Electromagnetic fields of buried sources in stratified anisotropic media

A general formulation to the problem of the radiation of arbitrary distribution of buried sources within a horizontally stratified anisotropic medium is presented. The fields are obtained in terms of appropriately defined electric and magnetic types of dyadic Green's functions which are dual to each other. The formulation is considerably simplified by the resolution of these dyadic Green's functions into transverse electric (TE) and transverse magnetic (TM) waves and by the existing duality between them. A systematic procedure for deriving the fields in an arbitrary layer in terms of the primary source excitation and appropriately defined wave amplitude matrices is described.     

Copolar and cross-polar radiation of Vivaldi antenna on dielectricsubstrate

The copolar and cross-polar radiation patterns of the Vivaldi antenna on a dielectric substrate are calculated and validated by measurements. The method involves a two-step procedure. The electric field distribution across the antenna slot aperture is calculated first. The radiated fields are then calculated, using Green's functions. The continuous exponential tapered shape is approximated by annular linearly tapered sections. The conical transmission-line theory and a variational method yield the electric field in each section. The radiation calculation is based on closed-form expressions for the dyadic Green's function of an elementary electric field source in a conducting half sheet. Both copolar and cross-polar radiation patterns of the Vivaldi antenna are calculated by integrating the Green's functions weighted by the electric field distribution over the antenna aperture. The effect of lateral truncation is taken into account by defining weighting patterns. The method is validated by original measurements and limitations of the model are discussed. Antenna directivity and sensitivity are calculated     

Dyadic Green's Functions for Integrated Electronic and Optical Circuits

Layered structures play an important role in both integrated microwave circuits and optical integrated circuits. Accurate prediction of device behavior requires evaluation of fields in the system. An increasingly used mathematical formulation refies on integral equations the electric field in the device is expressed in terms of the device current integrated into an electric Green's function. Details of the development of the specialized Green's functions used by various researchers have not appeared in the literature. We present the development of general dyadic electric Green's functions for layered structures; this dyadic formulation allows extension of previous analyses to cases where currents are arbitrarily directed. The electric-field Green's dyads are found in terms of associated Hertzian potential Green's dyads, developed via Sommerfeld's classic method. Incidently, boundary conditions for electric Hertzian potential are utiltzed; these boundary conditions, which have been a source of confusion in the research community, are developed in full generality. The dyadic forms derived herein are reducible in special cases to the Green's functions used by other workers.     

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     

Electromagnetic scattering from a chiral cylinder of arbitrarycross section

A simple moment solution is presented to the problem of electromagnetic scattering from a homogeneous chiral cylinder of arbitrary cross-section. The cylinder is assumed to be illuminated by either a TE or a TM wave. The surface equivalence principle is used to replace the cylinder by equivalent and magnetic-surface currents. These currents radiating in unbounded external medium produce the correct scattered field outside. When radiating in an unbounded chiral medium, they produce the correct total internal field. By enforcing the continuity of the tangential components of the total electric field on the surface of the cylinder, a set of coupled integral equations is obtained for the equivalent surface currents. Unlike a regular dielectric, the chiral scatterer produces both copolarized and cross-polarized scattered fields. Hence, both the electric and magnetic current each have a longitudinal and a circumferential component. These four components of the currents are obtained by using the method of moments (MoM) to solve the coupled set of integral equations. Pulses are used as expansion functions and point matching is used. The Green's dyads are used to develop explicit expressions for the electric field produced by two-dimensional surface currents radiating in an unbounded chiral medium. Some of the advantages and limitations of the method are discussed. The computed results include the internal field and the bistatic and monostatic echo widths. The results for a circular cylinder are in very good agreement with the exact eigenfunction solution     

The Green's Dyadic for Radiation in a Bounded Simple Moving Medium

The studies here show that the wave equation for electromagnetic wave propagation in an isotropic and uniformly moving medium is solvable by the separation method in four coordinate systems. Solutions in the form of complete sets of eigenfunctions are possible for problems where boundary surfaces are presented. A Green's dyadic for finite or semi-infinite domain problems involving sources in the moving medium has been formulated through vector operation on the eigenfunction solutions of the homogeneous wave equation. The case of electromagnetic waves excited by a current loop, immersed in a moving medium, and confined by a circular cylindrical waveguide, was examined. The electric and magnetic field intensities in such a waveguide were compared with those obtained through a different approach. The Green's dyadic for electromagnetic waves in an infinite domain moving medium was shown to be obtainable from the finite domain Green's dyadic through a limiting process.     

Full-wave analysis of quasi-optical structures

A full-wave moment method implementation, using a combination of spatial and spectral domains, is developed for the analysis of quasi-optical systems. An electric field dyadic Green's function, including resonant and nonresonant terms corresponding to coupling from modal and nonmodal fields, is employed in a Galerkin routine. The dyadic Green's function is derived by separately considering paraxial and nonparaxial fields and is much easier to develop than a mixed, scalar and vector, potential Green's function. The driving point impedance of several antenna elements in a quasi-optical open cavity resonator and a 3×3 grid in free space are computed and compared with measurements     

The equivalence of the electric and magnetic surface current approaches in microstrip antenna studies

It is shown that the fields produced by the electric surface currents on the conducting patch of a microstrip antenna are equivalent to those produced by a magnetic surface current sheet bounding the patch in the substrate only when dyadic Green's functions for the two-layer stratified medium are used.     

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.     

Domain integral equation analysis of integrated optical channel andridge waveguides in stratified media

A domain integral equation approach to computing both the propagation constants and the corresponding electromagnetic field distributions of guided waves in an integrated optical waveguide is discussed. The waveguide is embedded in a stratified medium. The refractive index of the waveguide may be graded, but the refractive indices of the layers of the stratified medium are assumed to be piecewise homogeneous. The waveguide is regarded as a perturbation of its embedding, so the electric field strength can be expressed in terms of domain integral representation. The kernel of this integral consists of a dyadic Green's function, which is constructed using an operator approach. By investigating the electric field strength within the waveguide, it is possible to derive an integral equation that represents an eigenvalue problem that is solved numerically by applying the method of moments. The application of the domain integral equation approach in combination with a numerically stable evaluation of the Green's kernel functions provides a new and valuable tool for the characterization of integrated optical waveguides embedded in stratified media. Numerical results for various channel and ridge waveguides are presented and are compared with those of other methods where possible     

Far field radiation from an arbitrarily oriented Hertzian dipole in the presence of a layered anisotropic medium

Far field radiation from an arbitrarily oriented Hertzian dipole for two-layered uniaxially anisotropic medium with a tilted optic axis is treated analytically by using the dyadic Green's function of the problem when the dipole is placed over or embedded in a two-layered uniaxially anisotropic medium. The radiation fields are evaluated using the steepest descent method. Parameter studies including anisotropy, layer thickness and dipole location are performed to investigate the effects of changing different variables on the radiation fields. Results of this work can be applied in microstrip circuits and antennas.     

Scattering of TE-polarized EM wave by discontinuity in groundeddielectric layer

The two-dimensional problem of EM wave interaction with a dielectric discontinuity in an infinite grounded dielectric layer is studied. An electric field integral equation (EFIE) for TE illumination has been derived based on the Green's function for the electric field produced by induced polarization currents in the discontinuity region. Impressed electric fields consist of either plane waves incident from space above the dielectric layer or surface waves supported by that layer. Method of Moments (MoM) numerical solutions for the induced electric field in the discontinuity region are implemented. The amplitudes of surface waves excited by excess discontinuity-region polarization currents are calculated, as well as the pattern of the scattered field and the associated scattering width. It is observed that the excitation of a surface-wave mode reduces the back scattered radiation for TE-polarized plane wave incidence. The accuracy of the theory is verified by comparison of numerical results with those of existing studies     

Closed form expression of the Green's function for the time-domain wave equation for a lossy two-dimensional medium

The Green's function that relates the electric field to a line current source in a conductive, homogeneous medium is evaluated in the space-time domain in closed form. Early and late time asymptotes are supplied.     

Integral equation analysis of vertical current sheets in planarcircuits and antennas

The electric field integral equation (EFIE) for planar circuits and antennas is usually solved with a spectral computation of the Green's functions. The method of moments solution of the EFIE becomes cumbersome for three-dimensional (3D) metallic surfaces in an arbitrary multilayered medium. Here, it is demonstrated how some of the numerical work can be replaced by analytical computations for 3D planar structures by using the closed form expressions for the spectral Green's functions. An example of a two-conductor line short circuited with a vertical metallic plate is presented     

平面分层媒质中二维非均匀结构电磁散射的研究

本文研究埋藏在平面分层媒质中的二维非均匀结构的电磁散射分析方法和散射特性。在推导平面分层介质中电流丝辐射的Green函数的基础上,建立非均匀结构相对于分层媒质的等效电流所产生散射场的电场积分方程,进而在离散的条件下求解。利用文中提出的方法,对于不同介质目标的散射进行了计算,并比较了埋藏深度、周围介质、分层结构等因素对埋藏目标散射特性的影响。     

多层介质中谱域格林函数的解析公式及在微带天线中的应用

首先假定平面电流源位于任一层介质中，然后利用谱域法和波矩阵技术，通过求解矢量电波场动方程，推导出了多层介质中谱域格林函数的解析公式，将所得公式应用于多层介质微带 天线的分析中，得 到了天线辐射场的理论计算公式，分析计算了一些工程实例，实验结果证实了理论计算的正确性。     

用谱域导抗法推导平面分层介质格林函数的一般表达式

本文应用谱域导抗法推导了不同源激励产生的电场、磁场格林函数的一般表达式.它的基本思路是,找到电流源、磁流源分别对应的等效传输线.应用传输线理论求出电场、磁场所对应的量,通过坐标变换回到原来坐标系中,求得所需的谱域格林函数.这样问题变成了确定不同等效传输线上的电流和电压,大大简化了谱域格林函数的推导过程,尤其是对于多层介质的情况.本文最后给出了四种不同类型的谱域格林函数,证明了此方法的正确性.     

单层和双层手征介质柱域的并矢格林函数理论及其应用

本文应用散射叠加法,分别导出了单层和双层手征介质圆柱区域中的并矢格林函数。由此分析了位于手征介质圆柱和手征介质圆柱罩中心轴线上点偶极天线的辐射特性。结果表明,通过改变手征介质圆柱的尺寸和手征介质圆柱罩的厚度,可以任意调节辐射场的极化特性。另外,本文给出的并矢格林函数公式还可用于分析柱形手征微带天线的辐射特性。     

Waveguide excited microstrip patch antenna-theory and experiment

An arbitrarily shaped microstrip patch antenna excited through an arbitrarily shaped aperture in the mouth of a rectangular waveguide is investigated theoretically and experimentally. The metallic patch resides on a dielectric substrate grounded by the waveguide flange and may be covered by a dielectric superstrate. The substrate (and superstrate, if present) consists of one or more planar, homogeneous layers, which may exhibit uniaxial anisotropy. The analysis is based on the space domain integral equation approach. More specifically, the Green's functions for the layered medium and the waveguide are used to formulate a coupled set of integral equations for the patch current and the aperture electric field. The layered medium Green's function is expressed in terms of Sommerfeld-type integrals and the waveguide Green's function in terms of Floquet series, which are both accelerated to reduce the computational effort. The coupled integral equations are solved by the method of moments using vector basis functions defined over triangular subdomains. The dominant mode reflection coefficient in the waveguide and the far-field radiation patterns are then found from the computed aperture field and patch current distributions. The radar cross section (RCS) of a plane-wave excited structure is obtained in a like manner. Sample numerical results are presented and are found to be in good agreement with measurements and with published data     

Dyadic Green's Functions for an Anisotropic, Non-Local Model of Biased Graphene

Dyadic Green's functions are presented for an anisotropic surface conductivity model of biased graphene. The graphene surface can be biased using either a perpendicular static electric field, or by a static magnetic field via the Hall effect. The graphene is represented by an infinitesimally-thin, two-sided, non-local anisotropic conductivity surface, and the field is obtained in terms of Sommerfeld integrals. The role of spatial dispersion is accessed, and the effect of various static bias fields on electromagnetic field behavior is examined. It is shown that by varying the bias one can exert significant control over graphene's electromagnetic propagation characteristics, including guided surface wave phenomena, which may be useful for future electronic and photonic device applications.