Improved Locally Conformal Finite-Difference Time-Domain method for edge inclined slots in a finite wall thickness waveguide

An Improved Locally Conformal Finite-Difference Time-Domain (ILC-FDTD) method is presented in this paper, which is used to analyze the edge inclined slots penetrating adjacent broadwalls of a finite wall thickness waveguide. ILC-FDTD not only removes the instability of the original locally conformal FDTD algorithm, but also improves the computational accuracy by locally modifying magnetic field update equations and the virtual iterative electric fields according to the complexity of the slot fringe fields. The mutual coupling between two edge inclined slots can also be analyzed by ILC-FDTD effectively.     

FDTD Maxwell's equations models for nonlinear electrodynamics andoptics

This paper summarizes algorithms which extend the finite-difference time-domain (FDTD) solution of Maxwell's equations to nonlinear optics. The use of the FDTD in this field is novel. Previous modeling approaches were aimed at modeling optical-wave propagation in electrically long structures such as fibers and directional couplers, wherein the primary flow of energy is along a single principal direction. However, the FDTD is aimed at modeling compact structures having energy flow in arbitrary directions. Relative to previous methods, the FDTD achieves robustness by directly solving, for fundamental quantities, the optical E and H fields in space and time rather than performing asymptotic analyses or assuming paraxial propagation and nonphysical envelope functions. As a result, it is almost completely general. It permits accurate modeling of a broad variety of dispersive and nonlinear media used in emerging technologies such as micron-sized lasers and optical switches     

Analysis of edge slots in rectangular waveguide with finitewaveguide wall thickness

A novel analysis for computing the admittance characteristics of edge slots with a salient feature in successfully considering the finite waveguide wall thickness is presented. The variational equation for the electric field in the slot region between the inner and outer waveguide walls is derived by applying the variational reaction theory and solved by the finite-element method. The division of the slot region into small elements of triangular cylinders and the basis function for each element are described in detail. In the limiting case of zero wall thickness, this finite-element analysis is reduced to a moment-method analysis using Galerkin's approach with triangular basis functions. The effects of waveguide wall thickness on the characteristics of the slot are investigated by comparing the numerical results with and without considering the wall thickness. Negligence of the wall thickness may result in a severe underestimation of the resonant length by as large as 14% for edge slots cut in typical X-band waveguides. The computed results with the finite wall thickness taken into account have been checked with the measured data published in previous literature and those obtained by a carefully devised experimental setup. Good agreement between theoretical and experimental results is obtained to demonstrate the validity of the analysis     

Grid decoupling in finite element solutions for Maxwell's equations

Certain finite-element discretization methods used in time-domain electromagnetic modeling reduce to a type of finite-difference method when applied on a regular mesh. The form of this underlying finite-difference method is unusual; it consists of two decoupled grids, rotated 45° from the original finite element mesh     

High-accuracy FDTD solution of the absorbing wave equation, and conducting Maxwell's equations based on a nonstandard finite-difference model

We previously introduced high-accuracy finite-difference time-domain (FDTD) algorithms based on nonstandard finite differences (NSFD) to solve the nonabsorbing wave equation and the nonconducting Maxwell equations. We now extend our methodology to the absorbing wave equation and the conducting Maxwell equations. We first derive an exact NSFD model of the one-dimensional wave equation, and extend it to construct high-accuracy FDTD algorithms to solve the absorbing wave equation, and the conducting Maxwell's Equations in two and three dimensions. For grid spacing h, and wavelength /spl lambda/, the NSFD solution error is /spl epsiv//spl sim/(h//spl lambda/)/sup 6/ compared with (h//spl lambda/)/sup 2/ for ordinary FDTD algorithms using second-order central finite-differences. This high accuracy is achieved not by using higher-order finite differences but by exploiting the analytical properties of the decaying-harmonic solution basis functions. Besides higher accuracy, in the NSFD algorithms the maximum time step can be somewhat longer than for the ordinary second-order FDTD algorithms.     

非均匀网格FDTD分析波导宽边辐射缝隙特性

波导宽边辐射缝隙被广泛应用于波导缝隙阵列中，为了比较准确地对波导缝隙进行建模，同时考虑到计算资源限制，本文引入一种采用非均匀网格的时域有限差分方法对其S参数特性进行了计算。数值结果表明该方法分析波导辐射缝隙特性问题的有效性。     

基于PSO/FDTD的波导缝隙天线优化设计

设计了一种16阵元波导缝隙天线,其阵元在波导宽边中心线一侧排列。该设计采用泰勒分布进行阵列综合,利用粒子群优化算法(PSO)与时域有限差分法(FDTD)在不同偏置位置对谐振长度进行优化。由于该天线属于非谐振式波导缝隙阵,设计的关键是调整缝隙对宽边中心线的偏移。仿真结果表明天线指标与设计要求吻合,证明了设计方法的可行性。     

A technique for solution of Maxwell's equations in a moving dielectric medium

A simple technique is presented for converting a known solution for the electric and magnetic vector fields in a dielectric medium at rest into the corresponding fields in a moving dielectric medium. The technique combines methods presented by Tai [1] with a scaling procedure developed by Clemmow [2]. Tai's work reduces the moving medium problem to the solution of Maxwell's equations in a uniaxial medium, and Clemmow's procedure enables one to convert a known solution in an isotropic medium to the corresponding solution in a uniaxial medium. Thus by first solving for the fields in the medium at rest, then following Clemmow's procedure to obtain the fields in Tai's uniaxial medium, and finally applying Tai's reasoning, one may easily obtain the solution of Maxwell's equations in the moving medium.     

一种波导窄边裂缝天线缝隙倾角的改进方法

为减小波导窄边裂缝天线缝隙间互耦对天线性能的影响, 实现低副瓣的设计, 提出了一种倾角波动分布的设计方法.天线电流分布选用泰勒分布, 利用HFSS软件确定缝隙倾角初值, 在此基础上得到波动分布的倾斜角度, 并通过遗传算法对缝隙倾角进行优化.使用Matlab与HFSS软件联合仿真, 省略了建模、设置参数等大量操作, 提高了设计效率.基于此, 设计了一款长度为1.2 m的X波段波导窄边裂缝天线, 仿真发现副瓣电平比传统设计方法低2.17 dB, 加工了天线实物并进行了测试, 天线实测增益和副瓣电平分别为20.9 dBi和-28.7 dB, 验证了方法的有效性.     

Iterative FEM for characterising radiating slot in broad wall ofrectangular waveguide

It is shown that the iterative finite element method with the radiation-type boundary condition can give an efficient and accurate solution to the radiation problem. The proposed method is applied to the characterisation of a radiating slot on the broad wall of a rectangular waveguide. The result is compared with those of other conventional methods, and shows a good agreement     

Finite-difference time-domain solution of Maxwell's equations forthe dispersive ionosphere

The application of the finite-difference time-domain (FDTD) technique to problems in ionospheric radio wave propagation is complicated by the dispersive nature of the ionospheric plasma. In the time domain, the electric displacement is the convolution of the dielectric tensor with the electric field, and thus requires information from the entire signal history. It is shown that this difficulty can be avoided by returning to the dynamical equations from which the dielectric tensor is derived. By integrating these differential equations simultaneously with the Maxwell equations, temporal dispersion is fully incorporated. An FDTD approach utilizing the vector wave equation is also presented. The accuracy of the method is shown by comparison for a special case for which an analytic solution is available. The method is demonstrated with examples of pulse propagation in one and two dimensions. The computational limitations of present-generation computers are discussed. The application of this approach to the study of wave propagation in randomly structured ionization is addressed     

Investigation of a method for numerical solution of nonstationary waveguide equations

Results of numerical time-domain calculation of propagation and transformation of ultrawideband electromagnetic pulses in irregular metal waveguides with a variable section are presented for the example of a coaxial corrugated structure. The calculation is performed with the use of a system of nonstationary waveguide equations. A method for estimation of the computation error is described. The method involves the following components (below, referred to as features): monitoring the energy balance, integral estimation of the error in the calculated field, and estimation of the accuracy of the computational realization of the boundary condition on the boundary of the perfect conductor. With the use of a coaxial corrugated structure as an example, it is shown that, for each of the above features, the application of the proposed polynomial basis in the calculations guarantees an accuracy that substantially exceeds the accuracy of measurements. It is shown that the basis of comparison waveguides provides for highly accurate computations in the rms approximation, in spite of the fact that the application of the third feature is impeded because, for a waveguide with a variable section, the boundary conditions cannot be satisfied on perfectly conducting boundary Γ.     

An a posteriori error reduction scheme for the three-dimensionalfinite element solution of Maxwell's equations

The accuracy of the finite element method (FEM) depends on the properties of the mesh which covers the problem geometry. The accuracy can usually be improved by increasing the element density in the mesh or the order of the shape functions in the elements at the expense of a significant increase in computation time. Instead, in this paper an a posteriori error reduction scheme is applied to improve the accuracy in the solution of three-dimensional electromagnetic boundary value problems. In this scheme, first the FEM, solution is generated by the use of lower-order shape functions. Then the numerical error is expressed in terms of higher-order shape functions and calculated on an element-by-element basis from information derived from the FEM solution. Finally, this error is added to the FEM solution to improve its accuracy. The degree of error reduction which is achieved with the application of this scheme is demonstrated by means of several simple electromagnetic boundary value problems     

Output performance of a slot in a waveguide with dielectric insert of finite length

Characteristics of a narrow longitudinal slot positioned over a dielectric insert of finite length completely filling the cross section of a rectangular waveguide have been investigated. The magnetic field excited by a slot in the dielectric insert in the area directly under the slot was determined. Internal admittance of the slot and its energy parameters were numerically investigated.     

Integral equation solution of Maxwell's equations from zerofrequency to microwave frequencies

We develop a new method to precondition the matrix equation resulting from applying the method of moments (MoM) to the electric field integral equation (EFIE). This preconditioning method is based on first applying the loop-tree or loop-star decomposition of the currents to arrive at a Helmholtz decomposition of the unknown currents. However, the MoM matrix thus obtained still cannot be solved efficiently by iterative solvers due to the large number of iterations required. We propose a permutation of the loop-tree or loop-star currents by a connection matrix, to arrive at a current basis that yields a MoM matrix that can be solved efficiently by iterative solvers. Consequently, dramatic reduction in iteration count has been observed. The various steps can be regarded as a rearrangement of the basis functions to arrive at the MoM matrix. Therefore, they are related to the original MoM matrix by matrix transformation, where the transformation requires the inverse of the connection matrix. We have also developed a fast method to invert the connection matrix so that the complexity of the preconditioning procedure is of O(N) and, hence, can be used in fast solvers such as the low-frequency multilevel fast multipole algorithm (LP-MLFMA). This procedure also makes viable the use of fast solvers such as MLFMA to seek the iterative solutions of Maxwell's equations from zero frequency to microwave frequencies     

Conservation of complex power technique for waveguide junctionswith finite wall conductivity

Scattering at the junction of two waveguides with finite wall conductivity is rigorously treated using E-field mode matching and the conservation of complex power technique. At the transverse junction discontinuity between the two waveguides, the complex power absorbed by the junction wall is taken into account along with the usual transfer of complex power from one guide to the other. This leads to a generalized form of the scattering matrix [S] of the lossy junction which incorporates the surface impedance Z_m of the transverse metallic wall, assumed to be a good conductor. The specific case of a copper transverse diaphragm with centered circular iris in an X-band guide is considered and the equivalent TE₁₀ shunt admittance is computed. Numerical results are also given for lossy X-band cavity resonators with circular coupling holes     

Analysis of a centered-inclined waveguide slot coupler

Integral equations are developed for a centered-inclined coupling slot (including the effect of finite wall-thickness of the common broad-wall) and the slot-aperture electric intensity field is found using the method of moments. Numerical results for resonant length, backscattered wave amplitude, and phase variation off-resonance are presented over a range of values of the waveguide b dimension, wall thickness, slot width, and frequency. It is shown that the resonant length is relatively insensitive to slot tilt, &thetas;, for a standard-height X-band waveguide, whereas its dependence on &thetas; is significant for reduced-height waveguides. The phase variation of scattered TE₁₀ waves in both waveguides off-resonance is less for wider slots and smaller b dimensions. Shunt-series coupling slots exhibit greater phase variation off resonance when compared to a centred-inclined coupling slot. Also, the former has a longer resonant length for a smaller b dimension and for a wider slot. Thus the centred-inclined slot coupler possesses superior characteristics. The higher-order mode coupling between a centred-inclined slot coupler and a pair of straddling radiating slots in the branch waveguide is significant     

High-order accurate split-step FDTD method for solution of maxwell?s equations

The split-step finite difference time domain (SS-FDTD) method characterised by unconditional stability is becoming an important numerical method in computational electromagnetics. Proposed is a new high-order accurate unconditionally stable SS-FDTD method, which is derived from the exponential evolution operator. Compared with the conventional SS-FDTD method, the numerical dispersion of the new method is greatly reduced     

Spectral Lanczos decomposition method for time domain and frequencydomain finite-element solution of Maxwell's equations

A technique that combines the spectral Lanczos decomposition method and the finite-element method is introduced that can be used to solve Maxwell's equations in both the frequency and time domains. The present technique is an implicit, unconditionally stable finite-element time and frequency domain scheme. The Lanczos process is implemented only at the largest time or frequency of interest. The efficiency and effectiveness of this new technique are illustrated by using the numerical example of a three-dimensional dielectric-loaded cavity resonator     

Form of field in small-offset longitudinal slot in broad wall of rectangular waveguide

A surface-patch moment method approach is used to examine the electric field distribution in longitudinal slots that have small offsets from the host rectangular waveguide centreline. It is shown that the phase of the transverse electric field in the slot may display a large variation across the slot narrow dimension in such instances.<>