylinder and where the material of the cylinder is isorefractive are also considered, and the same analytical solutions in both cases are obtained.     

Spheroidal vector wave eigenfunction expansion of dyadic Green'sfunctions for a dielectric spheroid

The dyadic Green's functions for defining the electromagnetic (EM) fields for the inner and outer regions of a dielectric spheroid are formulated. The dyadic Green's function for an unbounded medium is expanded in terms of the spheroidal vector wave functions and the singularity at source points is extracted. The principle of scattering superposition is then applied into the analysis to obtain the scattering spheroidal dyadic Green's functions due to the existing interface. Coupled equation systems satisfied by scattering (i.e., reflection and transmission) coefficients of the dyadic Green's functions are obtained so that these coefficients can be uniquely solved for. The characteristics of the spheroidal dyadic Green's functions as compared with the spherical and cylindrical Green's dyadics are described and the improper developments of the spheroidal dyadic Green's function for the outer region of a conducting spheroid in the existing work are pointed out     

构造平面分层均匀媒质并矢Green函数的本征谱方法

本文从自由空间中的并矢Green函数出发,引入一种构造平面分层均匀媒质中并矢Green函数的新方法。根据平面分层均匀媒质中不同取向的点源辐射在场点处的响应得到并矢Green函数的谱矢量,进而得出平面分层均匀媒质中并矢Green函数的积分表达式。     

On the dyadic Green's function for a planar multilayereddielectric/magnetic media

A complete plane wave spectral eigenfunction expansion of the electric dyadic Green's function for a planar multilayered dielectric/magnetic media is given in terms of a pair of the (zˆ)-propagating solenoidal eigenfunctions, where (z ˆ) is normal to the interface, and it is developed via a utilization of the Lorentz reciprocity theorem. This expansion also contains an explicit dyadic delta function term which is required for completeness at the source point. Some useful concepts such as the effective plane wave reflection and transmission coefficients are employed in the present spectral domain eigenfunction expansion. The salient features of this Green's function are also described along with a physical interpretation     

A spectral recursive transformation method for electromagneticwaves in generalized anisotropic layered media

A transition-matrix method is commonly used to deal with the problems of plane wave scattering from and the Green's function for multilayered generalized anisotropic media. The boundary conditions at the source interfaces are matched numerically. This method, although rigorous analytically, causes numerical singularities in the matrix inversion when the spectral fields are highly attenuating. A recursive variable transformation method is developed to deal with the exponentially growing or decaying terms associated with the spectral matrix method. The proposed scheme is suitable for numerical analysis of generalized anisotropic layers including uniaxial and biaxial materials, biased ferrites, magnetoplasmas, chiral and bi-anisotropic materials without increasing computer time. Applications of the recursive method are highlighted through examples of radiation and scattering from a three-layer ferrite structure and a conductor-backed magnetoplasma layer     

Efficient analysis of planar circulators by a new boundary-integraltechnique

The application of a new boundary-integral technique to the study of planar circulators in stripline/microstrip technology is described. The technique employs Green's second identity with plane waves as weighting functions, and leads to a very efficient algorithm for the analysis of planar devices in anisotropic media. Extensive comparison is made with results from the standard contour-integral formulations with very good agreement between the two techniques. The new technique is more stable in the critical region (μ_eff close to 0) and is somewhat faster     

多层媒质中散射DGF的系数

长期以来,多层媒质中并矢格林函数的系数一直难以求解。本文给出了多层媒质中并矢格林函数的系数所满足的方程组,利用散射叠加法,求得了任意多层媒质中散射DGF的系数,给出了其一般表达式。     

Multilayered media Green's functions in integral equationformulations

A compact representation is given of the electric- and magnetic-type dyadic Green's functions for plane-stratified, multilayered, uniaxial media based on the transmission-line network analog along the aids normal to the stratification. Furthermore, mixed-potential integral equations are derived within the framework of this transmission-line formalism for arbitrarily shaped, conducting or penetrable objects embedded in the multilayered medium. The development emphasizes laterally unbounded environments, but an extension to the case of a medium enclosed by a rectangular shield is also included