Millimeter Wave Gunn Diode Oscillator Design Based on FDTD Method*

In this paper, a millimeter wave Gunn diode oscillator is analyzed and designed by the finite-difference time-domain (FDTD) method. The design results indicate that the oscillator has an oscillation frequency of 45.0GHz and a higher oscillation voltage. Based on the circuit equations and an integral transform, an improved matrix method is utilized for the oscillator design. This method is also extended to model the hybrid network which is constructed by the high order linear elements and the nonlinear elements with arbitrary connections. The experience shows that the improved FDTD method is stable with the time step length Δt based on the Courant condition. *This work was supported by the National Natural Science Foundation of China.     

屏蔽多导体强电磁脉冲响应的FDTD-MTL混合计算方法研究

 利用电缆的转移阻抗,将空间电磁场在电缆屏蔽层产生的电流作为多导体传输线（MTL）方程中的激励源,提出了计算编织屏蔽多导体电磁脉冲(EMP)响应的FDTD-MTL混合计算方法。分析了电缆转移阻抗的计算模型,并同实验结果进行了比较,证明Tyni提出的转移阻抗模型更符合实验结果。最后,利用该混合方法得到了三导体屏蔽电缆的强电磁脉冲响应。     

NOR and NAND gates using two photon absorption in silicon wire waveguide

Ultrafast all-optical NOR gate based on two photon absorption (2PA) process in SOI waveguide is already established. We have designed NAND gate also based on this process with a novel waveguide coupler structure. Power attenuation due to 2PA process and the working of these gates is developed with FDTD simulation. Dominant 2PA process is incorporated in FDTD update equations and it is shown that the influence of high intensity pump pulses on a different frequency continuous probe beam can be utilized to form NOR as well as NAND gates.     

Sound field of thermoacoustic tomography based on a modified finite-difference time-domain method

A modified finite-difference time-domain （FDTD） method is proposed for the sound field simulation of the thermoacoustic tomography （TAT） in the acoustic speed inhomogeneous medium. First, the basic equations of the TAT are discretized to difference ones by the FDTD. Then the electromagnetic pulse, the excitation source of the TAT, is modified twice to eliminate the error introduced by high frequency electromagnetic waves. Computer simulations are carried out to validate this method. It is shown that the FDTD method has a better accuracy than the commonly used time-of-flight （TOF） method in the TAT with the inhomogeneous acoustic speed. The error of the FDTD is ten times smaller than that of the TOF in the simulation for the acoustic speed difference larger than 50%. So this FDTD method is an efficient one for the sound field simulation of the TAT and can provide the theoretical basis for the study of reconstruction algorithms of the TAT in the acoustic heterogeneous medium.     

Electric and magnetic losses modeled by a stable hybrid with explicit–implicit time-stepping for Maxwell’s equations

A stable hybridization of the finite-element method (FEM) and the finite-difference time-domain (FDTD) scheme for Maxwell’s equations with electric and magnetic losses is presented for two-dimensional problems. The hybrid method combines the flexibility of the FEM with the efficiency of the FDTD scheme and it is based directly on Ampère’s and Faraday’s law. The electric and magnetic losses can be treated implicitly by the FEM on an unstructured mesh, which allows for local mesh refinement in order to resolve rapid variations in the material parameters and/or the electromagnetic field. It is also feasible to handle larger homogeneous regions with losses by the explicit FDTD scheme connected to an implicitly time-stepped and lossy FEM region. The hybrid method shows second-order convergence for smooth scatterers. The bistatic radar cross section (RCS) for a circular metal cylinder with a lossy coating converges to the analytical solution and an accuracy of 2% is achieved for about 20 points per wavelength. The monostatic RCS for an airfoil that features sharp corners yields a lower order of convergence and it is found to agree well with what can be expected for singular fields at the sharp corners. A careful convergence study with resolutions from 20 to 140 points per wavelength provides accurate extrapolated results for this non-trivial test case, which makes it possible to use as a reference problem for scattering codes that model both electric and magnetic losses.     

The extended Fourier pseudospectral time-domain method for atmospheric sound propagation

An extended Fourier pseudospectral time-domain (PSTD) method is presented to model atmospheric sound propagation by solving the linearized Euler equations. In this method, evaluation of spatial derivatives is based on an eigenfunction expansion. Evaluation on a spatial grid requires only two spatial points per wavelength. Time iteration is done using a low-storage optimized six-stage Runge-Kutta method. This method is applied to two-dimensional non-moving media models, one with screens and one for an urban canyon, with generally high accuracy in both amplitude and phase. For a moving atmosphere, accurate results have been obtained in models with both a uniform and a logarithmic wind velocity profile over a rigid ground surface and in the presence of a screen. The method has also been validated for three-dimensional sound propagation over a screen. For that application, the developed method is in the order of 100 times faster than the second-order-accurate FDTD solution to the linearized Euler equations. The method is found to be well suited for atmospheric sound propagation simulations where effects of complex meteorology and straight rigid boundary surfaces are to be investigated.     

Simulation of photodetection using finite-difference time-domain method with application to near-field subwavelength imaging based on nanoscale semiconductor photodetector array

Simulation of detecting photoelectrons using multi-level multi-electron (MLME) finite-difference time-domain (FDTD) method with an application to near-field subwavelength imaging based on semiconductor nanophotodetector (NPD) array is reported. The photocurrents from the photodiode pixels are obtained to explore the resolution of this novel NPD device for subwavelength imaging. One limiting factor of the NPD device is the optical power coupling between adjacent detector pixels. We investigate such power coupling in the presence of absorbing media as well as the spatial distributions of the electric field and photoelectron density using the MLME FDTD simulation. Our results show that the detection resolution is about one tenth of the operating wavelength, which is comparable to that of a near-field scanning optical microscope based on metal clad tapered fiber.     

光子晶体传输特性的时域精细积分法分析

将精细积分法应用于时域有限差分法中,提出了一种求解光子晶体传输特性的时域精细积分法,并对其计算精度及稳定性进行了分析.从一阶麦克斯韦方程出发,在空间上采用Yee元胞进行差分离散,结合吸收边界条件及激励源表达式将方程整理为标准的一阶常微分方程组形式.通过时间步长的精细划分和指数矩阵的加法定理,在时间上利用精细积分法对齐次微分方程进行积分求解,并结合激励向量的特解得到空间离散的场分量,最终通过傅里叶变换求得方程的解.利用时域精细积分法对光子晶体进行了实例计算,并将其结果分别与时域有限差分法和四阶龙格库塔法在精度、稳定性等方面进行了比较,结果表明时域精细积分法具有更高的计算精度,并且克服了时域有限差分法以及四阶龙格库塔法在计算稳定性上对时间步长的限制.提出的方法具有精确、稳定的特点,为光子晶体传输特性的研究提供了一种新的有效的分析方法.     

BOR-FDTD subgridding based on finite element principles

In this paper a recently developed provably passive and stable 3D FDTD subgridding technique, based on finite elements principles, is extended to body-of-revolution (BOR) FDTD. First, a suitable choice of basis functions is presented together with the mechanism to assemble them into an overall mesh consisting of coarse and fine mesh cells. Invoking appropriate mass-lumping concepts then leads to an explicit leapfrog time stepping algorithm for the amplitudes of the basis functions. Attention is devoted to provide the reader with insight into the updating equations, in particular at a subgridding boundary. Stability, grid reflection and dispersion are also discussed. Finally, some numerical examples for toroidal and cylindrical cavities demonstrate the stability and accuracy of the method.     

Low threshold laser cavities of two-dimensional photonic crystal line defect mode

Two-dimensional (2D) rod-type photonic crystal (PC) line defect waveguide (LDW) laser cavities based on three types of line defect modes with zero group velocity are studied by using finite-difference time-domain (FDTD) method. These laser cavities have high quality (Q) factor, better localization of light, non-uniform gain distribution and small overlap between gain medium and light field. Therefore, they have the advantages over conventional and air-bridge PC cavities with uniform gain, such as low threshold, single mode lasing and effectively avoiding thermal effect. From their comparison, one can find the mode at middle Brillouin zones (BZ) is the best one to be used as lasing mode. Its dynamic lasing process and lasing features are demonstrated by the numerical experiment where the FDTD method coupling Maxwell's equations with the rate equations of electronic population is used.     

旋转体时域有限差分法对轴对称亚波长衍射光学元件的分析

采用旋转体时域有限差分法对轴对称亚波长衍射光学元件进行严格的矢量分析.推导了旋转体时域有限差分法的基本计算公式;给出了入射波的设置方法;采用了完全匹配层吸收边界条件;改进了平面波谱传播算法,大大简化了计算过程并提高了计算速度.对多台阶微透镜和二元亚波长微透镜进行分析给出了它们焦平面的电场强度分布.数值计算结果表明,本文的算法可以准确且高效地分析轴对称亚波长衍射光学元件.     

乳腺癌检测的三维微波热声成像技术

提出了三维微波热声成像技术检测早期乳腺肿瘤,成像同时具有高对比度和高分辨率的特点.该技术利用自适应的鲁棒Capon波束成形(RCB)算法进行信号处理和图像重建.基于电磁学和声学时域有限差分(FDTD)法,进行微波热声成像仿真,算例结果证实了该技术用于诊断早期乳腺肿瘤的可行性. 关键词： 乳腺癌检测 微波热声成像 鲁棒的Capon波束成形 时域有限差分     

一种计算多导体传输线电磁脉冲响应的时域方法

基于波形松弛技术, 提出一种计算外界电磁脉冲激励下理想大地上无损多导体传输线瞬态响应的时域迭代方法。首先利用波形松弛技术对复频域内多导体传输线的电报方程进行解耦, 其中相邻导线的耦合作用等效为线上的分布源, 从而使电报方程转换为一系列关于独立导线的解耦方程组; 然后将复频域内传输线的解耦方程转换到时域, 根据时域方程建立相应的等效电路; 最后利用电路仿真软件PSCAD计算电磁脉冲激励下多导体传输线的瞬态响应。本文时域方法的计算结果与时域有限差分(FDTD) 法计算的结果进行对比, 证实了该时域方法的有效性和准确性, 这为工程和科研人员快速评估、分析电磁脉冲激励下多导体传输线的瞬态响应问题提供了一种可靠方法。     

基于移位算子时域有限差分的色散薄层节点修正算法

提出了一种时域有限差分（FDTD）计算中色散介质薄层问题处理的新算法.对于厚度小于一个元胞尺度的电小尺寸色散介质薄层问题,采用将元胞内电位移矢量和磁感应强度加权平均的方法,求得薄层所在元胞内修正点处的等效介质参数.然后根据常见色散介质模型,包括Debye模型、Lorenz模型、Drude模型等,介电常数和磁导率可以表示为jω分式多项式的特点,结合频域到时域的转换关系（即用/t代替jω）和移位算子方法得到了修正点处的时域本构关系,进而获得时域递推计算式.数值结果表明,该方法具有通用、节省计算时间、节省内存和计算精度良好等优点. 关键词： 色散介质薄层 节点修正 移位算子 时域有限差分     

Numerical Analysis of Electromagnetic Fields in Multiscale Model

Modeling technique for electromagnetic fields excited by antennas is an important topic in computational electromagnetics, which is concerned with the numerical solution of Maxwell's equations. In this paper, a novel hybrid technique that combines method of moments(MoM) with finite-difference time-domain(FDTD) method is presented to handle the problem. This approach employed Huygen's principle to realize the hybridization of the two classical numerical algorithms. For wideband electromagnetic data, the interpolation scheme is used in the MoM based on the dyadic Green's function. On the other hand, with the help of equivalence principle, the scattered electric and magnetic fields on the Huygen's surface calculated by MoM are taken as the sources for FDTD. Therefore, the electromagnetic fields in the environment can be obtained by employing finite-difference time-domain method. Finally, numerical results show the validity of the proposed technique by analyzing two canonical samples.     

Equations for finite-difference, time-domain simulation of sound propagation in moving inhomogeneous media and numerical implementation

Finite-difference, time-domain (FDTD) calculations are typically performed with partial differential equations that are first order in time. Equation sets appropriate for FDTD calculations in a moving inhomogeneous medium (with an emphasis on the atmosphere) are derived and discussed in this paper. Two candidate equation sets, both derived from linearized equations of fluid dynamics, are proposed. The first, which contains three coupled equations for the sound pressure, vector acoustic velocity, and acoustic density, is obtained without any approximations. The second, which contains two coupled equations for the sound pressure and vector acoustic velocity, is derived by ignoring terms proportional to the divergence of the medium velocity and the gradient of the ambient pressure. It is shown that the second set has the same or a wider range of applicability than equations for the sound pressure that have been previously used for analytical and numerical studies of sound propagation in a moving atmosphere. Practical FDTD implementation of the second set of equations is discussed. Results show good agreement with theoretical predictions of the sound pressure due to a point monochromatic source in a uniform, high Mach number flow and with Fast Field Program calculations of sound propagation in a stratified moving atmosphere.     

任意形状金属腔体内电磁脉冲的三维计算

提出了模拟任意形状腔体中的内电磁脉冲的三维直角坐标系时域有限差分(FDTD)算法。该算法采用FDTD共形网格技术模拟任意形状腔体的边界,可以解决腔体内非对称的边界问题。推导了射线斜入射的差分方程,进行了三维数值计算,并采用直角坐标系FDTD算法和柱坐标系FDTD算法计算了射线斜入射圆柱腔体产生的内电磁脉冲,二者吻合很好,验证了直角坐标系FDTD算法正确性。     

色散周期结构的辅助场时域有限差分法分析

利用辅助场时域有限差分(FDTD)方法分析色散周期结构的斜入射问题. 主要基于Floquet定理, 在FDTD迭代式中引入辅助场量, 结合变换的周期及吸收边界条件,解决了周期结构斜入射问题的电磁特性仿真. 进一步将辅助场FDTD方法引入至色散周期结构的模拟, 结合Z变换方法,给出了基于Drude色散模型的具体迭代公式. 数值计算结果表明所构建方法的有效性及普适应.     

一维随机激光器中准态模的饱和特性研究

针对随机激光器的半经典理论是应用电磁场时域有限差分法数值求解半经典随机激光模型方程组，基于半经典理论数值研究了一维随机激光器中准态模式的饱和特性，获得了不同准态模的空间分布和频谱分布图。计算结果分析显示：准态模式的某些特征参数如局域程度将会影响系统的饱和特性。利用这一结果，可以通过单频抽运方法选择具有低阈值、高饱和强度的准态模式作为整个激光系统的稳态输出模式。     

二维周期性多孔La_(0.83)Sr_(0.17)Mn_(0.9)Zn_(0.1)O_3发射率研究

基于麦克斯韦方程组,利用时域有限差分方法(FDTD)计算了二维周期性多孔钙钛矿型氧化物La_(0.83)Sr_(0.17)Mn_(0.9)Zn_(0.1)O_3(LSMZO)的光谱特性,讨论了结构尺寸对光谱特性的影响。计算结果表明,当孔径约比热辐射波长小一个量级时,周期性多孔LSMZO的发射率比块体材料有所提高,这对改善热致变色材料的性能具有一定的指导意义。