Propagation and coupling properties of integrated opticalwaveguides-an integral equation formulation

The propagation and coupling properties of integrated optical waveguides are analyzed by means of the electric field integral equation approach. The kernel of the integral equation is the Green's function of a two-layered medium. The Galerkin's method is then employed to solve the integral equation numerically. The set of basis and test functions consists of entire domain plane wave functions. Fast convergence and superior accuracy are the advantages of the chosen set of basis and test functions. The method is used to compute the propagation and coupling properties of several structures. Very good agreement is observed with previously published results. Field distributions of several coupled mode structures, such as the symmetrical and asymmetrical coupler are also investigated and presented. Finally, the same method is used to produce the field distribution of waveguides having more complex cross section like the trapezoidal waveguide     

Comparison of a class of subdomain and entire domain basisfunctions automatically satisfying KCL

Accuracy, number of unknowns, and CPU time are compared for piecewise linear subdomain basis functions and polynomial entire domain basis functions. Both types of functions automatically satisfy a continuity equation at wire ends and junctions, according to Kirchoff's current law (KCL). The relative root mean square (RMS) current deviation is chosen as the error metric. An electrically short scatterer, a crossed wire scatterer and an electrically long scatterer are used for comparison. Currents are obtained by solving the electric field integral equation (EFIE), by means of the Galerkin method. It was shown that in most cases, for the same accuracy required, the entire domain approximation uses three to five times less numbers of unknowns and 10-100 times less CPU time than the subdomain approximation. Generally, such efficiency is achieved by using entire domain expansions the order of which is up to n=5 and cannot be significantly improved by using higher order expansions     

Radiation and scattering from structures involving finite-sizedielectric regions

A full-wave approach is presented for calculating the scattered fields produced by structures that involve finite-size dielectric regions. The dielectric is first approximated by an array of interlocking thin-wall sections; the electric field boundary conditions are then applied through the use of appropriate surface impedances. Rooftop basis functions, chosen to represent the surface current, are appropriately placed on the thin-wall sections in such a way as to accurately represent the polarization current while preventing fictitious charge within the dielectric. Rooftop currents are also used to represent the current on any conductor that may be present. The matrix elements are calculated, depending upon the distance between the source and field locations, through a scheme that employs Taylor series expansions and point source approximations. The technique is applied to scattering from dielectric cubes and composite dielectric-conductor structures, and to radiation from microstrip structures. Numerical convergence and agreement with the literature are demonstrated     

A method of moments solution for electromagnetic scattering by inhomogeneous dielectric bodies of revolution

A method of calculating the electromagnetic scattering from and internal field distribution of inhomogeneous dielectric bodies of revolution (BOR) is presented. The method uses a typical mode-by-mode solution scheme. The electric flux density is chosen as the unknown quantity, which, together with the special construction of basis and testing functions, enables considerable reduction of the number of unknowns. A key element in this technique is expressing of the azimuthal field components of basis functions in terms of transverse components. A Galerkin testing procedure is used, with special attention put on the efficiency of calculating scalar potential term. Results of calculation for a few classes of dielectric bodies are given and compared with calculations done by other authors.     

Note on interpolational basis functions in the method of moments[EM scattering]

Efficient basis sets for the method of moments may be obtained using quasi-localized bandlimited interpolational functions that, broadly speaking, are defined relative to a mean sampling rate that is adjusted to curvature and proximity to edges, thus reflecting the local spatial-frequency bandwidth. Computed scattering data in a number of structures, including perfectly conducting circular and elliptical two-dimensional cylinders as well as a flat infinite strip, indicate that reasonable accuracy can be obtained with an average rate of between 2.5 and 3 basis functions per wavelength. Average sampling rates need not correspond strictly to the bandwidth of the basis functions, and there is considerable latitude with respect to random variation of sampling intervals. Although each basis function typically extends over several sample points, required integrals can be obtained speedily by the use of standard sampling-theoretical methods     

利用高阶矢量基函数求解时域磁场积分方程

本文利用一种新的高阶矢量基函数求解了三维时域磁场积分方程,该基函数定义在一个曲边三角形贴片上并用拉格朗日插值多项式来表示每一个贴片内的未知电流密度.该基函数的实质就是将拉格朗日插值多项式的插值点选为高斯积分结点,极大地简化和加快了时域积分方程矩量法的繁琐的时间和空间积分运算;另外,该基函数不要求网格为规范网格,给复杂目标的网格剖分带来很大方便.在空间上利用点匹配方法求解了时域磁场积分方程,数值计算结果表明了该方法求解时域积分方程的精确性和高效性.     

An efficient curved-wire integral equation solution technique

Computation of the currents on curved-wires by integral equation methods is often inefficient when the structure is tortuous but the length of wire is not large relative to the wavelength at the frequency of operation. The number of terms needed in an accurate piecewise straight model of a highly curved-wire can be large, yet, if the total length of wire is small relative to the wavelength, the current can be accurately represented by a simple linear function. A new solution method for the cured-wire integral equation is introduced. It is amenable to uncoupling of the number of segments required to accurately model the wire structure from the number of basis functions needed to represent the current. This feature lends itself to high efficiency. The principles set forth can be used to improve the efficiency of most solution techniques applied to the curved-wire integral equation. New composite basis and testing functions are defined and constructed as linear combinations of other commonly used basis and testing functions. We show how the composite basis and testing functions can lead to a reduced-rank matrix, which can be computed via a transformation of a system matrix created from traditional basis and testing functions. Supporting data demonstrate the accuracy of the technique and its effectiveness in decreasing matrix rank and solution time for curved-wire structures     

线面结构天线的电磁建模与计算

应用矩量法对线面结构的天线进行建模,针对天线中的不同结构,选用了不同的基函数进行建模,对于线结构和面结构,分别采用了经典的三角形基函数和RWG 矢量基函数。而对于线面结合处这一复杂结构,在分析传统线面基函数表达式的基础上推导出一种新的基函数,该基函数中增加了描述天线粗细的项,且其散度为一常数,避免了复杂的差分计算,有效解决了传统线面结合基函数分析粗天线模型时误差大且存在奇异点的缺点。在此基础上,给出了线面结构天线阻抗矩阵及散射场的计算方法。最后通过两个天线的算例验证了该算法的正确性和通用性。     

Cortical patch basis model for spatially extended neural activity

A new source model for representing spatially distributed neural activity is presented. The signal of interest is modeled as originating from a patch of cortex and is represented using a set of basis functions. Each cortical patch has its own set of bases, which allows representation of arbitrary source activity within the patch. This is in contrast to previously proposed cortical patch models which assume a specific distribution of activity within the patch. We present a procedure for designing bases that minimize the normalized mean squared representation error, averaged over different activity distributions within the patch. Extension of existing algorithms to the basis function framework is straightforward and is illustrated using linearly constrained minimum variance (LCMV) spatial filtering and maximum-likelihood signal estimation/generalized likelihood ratio test (ML/GLRT). The number of bases chosen for each patch determines a tradeoff between representation accuracy and the ability to differentiate between distinct patches. We propose choosing the minimum number of bases that satisfy a constraint on the normalized mean squared representation accuracy. A mismatch analysis for LCMV and ML/GLRT is presented to show that this is an appropriate strategy for choosing the number of bases. The effectiveness of the patch basis model is demonstrated using real and simulated evoked response data. We show that significant changes in performance occur as the number of basis functions varies, and that very good results are obtained by allowing modest representation error.     

Improved computational efficiency via near-field localization

The coefficient matrix which results when one applies the method of moments to the solution of the electric field integral equation is rendered sparse by appropriate selection of basis functions. These new basis functions arise when equivalent sources are arranged in such a manner as to produce a field focused on the bounding surface. The local nature of the focused fields reduces to a negligible level the interactions represented by many of the off-diagonal elements of the coefficients matrix. Moreover, the resulting basis appears to represent the surface fields more efficiently than many of the commonly used bases. The technique is currently limited to closed structures. Its application is demonstrated in two dimensions by computing the scattering of a plane wave by circular and square perfectly conducting cylinders. As the electrical size of the structure is increased and the number of unknowns is correspondingly increased, that the number of significant matrix elements per row is shown to remain approximately constant     

A novel grid-robust higher order vector basis function for themethod of moments

A set of novel, grid-robust, higher order vector basis functions is proposed for the method-of-moments (MoM) solution of integral equations for three-dimensional (3-D) electromagnetic (EM) problems. These basis functions are defined over curvilinear triangular patches and represent the unknown electric current density within each patch using the Lagrange interpolation polynomials. The highlight of these basis functions is that the Lagrange interpolation points are chosen to be the same as the nodes of the well-developed Gaussian quadratures. As a result, the evaluation of the integrals in the MoM is greatly simplified. Additionally, the surface of an object to be analyzed can be easily meshed because the new basis functions do not require the side of a triangular patch to be entirely shared by another triangular patch, which is a very stringent requirement for traditional vector basis functions. The proposed basis functions are implemented with point matching for the MoM solution of the electric-field integral equation, the magnetic-field integral equation, and the combined-field integral equation. Numerical examples are presented to demonstrate the higher order convergence and the grid robustness for defective meshes using the new basis functions     

网络分解法的误差分析

网络分解法是求解电大尺寸复杂结构电磁问题的重要方法之一,关于网络分解法误差分析的研究有着重要的理论意义和实用价值.本文给出了网络分解法的误差估计,并对于脉冲基函数转换成三角基函数的情况给出了三角基函数个数的最优公式,数值结果表明了分析的正确性.     

Matching pursuits with time-frequency dictionaries

The authors introduce an algorithm, called matching pursuit, that decomposes any signal into a linear expansion of waveforms that are selected from a redundant dictionary of functions. These waveforms are chosen in order to best match the signal structures. Matching pursuits are general procedures to compute adaptive signal representations. With a dictionary of Gabor functions a matching pursuit defines an adaptive time-frequency transform. They derive a signal energy distribution in the time-frequency plane, which does not include interference terms, unlike Wigner and Cohen class distributions. A matching pursuit isolates the signal structures that are coherent with respect to a given dictionary. An application to pattern extraction from noisy signals is described. They compare a matching pursuit decomposition with a signal expansion over an optimized wavepacket orthonormal basis, selected with the algorithm of Coifman and Wickerhauser see (IEEE Trans. Informat. Theory, vol. 38, Mar. 1992)     

RBFN restoration of nonlinearly degraded images

We investigate a technique for image restoration using nonlinear networks based on radial basis functions. The technique is also based on the concept of training or learning by examples. When trained properly, these networks are used as spatially invariant feedforward nonlinear filters that can perform restoration of images degraded by nonlinear degradation mechanisms. We examine a number of network structures including the Gaussian radial basis function network (RBFN) and some extensions of it, as well as a number of training algorithms including the stochastic gradient (SG) algorithm that we have proposed earlier. We also propose a modified structure based on the Gaussian-mixture model and a learning algorithm for the modified network. Experimental results indicate that the radial basis function network and its extensions can be very useful in restoring images degraded by nonlinear distortion and noise.     

Modeling of corneal surfaces with radial polynomials

We consider analytical modeling of the anterior corneal surface with a set of orthogonal basis functions that are a product of radial polynomials and angular functions. Several candidate basis functions were chosen from the repertoire of functions that are orthogonal in the unit circle and invariant in form with respect to rotation about the origin. In particular, it is shown that a set of functions that is referred herein as Bhatia-Wolf polynomials, represents a better and more robust alternative for modeling corneal elevation data than traditionally used Zernike polynomials. Examples of modeling corneal elevation are given for normal corneas and for abnormal corneas with significant distortion.     

Moment-method calculations on apertures using basis singularfunctions

The transmission properties of perforated perfectly conducting screens are of practical interest. The treatment of nonperiodical structures by numerical techniques, such as the method of moments, is very computer intensive. In this paper it is shown that using basis functions that incorporate the edge as well as the corner singularities, the number of unknowns can be drastically reduced. The advantages and limitations of the method are discussed. Numerical results are presented illustrating the transmission properties of arrays of square and rectangular apertures     

复杂金属载体上线天线的MoM分析

各类金属载体上线天线的特性分析具有很重要的实用价值。本文运用矩量法处理各种载体上线天线问题。首先将线天线模拟为带状线,天线和载体表面均采用平面三角形单元进行剖分,RWG基函数作电流展开函数。然后介绍了线面连接处贴片单元的剖分方法,以及在连接处定义基函数和添加电压源模型。本文分析了各种形状金属载体上线天线的特性,研究了角度和位置对天线输入阻抗或辐射特性的影响。数值结果验证了方法的正确性。     

Number theoretic transforms to implement fast digital convolution

Transforms using number theoretic concepts are developed as a method for fast and error-free calculation of finite digital convolution. The transforms are defined on finite fields and rings of integers with arithmetic carried out modulo an integer and it is shown that under certain conditions this gives the same results as conventional digital convolution. Because of these characteristics they are ideally suited to digital computation by taking into account quantization of amplitude as well as time in their definition. When the modulus is chosen as a Fermat number a transform results that requires only on the order of N log N additions and word shifts but no multiplications. In addition to being efficient, they have no roundoff error and do not require storage of basis functions. There is a restriction on sequence length imposed by word length and a problem with overflow but methods for overcoming these are presented. Results of an implementation on an IBM 370/155 are presented and compared with the fast Fourier transform showing a substantial improvement in efficiency and accuracy. Variations on the basic number theoretic transforms are also presented.     

Time-varying filter banks and wavelets

Time-varying filter banks and wavelets are studied and a design procedure is presented. In the resulting analysis-synthesis structures, the analysis filters and the corresponding synthesis filters, the number of bands, and the decimation rates can be changed with time. Such structures can be considered as time-frequency overlapping block transforms. From this viewpoint, the tiling of the time-frequency plane and the corresponding basis functions are changed in time. The time-varying discrete wavelet transforms can be considered a special case of time-varying overlapping block transforms and are studied in detail. The formulation is based on the time domain formulation of time-varying analysis-synthesis structures. The design procedure can be used to design time-varying perfectly invertible transformations with a finite number of distinct analysis structures. For adaptive filter bank application, a least squares design method is also studied