Closed-form Green's functions for cylindrically stratified media

A numerically efficient technique is developed to obtain the spatial-domain closed-form Green's functions of the electric and magnetic fields due to z- and φ-oriented electric and magnetic sources embedded in an arbitrary layer of a cylindrical stratified medium. First, the electric- and magnetic-field components representing the coupled TM and TE modes are derived in the spectral domain for an arbitrary observation layer. The spectral-domain Green's functions are then obtained and approximated in terms of complex exponentials in two consecutive steps by using the generalized pencil of function method. For the Green's functions approximated in the first step, the large argument behavior of the zeroth-order Hankel functions is used for the transformation into the spatial domain with the use of the Sommerfeld identity. In the second step, the remaining part of the Green's functions are approximated on two complementary parts of a proposed deformed path and transformed into the spatial domain, analytically. The results obtained in the two consecutive steps are combined to yield the spatial-domain Green's functions in closed forms     

One- and two-dimensional dyadic Green's functions in chiral media

The one-dimensional and two-dimensional dyadic Green's functions are calculated for 1D and 2D electric sources in an unbounded, lossless, reciprocal chiral medium which is electromagnetically described by a set of symmetric constitutive relations. It is shown that in two- and one-dimensional cases, similar to the three-dimensional case, the medium supports two eigenmodes of propagation with two different wavenumbers. One of them corresponds to the right-circularly polarized wave and the other one to the left-circularly polarized wave. The eigenmode amplitudes a and b are similar to those of the three-dimensional case     

快速计算平面分层介质的闭式格林函数

使用离散复镜像方法(DCIM)快速得到平面分层介质的空间域的闭式格林函数,避免了费时的索末菲尔德积分.给出闭式格林函数在矩量法中的应用,为研究微带天线的性能提供了一种数值方法.数值结果表明离散复镜像方法能够快速、准确地计算平面分层介质的闭式格林函数.     

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     

Evaluation of layered media Green's functions via rational function fitting

An efficient rational function fitting methodology, called VECTFIT, is utilized toward the closed-form evaluation of the Sommerfeld integrals associated with electromagnetic Green's functions in planar layered media. VECTFIT approximates the component of the spectrum of the Green's function that remains after the extraction of the primary source contribution and the quasistatic part with a rational function, thus enabling a robust and expedient closed-form evaluation of the Sommerfeld integral for electromagnetic potentials and associated field quantities.     

Time domain Green's functions for lossy and dispersive multilayered media

We have introduced a fast method of calculating the time domain Green's functions for multilayered media. In this paper, we demonstrate the use of this method to compute the scalar potential Green's function for a multilayer lossy dispersive medium on a PEC ground. The strength of the method lies in obtaining the Green's function for many source-to-field distances /spl rho/ and time instances t simultaneously. It only takes 6 min 28 s to compute 100/spl times/336=33 600 space time Green's function points in Matlab on a Pentium III 867 MHz processor with 1 GB of RAM for a multilayered lossy dispersive medium.     

On the fast approximation of Green's functions in MPIE formulationsfor planar layered media

The numerical implementation of the complex image approach for the Green's function of a mixed-potential integral-equation formulation is examined and is found to be limited to low values of κ_oρ (in this context κ₀ρ = 2πρ/λ₀, where ρ is the distance between the source and the field points of the Green's function and λ₀ is the free space wavelength). This is a clear limitation for problems of large dimension or high frequency where this limit is easily exceeded. This paper examines the various strategies and proposes a hybrid method whereby most of the above problems can be avoided. An efficient integral method that is valid for large κ₀ρ is combined with the complex image method in order to take advantage of the relative merits of both schemes. It is found that a wide overlapping region exists between the two techniques allowing a very efficient and consistent approach for accurately calculating the Green's functions. In this paper, the method developed for the computation of the Green's function is used for planar structures containing both lossless and lossy media     

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。     

球形分层媒质中并矢格林函数的求解域: 并矢格林函数快速计算*

首先,采用勒让德多项式的加法定理,对PartΙ部分得到的并矢格林函数进行化简,将双级数和形式转换成单级数和形式。然后,将场型格林函数转换成位型格林函数,将九个分量中收敛慢的TM 分量统一合并成公共的标量位函数。接着,利用球贝塞尔函数和汉克尔函数的渐近公式,导出并矢格林函数的渐近函数,以加速格林函数的收敛速度。最后,计算了球面共形微带天线的输入阻抗,与文献计算结果吻合,说明了处理的正确性和有效性。     

A direct discrete complex image method from the closed-form Green's functions in multilayered media

Sommerfeld integration is introduced to calculate the spatial-domain Green's functions (GF) for the method of moments in multilayered media. To avoid time-consuming numerical integration, the discrete complex image method (DCIM) was introduced by approximating the spectral-domain GF by a sum of exponentials. However, traditional DCIM is not accurate in the far- and/or near-field region. Quasi-static and surface-wave terms need to be extracted before the approximation and it is complicated to extract the surface-wave terms. In this paper, some features of the matrix pencil method (MPM) are clarified. A new direct DCIM without any quasi-static and surface-wave extraction is introduced. Instead of avoiding large variations of the spectral kernel, we introduce a novel path to include more variation before we apply the MPM. The spatial-domain GF obtained by the new DCIM is accurate both in the near- and far-field regions. The CPU time used to perform the new DCIM is less than 1 s for computing the fields with a horizontal source-field separation from 1.6/spl times/10/sup -4//spl lambda/ to 16/spl lambda/. The new DCIM can be even accurate up to 160/spl lambda/ provided the variation of the spectral kernel is large enough and we have accounted for a sufficient number of complex images.     

General analytical solutions of static Green's functions forshielded and open arbitrarily multilayered media

In this paper, we present for the first time general analytical solutions of the static Green's functions for shielded and open arbitrarily multilayered media. The analytical formulas for the static Green's functions, which are expressed in the form of the Fourier series or the Fourier integrals, have simple form and are applicable to arbitrary number of the dielectric layers. The derivation of the formulas is primarily based on a technique by which a recurrence relation between L layers and L+1 layers is developed. Green's functions for a three-layered dielectric structure are given as an example of the general formulas. These general analytical solutions will provide a new and efficient tool to the analysis of the multilayered medium structures     

On the electromagnetic dyadic Green's functions for planar multi-layered anistropic uniaxial material media

A complete, plane-wave spectral, vector-wave function expansion of the electromagnetic, electric, and magnetic, dyadic Green's function for electric, as well as magnetic, point currents for a planar, anisotropic uniaxial multi-layered medium is presented. It is given in terms ofz-propagating, source-free vector-wave functions, where ? is normal to the interfaces, and it is developed via a utilization of the Lorentz reciprocity theorem. The electromagnetic dyadic Green's function for periodic electric as well as magnetic point current sources is also presented. Some salient features of the Green's dyadics, along with a physical interpretation are also described.     

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。     

Dyadic Green's function in bounded media

A new theory for the evaluation of the dyadic Green's functions in a homogeneous medium bounded by perfectly conducting walls is presented. The peculiarities of this theory are 1) the Green's functions are systematically and explicitly decomposed in a singular and an analytical part, and 2) these two parts are formulated in a general manner, i.e., independent on the boundaries. As an application, the Green's functions in a conical guide are evaluated.     

Some methods of solving for the coefficients of dyadic Green's functions in isotropic stratified media

Dyadic Green's functions in multi-layered isotropic media are analysed in this paper. Three different kinds of method for obtaining the coefficients of dyadic Green's functions in multi-layered media are given, these are (a) the boundary condition method, which is well-known; (b) the recurrence matrix equation method; and (c) the ray trail method. Using these methods, several examples are considered. Some results are the same as those obtain previously. Some are obtained for the first time.     

Green's functions in lossy layered media: integration along the imaginary axis and asymptotic behavior

This paper presents an efficient technique for evaluating Green's functions associated to layered media, when formulated as Sommerfeld integrals in the space domain. The key step in the formulation is that Sommerfeld integrals are computed choosing a suitable integration path which is closed through the imaginary axis of the complex spectral plane. It is shown that with this original choice of the integration contour, the numerical effort usually involved in the evaluation of Sommerfeld integrals can be greatly reduced, specially when large source-observer distances are involved. One asset of this technique is that it can be easily incorporated into integral equation based CAD packages for the efficient analysis of complex printed microwave circuit and antennas. In addition, the theoretical developments needed to set up the numerical algorithm throw a new light on the asymptotic behavior of the layered media Green's functions for large source-observer distances.     

Green's functions and magnetized ferrites

Magnetized ferrites play an important role in the field of microwaves as substrates in various electronic elements. The dyadic Green's functions method is used to solve the electromagnetic field problem for such anisotropic (magnetically gyrotropic) materials. The full dyadic problem is reduced to a scalar one where the complete information is contained within a single scalar Green's function. A connection between the Green's functions formalism and that of scalar Hertz potentials is established and some progress is made towards the calculation of the scalar Green's function.     

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     

Evaluation of Green's function integrals in conducting media

This work presents an accurate integration method for computing Green's function operators related to lossy conducting media. The presented approach is ultrawideband, i.e., the integration schemes cover the entire range of frequency behavior, from high frequencies where skin current is prevalent to low frequencies where volume current flow dominates. The scheme is a step toward permitting exact ultrawide-band frequency domain surface-only-based integral-equation simulation of arbitrarily-shaped three-dimensional conductors, and toward obviating the need for volume-based explicit frequency-dependent skin effect modeling. This work deals specifically with the computation of Green's functions and not with the unrelated but important low-frequency conditioning issue associated with the standard electric field integral equation.     

A new technique for the derivation of closed-form electromagnetic Green's functions for unbounded planar layered media

A closed-form electromagnetic Green's function for unbounded, planar, layered media is derived in terms of a finite sum of Hankel functions. The derivation is based on the direct inverse Hankel transform of a pole-residue representation of the spectral-domain form of the Green's function. Such a pole-residue form is obtained through the solution of the spectral-domain form of the governing Green's function equation numerically, through a finite-difference approximation, rather than analytically. The proposed methodology can handle any number of layers, including the general case where the planar media exhibit arbitrary variation in their electrical properties in the vertical direction. The numerical implementation of the proposed methodology is straightforward and robust, and does not require any preprocessing of the spectrum of the Green's function for the extraction of surface-wave poles or its quasi-static part. The number of terms in the derived closed-form expression is chosen adaptively with the distance between source and observation point as parameter. The development of the closed-form Green's function is presented for both vertical and horizontal dipoles. Its accuracy is verified through a series of numerical examples and comparisons with results from other established methods.