An observation on the Sommerfeld-integral representation of theelectric dyadic Green's function for layered media

The authors discuss the electric dyadic Green's function for layered dielectrics. It is known that for the free-space electric dyadic Green's function, evaluation of the electric field at observation points within the source region requires specification of a principal volume along with the corresponding depolarizing dyad. Special considerations are invoked for layered background media which are appropriate for the electromagnetics of integrated electronics. It is shown that use of the Sommerfeld-integral representation of the electric dyadic Green's function leads to an innate choice for the depolarizing dyad. A corresponding principal volume is subsequently identified; it is demonstrated that there exists an alternative choice for this excluding region which leads to the same depolarizing dyad     

On the longitudinal component of the Green's function dyadic

Discussion of the divergenceless property of the right-hand side of the dyadic-wave equation for the Green's dyad has centered on the inconsistency of expanding the Green's dyad only in terms of transverse-wave functions. By including the longitudinal functions in the Ohm-Rayleigh expansion of the dyad, a simple closed form expression for the longitudinal component is derived which yields the expected singular quasi-static field. The result is verified in a coordinate independent manner with the aid of the Helmholtz theorem.     

Dyadic Green's function of multilayer cylindrical closed and sector-structures for waveguide, microstrip-antenna, and network analysis

A clear and systematic method to derive the spectral- and space-domain dyadic Green's function of arbitrary cylindrical multilayer and multiconductor structures is proposed. The derivation is either done for a circumferentially closed or a cylindrical sector structure, which is bounded by electric or magnetic walls in an azimuthal direction. The solution for the dyadic Green's function in the spectral domain is obtained via an equivalent circuit. Relations between the spectral and space domains for the dyadic Green's functions are derived using eigensolution expansions. Finally, the dyadic Green's function is applied to the problem of finding the propagation constants of the two-layer dielectric rod.     

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     

On the singularity of the full spectral Green's dyad

The full3 times 3spectral dyadic Green's function exhibits certain properties that its popular2 times 2transversal portion does not. In particular, it is shown that the dyad is identically singular, the singularity being a manifestation of the plane wave properties of each spectral component. This singularity has an impact on the use of certain computational algorithms which in general would require an inversion of the dyad. Other plane wave properties, being dual to Maxwell's equations, are also discussed.     

An efficient numerical spectral domain method to analyze a largeclass of nonreciprocal planar transmission lines

Presents an efficient numerical application of the Galerkin method in the spectral domain (SD) to the analysis of striplike/slotlike coplanar transmission lines embedded in a bianisotropic multilayered medium. The method is based on obtaining the spectral dyadic Green's function by the equivalent boundary method (EBM), a suitable third order extraction technique of the asymptotic behavior of the Green's dyad, an enhanced numerical integration scheme, and the use of an adequate contour integral method for searching zeros in the complex plane. This method, namely the SD-EBM, has been found to be very suitable for analyzing transmission lines with semiconductors and/or ferrites magnetized at an arbitrary direction, including the study of magnetostatic wave propagation phenomena     

A Generalized Spectral-Domain Green's Function for Multilayer Dielectric Substrates with Application to Multilayer Transmission Lines

A generalized full-wave Green's function completely defining the field inside a multilayer dielectric structure due to a current element arbitrarily placed between any two layers is derived in two-dimensional spectral-domain form. It is derived by solving a "standard" form containing the current element with two substrates on either side of it, and using an iterative algorithm to take care of additional layers. Another iterative algorithm is then used to find the field in any layer in terms of the field expressions in the two layers of the "standard" form. The locations of the poles of the Green's function are predicted, and an asymptotic form is derived along with the asymptotic limit, by use of which the multilayer Green's function can be used in numerical methods as efficiently as the single-layer grounded-dielectric-substrate Green's function. This Green's function is then applied to a few multilayer transmission lines for which data are not found in the literature to date.     

Closed-Form Expressions of Multilayered Planar Green's Functions That Account for the Continuous Spectrum in the Far Field

The rational function fitting method has been found useful in the derivation of closed-form expressions of spatial-domain Green's functions for multilayered media. However, former implementations of the rational function fitting method lead to Green's functions expressions that are not accurate in the far field when this far field is dominated by the continuous spectrum instead of being dominated by surface waves (as it happens, for instance, in the case of lossy multilayered media). In this paper, the authors introduce a novel implementation of the rational function fitting method, which leads to Green's functions expressions that are accurate in the far field when this is dominated either by the continuous spectrum or by surface waves. In the new approach, the far-field contribution of the continuous spectrum to the Green's functions is numerically fitted in terms of functions with closed-form Hankel transforms, and this far-field contribution is explicitly added to the total least squares approximations of the Green's functions. The numerical results obtained for the Green's functions with the new approach have been compared with numerical results obtained via direct numerical integration of Sommerfeld integrals, and excellent agreement has been found despite the contribution—continuous spectrum or surface waves—dominating the far field.      

A Correlation method for the determination of the dyadic Green's function of the electromagnetic field in diffraction problem

A correlation method is developed for the determination of the dyadic Green's function of the electromagnetic field in the presence of diffracting body. The dyadic Green's function G(r, t/rs, t') is determined by the temporal correlation function between a Gaussian and white random current source J(t') situated at rsand the electric field E(r, t) observed at a point r.     

Green's function in the spectral domain for biaxial and uniaxial anisotropic planar dielectric structures

Green's function solutions of the biaxial and uniaxial anisotropic layered-medium planar-structure is formulated in terms of Maxwell's equations. Diagonalized biaxial and uniaxial permittivity tensors in the coordinate system of interest are treated. The Green's function is found in the double Fourier transformed domain for three longitudinal-to-an-axis coupled electric-magnetic field sets applied to a simple layered structure. The approach is applicable to structures having discontinuities in two orthogonal planar directions such as patch radiators or resonators. Spectral Green's function is usable in method-of-moment calculations assisted by Galerkin's method.     

用电磁场算子理论求波导复合系统的本征值

该文用并矢格林函数方法通过虚拟边界的电场和磁场的耦合求解波导复合结构的本征值,所采用的并矢格林函数没有奇异项,可以用标量格林函数来表示并进行计算,因此不仅可以计算横电与横磁模的基模和高次模式,还可以计算存在两个孪生模式的复合系统。该文同时还对经典场论中常用的一些定理,如面旋度定理进行了探讨。     

An asymptotic closed-form microstrip surface Green's function forthe efficient moment method analysis of mutual coupling in microstripantennas

A relatively simple closed-form asymptotic representation for the single-layer microstrip dyadic surface Green's function is developed. The large parameter in this asymptotic development is proportional to the lateral separation between the source and field points along the air-dielectric interface. This asymptotic solution remains surprisingly accurate even for very small (a few tenths of a free-space wavelength) lateral separation of the source and field points. Thus, using the present asymptotic approximation of the Green's function can lead to a very efficient moment method (MM) solution for the currents on an array of microstrip antenna patches and feed lines. Numerical results based on the efficient MM analysis using the present closed-form asymptotic approximation to the microstrip surface Green's function are given for the mutual coupling between a pair of printed dipoles on a single-layer grounded dielectric slab. The accuracy of the latter calculation is confirmed by comparison with numerical results based on a MM analysis which employs an exact integral representation for the microstrip Green's function     

A NEW METHOD FOR SOLVING DYADIC GREEN''''S FUNCTION OF ELECTROMAGNETIC FIELD

A new method for solving electromagnetic field boundary value problem is given.Byusing this method,the boundary value problem of the vector wave equation can be transformedinto the independent boundary value problem of scalar wave equations and the two additionalvector differential operations.All the dyadic Green's functions got by eigenfunction expansionof the dyadic Green's function can be got by this method easily and some of the dyadic Green'sfunctions for complex systems which are very difficult to get by the ordinary method have beengot by this new method.The dyadic Green's function for a dielectric loaded cavity is one of thegiven examples.     

Spectral domain iterative analysis of single- and double-layeredmicrostrip antennas using the conjugate gradient algorithm

An analysis for single- and double-layered microstrip antennas is described. The planarity of these structures makes it possible to construct a general spectral representation for any number of layers and to derive the spectral Green's dyad in a compact fashion using a transmission-line analogy. A formulation of the antenna problem in the spectral domain, incorporating this dyad, is coupled with the conjugate gradient algorithm, whose applicability as an efficient way of analyzing a number of microstrip antennas is studied. Results are quite accurate. Conclusions pertaining to the applicability of the method, including effects of problem parameters on convergence rates, are drawn     

Transient temperature fields with general nonlinear boundary conditions in electronic systems

Green's function representations of the solution of the heat conduction equation for general boundary conditions are generalized for the nonlinear, i.e., temperature dependent case. Temperature dependent heat transfer coefficients lead to additional terms in the Green's function representation of the temperature field. For a rectangular structure with averaged homogeneous material parameters several types of Green's functions can be chosen especially simple, because of the new representation with the possibility of differing types of boundary conditions for the temperature field and the Green's function. Exact finite closed form expressions for three-dimensional-Green's functions in the time domain using elliptic theta functions are presented. The temperature field is a solution of a nonlinear integral equation which is solved numerically by iteration. The resulting algorithm is very robust, stable and accurate with reliable convergence properties and avoids matrix inversions completely. The algorithm can deal with all sizes of volume heat sources without additional grid generation. Large and small size volume heat sources are treated simultaneously in the calculations that will be presented. Heat transfer coefficients are chosen representing radiative and convective boundary conditions. An extension of the solution algorithm to composed multilayer systems of arbitrary geometry is outlined.     

Green's Function Techniques for Inhomogeneous Anisotropic Media (Correspondence)

In many problems involving the guiding and radiation of electromagnetic raves the solution for the field quantities at points in space is given in terms of integrals of the field quantities over their values on a closed surface. These integrals are often derived through the application of vector Green's theorems. The Green's function used in any particular application is usually determined by the special considerations of that problem, but it is convenient to use, as the Green's function, a solution of the vector wave equation which is singular at the point where the field is to be computed. In this article the concept is extended to iuclude media which are anisotropic and maybe inhomogeneous as well. Use is made of the generalized reciprocity relationships for anisotropic media. This involves the use of the media of a given problem termed "original media" and those characterized by transposed tensor parameters and termed "transposed media."     

Electric dyadic Green's functions in the source region

A straightforward approach that does not involve delta-function techniques is used to rigorously derive a generalized electric dyadic Green's function which defines uniquely the electric field inside as well as outside the source region. The electric dyadic Green's function, unlike the magnetic Green's function and the impulse functions of linear circuit theory, requires the specification of two dyadics: the conventional dyadic G^-eoutside its singularity and a source dyadic L^-which is determined solely from the geometry of the "principal volume" chosen to exclude the singularity of G^-e. The source dyadic L^-is characterized mathematically, interpreted physically as a generalized depolarizing dyadic, and evaluated for a number of principal volumes (self-cells) which are commonly used in numerical integration or solution schemes. Discrepancies at the source point among electric dyadic Green's functions derived by a number of authors are shown to be explainable and reconcilable merely through the proper choice of the principal volume. Moreover, the ordinary delta-function method, which by itself is shown to be inadequate to extract uniquely the proper electric dyadic Green's function in the source region, can be supplemented by a simple procedure to yield unambiguously the correct Green's function representation and associated fields.     

A compact recursive trans-impedance Green's function for the inhomogeneous ferrite microwave circulator

A detailed analytical investigation of the circular ferrite circulator is provided in this paper. The ferrite is assumed to be radially inhomogeneous as a result of an azimuthally invariant demagnetization field. The cavity model of Bosma and the stratified ferrite model of Krowne and Neidert are used to construct a compact recursive Green's function in terms of wave impedances and azimuthal modes. The Green's function logarithmic singularity is treated separately and extracted to improve the convergence characteristics of the modal series. The impedance parameters of the circulator are obtained via an integration of the Green's function and its singular term; to obtain the scattering parameters, various matrix manipulations of the impedance parameters are invoked. Data are provided and compared with independent sources to demonstrate the veracity of the Green's function approach. Finally, a circulator design is offered using the Green's function method and scattering-parameter data associated with that design are compared with data from a three-dimensional finite-element electromagnetic simulation of a microstrip circulator. The correlation between both data sets further supports the validity of the inhomogeneous cavity model and the Green's function approach.     

The expansion wave concept. I. Efficient calculation of spatialGreen's functions in a stratified dielectric medium

A procedure is given to perform the inverse Fourier transformation relating a spatial Green's function to its spectral equivalent. The procedure is applied to the spectral Green's functions of the double scalar mixed-potential integral expression formulation of the electromagnetic field in a stratified dielectric medium. The extraction technique is used to annihilate every type of “problematic” behavior of the spectral Green's functions. Every annihilating function is inverse Fourier transformed analytically. It is shown that the annihilation of both the surface wave poles and the singularities at the branch point results in a set of analytical spatial functions, which are a very good approximation of the exact spatial Green's function down to relatively small lateral distances     

Integral equation formulation for inhomogeneous anisotropic mediaGreen's dyad with application to microstrip transmission linepropagation and leakage

A straightforward numerical technique based on the equivalence principle is presented to determine the complete spectral Green's dyad for inhomogeneous anisotropic media. This method is relevant to guided-wave problems where propagation characteristics are desired in the axial transform domain. Spectral Green's components are determined from a one-dimensional polarization-type integral equation. This method is very simple and versatile, and can be used to model continuously varying or stratified dielectric media with permittivity dyads of the most general form. As an application, a microstrip transmission line residing on a generally orientated uniaxial and biaxial substrate is considered, and new results for higher-order mode leakage are presented