Efficient multiresolution time-domain analysis of arbitrarily shaped photonic devices

A multiresolution time-domain (MRTD) technique is proposed and applied to the analysis of arbitrarily shaped photonic devices. The suggested method implements the multiresolution analysis in the context of method-of-moments for the solution of Maxwell?s equations. To improve the capabilities of the proposed method, the uniaxial perfectly matched layers absorber for the MRTD is rigorously incorporated and better performance is reported over the conventional finite-difference time-domain. Various numerical examples demonstrate the stability and numerical precision of the suggested MRTD method for both linear and nonlinear applications. Moreover, the application of the suggested MRTD scheme for the design of a photonic crystal-based optical wavelength filter and for the analysis of a frequency converter is presented.     

Parallel implementation of the finite element method using compressed data structures

This paper presents a parallel implementation of the finite element method designed for coarse-grain distributed memory architectures. The MPI standard is used for message passing and tests are run on a PC cluster and on an SGI Altix 350. Compressed data structures are employed to store the coefficient matrix and obtain iterative solutions, based on Krylov methods, in a subdomain-by-subdomain approach. Two mesh partitioning schemes are compared: non-overlapping and overlapping. The pros and cons of these partitioning methods are discussed. Numerical examples of symmetric and non-symmetric problems in two and three dimensions are presented.     

Parallel implementation of spectral element method for Lamb wave propagation modeling

The proposed spectral element method implementation is based on sparse matrix storage of local shape function derivatives calculated at Gauss–Lobatto–Legendre points. The algorithm utilizes two basic operations: multiplication of sparse matrix by vector and element‐by‐element vectors multiplication. Compute‐intensive operations are performed for a part of equation of motion derived at the degree of freedom level of 3D isoparametric spectral elements. The assembly is performed at the force vector in such a way that atomic operations are minimized. This is achieved by a new mesh coloring technique The proposed parallel implementation of spectral element method on GPU is applied for the first time for Lamb wave simulations. It has been found that computation on multicore GPU is up to 14 times faster than on single CPU. Copyright © 2015 John Wiley & Sons, Ltd.     

双正交冗余小波变换的图像去噪方法

由于正交小波变换的不具备线性相位、不具有平移不变性等特性,导致其在图像去噪领域仍存在很多问题,本文将双正交冗余离散小波变换应用到几种经典小波阈值图像去噪方法中,以克服标准正交小波变换在阈值图像去噪中存在的问题.实验证明该方法的去噪效果明显优于正交小波方法和普通双正交小波变换的去噪效果.     

Adaptive filter with a time-domain implementation using correlation cancellation loops

The results of a feasibility study of an optical adaptive filter are presented. The processor is a time-domain implementation using correlation cancellation loops. Included is a theoretical verification of the correlation cancellation loop approach for linear prediction. The processor architecture and performance are described in detail. The results are encouraging although limited by laboratory equipment.     

Parallel implementation of the boundary element method for linear elastic problems on a MIMD parallel computer

The parallel implementation of the boundary element method (BEM) for linear elastic 2D-problems on a MIMD parallel computer is treated. The parallelization is performed by data decomposition. The use of collocation method leads to a non-symmetric system of linear equations which is solved by direct or iterative methods. Focusing on the parallel implementation, these solvers are compared with respect to their efficiency using a Parsytec MultiCluster2 with 32 T805 transputers.     

Calculation method of reflectance distributions for computer-generated holograms using the finite-difference time-domain method

The research on reflectance distributions in computer-generated holograms (CGHs) is particularly sparse, and the textures of materials are not expressed. Thus, we propose a method for calculating reflectance distributions in CGHs that uses the finite-difference time-domain method. In this method, reflected light from an uneven surface made on a computer is analyzed by finite-difference time-domain simulation, and the reflected light distribution is applied to the CGH as an object light. We report the relations between the surface roughness of the objects and the reflectance distributions, and show that the reflectance distributions are given to CGHs by imaging simulation.     

Implementing the near- to far-field transformation in the finite-difference time-domain method

When the finite-difference time-domain (FDTD) method is applied to light-scattering computations, the far fields can be obtained by means of integrating the near fields either over the volume bounded by the particle's surface or on a regular surface encompassing the scatterer. For light scattering by a sphere, the accurate near-field components on the FDTD-staggered meshes can be computed from the rigorous Lorenz-Mie theory. We investigate the errors associated with these near- to far-field transform methods for a canonical scattering problem associated with spheres. For a scatterer with a small refractive index, the surface-integral approach is more accurate than its volume counterpart for computation of the phase functions and extinction efficiencies; however, the volume-integral approach is more accurate for computation of other scattering matrix elements, such as P12, P32, and P43, especially for backscattering. If a large refractive index is involved, the results computed from the volume-integration method become less accurate, whereas the surface method still retains the same order of accuracy as in the situation for the small refractive index.     

Parallel fractional correlation: an optical implementation

An optical setup to obtain all the fractional correlations of a one-dimensional input in a single display is implemented. The system works as a multichannel parallel correlator for a continuous set of fractional orders and presents a variable shift variance. Some experimental results together with computer simulations are performed to illustrate the performance of our proposal.     

Two-step preconditioning technique for hierarchical time-domain finite-element method

A two-step factorised sparse approximation inverse and symmetric successive over relaxation preconditioned conjugate gradient (CG) algorithm is proposed to solve the large system of linear equations resulted from the hierarchical implicit time-domain finite-element method (TDFEM). Convergence properties and CPU time of the proposed algorithm are compared with those of other preconditioned CG schemes. Numerical results demonstrate that the present approach is efficient for solving the large sparse system from hierarchical implicit TDFEM.     

A time-domain symplectic method for finite viscoelastic cylinders

The symplectic method is introduced for boundary-condition problems of finite viscoelastic cylinders. On the basis of the state space formalism and the use of the Laplace integral transform, the general solution of the governing equations, zero- and nonzero-eigenvalue eigenvectors, are obtained. Since the eigenvectors are expressed in concise analytical forms, the adjoint symplectic relation of the Laplace domain is generalized to the time domain. Therefore, the particular solution and the eigenvector expansion method can be discussed directly in the eigenvector space of the time domain, without employing the iterative application of the inverse Laplace transformation. Using this method, various boundary conditions, the particular solution of nonhomogeneous equations, especially the interfacial continuity conditions of composite materials, can be conveniently described by combinations of the eigenvectors.     

Simulation of subwavelength metallic gratings using a new implementation of the recursive convolution finite-difference time-domain algorithm

We introduce a new implementation of the finite-difference time-domain (FDTD) algorithm with recursive convolution (RC) for first-order Drude metals. We implemented RC for both Maxwell's equations for light polarized in the plane of incidence (TM mode) and the wave equation for light polarized normal to the plane of incidence (TE mode). We computed the Drude parameters at each wavelength using the measured value of the dielectric constant as a function of the spatial and temporal discretization to ensure both the accuracy of the material model and algorithm stability. For the TE mode, where Maxwell's equations reduce to the wave equation (even in a region of nonuniform permittivity) we introduced a wave equation formulation of RC-FDTD. This greatly reduces the computational cost. We used our methods to compute the diffraction characteristics of metallic gratings in the visible wavelength band and compared our results with frequency-domain calculations.     

Comparison of the born iterative method and tarantola's method for an electromagnetic time-domain inverse problem

Two methods of solving the nonlinear two-dimensional electromagnetic inverse scattering problem in the time domain are considered. These are the Born iterative method and the method originally proposed by Tarantola for the seismic reflection inverse problems. The former is based on Born-type iterations on an integral equation, whereby at each iteration the problem is linearized, and its solution is found via a regularized optimization. The latter also uses an iterative method to solve the nonlinear system of equations. Although it linearizes the problem at each stage as well, no optimization is carried out at each iteration; rather the problem as a whole is posed as a (regularized) optimization. Each method is described briefly and its computational complexity is analyzed. Tarantola's method is shown to have a lower numerical complexity compared to the Born iterative method for each iteration, but in the examples considered, required more iterations to converge. Both methods perform well when inverting a smooth profile; however, the Born iterative method gave better results in resolving localized point scatterers.     

水中目标强度的一致性时域有限差分计算

本文应用一致性时域有限差分法（FDTD）和近场-远场变换计算散射声目标的反射声压强度，找出反射声压级与目标声中心到换能器间距离的关系。数值计算中考虑了自由场和有海面及海面波浪影响时的不同情况。根据声源和目标的几何特征对入射波和散射波分别作了球面和柱面扩散修正，并将计算结果与水池实验结果进行了比较。本文的讨论可对水下目标强度测量方法提供参考。     

Three-dimensional analysis of subwavelength diffractive optical elements with the finite-difference time-domain method

We present a three-dimensional (3D) analysis of subwavelength diffractive optical elements (DOE's), using the finite-difference time-domain (FDTD) method. To this end we develop and apply efficient 3D FDTD methods that exploit DOE properties, such as symmetry. An axisymmetric method is validated experimentally and is used to validate the more general 3D method. Analyses of subwavelength gratings and lenses, both with and without rotational symmetry, are presented in addition to a 2 x 2 subwavelength focusing array generator.     

Application of the pseudospectral time-domain method to the scattering of light by nonspherical particles

The pseudospectral time-domain (PSTD) method is a powerful approach for computing the single-scattering properties of arbitrarily shaped particles with small-to-moderate-sized parameters. In the PSTD method, the spatial derivative approximation based on the spectral method is more accurate than its counterpart based on the finite-difference technique. Additionally, the PSTD method can substantially diminish accumulated errors that increase with the spatial scale and temporal duration of simulation. We report on the application of the PSTD method to the scattering of light by nonspherical ice particles. The applicability of the PSTD method is validated against the Lorenz-Mie theory and the T-matrix method. The phase functions computed from the PSTD method and the Lorenz-Mie theory agree well for size parameters as large as 80. Furthermore, the PSTD code is also applied to the scattering of light by nonspherical ice crystals, namely, hollow hexagonal columns and aggregates, which are frequently observed in cirrus clouds. The phase functions computed from the PSTD method are compared with the counterparts computed from the finite-difference time-domain (FDTD) method for a size parameter of 20 and an incident wavelength of 3.7 microm. The comparisons show good agreement between the two methods.     

Formulation of the finite-difference time-domain method for the analysis of axially symmetric metal nanodevices

A systematic finite-difference time-domain method, established in the cylindrical coordinate and integrated with the six-pole Lorentz–Drude model using the auxiliary differential equation method, is formulated. The model is appropriate for analyzing metal photonic devices with an axially symmetric nanostructure, such as metal nanowires, metal particles, and plasmonic lenses. As an example, an experimentally demonstrated plasmonic lens is analyzed based on the Drude model, the Lorentz–Drude model, and the Lorentz model. Depending on the different dispersion models, distinct electric field distributions for the plasmonic lens are obtained. The interesting numerical results, which are explained in this paper, show the high efficiency and accuracy of the simulation model.     

Application of the symplectic finite-difference time-domain method to light scattering by small particles

A three-dimensional fourth-order finite-difference time-domain (FDTD) program with a symplectic integrator scheme has been developed to solve the problem of light scattering by small particles. The symplectic scheme is nondissipative and requires no more storage than the conventional second-order FDTD scheme. The total-field and scattered-field technique is generalized to provide the incident wave source conditions in the symplectic FDTD (SFDTD) scheme. The perfectly matched layer absorbing boundary condition is employed to truncate the computational domain. Numerical examples demonstrate that the fourth-order SFDTD scheme substantially improves the precision of the near-field calculation. The major shortcoming of the fourth-order SFDTD scheme is that it requires more computer CPU time than a conventional second-order FDTD scheme if the same grid size is used. Thus, to make the SFDTD method efficient for practical applications, one needs to parallelize the corresponding computational code.