Complex Frequency-shifted Perfectly Matched Layer Research Articles

Optimization of the Perfectly Matched Layer for the Finite-Element Time-Domain Method

We present a new formulation to implement the complex frequency shifted-perfectly matched layer (CFS-PML) for boundary truncation in 2-D vector finite-element time-domain method directly applied to Maxwell's equations. It is shown that the proposed method is highly absorptive to evanescent modes when computing the wave interaction of elongated structures or sharp corners. The impact of the CFS-PML parameters on the reflection error is investigated and optimal choices of these parameters are derived

Z-Transform Implementations of the CFS-PML

Four implementations of the complex frequency-shifted perfectly matched layer (CFS-PML) based on the uniaxial anisotropic PML (UPML) formulations and Z-transform methods are presented for truncating the finite-difference time-domain (FDTD) lattices. These formulations are independent of the material properties of the FDTD computational domain and hence can be applied to the modeling of general media. Particularly, a new algorithm to minimize memory requirement is introduced. Two numerical simulations of the dispersive media have been carried out in three dimensions to validate these formulations. It is shown that the proposed formulations with the CFS scheme are efficient in attenuating of evanescent waves and reducing late-time reflections.

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.

Numerical reflection from FDTD-PMLs: a comparison of the split PML with the unsplit and CFS PMLs

Although perfectly matched layer (PML) absorbing boundary conditions are perfect in theory, an amount of spurious reflection is present in actual computations with the finite-difference time-domain (FDTD) method. This paper compares the reflections produced by three different PMLs, namely the split PML, the unsplit PML, and the recently introduced complex frequency shifted (CFS) PML. It is shown that the reflections from the split and unsplit PMLs are identical, while the CFS PML allows the reflection of evanescent waves to be significantly reduced.

Convolution PML (CPML): An efficient FDTD implementation of the CFS-PML for arbitrary media

A novel implementation of perfectly matched layer (PML) media is presented for the termination of FDTD lattices. The implementation is based on the stretched coordinate form of the PML, a recursive convolution, and the use of complex frequency, shifted (CFS) PML parameters. The method, referred to here as the convolutional PML (CPML), offers a number of advantages over the traditional implementations of the PML. Specifically, the application of the CPML is completely independent of the host medium. Thus, no modifications are necessary when applying it to inhomogeneous, lossy, anisotropic, dispersive, or nonlinear media. Secondly, it is shown that the CFS–PML is highly absorptive of evanescent modes and can provide significant memory savings when computing the wave interaction of elongated structures, sharp corners, or low-frequency excitations. © 2000 John Wiley & Sons, Inc. Microwave Opt Technol Lett 27: 334–339, 2000.