Modal analysis of deep-etched low-contrast two-port beam splitter grating

Modal analysis of a deep-etched low-contrast two-port beam splitter grating under Littrow Mounting is presented. The guideline for the design of a subwavelength transmission fused-silica phase grating as high-efficiency grating, polarizing beam splitter (PBS), and two-port beam splitter, is summarized. As an example, a polarization-independent two-port beam splitter grating is designed at wavelength of 1064 nm. We firstly analyzed the physical essence of the grating by the simplified modal method. The guideline for the grating design and the approximate grating parameters are obtained. Then using the rigorous coupled-wave analysis (RCWA) with parameters varying around the approximate ones, Optimum grating parameters can be determined. With the design guideline, the time for the rigorous calculation of the grating profile parameters can be reduced significantly. (C) 2008 Elsevier B.V. All rights reserved

Crack propagation in structures subjected to periodic excitation

In the present paper, a simple mechanical model is developed to predict the dynamic response of a cracked structure subjected to periodic excitation, which has been used to identify the physical mechanisms in leading the growth or arrest of cracking. The structure under consideration consists of a beam with a crack along the axis, and thus, the crack may open in Mode I and in the axial direction propagate when the beam vibrates. In this paper, the system is modeled as a cantilever beam lying on a partial elastic foundation, where the portion of the beam on the foundation represents the intact portion of the beam. Modal analysis is employed to obtain a closed form solution for the structural response. Crack propagation is studied by allowing the elastic foundation to shorten (mimicking crack growth) if a displacement criterion, based on the material toughness, is met. As the crack propagates, the structural model is updated using the new foundation length and the response continues. From this work, two mechanisms for crack arrest are identified. It is also shown that the crack propagation is strongly influenced by the transient response of the structure.

Nonlinear dynamics of atomic force microscopy with intermittent contact

When the atomic force microscopy (AFM) in tapping mode is in intermittent contact with a soft substrate, the contact time can be a significant portion of a cycle, resulting in invalidity of the impact oscillator model, where the contact time is assumed to be infinitely small. Furthermore, we demonstrate that the AFM intermittent contact with soft substrate can induce the motion of higher modes in the AFM dynamic response. Traditional ways of modeling AFM (one degree of freedom (DOF) system or single mode analysis) are shown to have serious mistakes when applied to this kind of problem. A more reasonable displacement criterion on contact is proposed, where the contact time is a function of the mechanical properties of AFM and substrate, driving frequencies/amplitude, initial conditions, etc. Multi-modal analysis is presented and mode coupling is also shown. (c) 2006 Published by Elsevier Ltd.

A metal-mirror-based reflecting polarizing beam splitter

We theoretically investigated the design of a metal-mirror-based reflecting polarizing beam splitter (RPBS). The metal mirror is a silver slab, which is embedded in the substrate of a rectangular silica transmission grating. By using a modal analysis and rigorous coupled-wave analysis, an RPBS grating is designed for operation at 1550 nm. When it is illuminated in Littrow mounting, the transverse electric (TE) and transverse magnetic (TM) waves will be mainly reflected in the minus-first and zeroth orders, respectively. Moreover, a wideband RPBS grating is obtained by adopting the simulated annealing algorithm. The RPBS gratings exhibit high diffraction efficiencies (similar to 95%) and high extinction ratios over a certain angle and wavelength range, especially for the minus-first-order reflection. This kind of RPBS should be useful in practical optical applications.

穿甲弹发射故障的动态诊断

对某研制阶段的高膛压火炮发射穿甲弹研究发现,当静强度安全系数较大时多次发生断弹事故,这说明此时动强度已成为主要矛盾,应用模态实验技术研究了脱壳穿甲弹动态特性,获得了该脱壳穿甲弹结构模态参数,模态分析方法所获得的动态薄弱截面位置与试验弹断弹情况相吻合,为其发射故障诊断提供了实验依据。

Modelling and analysis of modal behaviour in SOI slot waveguides

Mode behaviour for SOI slot waveguides is modelled and analysed using a numerical full vectorial method based on the film mode matching method (MMM). Only the quasi-TE mode is investigated. Waveguide heights and slot widths, as well as silicon widths are properly chosen with respect to the single mode behaviour in the slot region. Comparison between the effective index method and our side loss method shows that our single mode condition is creditable. The optical power confinement in slot region for the quasi-TE mode is also studied and presented. We demonstrate that the maximum achievable optical power confinement P-slot and the maximum normalized average optical intensity I-slot are 42% and 26 mu m(-2), respectively.

Theoretical analysis of modal gain in p-doped 1.3 mu m InAs/GaAs quantum dot lasers

A theoretical study of modal gain in p-doped 1.3 mu m InAs/GaAs quantum dot (QD) lasers is presented. The expression of modal gain is derived, which includes an effective ratio that describes how many QDs contribute to the modal gain. The calculated results indicate that the modal gain with the effective ratio is much smaller than that without the effective ratio. The calculated maximum modal gain is is a good agreement with the experimental data. Furthermore, QDs with lower height or smaller aspect ratio are beneficial in achieving a larger maximum modal gain that leads to lower threshold current density and higher differential modal gain. (C) 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

A finite-element analysis of viscoelastically damped sandwich plates

A finite element analysis associated with an asymptotic solution method for the harmonic flexural vibration of viscoelastically damped unsymmetrical sandwich plates is given. The element formulation is based on generalization of the discrete Kirchhoff theory (DKT) element formulation. The results obtained with the first order approximation of the asymptotic solution presented here are the same as those obtained by means of the modal strain energy (MSE) method. By taking more terms of the asymptotic solution, with successive calculations and use of the Padé approximants method, accuracy can be improved. The finite element computation has been verified by comparison with an analytical exact solution for rectangular plates with simply supported edges. Results for the same plates with clamped edges are also presented.

Analysis of flexural vibration of viscoelastically damped sandwich plates

The simplified governing equations and corresponding boundary conditions of flexural vibration of viscoelastically damped unsymmetrical sandwich plates are given. The asymptotic solution of the equations is then discussed. If only the first terms of the asymptotic solution of all variables are taken as an approximate solution, the result is identical with that obtained from the Modal Strain Energy (MSE) Method. As more terms of the asymptotic solution are taken, the successive calculations show improved accuracy. With the natural frequencies and the modal loss factors of a damped sandwich plate known, one can calculate the response of the plate to various loads providing a reliable basis for engineering design.

Design and analysis of a kind of large flattened mode optical fibre

In this paper, a refractive index pro. le design enabling us to obtain a. at modal field around the fibre centre is investigated. The theoretical approach for designing such multilayer large flattened mode (LFM) optical fibres is presented. A comparison is made between the properties of a three-layer LFM structure and a standard step-index pro. le with the same core size. The obtained results indicate that the effective area of the LFM fibre is about twice as large as that of the standard step-index fibre, but the LFM fibre has less effective ability to filter out the higher order modes than the standard step-index fibre with the same bending radius.

Study on tapered crossed subwavelength gratings by Fourier modal method

Fourier modal method incorporating staircase approximation is used to study tapered crossed subwavelength gratings in this paper. Three intuitive formulations of eigenvalue functions originating from the prototype are presented, and their convergences are compared through numerical calculation. One of them is found to be suitable in modeling the diffraction efficiency of the circular tapered crossed subwavelength gratings without high absorption, and staircase approximation is further proven valid for non-highly-absorption tapered gratings. This approach is used to simulate the "moth-eye" antireflection surface on silicon, and the numerical result agrees well with the experimental one.

Non-modal instabilities of two-dimensional disturbances in plane Couette flow of a power-law fluid

Instabilities of fluid flows have traditionally been investigated by normal mode analysis, i.e. by linearizing the equations of flow and testing for unstable eigenvalues of the linearized problem. However, the results of eigenvalue analysis agree poorly in many cases with experiments, especially for shear flows. In this paper we study the instabilities of two-dimensional Couette flow of a polymeric fluid in the framework of non-modal stability theory rather than normal mode analysis. A power-law model is used to describe the polymeric liquid. We focus on the response to external excitations and initial conditions by examining the pseudospectra structures and the transient energy growths. For both Newtonian and non-Newtonian flows, the results show that there can be a rather large transient growth even though the linear operator of Couette flow has no unstable eigenvalue. The effects of non-Newtonian viscosity on the transient behaviors are examined in this study. The results show that the "shear-thinning/shear-thickening" effect increases/decreases the amplitude of responses to external excitations and initial conditions. (C) 2010 Elsevier B.V. All rights reserved.

Preliminary analysis of grain-size populations with environmentally sensitive terrigenous components in marginal sea setting

Terrigenous components were separated from the bulk sediment of Core A7 from the Okinawa Trough and Core A37 from the Ryukru Trench and grain-size distributions of these sub-samples were analyzed. Based upon an analysis of the grain-size data of the two sedimentary sequences, grain-size populations are identified to be sensitive to sedimentary environmental changes. The modal values and size ranges of the two main grain-size populations in Core A7 are evidently different from those of Core A37, indicating the spatial variability of sediment sources and transport processes between the two places. The downcore variations in the content of the environmentally sensitive grain-size populations reveal that during the accumulation of sedimentary material the environment remained relatively stable at the site where Core A7 was collected, except for the apparent events for the formation of two turbidite layers and a volcanic ash layer. However, the sedimentary sequence of Core A37 shows six sedimentary cycles, indicating a highly variable sedimentary environment at this location.