一种基于波动方程的新高阶FDTD方法

 提出了一种基于二阶波动方程的（2M,4）高阶时域有限差分(FDTD)方法，通过使用辛积分传播子(SIP)在时域上获得4阶精度，使用离散奇异卷积(DSC)方法在空域上达到2M阶精度。与已有的(2M，4) 阶FDTD方法相比，虽然两者都采用SIP和DSC方法，但是此二者的不同点在于：第一，新方法基于二阶波动方程；第二，在离散计算空间时使用单一网格而不是传统的Yee网格；第三，单独计算某一场分量从而节约内存并减少计算量。数值计算结果表明，与传统高阶算法相比，基于波动方程的高阶FDTD方法耗费的机时只有它的50%,内存消耗下降10%, 而两者的计算结果之间相对误差小于5‰。     

细缝算法在细缝结构屏蔽效能计算中的应用

通过比较不同细缝算法(TSF)计算误差随细缝宽度相对网格步长占比和频率的变化,以及各TSF算法计算获得的孔缝处及远离孔缝位置场分布的差异,给出了时域有限差分（FDTD）计算中不同TSF算法的适用性。在此基础上,将TSF算法用于分析工程中搭接缝结构的屏蔽效能问题,结果表明:将工程搭接缝等效模型与TSF算法结合,能够使用FDTD快速地计算其屏蔽效能,有效解决了基于FDTD的含细缝复杂结构的屏蔽效能评估问题。     

交隐式BOR-FDTD在非核电磁脉冲导线耦合分析中的应用

 交隐式BOR-FDTD能将3维空间电磁问题转换到2维空间处理,具有节省计算时间和计算机内存的优点。运用该算法结合平面波的柱面波展开,通过总场/散射场连接边界条件引入入射平面波,计算了高功率微波和超宽带电磁脉冲作用下自由空间有限长导线上的感应电流,并对感应电流峰值和导线长度之间的变化关系进行了分析。计算结果表明:与传统3维FDTD算法比较,交隐式BOR-FDTD算法在节省大量计算机内存的同时可将计算速度提高数倍。     

基于FDTD方法的光栅结构光谱特性研究

基于时域有限差分(FDTD)法,从麦克斯韦方程组出发,结合周期边界条件将完全匹配层SAC-PML吸收边界条件应用到所建立的光栅数值模型中.对光栅结构和光滑表面结构的光谱特性进行了数值计算,得到了TM波入射时结构的吸收率,讨论了金属光栅耦合的表面等离子极化(SPPs)和空腔谐振模(Microcavity Mode)现象....     

基于紧致差分格式的高效时域有限差分算法

探讨一种基于紧致差分格式的高效时域有限差分算法(high-order compact-FDTD),该方法不仅提高计算精度,而且网格结点少、内存使用率和CPU时间大为降低.利用紧致格式FDTD方法实现无耗波导系统及光子晶体光纤中电磁波传播的数值模拟.通过计算实例验证算法的高效性.     

带阻性负载细导线对电磁脉冲响应的有限差分算法

在原始的FDTD细线算法基础上,把带负载细导线模型分成导线、电阻和吸收三个部分,分别用不同的偏微分方程描述,使其可以处理两端带有纯电阻性负载细线电磁脉冲散射问题,进而得到电阻负载上消耗的总能量及对应的功率消耗。用该方法计算得到的结果与文献结果进行了比较,证明了该方法的有效性。最后用此方法对一种典型情况进行了计算,并对结果进行了分析。该方法是对FDTD方法中细线算法的补充和提高,经过修改也可以用于非阻性负载的情况。     

基于JASMIN的并行CP-FDTD建模与屏蔽效能评估应用

时域有限差分(FDTD)中采用环路法(CP)进行复杂金属细缝结构建模,可突破细缝结构对空间步长的约束而大大减少计算资源的消耗。提出CP-FDTD在大规模并行化平台的建模方法,通过对工程金属细缝结构自动建模以及对CP算法的自动适配,实现CP-FDTD的并行化处理。利用所开发的并行CP-FDTD算法分析了开不同工程细缝金属腔在0.05~3.00 GHz内的电磁屏蔽效能,结果表明所开发的具有金属细缝建模功能的并行化CP-FDTD自动适配处理技术,与加密网格的传统FDTD(fine-FDTD)计算结果吻合良好,且计算效率显著提升。     

1维介质光栅近场及其衍射的FDTD分析

 应用FDTD方法计算了单色平面波斜入射时1维介质光栅的近场，进而求出介质光栅的衍射效率。借助于周期边界条件，整个计算区域为周期结构的一个单元。考虑入射波在两种介质界面上会产生反射和透射，故在总场边界上引入入射波、反射波和透射波。给出了光栅单元截面为矩形和梯形的算例。该方法可用于斜入射情形下具有复杂结构和任意单元截面的介质栅近场及其衍射特性分析。     

三维周期结构弱无条件稳定时域有限差分算法

从麦克斯韦方程出发,导出了适用于周期结构的三维弱无条件稳定时域有限差分（FDTD）算法的迭代式,在理论上证明了其稳定性条件,其稳定性条件比普通FDTD的稳定性条件要宽松,并将周期边界条件应用到迭代式中,得到了可直接编程迭代的方程,给出了对其特有的一类非三对角阵的解决办法。最后通过算例将计算结果与常规FDTD及ADI-FDTD计算结果比较,验证了算法的精确性和有效性。     

瞬变电磁场模拟中的CPML吸收边界条件

提出用于瞬变电磁法(TEM)模拟的时域有限差分(FDTD)算法中的卷积完全匹配层(CPML)吸收边界条件.首先,在磁场散度方程显式处理条件下,计算磁场z分量时,构造出一种计算时域卷积项的方法,并详细推导计算磁场z分量的表达式.而后,对均匀半空间模型进行数值计算.结果表明,提出的CPML吸收边界条件在保证计算精度的前提下,实现了瞬变电磁法时域有限差分高效正演计算.     

Bandgap characteristics of 2D plasma photonic crystal with oblique incidence:TM case

A novel periodic boundary condition (PBC), that is the constant transverse wavenumber (CTW) method, is introduced to solve the time delay in the transverse plane with oblique incidence. Based on the novel PBC, the FDTD/PBC algorithm is proposed to study periodic structure consisting of plasma and vacuum. Then the reflection coefficient for the plasma slab from the FDTD/PBC algorithm is compared with the analytic results to show the validity of our technique. Finally, the reflection coefficients for the plasma photonic crystals are calculated using the FDTD/PBC algorithm to study the variation of bandgap characteristics with the incident angle and the plasma parameters. Thus it has provided the guiding sense for the actual manufacturing plasma photonic crystal.     

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.     

Theoretical and computational aspects of scattering from periodic surfaces: two-dimensional perfectly reflecting surfaces using the spectral-coordinate method

We consider the scattering from a two-dimensional periodic surface. From our previous work on scattering from one-dimensional surfaces (1998 Waves Random Media 8 385) we have learned that the spectral-coordinate (SC) method was the fastest method we have available. Most computational studies of scattering from two-dimensional surfaces require a large memory and a long calculation time unless some approximations are used in the theoretical development. By using the SC method here we are able to solve exact theoretical equations with a minimum of calculation time.

We first derive in detail (part I) the SC equations for scattering from two-dimensional infinite surfaces. Equations for the boundary unknowns (surface field and/or its normal derivative) result as well as an equation to evaluate the scattered field once we have solved for the boundary unknowns. Special cases for the perfectly reflecting Dirichlet and Neumann boundary value problems are presented as is the flux-conservation relation.

The equations are reduced to those for a two-dimensional periodic surface in part II and we discuss the numerical methods for their solution. The two-dimensional coordinate and spectral samples are arranged in one-dimensional strings in order to define the matrix system to be solved.

The SC equations for the two-dimensional periodic surfaces are solved in part III. Computations are performed for both Dirichlet and Neumann problems for various periodic sinusoidal surface examples. The surfaces vary in roughness as well as period and are investigated when the incident field is far from grazing incidence ('no grazing') and when it is near-grazing. Extensive computations are included in terms of the maximum roughness slope which can be computed using the method with a fixed maximum error as a function of the azimuthal angle of incidence, the polar angle of incidence and the wavelength-to-period ratio.

The results show that the SC method is highly robust. This is demonstrated with extensive computations. Furthermore, the SC method is found to be computationally efficient and accurate for near-grazing incidence. Computations are presented for grazing angles as low as 0.01°. In general, we conclude that the SC method is a very fast, reliable and robust computational method to describe scattering from two-dimensional periodic surfaces. Its major limiting factor is high slopes and we quantify this limitation.     

二维声表面波压电声子晶体在射频段的时域有限差分法

对二维声表面波压电声子晶体在射频段的带隙特性,进行了时域有限差分法(FDTD)理论推导和计算,并提出实验方法对比验证。FDTD计算模型考虑了压电效应,引入周期边界条件以节省计算空间和时间,采用完全匹配层以解决声表面波在截断边界处的虚拟反射问题。实验上分别设计有/无二维压电声子晶体的两种宽频带延迟线结构,测量两种延迟线的传输系数取差值,得到了二维压电声子晶体的带隙;其中通过时域加窗函数保留一次传输信号,进行干扰信号的去除。以铝/128°YX-LiNbO3二维压电声子晶体为例,该FDTD方法、商业有限元软件COMSOL、实验方法均得到了100500 MHz射频段内的多个带隙,三种带隙对比证明了FDTD计算带隙与实验测量带隙一致,比COMSOL计算的计算带隙精度更高。      

Finite-difference time-domain modeling of curved material interfaces by using boundary condition equations method

To deal with the staircase approximation problem in the standard finite-difference time-domain(FDTD) simulation,the two-dimensional boundary condition equations(BCE) method is proposed in this paper.In the BCE method,the standard FDTD algorithm can be used as usual,and the curved surface is treated by adding the boundary condition equations.Thus,while maintaining the simplicity and computational efficiency of the standard FDTD algorithm,the BCE method can solve the staircase approximation problem.The BCE method is validated by analyzing near field and far field scattering properties of the PEC and dielectric cylinders.The results show that the BCE method can maintain a second-order accuracy by eliminating the staircase approximation errors.Moreover,the results of the BCE method show good accuracy for cylinder scattering cases with different permittivities.     

FDTD analysis of photonic crystal defect layers filled with liquid crystals

Dielectric and metallic photonic crystals comprising nematic liquid crystal materials as defect layers or elements are investigated by the Finite Difference Time Domain (FDTD) method. Appropriate formulations of the FDTD algorithm, for the simulation of anisotropic and dispersive media as well as periodic geometries, are utilised and combined with the proper absorbing and periodic boundary conditions. The spectral properties of the presented structures are tuned by means of applying static electric fields across the defect layers, thus affecting the molecular orientation of the liquid crystal material. Numerical results show that sufficient tuning ranges are achieved, requiring low operating voltages. Moreover, high and sharp resonance peaks are observed.     

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.     

粒子模拟中激励源的一种等效设置方法

 基于计算电磁学中对强迫激励源消除虚假反射的算法分析，提出了用等效电流和等效磁流在FDTD公式中引入电场激励源和磁场激励源的方法。从粒子模拟方法的基本方程和迭代公式出发，分析了激励源的引入过程，推导出激励源所等效的电流项和磁流项表达式，实现了新的激励源设置方法，并进行了数值验证和结果讨论。研究表明：这类等效模型与标准FDTD公式能紧密结合，引入非常方便；不必专门设置一个附加的散射场区来处理散射场的计算，大大节省了计算时间和计算内存，比常规总场/散射场体系方法的效率高20%以上，对粒子模拟这类耗时的计算较为适用。通过对2维柱坐标系下相对论速调管放大器(RKA)的模拟，证明了此类激励源设置方法的实用性。     

一维周期结构散射近-远场外推的两种方法

 首先讨论了自由空间中一维周期结构近-远场外推的Floquet模方法,即对FDTD计算所得散射近场中输出边界上散射场进行级数展开,求出各阶Floquet模的复数幅值,再求得远区场。接着介绍了求解一维周期结构远区散射场的周期Green函数方法,即根据FDTD计算所得散射近场中输出边界上散射场,求得等效面电磁流后,再借助周期Green函数进行外推得到远区场。两种方法均仅用一个周期单元内的散射近场进行外推。计算结果验证了上述两种方法外推的有效性。     

Group-theoretic approach to enhancing the Fourier modal method for crossed gratings with equilateral triangular symmetry

The Fourier modal method for crossed gratings is reformulated by use of a group-theoretic approach when the grating structures have the equilateral triangular symmetry. In the new formulation, a grating problem is first decomposed into four symmetrical basis problems whose field distributions are the symmetry modes (two are nondegenerate and the other two are doubly degenerate) of the grating. Then the symmetry relations of fields in the symmetry modes are used to reduce the number of unknowns in numerical computation. After the symmetrical basis problems are solved, their solutions are superposed to get the solution of the original problem. It is shown that when the grating is at some incident mountings, the memory occupation can be saved by 2/3 and the computation time can be reduced to 1/12 to 1/13.5 of the original one for different incident cases. Numerical examples are given to illustrate the effectiveness of the new formulation and verify the improved computation efficiency.