The perfectly matched layer boundary condition for scalarfinite-difference time-domain method

The perfectly matched layer (PML) boundary condition for the scalar finite-difference time-domain (FDTD) method is developed in this letter. It is demonstrated that the PML is suitable and effective in computation of optical waveguides. The results also show how to optimize the parameters of PML     

The perfectly matched layer boundary condition for modal analysis of optical waveguides: leaky mode calculations

The perfectly matched layer (PML) boundary condition is applied to modal analysis for optical waveguides. It is demonstrated that the PML is suitable and effective in computation of leaky modes.     

The perfectly matched layer (PML) boundary condition for the beam propagation method

The perfectly matched layer (PML) boundary condition for the Helmoltz equation is developed and applied to the finite-difference beam propagation method. Its effectiveness is verified by way of examples.     

Arbitrarily oriented perfectly matched layer in the frequencydomain

An arbitrarily oriented perfectly matched layer (PML) is introduced by using complex space mapping for more flexible meshing of microwave engineering problems. The PML can be oriented in any direction. The discussion is extended to two-direction PMLs for matching the interface between one-direction PMLs, and three-direction PMLs for two-direction ones. An example having analytical solution is calculated, Numerical results agree with the analytical solution very well within 0.1%     

A mode-preserving perfectly matched layer for optical waveguides

For numerical simulation of wave propagation in optical waveguides, we develop a mode-preserving boundary condition for the popular perfectly matched layer, which truncates the unbounded transverse plane. The method is particularly useful for single-mode longitudinally varying wave-guiding structures and it is easy to use for step-index planar waveguides. With this boundary condition, accurate numerical solutions can be obtained in a much smaller computational window. Numerical results based on the beam propagation method for a tapered waveguide are used to demonstrate the capacity of this boundary condition.     

三维新型非分裂场完全匹配层吸收边界条件

研究了一种3D新型时域有限差分法（FDTD）非分裂场近似完全匹配层（NPML）吸收边界。在直角坐标系中,通过直接对麦克斯韦方程组中的空间偏导的变量进行空间坐标拉伸,得到三维非分裂场的NPML吸收边界,这种吸收边界相对于PML吸收边界编程实现简单,编程复杂度低。通过对三维算例的电磁散射分析,验证了NPML吸收边界的正确性。计算结果表明了该方法是一个完美的吸收边界,可以用于实际目标的电磁散射问题分析。     

Z-transform-based FDTD algorithm for anisotropic perfectly matched layer

An efficient method based on the Z-transform theory and the D-H anisotropic perfectly matched layer formulations is presented for truncating general FDTD grids. The formulations are simple and independent of the material properties of the FDTD domain. Numerical examples for radiation and guided-wave problems are included to validate the proposed formulations.     

State-space FDTD implementation of anisotropic perfectly matched layer

New formulations based on the state-space approach are presented for implementing the anisotropic perfectly matched layer into the finite difference time domain (FDTD) algorithm. The formulations are simple and independent from the material properties of the FDTD computational domain. Numerical tests are included to validate the proposed formulations.     

On the reflection from Cummer's nearly perfectly matched layer

This letter shows that the nearly perfectly matched layer (NPML) recently introduced by Cummer is a true reflectionless absorbing boundary condition in continuous space, and is as effective as previous implementations of PMLs in discretized finite difference space.     

Application of an anisotropic perfectly matched layer absorber for open boundary truncation in the multiresolution time domain scheme

We apply an anisotropic perfectly matched layer (APML) absorber for open boundary truncation in implementation of the multiresolution time domain (MRTD) scheme. We develop an APML update algorithm to handle a general APML region in the MRTD formulations with the content of the leapfrog algorithm applied in the conventional finite-difference time-domain method. We also discuss the boundary truncations for both perfectly electric conductor (PEC) and perfectly magnetic conductor (PMC) walls using the image techniques. We validate the algorithm by analyzing various guided wave and antenna structures. It is found that the APML performs well for absorbing electromagnetic waves in the MRTD algorithm.     

A perfectly matched layer for free-space simulation in finite-difference computer codes

Some results of fdtd computations are presented to illustrate the actual possibilities of a new technique of free-space simulation. It is shown that this technique improves the absorption of the outgoing waves and allows the computational requirements to be widely reduced when solving wave-structure interaction problems.     

A simple, nearly perfectly matched layer for general electromagnetic media

A new implementation of the perfectly matched layer (PML) absorbing boundary condition is presented. This formulation is designed such that the partial differential equations in the PML are identical to those in the regular medium for any linear electromagnetic material. This makes this method particularly simple to implement, especially in dispersive and anisotropic materials. We call this method the nearly perfectly matched layer (NPML) because it employs variable changes that are not strictly exact when the PML conductivity is spatially variant. Comparisons with the convolutional PML in a Lorentz dielectric show that the NPML is as effective an absorber as exact PML formulations.     

DSP techniques for implementation of perfectly matched layer fortruncating FDTD domains

A new algorithm for implementing the perfectly matched layer (PML) using digital signal processing (DSP) is presented for truncating finite difference time-domain (FDTD) domains. The algorithm is based on incorporating digital filtering techniques into the PML formulation. A simple, unsplit-field and material independent PML formulation is achieved     

Z-transform implementation of the perfectly matched layer for truncating FDTD domains

A simple algorithm for implementing the perfectly matched layer (PML) is presented for truncating finite difference time domain (FDTD) computational domains. The algorithm is based on incorporating the Z-transform method into the PML FDTD implementation. The main advantage of the algorithm is its simplicity as it allows direct FDTD implementation of Maxwell's equations in the PML region. In addition, the formulations are independent of the material properties of the FDTD computational domain. Numerical examples are included to demonstrate the effectiveness of these formulations.     

Evaluation of perfectly matched layer mesh terminations infinite-element bioelectromagnetic scattering computations

There has been considerable interest in and development of perfectly matched layer (PML) mesh terminations for electromagnetic scattering problems. For the most part, PML performance has been characterized on benchmarks which involve scattering from perfectly conducting objects. In this paper, we evaluate a recent PML implementation for node-based finite-element formulations using a prototype problem which is relevant to bioelectromagnetic computations. Variables under consideration include the layer material properties, layer thickness, and layer distance from the biological body. The results demonstrate that distance from the body is the strongest determinant of solution accuracy with increasing errors occurring with increasing frequency at a fixed distance, although average solution variations of less than 10% are observed in most cases where layers are located at a distance of at least 1.5 times the smallest body dimension. In addition, the PML need only consist of two to three layers in order to reduce solution variations resulting from layer thickness, and this thickness requirement is largely independent of layer distance from the body. This is in contrast to results from perfectly conducting scatterers where six to eight or more layers have been recommended. Further, the computed solutions are not a strong function of the layer material property and this parameter can easily be determined from a simple analytical decay formula without compromising PML performance. These findings are encouraging from a computational economy perspective and they suggest that the PML concept is an excellent choice for finite-element mesh truncation in bioelectromagnetic computations     

A new anisotropic perfectly matched layer medium for mesh truncation in finite difference time domain analysis

In this paper an unsplit anisotropic perfectly matched layer (PML) medium, previously utilized in the context of finite element analysis, is implemented in the finite difference time domain (FDTD) algorithm. The FDTD anisotropic PML is easy to implement in the existing FDTD codes, and is well suited for truncating inhomogeneous and layered media without special treatment required in the conventional PML approach. A further advantage of the present approach is improved performance at lower frequencies. The applications of the unsplit anisotropic PML/FDTD method are illustrated by considering the problems of a plane wave propagation and an open microstrip line.     

基于Z变换的拉伸坐标完全匹配层的改进算法

针对基于Z变换方法的拉伸坐标完全匹配层(SC-PML)提出了一种改进算法.新算法采用匹配Z变换技术将复拉伸坐标变量仿真为无限脉冲响应数字滤波器.与以前发表的SC-PML实现方法相比,新算法的主要优点是在PML的角和棱上仅仅需要一个辅助变量,从而节约了许多内存.而且,所提出的方法在不用修改的情况下,就能应用于仿真广义的FDTD计算域,诸如有耗、色散、各向异性或非线性.另外,还提出了一种应用在高阶差分方程中最小化内存的新算法.两个三维数字仿真实例验证了新算法的有效性.     

A digital filter approach for complex frequency-shifted perfectly matched layer in semivectorial FDTD

A new formulation of the perfectly matched layer (PML) for the semivectorial finite-difference time-domain (FDTD) method in optical waveguide simulation is presented by incorporating the infinite-impulse response (IIR) digital filter technique. The complex frequency-shifted PML is implemented through Z transformation, where the second-order derivatives in semivectorial FDTD are realized by two cascaded first-order recursive IIR digital filters. The numerical examples indicate that the new scheme has better performance compared with the normal PML.     

Auxiliary differential equation formulation: an efficient implementation of the perfectly matched layer

An efficient algorithm for implementing the perfectly matched layer (PML) is presented for truncating finite-difference time-domain domains. The algorithm is based on incorporating the auxiliary differential equation method into the PML formulations. Simple, unsplit-field and material independent PML formulations are obtained. Two dimensional numerical examples are included to validate the proposed formulations.