A review on highly ordered, vertically oriented TiO2 nanotube arrays: Fabrication, material properties, and solar energy applications

The perfectly matched layer (PML) absorbing boundary condition has proven to be very efficient from a numerical point of view for the elastic wave equation to absorb both body waves with nongrazing incidence and surface waves. However, at grazing incidence the classical discrete PML method suffers from large spurious reflections that make it less efficient for instance in the case of very thin mesh slices, in the case of sources located close to the edge of the mesh, and/or in the case of receivers located at very large offset. We demonstrate how to improve the PML at grazing incidence for the differential seismic wave equation based on an unsplit convolution technique. The improved PML has a cost that is similar in terms of memory storage to that of the classical PML. We illustrate the efficiency of this improved convolutional PML based on numerical benchmarks using a finite-difference method on a thin mesh slice for an isotropic material and show that results are significantly improved compared with the classical PML technique. We also show that, as the classical PML, the convolutional technique is intrinsically unstable in the case of some anisotropic materials.

An unsplit convolutional perfectly matched layer improved at grazing incidence for the seismic wave equation

Absorbing PML boundary layers for wave-like equations

This lecture presents the perfectly matched layer (PML) absorbing boundary condition (ABC) used to simulate free space when solving the Maxwell equations with such finite methods as the finite difference time domain (FDTD) method or the finite element method. The frequency domain and the time domain equations are derived for the different forms of PML media, namely the split PML, the CPML, the NPML, and the uniaxial PML, in the cases of PMLs matched to isotropic, anisotropic, and dispersive media. The implementation of the PML ABC in the FDTD method is presented in detail. Propagation and reflection of waves in the discretized FDTD space are derived and discussed, with a special emphasis on the problem of evanescent waves. The optimization of the PML ABC is addressed in two typical applications of the FDTD method: first, wave-structure interaction problems, and secondly, waveguide problems. Finally, a review of the literature on the application of the PML ABC to other numerical techniques of elec...

/pdf/perfectly-matched-layer-pml-for-computational-1qe3zw59k0.pdf

Perfectly Matched Layer (PML) for Computational Electromagnetics

Noble metal nanowaveguides supporting plasmon polariton modes are able to localize the optical fields at nanometer level for high sensitivity biochemical sensing devices. Here we report on the design and fabrication of a novel photonic-plasmonic device which demonstrates label-free detection capabilities on single inorganic nanoparticles and on monolayers of organic compounds. In any case, we determine the Raman scattering signal enhancement and the device detection limits that reach a number of molecules between 10 and 250. The device can be straightforwardly integrated in a scanning probe apparatus with the possibility to match topographic and label-free spectroscopic information in a wide range of geometries.

/pdf/a-hybrid-plasmonic-photonic-nanodevice-for-label-free-39qznuxaz6.pdf

A hybrid plasmonic-photonic nanodevice for label-free detection of a few molecules

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.

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

Efficient implementation of the uniaxial-based pml media in three-dimensional nonorthogonal coordinates with the use of the fdtd technique

In this paper, a sufficient test for the numerical stability of generalized grid finite-difference time-domain (FDTD) schemes is presented. It is shown that the projection operators of such schemes must be symmetric positive definite. Without this property, such schemes can exhibit late-time instabilities. The origin and the characteristics of these late-time instabilities are also uncovered. Based on this study, nonorthogonal grid FDTD schemes (NFDTD) and the generalized Yee (GY) methods are proposed that are numerically stable in the late time for quadri- lateral prism elements, allowing these methods to be extended to problems requiring very long-time simulations. The study of numerical stability that is presented is very general and can be applied to most solutions of Maxwell's equations based on explicit time-domain schemes. Index Terms—FDTD methods, numerical stability.

https://ieeexplore.ieee.org/iel5/8/18033/00833072.pdf

J. Alan Roden

Papers

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

Efficient implementation of the uniaxial-based pml media in three-dimensional nonorthogonal coordinates with the use of the fdtd technique

Numerical Stability of NonorthogonalFDTD Methods