Closed-form Green's dyadics for a class of media with axialbi-anisotropy

The Green's dyadics are derived for a new combined nonreciprocal and uniaxial bi-anisotropic medium with material dyadics of the form μ⁼αϵ^=T, ξu⁼=ξu_zu_z, and ζ⁼=ζu_zu_z. The result can be expressed as an infinite series of exponential integrals. It is investigated for which media this series truncates to a closed-form expression and the result is checked with known Green's dyadics for special cases of the medium parameters     

Electromagnetic wave propagation in cylindrically stratified isotropic media

The general electromagnetic field, when independent of axial distance, may be expressed as the sum of E parallel and H parallel partial fields. Exact solutions of the wave equation for the radial variation of the H parallel field are not numerous. Generalised refractive-index profiles are presented which permit transcendental solutions to be made.     

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.     

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     

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.     

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.     

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     

Accurate approximation of Green's functions in planar stratified media in terms of a finite sum of spherical and cylindrical waves

A robust and computationally-expedient methodology is presented for accurate, closed-form approximation of the Green's functions used in the mixed-potential integral equation statement of the electromagnetic boundary value problem in planar stratified media. The proposed methodology is based on the fitting of the spectrum of the Green's function, after the extraction of the quasistatic part, making use of rational functions. The effectiveness and robustness of the proposed methodology rely upon the proper sampling of the spectrum in order to improve the accuracy of the rational function fit. The resulting closed-form approximation is in terms of both spherical and cylindrical waves. Thus, high accuracy is obtained in the approximation of the Green's function irrespective of the distance of the observation point from the source. The methodology is validated through its application to the approximation of the Green's function for a multi-layered, planar dielectric stack.     

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.     

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.     

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     

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.     

Application of Hill's functions to problems of propagation in stratified media

A novel method of solving Maxwell's equations in a plane-stratified dielectric layer is presented, The governing differential equations for each polarization are solved in terms of Hill's functions. The formulation yields solutions which are formally exact and applicable to an extremely wide range of dielectric variations within the layer, without restriction to any particular frequency regime. The method is used to study the reflection of a plane wave polarized parallel to the plane of incidence by an inhomogeneous layer separating two homogeneous regions of infinite extent. The effect of the graded boundary on the Brewster-angle phenomenon is discussed for the case where the two homogeneous regions have different dielectric properties. Reflections from a dielectric duct are also considered as an illustration of the utility of the method.     

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 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     

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     

Dyadic Green's functions for a coaxial line

The eigenfunction expansions of the dyadic Green's functions for a coaxial line have been derived based on the method ofbarbar{G}_{m}, whereby the irrotational vector wave functionbar{L}is not needed. A dyadic boundary condition for the discontinuity of the tangential component ofbarbar{G}_{m}has been used to facilitate the derivation of the expression for the electric dyadic Green's function.     

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.