Existence of positive solutions for a class of semilinear and quasilinear elliptic equations with supercritical case

In this paper, we consider a class of semilinear elliptic Dirichlet problems in a bounded regular domain with cylindrical symmetry involving concave-convex nonlinearities with supercritical growth. Using a new Sobolev embedding theorem and variational method, we show the existence of two positive solutions of the problem. Additionally, we study the quasilinear elliptic equation and obtain a similar result.     

Frequency/time domain modeling of a direct drive point absorber wave energy converter

Two different methods to model a point absorber wave energy converter(WEC)with direct drive linear power take-off(PTO)are proposed in the present study:the frequency domain(FD)method and the time domain(TD)method.In the FD analysis,the frequency response function(FRF)of the WEC device is obtained via the equation of motion,and the expressions of power capture width in regular and random waves are derived as well.In the TD modeling,based on a state space approximation of the convolution term in the motion equation,both regular wave and random wave simulations are carried out.The regular wave simulation results indicate that the state space approximation is sufficiently accurate and the capture width reaches the maximum in the vicinity of the natural frequency.In the random wave simulations,the effects of buoy size,the PTO damping and wave climate on the power capture width are discussed in detail,which leads to the conclusion that the capture widths are influenced by the natural frequency of the WEC device,peak frequency of the wave spectrum,the amplitude of FRF and PTO damping.Furthermore,the increase of the capture width is at the cost of a relatively large buoy size and PTO damping when control is not included.     

Temporal diffraction characteristics of transmitted multilayer volume holographic grating illuminated by an ultrashort pulse

Based on the coupled wave theory of Kogelnik and Fourier optics, the time-domain diffraction characteristics of tramsmitted multilayer volume holographic grating (MVHG) under an ultrashort pulse readout are investigated. It is shown that the temporal diffraction characteristics depend not only on the numbers of the grating layers, but also on the thicknesses of the grating layers and buffer layers, grating period and the refractive index modulation. Furthermore, using group velocity dispersion we give explanation on the time-delay of diffraction pulse with respect to the center of the readout pulse. Results of our discussion may find applications in optical communications, pulse shaping and processing.     

Double-mode electrostatic dispersing prism for electron pulse time-domain compression

The generalized theory of double-mode electrostatic dispersing prism for time-domain compressing electron pulse is presented. The fundamental difference between the two modes of o mode and e mode lies in the dispersive dependence of electron's time of flight on its initial kinetic energy at prism entrance: the electrons with higher initial axial energy definitely have longer time of flight for o mode, while not the case for e mode, which results from the electron pulse's U-shaped motion in the prism. The dispersive dependence of time of flight constitutes the mechanism of electron pulse compression for each mode. An example is given to demonstrate the issue of parameter choosing for the prism and to verify its tunable performance of compression.     

Design of high duty ratio nonlinear photonic crystal fiber with near-zero flattened dispersion after 1.205 μm

The paper presents a high nonlinear photonic crystal fiber (HN-PCF) with highly duty ratio for time-stretch analog-to-digital conversion (TSADC). The simulation results show that a nonlinear of 42.26 W⁻¹ km⁻¹ and the flattened dispersion of less than 1.0 ps/(nm km) are obtained in more than 495 nm waveband (1205–1700 nm). Owing to its high nonlinear coefficient and flattened dispersion, the high nonlinear PCF is expected to be suitable for supercontinuum (SC) generation. The numerical simulation results demonstrate that the proposed high duty ratio HN-PCF can generate wideband SC.     

A new multichannel time reversal focusing method for circumferential Lamb waves and its applications for defect detection in thick-walled pipe with large-diameter

This paper proposes a new multichannel time reversal focusing (MTRF) method for circumferential Lamb waves which is based on modified time reversal algorithm and applies this method for detecting different kinds of defects in thick-walled pipe with large-diameter. The principle of time reversal of circumferential Lamb waves in pipe is presented along with the influence from multiple guided wave modes and propagation paths. Experimental study is carried out in a thick-walled and large-diameter pipe with three artificial defects, namely two axial notches on its inner and outer surface respectively, and a corrosion-like defect on its outer surface. By using the proposed MTRF method, the multichannel signals focus at the defects, leading to the amplitude improvement of the defect scattered signal. Besides, another energy focus arises in the direct signal due to the partial compensation of dispersion and multimode of circumferential Lamb waves, alongside the multichannel focusing, during MTRF process. By taking the direct focus as a time base, accurate defect localization is implemented. Secondly, a new phenomenon is exhibited in this paper that defect scattered wave packet appears just before the right boundary of truncation window after time reversal, and to which two feasible explanations are given. Moreover, this phenomenon can be used as the theoretical basis in the determination of defect scattered waves in time reversal response signal. At last, in order to detect defects without prior knowing their exact position, a large-range truncation window is used in the proposed method. As a result, the experimental operation of MTRF method is simplified and defect detection and localization are well accomplished.     

Analytical investigation of response of birefringent fiber Bragg grating sensors in distributed monitoring system based on optical frequency domain reflectometry

When Fiber Bragg gratings (FBGs) are used as strain sensors, both longitudinal and lateral strain can be applied uniformly or non-uniformly over the length of the FBGs. In order for the demodulation of such FBG signal, this paper investigates the response of birefringent FBGs which are monitored by distributed measurement system based on optical frequency domain reflectometry. A numerical model of the distributed measurement system is built based on piece-wise uniform approach, which considers polarization states of propagating lights. The numerical model simulates analytical response of birefringent FBGs especially when birefringence induces power fluctuations in the distributed spectra, which can be noise or new opportunity for sensitive monitoring of birefringence. Simulation results show the relationships between the power fluctuations and the polarization states of the propagating lights. Consequently, appropriate methods of polarization control for sensitive distributed birefringent FBG monitoring are discussed.     

Electrical field analysis of metal‐surface plasmon resonance using a biaxially strained Si substrate

Electrical field components of metal‐surface plasmon resonance were analyzed in detail. Both longitudinal optical (LO) and transverse optical (TO) phonon modes of a biaxially strained Si layer can be excited by surface‐enhanced Raman spectroscopy (SERS). The z to y polarization ratio in SERS measurements was calculated to be 0.78 using the intensity ratio of TO to LO phonon modes. The electrical field components of SERS were also calculated by the finite‐difference time‐domain method. Copyright © 2014 John Wiley & Sons, Ltd.     

前后光栅周期对于双光栅结构薄膜太阳能电池光俘获效应的影响

本文用时域有限差分法对硅层等效厚度为100 nm的具有不同前后光栅周期的介质/金属双光栅结构薄膜太阳能电池进行了模拟分析,比较了三角形最佳相同与不同周期光栅结构的吸收光谱特性,分析了光栅高度、填充比、硅吸收层厚度对最佳相同和不同周期光栅结构光吸收特性的影响,以及相应结构中导致光吸收增强的共振模式.结果表明前后光栅周期为1:1的共形双光栅结构中存在光泄漏现象,偏离1:1后的光栅结构可有效地抑制低级次衍射光的泄漏,前光栅周期小于后光栅周期的结构光吸收性能的提高来自于平面波导模式在吸收层中的有效激发和传播,而前光栅周期大于后光栅周期的结构光吸收性能的提高则来自于后光栅界面上所激发的等离子体极化模式.在较厚的硅吸收层厚度,前后光栅周期比为1:2和1:3的电池结构也会出现光泄漏现象,从而使具有最大光吸收效率的结构偏离这些周期比结构的位置.