Stress analysis of silica-based arrayed waveguide grating by a finite element method

The stress distribution in silica optical waveguides on silicon is calculated by using finite element method (FEM). The waveguides are mainly subjected to compressive stress along the x direction and the z direction, and it is accumulated near the interfaces between the core and cladding layers. The shift of central wavelength of silica arrayed waveguide grating (AWG) on silicon-substrate with the designed wavelength and the polarization dependence are caused by the stress in the silica waveguides.

Measurement of respiratory acoustic impedance in children by a modified forced oscillation method

An introduction to a modified forced oscillation method, square-wave excitation technique, including fundamentals and methods, as used in respiratory function examination. On the basis of experimental results and theoretical predictions, we suggest that Respiratory Acoustic Impedance (RAI) measurement by spectral analysis can significantly improve estimation of contribution to RAI from different part of respiratory tract. The outcome is of considerable interest in the study of lung disease, such as COPD and asthma in young children.

Diffractive microlens with a cascade focal plane fabricated by single mask UV-photolithography and common KOH:H2O etching

A diffractive microlens with a cascade focal plane along the main optical axis of the device is fabricated using a low-cost technique mainly including single mask ultraviolet (UV) photolithography and dual-step KOH:H2O etching. Based on the evolutionary behavior of converse pyramid-shaped microholes (CPSMs) preshaped over a {100}-oriented silicon wafer in KOH etchant, the first-step KOH etching is performed to transfer initial square micro-openings in a SiO2 film grown by plasma enhanced chemical vapor deposition (PECVD) and patterned by single mask UV-photolithography, into CPSMs with needed dimension. After completely removing a thinned SiO2 mask, basic annular phase steps with a relatively steep sidewall and scheduled height can be shaped in the overlapped etching region between the neighboring silicon concave-arc microstructures evolved from CPSMs through the second-step KOH etching. Morphological measurements demonstrate a desirable surface of the silicon microlens with a roughness in nanometer scale and the feature height of the phase steps formed in the submicrometer range. Conventional optics measurements of the plastic diffractive microlens obtained by further hot embossing the fine microrelief phase map over the nickel mask made through a common electrochemical method indicate a highly efficient cascaded focusing performance.

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.

Design and optimization of highly nonlinear low-dispersion crystal fiber with high birefringence for four-wave mixing

We have proposed a novel type of photonic crystal fiber (PCF) with low dispersion and high nonlinearity for four-wave mixing. This type of fiber is composed of a solid silica core and a cladding with a squeezed hexagonal lattice elliptical airhole along the fiber length. Its dispersion and nonlinearity coefficient are investigated simultaneously by using the full vectorial finite element method. Numerical results show that the proposed highly nonlinear low-dispersion fiber has a total dispersion as low as +/- 2.5 ps nm(-1) km(-1) over an ultrabroad wavelength range from 1.43 to 1.8 mu m, and the corresponding nonlinearity coefficient and birefringence are about 150 W-1 km(-1) and 2.5 x 10(-3) at 1.55 mu m, respectively. The proposed PCF with low ultraflattened dispersion, high nonlinearity, and high birefringence can have important application in four-wave mixing. (C) 2010 Optical Society of America

Analytical method of predicating the instabilities of a micro arch-shaped beam under electrostatic loading

An arch-shaped beam with different configurations under electrostatic loading experiences either the direct pull-in instability or the snap-through first and then the pull-in instability. When the pull-in instability occurs, the system collides with the electrode and adheres to it, which usually causes the system failure. When the snap-through instability occurs, the system experiences a discontinuous displacement to flip over without colliding with the electrode. The snap-through instability is an ideal actuation mechanism because of the following reasons: (1) after snap-through the system regains the stability and capability of withstanding further loading; (2) the system flips back when the loading is reduced, i.e. the system can be used repetitively; and (3) when approaching snap-through instability the system effective stiffness reduces toward zero, which leads to a fast flipping-over response. To differentiate these two types of instability responses for an arch-shaped beam is vital for the actuator design. For an arch-shaped beam under electrostatic loading, the nonlinear terms of the mid-plane stretching and the electrostatic loading make the analytical solution extremely difficult if not impossible and the related numerical solution is rather complex. Using the one mode expansion approximation and the truncation of the higher-order terms of the Taylor series, we present an analytical solution here. However, the one mode approximation and the truncation error of the Taylor series can cause serious error in the solution. Therefore, an error-compensating mechanism is also proposed. The analytical results are compared with both the experimental data and the numerical multi-mode analysis. The analytical method presented here offers a simple yet efficient solution approach by retaining good accuracy to analyze the instability of an arch-shaped beam under electrostatic loading.

Instabilities and transient behaviors of a liquid film flowing down a porous inclined plane

The nonmodal linear stability of a falling film over a porous inclined plane has been investigated. The base flow is driven by gravity. We use Darcy's law to describe the flow in the porous medium. A simplified one-sided model is used to describe the fluid flow. In this model, the influence of the porous layer on the flow in the film can be identified by a parameter beta. The instabilities of a falling film have traditionally been investigated by linearizing the governing equations 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 the present paper, we have studied the linear stability of three-dimensional disturbances using the nonmodal stability theory. Particular attentions are paid to the transient behavior rather than the long time behavior of eigenmodes predicted by traditional normal mode analysis. The transient behaviors of the response to external excitations and the response to initial conditions are studied by examining the pseudospectral structures and the energy growth function G(t) Before we study the nonmodal stability of the system, we extend the results of long-wave analysis in previous works by examining the linear stabilities for streamwise and spanwise disturbances. Results show that the critical conditions of both the surface mode and the shear mode instabilities are dependent on beta for streamwise disturbances. However, the spanwise disturbances have no unstable eigenvalue. 2010 American Institute of Physics. [doi:10.1063/1.3455503]

Dynamics of Vortex-Wave under a Travelling-Wave Modulation

The mecha nism of destabilization is studied for the rotating vortices (scroll waves and spiral waves) in excitable media induced by a parameter modulation in the form of a travelling-wave. It is found that a rigid rotating spiral in the two-dimensional (2D) system undergoes asynchronized drift along a straightline, and a 3D scrolling with its filament closed into a circle can be reoriented only if the direction of wavenumber of a travelling-wave perturbation is parallel to the ring plane. Then, in order to describe the behaviour of the synchronized drift of spiral wave and the reorientation of scrollring, the approximate formulas are given to exhibit qualitative agreements with the observed results.

A discrete square global grid system based on the parallels plane projection

We developed a direct partitioning method to construct a seamless discrete global grid system (DGGS) with any resolution based on a two-dimensional projected plane and the earth ellipsoid. This DGGS is composed of congruent square grids over the projected plane and irregular ellipsoidal quadrilaterals on the ellipsoidal surface. A new equal area projection named the parallels plane (PP) projection derived from the expansion of the central meridian and parallels has been employed to perform the transformation between the planar squares and the corresponding ellipsoidal grids. The horizontal sides of the grids are parts of the parallel circles and the vertical sides are complex ellipsoidal curves, which can be obtained by the inverse expression of the PP projection. The partition strategies, transformation equations, geometric characteristics and distortions for this DGGS have been discussed. Our analysis proves that the DGGS is area-preserving while length distortions only occur on the vertical sides off the central meridian. Angular and length distortions positively correlate to the increase in latitudes and the spanning of longitudes away from a chosen central meridian. This direct partition only generates a small number of broken grids that can be treated individually.

Facile synthesis of highly uniform octahedral LuVO4 microcrystals by a facile chemical conversion method

Uniform octahedral LuVO4 microcrystals have been successfully prepared through a designed two-step hydrothermal method. One-dimensional lutetium precursor was first prepared through a simple hydrothermal route. Subsequently, a well-shaped octahedral LuVO4 sample was synthesized at the expense of the wirelike precursors during the hydrothermal process. The whole process in this method was carried out in aqueous conditions without the use of any organic solvents, surfactant, or catalyst. The conversion process from nanowire precursor to octahedral product has been investigated in detail. The LuVO4 : Ln(3+) (Ln Eu, Dy, Sm, and Er) phosphors show strong light emissions with different colors coming from different activator ions under ultraviolet light excitation or low-voltage electron beam excitation. Furthermore, this general and facile method may be of much significance in the synthesis of many other lanthanide compounds with polyhedral morphology.

Study of self-assembly of symmetric coil-rod-coil ABA-type triblock copolymers by self-consistent field lattice method

The self-assembly of symmetric coil-rod-coil ABA-type triblock copolymer melts is studied by applying self-consistent field lattice techniques in a three-dimensional space. The self-assembled ordered structures differ significantly with the variation of the volume fraction of the rod component, which include lamellar, wave lamellar, gyroid, perforated lamellar, cylindrical, and spherical-like phases. To understand the physical essence of these phases and the regimes of occurrence, we construct the phase diagram, which matches qualitatively with the existing experimental results. Compared with the coil-rod AB diblock copolymer, our results revealed that the interfacial grafting density of the separating rod and coil segments shows important influence on the self-assembly behaviors of symmetric coil-rod-coil ABA triblock copolymer melts. We found that the order-disorder transition point changes from f(rod)=0.5 for AB diblock copolymers to f(rod)=0.6 for ABA triblock copolymers. Our results also show that the spherical-like and cylindrical phases occupy most of the region in the phase diagram, and the lamellar phase is found stable only at the high volume fraction of the rod.

Third-order Stokes wave solutions for interfacial internal waves in a three-layer density-stratified fluid

Interfacial internal waves in a three-layer density-stratified fluid are investigated using a singular method, and third-order asymptotic solutions of the velocity potentials and third-order Stokes wave solutions of the associated elevations of the interfacial waves are presented based on the small amplitude wave theory. as expected, the third-order solutions describe the third-order nonlinear modification and the third-order nonlinear interactions between the interfacial waves. The wave velocity depends on not only the wave number and the depth of each layer but also on the wave amplitude.

Wave generation by the falling rock in the two-dimensional wave tank

Wave generation by the falling rock in the two-dimensional wave tank is experimentally and numerically studied, where the numerical model utilizes the boundary element method to solve the fully nonlinear potential flow theory. The wave profiles at different times are measured in the laboratory, which are also used to test the numerical model. Comparisons show that the experimental and numerical results are in good agreement, and the numerical model can be used to simulate the wave generation due to the submarine rock falling. Further numerical tests on the influences of the rock size, density, initial position and the falling angle on the wave elevation of the generated waves are performed, respectively. The results show that the size and density of the rock have strong effects on the maximum elevation of the generated wave, while the effects of the initial position and the falling angle of the rock are also significant. When the size or the density of the rock increases, the maximum elevation of the generated wave increases. The same effect on the generated wave would be produced if the initial position of the rock becomes closer to the surface, or the falling angle between the falling route and the vertical direction turns larger. In addition, the present numerical tests reveal that the submarine rock falling provides a new generation method for the breaking wave in the wave tank.

Influence of the earth rotation on the interfacial wave solutions and wave-induced tangential stress in a two-layer fluid system

Interfacial waves and wave-induced tangential stress are studied for geostrophic small amplitude waves of two-layer fluid with a top free surface and a flat bottom. The solutions were deduced from the general form of linear fluid dynamic equations of two-layer fluid under the f-plane approximation, and wave-induced tangential stress were estimated based on the solutions obtained. As expected; the solutions derived from the present work include as special cases those obtained by Sun et al. (2004. Science in China, Set. D, 47(12): 1147-1154) for geostrophic small amplitude surface wave solutions and wave-induced tangential stress if tire density of the upper layer is much smaller than that of the lower layer. The results show that the interface and the surface will oscillate synchronously, and the influence of the earth's rotation both on the surface wave solutions and the interfacial wave solutions should be considered.

Numerical wave flume study on wave motion around submerged plates

Nonlinear interaction between surface waves and a submerged horizontal plate is investigated in the absorbed numerical wave flume developed based on the volume of fluid (VOF) method. The governing equations of the numerical model are the continuity equation and the Reynolds-Averaged Navier-Stokes (RANS) equations with the k-epsilon turbulence equations. Incident waves are generated by an absorbing wave-maker that eliminates the waves reflected from structures. Results are obtained for a range of parameters, with consideration of the condition under which the reflection coefficient becomes maximal and the transmission coefficient minimal. Wave breaking over the plate, vortex shedding downwave, and pulsating flow below the plate are observed. Time-averaged hydrodynamic force reveals a negative drift force. All these characteristics provide a reference for construction of submerged plate breakwaters.