MRTD算法的APML实现及其在光波导仿真中的应用

实现了基于Daubechies紧支集尺度函数的时域多分辨分析(MRTD)算法的各向异性理想匹配层(APML)吸收边界条件,并将其应用到平面光波导的仿真和分析中。验证结果表明,APML吸收层性能主要由其层数和计算空间步长所决定。与传统的时域有限差分(FDTD)法相比,基于高阶消失矩Daubechies尺度函数的MRTD法可以提高吸收层性能。     

基于时域多分辨法微带线串扰分析

时域多分辨分析法作为一种时域计算方法,其吸收边界直接影响到计算的准确度。采用具有紧支撑性和对称性的CDF(2,6)尺度函数作为基函数得到了三维各向异性完全匹配层吸收边界;将时域多分辨分析法应用于微带线串扰分析中,给出了适用于任意尺度函数的集总电阻和阻抗电压源模拟方法,并用该方法分析了某印刷电路板上两根平行微带线的串扰问题。仿真结果表明:与传统的时域有限差分算法相比,以CDF(2,6)尺度函数为基函数的时域多分辨分析法只需要其一半的网格数,计算速度提高三倍,同时具有内存使用少、利用率高等特点。     

Multiple image technique (MIT) and anisotropic perfectly matchedlayer (APML) in implementation of MRTD scheme for boundary truncationsof microwave structures

This paper presents an adjustable multiple image technique (MIT) and an anisotropic perfectly matched layer (APML) employed in the context of multiresolution time-domain (MRTD) scheme for the truncation of the computational boundary, with the MIT used for perfect electrically conducting (PEC) shields and the APML for open structures. We begin by presenting a systematic formulation for developing the constitutive relations and update equations in the transform domain of the MRTD, when considering both the original and image regions. We then illustrate the applications of the above techniques by analyzing a two-layer dielectric-loaded cavity, printed circuit enclosed by a PEC, as well as open transmission lines. Although, in principle, one can employ a large number of images to ensure the accuracy of the MRTD computation, in practice, it is useful, from the point-of-view of computational efficiency, to develop a criterion that determines the number of requisite images. While its formulation may appear to be lengthy, the MIT is based on physical concepts that are fairly well suited for computer programming     

A nonlinear and dispersive APML ABC for the FD-TD methods

We have developed a modified anisotropic perfectly matched layer (APML) absorbing boundary condition (ABC) for the finite-difference time-domain (FD-TD) analysis of nonlinear and dispersive media. The formulation is a simple modification to the original nonsplit APML, and retains the robustness and the simple implementation in the FD-TD and the higher-order schemes. The proposed ABC has a broad area of application, and is especially suitable for the analysis of nonlinear optical waveguide problems.     

Optimization of nonlinear dispersive APML ABC for the FDTD analysis of optical solitons

We have investigated the parameter optimization for the nonlinear dispersive anisotropic perfectly matched layer (A-PML) absorbing boundary conditions (ABCs) for the two- and the three-dimensional (2D and 3D) finite-difference time-domain (FDTD) analyses of optical soliton propagation. The proposed PML is applied to the FDTD method of the standard and the high-spatial-order schemes. We first searched for the optimum values of the loss factor, permittivity, and the order of polynomial grading for particular numbers of APML layers in a two-dimensional (2-D) setting with Kerr and the Raman nonlinearity and Lorentz dispersion, and then we applied the optimized APML to a full three-dimensional (3-D) analysis of nonlinear optical pulse propagation in a glass substrate. An optical pulse of spatial and temporal soliton profile has been launched with sufficient intensity of electric field to yield a soliton pulse, and a reflection of -60dB has been typically obtained both for the 2-D and the 3-D cases.     

Unconditionally stable ADI-FDTD formulations of the APML for frequency-dependent media

Unconditional stable formulations of the anisotropic perfectly matched layer (APML) are presented for truncating frequency-dependent media. The formulations are based on the auxiliary differential equation and the alternating direction implicit finite-difference time-domain (ADI-FDTD) methods. Numerical examples carried out in one and two dimensions show that the proposed formulations remain unconditionally stable with inclusion of material dispersion into ADI-FDTD implementation of APML.     

High-order FDTD and auxiliary differential equation formulation of optical pulse propagation in 2-D Kerr and Raman nonlinear dispersive media

We reformulate the existing auxiliary differential equation (ADE) technique in the context of the finite-difference time-domain analysis of Maxwell's equations for the modeling of optical pulse propagation in linear Lorentz and nonlinear Kerr and Raman media. Our formulation is based on the polarization terms and allows simple and consistent implementation of such media together with the anisotropic perfectly matched layer (APML) absorbing boundary condition. The disadvantages of the ADE technique, i.e., requiring additional storage for auxiliary variables, has been overcome by adopting the high-order finite-difference schemes derived from the previously reported wavelet-based formulation. With those techniques, we demonstrate in two-dimensional setting an effective and accurate numerical analysis of the spatio-temporal soliton propagation as a consequence of the physically originated balanced phenomena between the self-focusing effect of nonlinearity and the pulse broadening effects of the temporal dispersion and of the spatial diffraction.     

A nonuniform FDTD technique for efficient analysis of propagationcharacteristics of optical-fiber waveguides

In this paper, we present a highly efficient one-dimensional cylindrical nonuniform finite-difference time-domain (1-D CNUFDTD) method, which utilizes the unsplit anisotropic perfectly matched layer (APML) for mesh truncation along the radial direction to analyze axisymmetric optical-fiber waveguides. As a first step, we validate the proposed FDTD algorithm by analyzing a uniform dielectric waveguide of circular cross section and show that the results are in excellent agreement with the conventional mode theory solutions. Next, we apply the algorithm to analyze propagation characteristics of a number of commonly used optical-fiber waveguides, i.e., step-index multimode, graded-index multimode, and single-mode step-index configurations     

Scattering analysis by the multiresolution time-domain method usingcompactly supported wavelet systems

We present a formulation of the multiresolution time-domain (MRTD) algorithm using scaling and one-level wavelet basis functions, for orthonormal Daubechies and biorthogonal Cohen-Daubechies-Feauveau (CDF) wavelet families. We address the issue of the analytic calculation of the MRTD coefficients. This allows us to point out the similarities and the differences between the MRTD schemes based on the aforementioned wavelet systems and to compare their performances in terms of dispersion error and computational efficiency. The remainder of the paper is dedicated to the implementation of the CDF-MRTD method for scattering problems. We discuss the approximations made in implementing material inhomogeneities and validate the method by numerical examples     

基于MRTD的天线电磁辐射分析

系统地研究了时域多分辨（MRTD）算法,并利用该算法计算天线的电磁辐射,验证与其他算法比较下所具有的优越性,推导出采用具有紧支撑特性的Daubechies小波作为展开基的MRTD算法的计算公式,分析其色散特性和吸收边界条件,通过模型分析圆柱形单极天线的电磁辐射,仿真出该天线的一系列电参数值,经过优化可以得出比较理想的结果。结果表明MRTD具有良好的色散特性和精度,同时还具有计算速度快、存储空间少和内存使用量小等优点,有效地弥补了其他计算机电磁算法的不足。     

Calculation of Cutoff Wavenumbers for TE and TM Modes in Tubular Lines with Offset Center Conductor (Short Paper)

The cutoff wavenumbers of TE and TM modes (higher order modes) in a tubular line having an offset center conductor have heen calculated. Whereas most previous methods used to study this structure were of an approximate nature, the analytical method developed by Singh and Kothari leads to a rigorous analytical formulation. The boundary conditions on both conductor boundaries, assumed to be perfectly conducting, are satisfied exactly. The cutoff values calculated show that some results previously reported are inaccurate.     

Application of Haar-wavelet-based multiresolution time-domainschemes to electromagnetic scattering problems

The multiresolution time-domain (MRTD) algorithm is applied to the problem of general two-dimensional electromagnetic scattering. A Haar wavelet expansion is utilized. A parallel between Haar MRTD and the classic Yee finite-difference time-domain (FDTD) algorithm is discussed, and results of simulations on canonical targets are shown for comparison. We focus on the incident-field implementation, which, in our case, consists of a pulsed plane wave. Also, we consider scattering in a half-space environment, with application to subsurface sensing. The results illustrate the advantage of the Haar MRTD method as compared with the classic FDTD, which consists of reduced memory and execution time requirements, without sacrificing accuracy     

A novel efficient algorithm for scattering from a complex BOR usingmixed finite elements and cylindrical PML

An efficient finite-element method (FEM) is developed to compute scattering from a complex body of revolution (BOR). The BOR is composed of a perfect conductor and impedance surfaces and arbitrary inhomogeneous materials. The method uses edge-based vector basis functions to expand the transverse field components and node-based scalar basis functions to expand the angular component. The use of vector basis functions eliminates the problem of spurious solutions suffered by other three component FEM formulations. The FEM mesh is truncated with a perfectly matched layer (PML) in cylindrical coordinates. The use of PML in cylindrical coordinates avoids the wasted computation which results from a spherical mesh boundary with an elongated scatterer. The FEM equations are solved by ordering the unknowns with a reverse Cuthill-McKee algorithm and applying a banded-matrix solution algorithm. The method is capable of handling large, realistic radar targets, and good agreement with measured results is achieved for benchmark targets     

Three-dimensional diffraction by infinite conducting and dielectric wedges using a generalized total-field/scattered-field FDTD formulation

We extend the generalized total-field/scattered-field formulation of the finite-difference time-domain method to permit efficient computational modeling of three-dimensional (3-D) diffraction by infinite conducting and dielectric wedges. This new method allows: 1) sourcing a numerical plane wave having an arbitrary incident angle traveling into, or originating from, a perfectly matched layer absorbing boundary and 2) terminating the infinite wedge inside the perfectly matched layer with negligible reflection. We validate the new method by comparing its results with the analytical diffraction coefficients for an infinite 3-D right-angle perfect electric conductor wedge obtained using the uniform theory of diffraction. Then, we apply the new method to calculate numerical diffraction coefficients for a 3-D infinite right-angle dielectric wedge, covering a wide range of incident and scattering angles. Finally, we show means to compactly store the calculated diffraction coefficients in a manner which permits easy interpolation of the results for arbitrary incidence and observation angles.     

Multiresolution time-domain algorithm using CDF biorthogonalwavelets

A new approach to the multiresolution time-domain (MRTD) algorithm is presented in this paper by introducing a field expansion in terms of biorthogonal scaling and wavelet functions. Particular focus is placed on the Cohen-Daubechies-Feauveau (CDF) biorthogonal-wavelet class, although the methodology is appropriate for general biorthogonal wavelets. The computational efficiency and numerical dispersion of the MRTD algorithm are addressed, considering several CDF biorthogonal wavelets, as well as other wavelet families. The advantages of the biorthogonal MRTD method are presented, with emphasis on numerical issues     

Efficient Second Harmonic Generation Through Selective Photonic Crystal-Microcavity Coupling

In this paper, a new 2-D frequency converter based on second harmonic generation (SHG) in GaAs photonic crystal waveguides is proposed. The input waveguide, where the second order nonlinear process takes place, is coupled to a secondary waveguide that is designed to allow only SH propagation. A row of photonic crystal microcavity resonators is then placed parallel to the waveguides in order to assist the field coupling. By tuning the resonance of the microcavities at second harmonic wave, the waveguides-microcavities arrangement showed good enhancement of conversion efficiency and selectivity. The performance of the proposed frequency converter has been analyzed by using multiresolution time domain (MRTD) scheme developed for nonlinear problems in conjunction with uniaxial perfectly matched layer (UPML) boundary conditions that rigorously truncate the computational window.     

高阶各向异性阻抗边界条件的导出

在求解各向异性介质涂敷物体的电磁散射中 ,采用高阶各向异性阻抗边界条件可以简化求解过程 ,提高近似解的精度。文中采用谱域法导出各向异性介质涂敷平面的二阶张量阻抗边界条件 ,并通过例子证明其精确性。     

Unconditionally Stable Z-Transform ADI-PML Algorithm for Lorentzian Double Negative Meta-Materials

Unconditionally stable formulations of the anisotropic perfectly matched layer (APML) are presented for truncating double negative (DNG) meta-material finite difference time domain (FDTD) grids. In the proposed formulations, the Z-transform theory is employed in the alternating direction implicit FDTD (ADI-FDTD) scheme to obtain update equations for the field components in the DNG meta-material domains. Numerical examples carried out in one dimensional Lorentzian type DNG meta-material domains are included to show the validity of the proposed formulations.     

Three-dimensional biorthogonal multiresolution time-domain method and its application to electromagnetic scattering problems

A three-dimensional (3-D) multiresolution time-domain (MRTD) analysis is presented based on a biorthogonal-wavelet expansion, with application to electromagnetic-scattering problems. We employ the Cohen-Daubechies-Feauveau (CDF) biorthogonal wavelet basis, characterized by the maximum number of vanishing moments for a given support. We utilize wavelets and scaling functions of compact support, yielding update equations involving a small number of proximate field components. A detailed analysis is presented on algorithm implementation, with example numerical results compared to data computed via the conventional finite-difference time-domain (FDTD) method. It is demonstrated that for 3-D scattering problems the CDF-based MRTD often provides significant computational savings (in computer memory and run time) relative to FDTD, while retaining numerical accuracy.     

Generalized Form of Telegrapher's Equations for the Electromagnetic Field Coupling to Buried Wires of Finite Length

In this paper, a generalized form of telegrapher's equations for electromagnetic field coupling to buried wires is derived. The presented approach is based on thin-wire antenna theory. The effect of a dissipative half-space is taken into account via the reflection/transmission coefficient approximation. The conductor losses can be taken into account via the surface impedance per unit length. The derived equations are treated numerically via the Galerkin–Bubnov indirect boundary element method. Numerical results are presented for induced current along the wire, and compared with transmission-line (TL) and modified TL (MTL) approximations, respectively, for the case of perfectly conducting electrode buried in a lossy medium. It is shown that the TL and MTL approximations can result in an inaccurate induced current distribution along the conductor at HFs and for shorter electrode lengths, respectively.