Efficient evaluation of reaction integrals in the EFIE analysis ofplanar layered structures with uniaxial anisotropy

This paper presents an efficient implementation of the electric-field integral-equation (EFIE) method to deal with planar anisotropic layered printed structures. A convenient treatment of the kernel of the integral equation gives rise to reaction integrals that only involve quasi-singularities and R^-1-type singularities. When the well-known Rao-Wilton-Glisson triangular basis functions are used in conjunction with the Galerkin's method, closed-form expressions are found for the singular parts of the self-reaction integrals, as well as for the inner convolution integrals of the remaining singular/quasi-singular reaction integrals. Thus, the present procedure sets the EFIE method as a competitive alternative to other formulations     

Extrapolation methods for Sommerfeld integral tails

A review is presented of the extrapolation methods for accelerating the convergence of Sommerfeld-type integrals (i.e. semi-infinite range integrals with Bessel function kernels), which arise in problems involving antennas or scatterers embedded in planar multilayered media. Attention is limited to partition-extrapolation procedures in which the Sommerfeld integral is evaluated as a sum of a series of partial integrals over finite subintervals and is accelerated by an extrapolation method applied over the real-axis tail segment (α,∞) of the integration path, where α>0 is selected to ensure that the integrand is well behaved. An analytical form of the asymptotic truncation error (or the remainder), which characterizes the convergence properties of the sequence of partial sums and serves as a basis for some of the most efficient extrapolation methods, is derived. Several extrapolation algorithms deemed to be the most suitable for the Sommerfeld integrals are described and their performance is compared. It is demonstrated that the performance of these methods is strongly affected by the horizontal displacement of the source and field points ρ and by the choice of the subinterval break points. Furthermore, it is found that some well-known extrapolation techniques may fail for a number of values of ρ and ways to remedy this are suggested. Finally, the most effective extrapolation methods for accelerating Sommerfeld integral tails are recommended     

TE-scattering by conducting strips right on the planar interface ofa three-layered medium

Two-dimensional scattering by one or two coplanar strips printed right on the interface of three-layered planar structures is investigated by combining the Fourier transform with powerful singular integral equation methods. The excitation is either the lowest incident TE (to strip axis) surface-wave mode or an incident, H-polarized plane wave. The kernel is most advantageously decomposed into a singular closed-form term and a fast convergent inverse Fourier integral. Treating all singular integrals by analytical and uniformly convergent algorithms leads to an efficient, accurate, and stable numerical code. Plotted numerical results reveal that, by a proper choice of certain geometrical parameters, the structures may become very efficient radiators     

Finite-element method coupled with method of lines for the analysis of planar or quasi-planar transmission lines

A full-wave analysis incorporating the finite-element method (FEM) and the method of lines (MoL) is presented in this paper to investigate a planar or quasi-planar transmission-line structure containing complex geometric/material features. For a transmission-line structure being considered, the regions containing complex media are modeled by the FEM while those consisting of simple media with simple geometry are analyzed using the MoL. From the field solutions calculated by MoL, the boundary conditions are constructed. The boundary integrals involved in finite-element analysis are then carried out using these boundary conditions. Since the finite-element analysis is employed only in the complex parts of the structures, while other parts are handled by the MoL, this approach not only retains the major advantage of the FEM in simulating complex structures but also becomes more efficient than the conventional finite-element analysis. Good agreement between the calculated results and those reported in the available literature is obtained and thus validates the present approach. Furthermore, proficient computational efficiency of this method is demonstrated by examining its convergence property. Finally, a number of relevant transmission-line structures are analyzed to illustrate the applications of this approach.     

Spectral and variational analysis of generalized cylindrical andelliptical strip and microstrip lines

The variational technique in the spectral domain (VTSD) is shown to be an efficient method for computing the quasi-TEM parameters of arbitrary multiconductor and multidielectric cylindrical or elliptical strip configurations. Simple conformal mappings reduce the cylindrical or elliptical geometries to an equivalent rectangular one with periodic boundary conditions. The analysis of this equivalent structure is achieved by taking advantage of previous work on boxed planar structures. The numerical convergence of the programs is greatly accelerated, incorporating the asymptotic behavior of the series appearing in the analysis in such a way that efficient programs have been written. It is pointed out that excessively simple approximations to the surface charge distribution yield meaningful numerical errors, mainly when strong coupling or wide strips are involved. As an application example, the behavior of the characteristic parameters of asymmetric coupled structures on multilayer substrates is shown     

Evaluation of Fourier transform integrals using FFT with improved accuracy and its applications

A new technique that significantly minimizes the aliasing error encountered in the conventional use of the fast Fourier transform (FFT) algorithms for the efficient evaluation of Fourier transforms of spatially limited functions (such as those that occur in the radiation pattern analysis of reflector antennas and planar near field to far field (NF-FF) transformation) is presented and illustrated through a typical example. Employing this technique and a discrete Fourier series (DFS) expansion for the integrand, a method for computing the radiation integrals of reflector antennas and planar NF-FF transformation integrals at arbitrary observation angles with optimum use of computer memory and time is also described.     

UtilisatIon D’un Processus de Renormalisation Pour L’étude Électromagnétique des Structures Fractales Bidimensionnelles

In this article, we apply the renormalization technique, used possibly in theorical physics, for electromagnetic studying of bi dimensional fractal structures. A recurrence relation based on the auto-similar nature of structures and on the model of the surface impedance, has permitted, thanks to the convergence to a fixed point, to determine the input impedance of these structures at any scale. Though, the suggested method has been validated by calculus of one-dimensional structures (Iris de Cantor) it may be applied easily to the analysis of planar circuits as the Sierpensky antenna.     

Spreading resistance calculations by the use of Gauss-Laguerre quadrature

The Gauss-Laguerre quadrature is proposed as a numerical method for calculating the correction factor integrals that occur in spreading resistance calculations. The method is very efficient in terms of computation time and memory storage, requiring only 33 integrand values for each integral evaluation. The accuracy of the method has been investigated for a variety of graded structures, and found to be better than 5%. As a test of its practical utility, the method has been used in the correction of the spreading resistance profile of a practical buried layer structure, and it has been found that the CPU time taken to correct the entire profile of 57 data points is 1.0 min on an IBM 1130 System with a 16K word (16 bit) memory or 0.4 sec on a UNIVAC 1100/10 Multiprocessor System with a 393K word (36 bit) memory. These times are a factor of 6 to 8 less than those required by using the previously proposed adaptive Simpson's rule to compute the correction factor integrals.     

A method of moments approach for the efficient and accuratemodeling of moderately thick cylindrical wire antennas

This paper introduces a moment-method formulation, which is capable of accurately modeling moderately thick cylindrical wire antennas. New algorithms are presented for the efficient computation of the cylindrical wire kernel and related impedance matrix integrals. These algorithms make use of exact series representations as well as efficient numerical procedures and lead to a significant reduction in overall computation time for thicker wires. Another major advantage of this moment-method technique is that it is no longer restricted by the segment length-to-radius ratio limitations inherent in past formulations, thereby making it possible to achieve solution convergence for a much wider class of wire antenna structures. Several examples illustrating the superior convergence properties of this new moment-method formulation are presented and discussed     

New plane wave spectrum formulations for the near-fields of circular and strip apertures

The plane wave spectrum (PWS) method has previously been applied to analyze the near-field of planar apertures. The main goal of this paper is to present new PWS formulations for the near-fields of strip and circular apertures. Only special cases are developed in detail. For example, the uniform and parabolic aperture distributions are developed for the circular aperture. These new formulations are expressed in terms of either elementary functions or Fresnel integrals. Consequently, they permit considerably more rapid and efficient calculations than previous near-field formulations, by either the PWS or the aperture integration approach. The new formulations are especially advantageous for large circularly symmetric apertures (on the order of100lambdaand larger) in that computational efficiencies are improved by an order of magnitude or two over the original PWS formulation. The improvement over aperture integration techniques is more than a factor of 1000 for the100lambdaaperture.     

RCS reduction of canonical targets using genetic algorithmsynthesized RAM

Radar cross section (RCS) reduction of canonical (planar, cylindrical, and spherical) conducting targets is the focus of this paper. In particular, a novel procedure is presented for synthesizing radar absorbing materials (RAM) for RCS reduction in a wide-band frequency range. The modal solutions of Maxwell's equations for the multilayered planar, cylindrical, and spherical canonical structures is integrated into a genetic algorithm (GA) optimization technique to obtain the best optimal composite coating. It Is shown that by using an optimal RAM, the RCS of these canonical structures can be significantly reduced. Characteristics of bistatic RCS of coated cylindrical and spherical structures are also studied and compared with the conducting structures without coating. It is shown that no optimal coating can be found to reduce the RCS in the deep shadow region. An in-depth study has been performed to evaluate the potential usage of the optimal planar coating as applied to the curved surfaces. It is observed that the optimal planar coating can noticeably reduce the RCS of the spherical structure. This observation was essential in introducing a novel efficient GA with hybrid planar/curved surface implementation using as part of its initial generation the best population obtained for the planar RAM design. These results suggest that the optimal RAM for a surface with arbitrary curvature may be efficiently determined by applying the GA with hybrid planar/curved surface population initialization     

基于固定实镜像平面波展开的快速多极子方法计算微带结构问题

将快速多极子算法应用于微带结构的一个关键技术是将矩量法中描述远区单元相互作用的Green函数用加法定理进行平面波展开.本文提出用固定实镜像方法拟合微带结构谱域Green函数进行平面波展开,对比目前常用的复镜像闭式平面波展开方法,该方法具有展开收敛性好,物理概念清晰,Green函数宽频插值方便等特点.计算实例表明了该方法的有效性和可靠性.     

Evaluation of Sommerfeld integrals using Chebyshev decomposition[antenna analysis]

Sommerfeld integrals ensue when one uses a spectral-domain transformation to calculate fields of a dipole source in a homogeneous space or in a layered medium with planar boundaries. A new and efficient method of evaluating these integrals is presented. This method still converge in the case of unbounded homogeneous media or when source and observer are both on the boundary itself, as in microstrip lines. The integration is based on decomposition of the integrand into Chebyshev polynomials. Numerical results are given and compared with published literature     

采用PML吸收边界条件的FDTD法在分析平面微带结构中的应用

本文将理想匹配层(PML)吸收边界条件用于平面微带结构的时域有限差分法(FDTD)分析中,给出平面微带结构的PML吸收边界条件,并编制程序,进行数值计算。结果表明,与传统的Mur吸收边界条件相比,采用PML吸收边界条件只需采用最简单的馈源模型就可明显地减小计算网格空间和加快收敛速度,并且可用于分析任意复杂结构的微带电路。本文方法对微带电路及微带天线的CAD设计将具有实际意义。     

Efficient hybrid spatial and spectral techniques in analyzingplanar periodic structures with nonuniform discretizations

A new efficient technique for analyzing planar periodic structures with arbitrary unit cell geometry rendered in a nonuniform discretization is proposed in this paper. The mixed potential integral equation is solved by the method of moments in conjunction with the Rao-Wilton-Glisson triangular discretization. The convergence of computing each element in the impedance matrix is accelerated using Ewald's method for contributions of quasi-dynamic and complex images and the lattice-sum method for the surface-wave contribution. Numerical efficiency and accuracy of this hybrid method are compared with the spectral-domain method     

A very short planar silica spot-size converter using a nonperiodicsegmented waveguide

To reduce the coupling loss of a fiber-to-ridge waveguide connection, a planar silica spot-size converter for a wavelength of 1.55 μm is implemented in the form of a nonperiodic segmented waveguide structure with irregular tapering. A simple single-step lithography process is sufficient for the fabrication of the planar structures. An evolutionary algorithm has been successfully applied for the optimization. The simulated results obtained with a three-dimensional (3-D) finite difference beam propagation method (FD-BPM) program are compared with measurements of implemented couplers, showing very good agreement. A waveguide-to-fiber coupling efficiency improvement exceeding 2 dB per converter is shown. Structures obtained with this approach are very short (~140 μm) and simple to integrate on the same wafer with other planar structures such as phased arrays or ring resonator structures     

Some convergence considerations in space-domain moment-methodanalysis of a class of wide-band microstrip antennas

The method of moments (MoM) analysis of probe-fed rectangular microstrip patches requires the inclusion of a probe-to-patch attachment mode-expansion function when the substrate thickness d⩾0.02λ, where λ is the free-space wavelength. The results for the input impedance showed increased divergence with measurements when the attachment mode was omitted from the full-wave analysis. The attachment mode can be expressed as an infinite eigenfunction series that increases the fill time of the impedance matrix in an MoM analysis. In an earlier investigation, the infinite eigenfunction series was reduced to a residue series that required one or two terms compared to about 55 terms for the eigenfunction series. In this paper, the convergence properties of the eigenfunction and residue series are investigated in view of rigorous MoM analysis. The relative errors resulting from replacing the eigenfunction by the residue series for the attachment mode, are compared by numerically evaluating a class of two-dimensional (2-D) spatial integrals shown to be closely related to the elements of an MoM impedance matrix. Additionally, the computation times for the evaluation of these integrals for the two forms of the attachment mode-expansion function are also included. Based on the superior convergence properties of the residue series for the attachment mode-expansion function, it is mathematically justified that this form can readily be used for analytic reduction of the spatial, reaction integrals from four to 2-D forms. This feature allows further reduction of the fill time of the MoM impedance matrix, suggesting the possibility of developing an efficient space-domain MoM technique for modeling of wide-band microstrip antennas     

Analytical evaluation of the MoM matrix elements

Derivation of the closed-form Green's functions has eliminated the computationally expensive evaluation of the Sommerfeld integrals to obtain the Green's functions in the spatial domain. Therefore, using the closed-form Green's functions in conjunction with the method of moments (MoM) has improved the computational efficiency of the technique significantly. Further improvement can be achieved on the calculation of the matrix elements involved in the MoM, usually double integrals for planar geometries, by eliminating the numerical integration. The contribution of this paper is to present the analytical evaluation of the matrix elements when the closed-form Green's functions are used, and to demonstrate the amount of improvement in computation time     

Efficient room-temperature continuous-wave AlGaInP/AlGaAs visible(670 nm) vertical-cavity surface-emitting laser diodes

Significant improvement in the performance of AlGaInP/AlGaAs visible vertical-cavity surface-emitting laser diodes has been achieved in gain-guided planar-geometry devices utilizing proton implants to define the current injection path. Threshold currents as low as 1.25 mA were measured on 10 μm-diameter devices, with maximum power output of 0.33 mW from larger devices. Continuous-wave (cw) lasing was achieved at temperatures as high as 45°C. The improved diode performance is attributed to better lateral heat-sinking and reduced parasitic heat generation afforded by the planar device structure, relative to previously-reported air-post structures. This work represents the first realization of efficient room-temperature operation of AlGaInP-based visible VCSEL diodes     

基于ILDC理论的平面结构电磁散射计算

增量长度绕射系数理论(ILDC)是对电大尺寸复杂目标进行边缘绕射计算的有效方法之一。本文基于散射总场、表面光学场和边缘绕射场三者之间的关系,针对几何建模的特点,从另一个角度推导出了ILDC在平表面结构中的应用形式,并验证了该方法的正确性,为目标电磁特性的研究提供了一种可行的计算方法。