Numerical study of sub-wavelength plasmonic waveguide

The authors present an analysis of a plasmonic waveguide, simulated using a two-dimensional finite-difference time-domain technique. With the surface structures located on the surface of the metal, the device is able to confine and guide light waves in a sub-wavelength scale. And two waveguides can be placed within 150 nm (∼6% of the incident wavelength) that will helpful for the optoelectronic integration. Within the 20 μm simulation region, it is found that the intensity of the guided light at the interface is roughly two to four times the peak intensity of the incident light, and the propagation length can reach approximately 40 μm at the wavelength of 2.44 μm.     

Analysis of disc brake squeal using the complex eigenvalue method

A new functionality of ABAQUS/Standard, which allows for a nonlinear analysis prior to a complex eigenvalue extraction in order to study the stability of brake systems, is used to analyse disc brake squeal. An attempt is made to investigate the effects of system parameters, such as the hydraulic pressure, the rotational velocity of the disc, the friction coefficient of the contact interactions between the pads and the disc, the stiffness of the disc, and the stiffness of the back plates of the pads, on the disc squeal. The simulation results show that significant pad bending vibration may be responsible for the disc brake squeal. The squeal can be reduced by decreasing the friction coefficient, increasing the stiffness of the disc, using damping material on the back plates of the pads, and modifying the shape of the brake pads.     

An improved quantum principal component analysis algorithm based on the quantum singular threshold method

Quantum principal component analysis (qPCA) is a dimensionality reduction algorithm for getting the eigenvectors corresponding to top several eigenvalues of the data matrix and then reconstructing. However, qPCA can only construct the quantum state contains all the eigenvectors and eigenvalues. In this paper, we present an improved quantum principal component analysis (Improved qPCA) algorithm with a fixed threshold. We can reduce the singular value less than the threshold to 0 and obtain a target quantum state which can be used to get an output similar to qPCA after phase estimation. Compared with qPCA, our algorithm has only the target eigenvalues and the probability that we get each target eigenvalue is greater. Furthermore, our algorithm can serve as an additional regularization method and a subroutine for subsequent data processing.     

The GW plus cumulant method and plasmonic polarons: application to the homogeneous electron gas*

We study the spectral function of the homogeneous electron gas using many-body perturbation theory and the cumulant expansion. We compute the angle-resolved spectral function based on the GW approximation and the “GW plus cumulant” approach. In agreement with previous studies, the GW spectral function exhibits a spurious plasmaron peak at energies 1.5ω_pl below the quasiparticle peak, ω_pl being the plasma energy. The GW plus cumulant approach, on the other hand, reduces significantly the intensity of the plasmon-induced spectral features and renormalizes their energy relative to the quasiparticle energy to ω_pl. Consistently with previous work on semiconductors, our results show that the HEG is characterized by the emergence of plasmonic polaron bands, that is, broadened replica of the quasiparticle bands, red-shifted by the plasmon energy.     

Polynomial potentials and a hidden symmetry of the Hill-determinant eigenvalue method

For the potential V(x) = g₁x² + g₂x⁴ + g₃x⁶ and its polynomial generalizations, the “true” and “false” energies of Killingbeck may both be interpreted as physical, corresponding to the two different forms of the potential. Thus, the Hill-determinant method has two non-equivalent forms, and neither of them gives spurious solutions.     

Finite element beam propagation method for analysis of plasmonic waveguide

The basic idea of the finite element beam propagation method (FE-BPM) is described. It is applied to calculate the fundamental mode of a channel plasmonic polariton (CPP) waveguide to confirm its validity. Both the field distribution and the effective index of the fundamental mode are given by the method. The convergence speed shows the advantage and stability of this method. Then a plasmonic waveguide with a dielectric strip deposited on a metal substrate is investigated, and the group velocity is negative for the fundamental mode of this kind of waveguide. The numerical result shows that the power flow direction is reverse to that of phase velocity.     

A numerical study of the solution of the partial eigenvalue problem

The partial eigenvalue problem that arises from the application of the finite element method is considered. A number of iterative methods are examined which consist in seeking the stationary points of the Rayleigh quotient and thus avoiding the physical assembling of the matrices involved. The computational efficiencies of the steepest descent, the conjugate gradient and the co-ordinate overrelaxation methods are compared. Several other modifications to the original conjugate gradient algorithm as well as an orthogonalization process are studied. The dependence of the convergence of the methods on the initial estimate of the eigenvectors and on different values of the relaxation parameter, in the case of the co-ordinate overrelaxation, are also examined.     

基于金属-电介质-金属波导结构的等离子体滤波器的数值研究

基于金属-电介质-金属波导结构, 提出了一种含双侧多支节型等离子波导滤波器, 采用有限元法研究了其透射特性. 在该结构的透射谱中观察到了基于电磁诱导透明效应的四个窄带透射峰, 并通过模场分布有效阐释了透射谱线中峰值、谷值的产生的物理机理. 数值研究同时表明当每个支节长度线性增加时, 透射峰中心波长也将线性增加. 这一结果可用于指导可调谐、多通道窄带滤波器的设计.     

An approximate solution scheme for the algebraic random eigenvalue problem

A reduced basis formulation is presented for the efficient solution of large-scale algebraic random eigenvalue problems. This formulation aims to improve the accuracy of the first order perturbation method, and also allow the efficient computation of higher order statistical moments of the eigenparameters. In the present method, the two terms of the first order perturbation approximation for the eigenvector are used as basis vectors for Ritz analysis of the governing random eigenvalue problem. This leads to a sequence of reduced order random eigenvalue problems to be solved for each eigenmode of interest. Since, only two basis vectors are used to represent each eigenvector, explicit expressions for the random eigenvalues and eigenvectors can readily be derived. This enables the statistics of the random eigenparameters and the forced response to be efficiently computed. Numerical studies are presented for free and forced vibration analysis of a linear stochastic structural system. It is demonstrated that the reduced basis method gives better results as compared to the first order perturbation method.     

An analytical method to compute an approximate value of the site percolation threshold P<Subscript>c</Subscript>

An analytical method to compute the site percolation threshold is introduced. This method yields an approximate value of larger or equal to the real value. As examples, the computation of is presented for 4 lattices in 2 dimensions: square, triangular, honeycomb and kagome. The results obtained are 0.592 871 6, 0.5, 0.765 069, 0.654 653 7, to be compared with the real values 0.592 746 0, 0.5, 0.697 043, 0.652 703 6. The method is not limited to 2 dimensions. Received 27 July 1999 and Received in final form 29 November 1999     

An optimal Galerkin scheme to solve the kinematic dynamo eigenvalue problem in a full sphere

The kinematic dynamo approximation describes the generation of magnetic field in a prescribed flow of electrically-conducting liquid. One of its main uses is as a proof-of-concept tool to test hypotheses about self-exciting dynamo action. Indeed, it provided the very first quantitative evidence for the possibility of the geodynamo. Despite its utility, due to the requirement of resolving fine structures, historically, numerical work has proven difficult and reported solutions were often plagued by poor convergence. In this paper, we demonstrate the numerical superiority of a Galerkin scheme in solving the kinematic dynamo eigenvalue problem in a full sphere. After adopting a poloidal–toroidal decomposition and expanding in spherical harmonics, we express the radial dependence in terms of a basis of exponentially convergent orthogonal polynomials. Each basis function is constructed from a terse sum of one-sided Jacobi polynomials that not only satisfies the boundary conditions of matching to an electrically insulating exterior, but is everywhere infinitely differentiable, including at the origin. This Galerkin method exhibits more rapid convergence, for a given problem size, than any other scheme hitherto reported, as demonstrated by a benchmark of the magnetic diffusion problem and by comparison to numerous kinematic dynamos from the literature. In the axisymmetric flows we consider in this paper, at a magnetic Reynolds number of O(100), a convergence of 9 significant figures in the most unstable eigenvalue requires only 40 radial basis functions; alternatively, 4 significant figures requires 20 radial functions. The terse radial discretization becomes particularly advantageous when considering flows whose associated numerical solution requires a large number of coupled spherical harmonics. We exploit this new method to confirm the tentatively proposed positive growth rate of the planar flow of Bachtiar et al. [4], thereby verifying a counter-example to the Zel’dovich anti-dynamo theorem in a spherical geometry.     

Thermodynamic stability of interacting fermions system with matrix eigenvalue method

A matrix eigenvalue method is applied to analyse the thermodynamic stability of two-component interacting fermions. The non-relativistic and ultra-relativistic d=1, 2,3 dimensions have been discussed in detail, respectively. The corresponding stability region has been given according to the two-body interaction strength and the particle number density ratio.     

Searching threshold effects in the interest rate: An application to Turkey case

This paper investigates the behaviour of interest rates in Turkey using a two-regime TAR model with an autoregressive unit root. This method recently developed by Caner and Hansen [Threshold autoregression with a unit roots, Econometrica 69 (6) (2001) 1555–1596] allows to simultaneously consider non-stationarity and non-linearity. Our finding indicates that the interest rate is a non-linear series and is characterized by a unit root process over the period 1990:1–2006:5.     

A new Monte Carlo power method for the eigenvalue problem of transfer matrices

We propose a new Monte Carlo method for calculating eigenvalues of transfer matrices leading to free energies and to correlation lengths of classical and quantum many-body systems. Generally, this method can be applied to the calculation of the maximum eigenvalue of a nonnegative matrix  such that all the matrix elements of Â^k are strictly positive for an integerk. This method is based on a new representation of the maximum eigenvalue of the matrix  as the thermal average of a certain observable of a many-body system. Therefore one can easily calculate the maximum eigenvalue of a transfer matrix leading to the free energy in the standard Monte Carlo simulations, such as the Metropolis algorithm. As test cases, we calculate the free energies of the square-lattice Ising model and of the spin-1/2XY Heisenberg chain. We also prove two useful theorems on the ergodicity in quantum Monte Carlo algorithms, or more generally, on the ergodicity of Monte Carlo algorithms using our new representation of the maximum eigenvalue of the matrixÂ.     

A new model of dispersion for metals leading to a more accurate modeling of plasmonic structures using the FDTD method

We present FDTD simulations results obtained using the Drude Critical points model. This model enables spectroscopic studies of metallic structures over wider wavelength ranges than usually used, and it facilitates the study of structures made of several metals.     

CCD二值化测量的阈值自动调节方法

设计了一种利用单脉冲正向峰值探测电路构成的CCD二值化阈值自动调节方法。分析了峰值探测电路产生漂移现象的原因,提出了解决方法。实验结果表明,该方法可达到100倍左右的自动调节范围,实现了野外自然光照明条件下的CCD输出信号二值化阈值的自动调节。     

Analyzing the effect of nonlocality on the scattering properties of a plasmonic nanocylinder using the discrete-source method

The problem of the diffraction of the field of a plane electromagnetic wave by a metal nanocylinder with an arbitrary cross section is considered. Based on the discrete-source method, a comparative analysis of both frequency and spatial scattering characteristics is performed taking the nonlocal effect into account. It is found that nonlocality produces a substantial effect on the scattering characteristics. It is demonstrated that the use of the Drude model for a refractive index of plasmonic particles in the ultraviolet region may lead to erroneous results.     

A relaxation method for large eigenvalue problems,with an application to flow stability analysis

Linear stability analysis of fluid flows usually involves the numerical solution of large eigenvalue problems. We present a spectral transformation allowing the computation of the least stable eigenmodes in a prescribed frequency range, based on the filtering of the linearized equations of motion. This “shift-relax” method has the advantage of low memory requirements and is therefore suitable for large two- or three-dimensional problems. For demonstration purposes, this new method is applied to compute eigenmodes of a compressible jet.     

An efficient directional coupling from dielectric waveguide to hybrid long-range plasmonic waveguide on a silicon platform

The silicon-based three-dimensional hybrid long-range plasmonic waveguide not only supports long-range propagation distance (~mm) but also has an ultra-small modal area (~10^?2 μm²) at 1.55 μm. Here, we propose a directional coupler for effective coupling from a dielectric slab-waveguide to the hybrid plasmonic waveguide on a silicon platform. Our simulation results show that the coupler is able to excite hybrid long-range plasmonic mode with short coupling length, low insertion loss, and high extinction ratio. With the arm separation of 0.3 μm, the coupling length can be made 5.2 % of the propagation length of the hybrid plasmonic waveguide, while the insertion loss and extinction ratio are ?0.12 and 22.4 dB, respectively. This coupler offers the potential applications in signal routing between the hybrid long-range plasmonic waveguide and dielectric waveguide in the photonic integrated circuits.