EFFECT OF PERIODIC DEFECTS ON ELECTROMAGENTIC SCATTERING BY THE TWO-DIMENSIONAL PHOTONIC CRYSTALS

Electromagnetic scattering from two-dimensional photonic crystals with two-dimensionally periodic defects is analyzed using a model of multilayered periodic arrays of parallel circular cylinders. The reflectance of the photonic crystals of finite thickness, which are free-standing or embedded in a dielectric slab, is obtained in terms of the lattice-sums, the T-matrix of a circular cylinder, and the generalized reflection matrix for a layered system. Numerical examples demonstrate that the refection and transmission bands of the crystals are reformed by introducing the periodic defects and their band natures are very sensitive to the polarization of excitation and the relative position of the defect element within a unit cell.     

多层介质平板结构的传输线等效面模型及相位修正算法

针对电大复杂多层介质结构目标电磁散射特性分析与应用对计算资源和效率的需求,提出了基于传输线理论的等效面模型,推导了相应的相位修正算法,实现对此类目标散射特性的快速准确预估.等效面模型将多层介质平板结构等效为平面,基于传输线理论,采用电路分析中常用的网络分析方法计算该平面的反射系数与透射系数,并通过引入多层介质结构厚度、入射和观测方向等信息实现对反射系数与透射系数的相位修正.仿真结果验证了该文方法的正确性和高效性.      

Quick quasi-TEM analysis of multiconductor transmission lines withrectangular cross section

This paper presents an efficient and accurate procedure for computing the quasi-static matrix parameters ([C], [L], [G], and [R]) of rectangular-shaped conductors embedded in a multilayered dielectric medium over an infinite ground plane. An additional top ground plane can also be considered., The problem is formulated in terms of the space-domain integral equation for the free-charge distribution on the slab conductor surfaces. The spatial Green's function is computed from its spectral counterpart using system identification techniques [Prony's method or matrix pencil method (MPM)]. The integral equation is solved by means of a Galerkin scheme employing entire domain basis functions. This results in a small matrix size. In addition, the quasi-analytical evaluation of the entries of the Galerkin matrix leads to a very efficient and accurate computer code. A detailed study on the convergence and accuracy of the method has been included     

Analysis of multilayered periodic structures using generalizedscattering matrix theory

The use of generalized scattering matrix theory is proposed as a fast, efficient approach for analyzing multilayer structures where in each layer is either a diffraction grating or a uniform dielectric slab, and all grating layers have the same periodicity. The overall scattering from the structure is determined by first evaluating a matrix of scattering parameters for each individual layer and then forming a scattering matrix for the entire structure by a procedure analogous to the cascading of networks in circuit theory. Higher-order spatial (Floquet) harmonics, including nonpropagating modes and cross-polarized fields, are taken into account as necessary. The approach is illustrated by computing the reflection coefficient of a multilayered resistive strip grating as a function of frequency     

Full-wave analysis of dielectric frequency-selective surfaces using a vectorial modal method

A novel vectorial modal method is presented for studying guidance and scattering of frequency-selective structures based on lossy all-dielectric multilayered waveguide gratings for both TE and TM polarizations. The wave equation for the transverse magnetic field is written in terms of a linear differential operator satisfying an eigenvalue equation. The definition of an auxiliary problem whose eigenvectors satisfy an orthogonality relationship allows for a matrix representation of the eigenvalue equation. Our proposed technique has been applied to the study of lossy all-dielectric periodic guiding media with periodicity in one dimension. This method yields the propagation constants and field distributions in such media. The reflection and transmission coefficients of a single layer under a plane-wave excitation can be obtained by imposing the boundary conditions. Study of the scattering parameters of the whole multilayered structure is accomplished by the cascade connection of components as characterized by their scattering parameters. Results obtained with this method for the propagation characteristics of a one-dimensional periodic dielectric medium are compared with those presented by other authors, and results for the scattering of several dielectric frequency-selective surfaces (DFSS) are compared with both theoretical and experimental results presented in the literature, finding a very good agreement. A symmetrical band-stop filter with a single waveguide grating is also demonstrated theoretically.     

A WH/GSMT-based full-wave analysis for planar transmission linesembedded in multilayered dielectric substrates

A new full-wave analysis method, referred to as the WH/GSMT, is developed to solve multilayered planar transmission line problems. First, the scattering of an obliquely incident parallel plate mode (PPM) by a PEC half plane embedded in a multilayered isotropic dielectric substrate within a PEC parallel plate region is analyzed via the Wiener-Hopf (WH) technique. The solution is then incorporated into the generalized scattering matrix technique (GSMT) to find the (complex) propagation constant and characteristic impedance of the planar transmission lines. The lateral power leakage is taken into account rigorously in the WH/GSMT. Numerical results including the microstrip line, conductor-backed slotline, coupled microstrip lines, and antipodal finlines are presented along with a discussion of the advantages/disadvantages of this method     

Effect of substrate dielectric anisotropy on the frequency behaviorof microstrip circuits

In this paper, we carry out a full-wave analysis of shielded two-port microstrip circuits, in which the metallizations are embedded in a multilayered substrate that may contain isotropic dielectrics and/or anisotropic dielectrics. The Galerkin's method in the spectral domain is applied for determining the current density on the metallizations of the circuits when their feeding lines are excited by means of delta-gap generators, and the matrix pencil technique is subsequently used for deembedding the scattering parameters from the computed current densities. Results are presented for the scattering parameters of some microstrip discontinuities and filters printed on both isotropic dielectric substrates and anisotropic dielectric substrates. These results show that when substrate dielectric anisotropy is ignored, errors arise when computing the scattering parameters of microstrip discontinuities and when predicting the operating frequency band of microstrip filters     

Scattering from composite laminate strips

An analytical model is developed for a composite laminate consisting of unidirectional fibers embedded in a dielectric slab on a conducting strip. The physics of the problem is formulated in terms of integral equations solved by the method of moments using an entire-domain Galerkin formulation. The effect of fiber spacing, the proximity of the ground plane, and the properties of the embedding dielectric are examined in relation to the nonspecular scattering characteristics of the laminate. Results of this analysis are presented for various limiting cases and are compared with experimental data     

Accurate analysis of two-dimensional electromagnetic scattering from multilayered periodic arrays of circular cylinders using lattice sums technique

A very efficient and accurate method to characterize two-dimensional (2-D) electromagnetic scattering from multilayered periodic arrays of parallel circular cylinders is presented, using the lattice sums technique, the aggregate T-matrix algorithm, and the generalized reflection and transmission matrices for a layered system. The method is quite general and applies to various configurations of 2-D periodic arrays. The unit cell of the array can contain two or more cylinders, which may be dielectric, conductor, gyrotropic medium, or their mixture with different sizes. The periodic spacing of cylinders along each array plane should be the same over all layers, but otherwise the cylinders in different layers may be different in material properties and dimensions. The numerical examples validate the usefulness and accuracy of the proposed method.     

Scattering and mode conversion of guided modes by an arbitrary cross-sectional cylindrical object in an optical slab waveguide

The scattering and mode conversion of guided modes caused by a cylindrical scatterer of arbitrary cross section embedded in, or placed on, a dielectric slab waveguide are investigated theoretically. The method employed for the analysis is the surface current integral equation technique. The total scattered power, mode-conversion coefficients, and scattering patterns for the typical numerical examples are shown.     

Interior Green's Function Solution for a Thick and Finite Dielectric Slab

An interior Green's function solution is presented for a two-dimensional thick and finite dielectric slab. In the present development, the source and the field points are assumed to be inside the dielectric slab. The result is composed of two parts. The first part which has a discrete spectrum of eigenfunctions includes the surface wave multiple interactions, and is obtained by using the generalized scattering matrix and method of moments. The second part, which is a closed-form integral, is obtained for a separable dielectric slab that is closely related to the finite slab. The closed form integral is evaluated numerically and added to the surface wave solution. The solution accounts for the mode conversions at the end caps which occur when surface waves are reflected and diffracted. Test cases show very good agreement with a finite-element solver, even when the source is near the end caps.     

Efficient computation of generalized scattering matrix foranalyzing multilayered periodic structures

An efficient technique is proposed for the computation of the generalized scattering matrix (GSM) of a dielectric interface with periodic metallizations. The technique is based on a spectral domain moment method, but assuming multiple incident Floquet-harmonics and computing the GSM directly. Also, some symmetry properties are exploited, and the whole GSM is computed with similar computer effort as that required for a single scattering coefficient. The technique has been applied to the analysis of periodic surfaces involving rectangular and arbitrarily-shaped metallizations using entire- and sub-domain basis functions, respectively. Losses in both dielectric layers and metallizations have been included in the formulation. Multilayered periodic structures are analyzed in a very flexible and efficient way by cascading iteratively the GSM of each interface with or without metallizations considered as building blocks. Numerical results have been provided for different multilayered structures, and a good agreement with other experimental and theoretical data has been obtained. The proposed technique is very appropriate for the analysis of composite structures when the separation between interfaces is small, and therefore higher-order Floquet-harmonic interaction cannot be neglected     

Novel Methods for Modeling of Multiple Vias in Multilayered Parallel-Plate Structures

This paper presents novel modeling methods for accurate and efficient analysis of coupling of multiple vias in finite-sized multilayered parallel-plate structures. The new modeling methods address two open problems related to the modal expansion with the T-matrix method for the analysis of via coupling. First, a novel boundary modeling method, called the frequency-dependent cylinder layer (FDCL), is proposed to resolve the open problem of boundary modeling. In the FDCL, virtual cylinders with dynamic radii are postulated to approximate the original finite-sized boundary of parallel-plate structures. Second, a generalized T-matrix model, which is derived by the mode-matching technique, is created to characterize the coupling effect for vias penetrating more than one layer in a multilayered structure. With the two open problems successfully solved, the modal expansion with the T-matrix method incorporating the FDCL boundary modeling method and the generalized T-matrix model can now be fully utilized for efficient and accurate analysis of finite-sized multilayered parallel-plate structures with a large number of vias. Both numerical and experimental verifications are presented to validate the new modeling methods.      

Capacitance computations in a multilayered dielectric medium usingclosed-form spatial Green's functions

An efficient method to compute the 2-D and 3-D capacitance matrices of multiconductor interconnects in a multilayered dielectric medium is presented. The method is based on an integral equation approach and assumes the quasi-static condition. It is applicable to conductors of arbitrary polygonal shape embedded in a multilayered dielectric medium with possible ground planes on the top or bottom of the dielectric layers. The computation time required to evaluate the space-domain Green's function for the multilayered medium, which involves an infinite summation, has been greatly reduced by obtaining a closed-form expression, which is derived by approximating the Green's function using a finite number of images in the spectral domain. Then the corresponding space-domain Green's functions are obtained using the proper closed-form integrations. In both 2-D and 3-D cases, the unknown surface charge density is represented by pulse basis functions, and the delta testing function (point matching) is used to solve the integral equation. The elements of the resulting matrix are computed using the closed-form formulation, avoiding any numerical integration. The presented method is compared with other published results and showed good agreement. Finally, the equivalent microstrip crossover capacitance is computed to illustrate the use of a combination of 2-D and 3-D Green's functions     

高速IC互连线分布参数提取的一种新方法:采用Pade逼近的介质格林函数法

本文提出采用Ｐａｄｅ逼近的介质格林函数方法计算多导体互连线分布参数。由于采用了分层介质的格林函数，只需在导体表面进行剖分，大大降低了未知变量的规模，本文首先提出利用Ｐａｄｅ逼近对Ｌａｐｌａｃｅ方程的级数形式的格林函数进行收敛性加速。文中给出了加速收敛的结果，表明这种方法是很有效的。     

Electromagnetic scattering from a dielectric-coated sphere with anembedded impedance film

The electromagnetic scattering from a multilayered sphere modal solution of Wait (1963) is modified to allow the inclusion of infinitesimally thin impedance films at layer boundaries. The modified solution is implemented in a computer algorithm and the scattering from an aluminum sphere coated with a dielectric Delrin^TM layer containing an embedded impedance film is computed. This target was fabricated and laboratory measurements performed in the 2-18 GHz region are in good agreement with computations     

Absorbing boundary conditions for the finite-element analysis ofplanar devices

The finite-element method is used to determine the scattering matrices of open devices in two dimensions. Microwave and optical devices in which the fields are not confined to a finite region can be analyzed with the finite-element method if special boundary conditions are used to absorb outgoing radiation. The absorbing boundary conditions can be imposed by the addition of two terms to the usual functional for the scalar Helmholtz equation. Universal matrices are introduced to allow the additional terms to be easily assembled, for polynomial orders one through four. Results are given for the impedance of a parallel-plate waveguide radiating into free space and for the scattering parameters of three dielectric slab waveguide devices: a rectangular discontinuity, a feed structure, and a junction     

Electromagnetic radiation of antennas in the presence of anarbitrarily shaped dielectric object: Green dyadics and theirapplications

Although numerical solutions to the electromagnetic scattering by an arbitrarily shaped object have been obtained using Waterman's (1971) T-matrix method (TMM), the general electromagnetic radiation due to an antenna of a three-dimensional (3-D) current distribution in the presence of an arbitrarily shaped object has not been well considered. In this paper, the technique of surface integral equations has been employed; and as a result, a terse and analytical representation of the dyadic Green's functions (DGFs) in the presence of an arbitrarily shaped dielectric object is obtained for the antenna radiation. In a form similar to that associated with the electromagnetic radiation in the presence of a dielectric sphere, the DGFs inside and outside of the object of arbitrary shape are expanded in terms of spherical vector wave functions. However, their coefficients are no longer decoupled due to the arbitrary surface of a 3-D object. The coupled coefficients are then determined using the surface integral equation approach, in a fashion similar to that in the T-matrix method. To confirm the applicability and correctness of the approach in this paper a dielectric sphere, as a special case, is utilized as an illustration. It is found that exactly the same expressions as in the rigorous analysis for the inner and outer spherical regions of the object are obtained using the different approaches. As applications of the approach in this paper, radiation problems of an electric dipole in the presence of superspheroids and rotational parabolic bodies are solved     

多层介质中通孔结构准静态电容参数的提取

本文采用维数缩减技术(DRT)提取了多层介质中通孔结构的准静态电容参数。由于该方法充分利用了集成电路结构分层性的特点,从而可以很方便地处理任意的介质层数和结构参数,而仅需很少的计算时间和内存.文中的计算结果与Ansoft软件结果符合较好。     

Scattering from non-spherical hydrometeors

A new theoretical formulation for scattering from a wide class of non-spherical hydrometeors has been developed recently using Waterman’s extended integral equation technique. The transition or T-matrix formulation is an exact solution to the scattering problem and computer programs have been developed to handle both homogeneous and imbedded bodies (e.g., a dielectric imbedded within another dielectric body). This theory will be briefly reviewed followed by sample computations of backscattering calculations of (a)oblate spheroidal icestones of varying sizes and eccentricities, (b)ice-stones with surface perturbations to model roughness, and (c)rough ice-stones covered with a thin coating of water. The method is realistically applicable for sizes up to D ≈3 λand for a wide range of dielectric constants. Comparisons with measurements of backscattering from a non-concentric dielectric-clad spherical perfect conductor is included.