The incorporation of microscopic material models into the FDTDapproach for ultrafast optical pulse simulations

We are developing full-wave vector Maxwell equation solvers for use in studying the physics and engineering of linear and nonlinear integrated photonics systems. Particular emphasis has been given to the interaction of ultrafast optical pulses with nonresonant and resonant optical materials and structures. Results are reviewed that simulate the interaction of ultrafast optical pulses with structures (e.g., gratings of finite length) filled with materials exhibiting resonant loss or gain. In particular, we consider structures loaded with atomic media resonant at or near the frequency of the incident optical radiation. Interest in these problems follows from our desire to design micron-sized linear and nonlinear guided-wave couplers, modulators, and switches. These resonant problems pose interesting FDTD modeling issues because of the many time and length scales involved. To understand the physics underlying the small-distance scale and short-time scale interactions, particularly in the resonance regime of the materials and the associated device structures, a first principles approach is desirable. Thus, the results presented are based upon a quantum mechanical two-level atom model for the materials. The resulting Maxwell-Bloch model requires a careful marriage between microscopic (quantum mechanical) material models of the resonant material systems and the multidimensional, macroscopic Maxwell's equations solver. The FDTD numerical issues are discussed. Examples are given to illustrate the design and control of these resonant large-scale optical structures. An optical triode is designed and characterized with the FDTD Maxwell-Bloch simulator     

An FDTD algorithm with perfectly matched layers for generaldispersive media

A three-dimensional (3-D) finite difference time domain (FDTD) algorithm with perfectly matched layer (PML) absorbing boundary condition (ABC) is presented for general inhomogeneous, dispersive, conductive media. The modified time-domain Maxwell's equations for dispersive media are expressed in terms of coordinate-stretching variables. We extend the recursive convolution (RC) and piecewise linear recursive convolution (PLRC) approaches to arbitrary dispersive media in a more general form. The algorithm is tested for homogeneous and inhomogeneous media with three typical kinds of dispersive media, i.e., Lorentz medium, unmagnetized plasma, and Debye medium. Excellent agreement between the FDTD results and analytical solutions is obtained for all testing cases with both RC and PLRC approaches. We demonstrate the applications of the algorithm with several examples in subsurface radar detection of mine-like objects, cylinders, and spheres buried in a dispersive half-space and the mapping of a curved interface. Because of their generality, the algorithm and computer program can be used to model biological materials, artificial dielectrics, optical materials, and other dispersive media     

A Highly Accurate FDTD Model for Simulating Lorentz Dielectric Dispersion

A highly accurate and numerically stable model of Lorentz dielectric dispersion for the finite-difference time-domain (FDTD) method is presented. The coefficients of the proposed model are optimally derived based on the Maclaurin series expansion (MSE) method and it is shown that the model is much better than the other four reported models in implementing the Lorentz dielectric dispersion with error of relative permittivity several orders lower. The model's stability and performance are also analyzed when it is incorporated into the practical second- and fourth-order accurate FDTD algorithms for an exemplified Lorentz medium. Interestingly, we find that all the mentioned models show nearly the same performance in the second-order algorithm due to its large intrinsic numerical dispersion and the superiority of the proposed MSE model begins to be manifested in the higher-order, say, fourth-order FDTD algorithms as implied by the governing numerical dispersion equations.      

Maxwellian material-based absorbing boundary conditions for lossymedia in 3-D

A two time-derivative Lorentz material (2TDLM), which has been shown previously to be the correct Maxwellian medium choice to match an absorbing layer to a lossy region, is extended here to a complete absorbing boundary condition (ABC) for three-dimensional (3-D) finite-difference time-domain (FDTD) simulators. The implementation of the lossy 2TDLM (L2TDLM) ABC is presented. It is shown that in contrast to the one-dimensional (1-D) and two-dimensional (2-D) versions, the full 3-D ABC requires a three time-derivative Lorentz material in the edge and corner regions to achieve a rigorous matching of the resulting Maxwellian absorbing layer to the lossy medium. The 3-D ABC implementation thus requires the introduction of an auxiliary field to handle the edge and corner regions to achieve a state-space form of the update equations in the ABC layers. Fully 3-D examples including pulsed dipole radiation and pulsed Gaussian beam propagation in lossless and lossy materials as well as pulse propagation along a microstrip over lossless and lossy materials are included to illustrate the effectiveness of the L2TDLM ABC     

一种新的简化行波边界条件在FDTD算法中的实现

本文提出一种新的边界条件。这种边界条件在边界处强加理想导体对计算场区进行截断,而将由此产生的反射场分离去除,从而减小反射所产生的干扰。与PML边界条件相比,由于它不需要吸收层,不需要PML层中人为的场量分解,因此节约了内存,提高了计算速度。文中给出一维、二维空间的计算实例,计算结果表明原理是可行的。     

3D crank-nicolson finite difference time domain method for dispersive media

The unconditionally stable Crank-Nicolson finite difference time domain (CN-FDTD) method is extended to incorporate frequency-dependent media in three dimensions. A Gaussian-elimination-based direct sparse solver is used to deal with the large sparse matrix system arising from the formulation. Numerical results validate and confirm that the scheme is unconditionally stable for time steps over the Courant-Friedrich-Lewy limit of classical FDTD.     

Robustness of Printed Patch Antennas

We address the question of robustness of damaged microstrip antennas, the damage being either penetrating, caused by fragment impact, or floating, caused by manufacturing imperfections. A simple analytic expression is derived to facilitate the prediction of robustness. To verify this expression a Monte Carlo method, based on a general 3D electromagnetic solver, is used to evaluate the robustness of the antennas. The simulations are verified by measurements and supplementary simulations in an alternative electromagnetic solver, using the finite difference time domain method (FDTD). The agreement between the simulated results and the analytic expression is found to be good in a qualitative comparison.     

Simple and Efficient PML Algorithm for Truncating Nonlinear FDTD Domains Based on the <Emphasis Type="Italic">Z</Emphasis>-Transform Method

Based on the Z-transform method, a simple, efficient and unsplit-field implementation of the Stretched Coordinate Perfectly Matched Layer (SC-PML) is proposed for truncating the nonlinear dispersive Finite Difference Time Domain (FDTD) lattices. In addition, the nonlinear FDTD formulations using the Z-transform method are reformulated with the advantage of a simple derivative process. The proposed algorithm is validated through two numerical examples carried out in one dimensional and two dimensional domains which include Lorentz dispersion as well as Kerr and Raman nonlinearities.     

A summary and systematic analysis of FDTD algorithms for linearlydispersive media

This paper examines the most popular advances in the FDTD algorithm development, as applied to electromagnetic wave propagation in linearly dispersive media. Several methodologies are presented, and comparisons are made in order to demonstrate the strengths and weaknesses of the various approaches. In particular, direct-integration and recursive-convolution schemes, associated with wave propagation in a cold plasma, Debye dielectrics, and Lorentz materials, are considered     

用于电磁散射分析的积分方程快速直接求解法研究及进展

介绍了一系列用于电磁散射分析的积分方程快速直接求解方法,旨在显著缓解或避免积分方程迭代求解收敛缓慢甚至不收敛的问题,为积分方程提供一个快速稳定的数值求解手段.文中详细介绍了快速直接求解方法的优点、应用以及国内外的研究动态;重点讨论了几种不同的方法,分别为分级矩阵（hierarchical matrices,-matrices）以及分级非对角低秩矩阵（hierarchically off-diagonal low-rank matrices,HODLR）,包括每种方法的构建以及分解求逆方式;对各个方法的优缺点展开了进一步讨论;给出了各个方法的分解以及内存复杂度和复杂飞机模型的电磁散射分析数值算例来证明各个方法的效率和精度.最后,对快速直接求解方法当前仍然存在的主要挑战和可能的策略进行了简略的讨论以及展望.     

Propagation in linear dispersive media: finite differencetime-domain methodologies

Finite difference time-domain (FDTD) methodologies are presented for electromagnetic wave propagation in two different kinds of linear dispersive media: an Nth order Lorentz and an Mth order Debye medium. The temporal discretization is accomplished by invoking the central difference approximation for the temporal derivatives that appear in the first-order differential equations. From this, the final equations are temporally advanced using the classical leapfrog method. One-dimensional scattering from a dielectric slab is chosen for a test case. Provided that the maximum operating frequency times the time step is small and that the wave is adequately resolved in space, as shown in the error analysis, the agreement between the computed and exact solutions will be excellent. The attached data, which are associated with the four pole Lorentz dielectric and the five pole Debye medium, verify this assertion     

Accurate FDTD Dispersive Modeling for Concrete Materials

This work presents an accurate finite‐difference time‐domain (FDTD) dispersive modeling of concrete materials with different water/cement ratios in 50 MHz to 1 GHz. A quadratic complex rational function (QCRF) is employed for dispersive modeling of the relative permittivity of concrete materials. To improve the curve fitting of the QCRF model, the Newton iterative method is applied to determine a weighting factor. Numerical examples validate the accuracy of the proposed dispersive FDTD modeling.     

An Alternative Algorithm for Both Narrowband and Wideband Lorentzian Dispersive Materials Modeling in the Finite-Difference Time-Domain Method

In this study, an alternative algorithm is proposed for modeling narrowband and wideband Lorentzian dispersive materials using the finite-difference time-domain (FDTD) method. Previous algorithms for modeling narrowband and wideband Lorentzian dispersive materials using the FDTD method have been based on a recursive convolution technique. They present two different and independent algorithms for the modeling of the narrowband and wideband Lorentzian dispersive materials, known as the narrowband and wideband Lorentzian recursive convolution algorithms, respectively. The proposed alternative algorithm may be used as a general algorithm for both narrowband and wideband Lorentzian dispersive materials modeling with the FDTD method. The second-order motion equation for the Lorentzian materials is employed as an auxilary differential equation. The proposed auxiliary differential-equation-based algorithm can also be applied to solve the borderline case dispersive electromagnetic problems in the FDTD method. In contrast, the narrowband and wideband Lorentzian recursive convolution algorithms cannot be used for the borderline case. A rectangular cavity, which is partially filled with narrowband and wideband Lorentzian dispersive materials, is presented as a numerical example. The time response of the electric field z component is used to validate and compare the results     

Conformal hybrid finite difference time domain and finite volumetime domain

A hybrid method that combines the finite difference time domain (FDTD) and the finite volume time domain (FVTD) methods is presented. The FVTD, based on a conformal and unstructured grid is used in the near vicinity of the surface of a scatterer, and the FDTD is used to model the fields in the surrounding area. The two are coupled together through interpolation. The vertex-based FVTD allows for more convenient and accurate interpolations than a conformal FDTD method. The hybrid method is validated through two examples-the scattering by a PEC cube and sphere-by comparison with the direct FDTD solution, and with an exact Mei series solution for the spherical case     

Circuit analysis of electromagnetic radiation and field couplingeffects for networks with embedded full-wave modules

With continually increasing operating frequencies, the analysis of electromagnetic interference (EMI)-related effects is becoming an important issue for high-speed designs. An algorithm is presented for fast analysis of radiation and incident field coupling effects in high-speed circuits. The proposed technique provides an efficient means for combining the solutions from full-wave field solvers such as the finite-difference time-domain (FDTD) method with circuit level simulators such as SPICE for calculating radiated/coupled fields in arbitrarily shaped interconnect structures. The technique speeds up the whole simulation process by employing a model-reduction-based approach, and also overcomes the numerical stability problems associated with the FDTD, in the presence of nonlinear terminations. In addition, the proposed algorithm provides a direct access to existing vast device libraries of SPICE in EMI analysis     

介质圆柱的单站微波成像方法

提出一种对介质圆柱实现单站微波成像的方法。该方法通过时域有限差分法进行电磁场正过程的仿真计算,采用整数微分进化策略实现逆过程的寻优计算。分别分析TE模式和TM模式的近场散射信号得到介质成像目标在电磁波传播方向上尺寸大小的估计,并以此为依据,确定成像目标的尺寸范围,从而确定逆过程的寻优区间。该方法无需像传统成像方法围绕成像目标设置多个发射/接收天线以获取成像信息,从而大大减少了成像的必要条件。采用该方法,在TE模式和TM模式下分别对介质圆柱目标进行仿真成像,获得了良好的效果。     

Unsplit-Field PML Algorithm for Truncating Nonlinear FDTD Domains

In this paper, unsplit-field Perfectly Matched Layer (PML) formulations are presented for truncating nonlinear dispersive Finite Difference Time Domain (FDTD) grids. The proposed scheme is based on incorporating the nonlinear Z-transform FDTD algorithm into the Auxiliary Differential Equation PML (ADE-PML) formulations. Numerical example carried out in one dimensional domain which includes Lorentz dispersion as well as Kerr and Raman nonlinearities is included to show the validity of the formulations.     

Electromagnetic Sensitivity Analysis and Shape Optimization Using Method of Moments and Automatic Differentiation

Sensitivity analysis is an important part of gradient-based optimization of electromagnetic devices. We demonstrate how sensitivity analysis can be incorporated into an existing in-house method of moments solver with a relatively small amount of labor by using a technique called automatic differentiation (AD). This approach enables us to obtain (geometrical) sensitivities of the discrete solution with accuracy up to numerical precision. We compare the assembly time and memory usage of the modified and original solvers. Moreover, we optimize the shape of a dipole antenna and the dimensions of a Yagi–Uda array using the presented AD technique, traditional response level finite difference sensitivities, and so-called feasible adjoint sensitivity technique.      

A Single-Boundary Implicit and FFT-Accelerated Time-Domain Finite Element-Boundary Integral Solver

A novel time-domain finite-element boundary integral (FE-BI) solver for analyzing broadband scattering and radiation from free-standing electromagnetically large and perfect electrically conducting platforms supporting inhomogeneous and geometrically intricate structures is presented. The solver has three distinctive features that render it especially attractive for broadband analysis of installed antennas. i) The FE and BI solver components are hybridized using a single-surface interface. ii) The hybrid equations are solved by an implicit time-marching scheme accelerated by an (outer) Jacobi iterative solver that leverages (inner) direct FE and iterative BI solvers. iii) The BI solver component is accelerated by a distributed memory parallel implementation of the time-domain adaptive integral method based on the message-passing interface. The accuracy, late-time stability, and performance of the proposed time-domain FE-BI solver are demonstrated via its application to various scattering and radiation problems; moreover, the solver is used to characterize conformally mounted antennas on several platforms including an aircraft     

The time-frequency interpretation for transient evolution of wavepropagation through dispersive medium

The propagation of electromagnetic waves in a linear, dispersive Lorentz medium is calculated using the finite-difference time-domain (FDTD) method; their time-frequency (TF) characteristics are studied using the Gabor extension. Numerical results show that the TF spectrum gives a clear interpretation for transient evolution of ultra wideband pulse propagation through a Lorentz medium