Nonlinear optics with structured light

The interest in tailoring light in all its degrees of freedom is steadily gaining traction,driven by the tremendous developments in the toolkit for the creation,control and detection of what is now called structured light.Because the complexity of these optical fields is generally understood in terms of interference,the tools have historically been linear optical elements that create the desired superpositions.For this reason,despite the long and impressive history of nonlinear optics,only recently has the spatial structure of light in nonlinear processes come to the fore.In this review we provide a concise theoretical framework for understanding nonlinear optics in the context of structured light,offering an overview and perspective on the progress made,and the challenges that remain.

Nonlinear Differential Equation of Macroeconomic Dynamics for Long-Term Forecasting of Economic Development

In this article we derive a general differential equation that describes long-term economic growth in terms of cyclical and trend components. Equation is based on the model of non-linear accelerator of induced investment. A scheme is proposed for obtaining approximate solutions of nonlinear differential equation by splitting solution into the rapidly oscillating business cycles and slowly varying trend using Krylov-Bogoliubov-Mitropolsky averaging. Simplest modes of the economic system are described. Characteristics of the bifurcation point are found and bifurcation phenomenon is interpreted as loss of stability making the economic system available to structural change and accepting innovations. System being in a nonequilibrium state has a dynamics with self-sustained undamped oscillations. The model is verified with economic development of the US during the fifth Kondratieff cycle (1982-2010). Model adequately describes real process of economic growth in both quantitative and qualitative aspects. It is one of major results that the model gives a rough estimation of critical points of system stability loss and falling into a crisis recession. The model is used to forecast the macroeconomic dynamics of the US during the sixth Kondratieff cycle (2018-2050). For this forecast we use fixed production capital functional dependence on a long-term Kondratieff cycle and medium-term Juglar and Kuznets cycles. More accurate estimations of the time of crisis and recession are based on the model of accelerating log-periodic oscillations. The explosive growth of the prices of highly liquid commodities such as gold and oil is taken as real predictors of the global financial crisis. The second wave of crisis is expected to come in June 2011.

Numerical Solution of Nonlinear System of Partial Differential Equations by the Laplace Decomposition Method and the Pade Approximation

In this paper, Laplace decomposition method (LDM) and Pade approximant are employed to find approximate solutions for the Whitham-Broer-Kaup shallow water model, the coupled nonlinear reaction diffusion equations and the system of Hirota-Satsuma coupled KdV. In addition, the results obtained from Laplace decomposition method (LDM) and Pade approximant are compared with corresponding exact analytical solutions.

SYNTHESIS AND CHARACTERIZATI0N OF POLYMETHACRYLATES BEARING HETEROCYCLIC AZO GROUP AND MESOGENIC GROUP FOR NONLINEAR OPTICS

The methacrylate monomers bearing mesogenic group and heterocyclicazo dye have been synthesized. The monomeric dye was copolymerized with the mesogenicmonomer using a free radical initiator to produce polymers useful for nonlinear optics. Themonomers and polymers were characterized by IR,;H-NMR, and UV-Vis spectra. Theaverage molecular weight （M;and M;） of the polymers were determined by gel permeationchromatography. The thermal properties of the polymers such as thermal stability andphase transition behavior were studied by thermogravimetric analysis, differential thermalanalysis, polarizing optical microscope and X-ray diffractometer. The results demonstratethat the synthesized polymers are crystalline polymers at room temperature and no liquidcrystalline phases were observed for all of them.

Fluorine-Mediated Benzothiadiazole Derivatives for Second-Order Nonlinear Optics

With increasing research interests in the field of light-matter interactions,various methods have been developed for regulating nonlinear optical(NLO)materials.However,the design and synthesis of organic molecular materials for second-order nonlinear optics remain a great challenge because of the strict requirement of the materials to possess a noncentrosymmetric structure.In this work,two benzothiadiazole(BTD)derivatives referred to as BTD-H and BTD-F were synthesized,and their NLO properties in the crystalline states were studied.It was found that introducing fluorine into the BTD backbone effectively tuned the crystal packing styles of BTD derivatives to a noncentrosymmetric system for effective second-order NLO responses.Such a strategy to induce the noncentrosymmetric structure by introducing the fluorine atoms and halogen interactions may provide guidance for future engineering of organic NLO molecular materials.

Localized waves of the coupled cubic–quintic nonlinear Schrdinger equations in nonlinear optics

We investigate some novel localized waves on the plane wave background in the coupled cubic-quintic nonlinear Schrdinger （CCQNLS） equations through the generalized Darboux transformation （DT）. A special vector solution of the Lax pair of the CCQNLS system is elaborately constructed, based on the vector solution, various types of higher-order localized wave solutions of the CCQNLS system are constructed via the generalized DT. These abundant and novel localized waves constructed in the CCQNLS system include higher-order rogue waves, higher-order rogues interacting with multi-soliton or multi-breather separately. The first-and second-order semi-rational localized waves including several free parameters are mainly discussed：（i） the semi-rational solutions degenerate to the first-and second-order vector rogue wave solutions; （ii） hybrid solutions between a first-order rogue wave and a dark or bright soliton, a second-order rogue wave and two dark or bright solitons; （iii） hybrid solutions between a first-order rogue wave and a breather, a second-order rogue wave and two breathers. Some interesting and appealing dynamic properties of these types of localized waves are demonstrated, for example, these nonlinear waves merge with each other markedly by increasing the absolute value of α. These results further uncover some striking dynamic structures in the CCQNLS system.

More Compactification for Differential Systems

This article is a review and promotion of the study of solutions of differential equations in the “neighborhood of infinity” via a non traditional compactification. We define and compute critical points at infinity of polynomial autonomuos differential systems and develop an explicit formula for the leading asymptotic term of diverging solutions to critical points at infinity. Applications to problems of completeness and incompleteness (the existence and nonexistence respectively of global solutions) of dynamical systems are provided. In particular a quadratic competing species model and the Lorentz equations are being used as arenas where our technique is applied. The study is also relevant to the Painlevé property and to questions of integrability of dynamical systems.

THE DYNAMICAL BEHAVIOR OF FULLY DISCRETE SPECTRAL METHOD FOR NONLINEAR SCHRODINGER EQUATION WITH WEAKLY DAMPED

Nonlinear Schrodinger equation (NSE) arises in many physical problems. It is a very important equation. A lot of works studied the wellposed, the existence of solution of NSE etc. And there are many works studied the numerical methods for it. Recently, since the development of infinite dimensional dynamic system the dynamical behavior of NSE has been investigated. The paper [1] studied the long time wellposedness, the existence of universal attractor and the estimate of Lyapunov exponent for NSE with weakly damped. At the same time it was need to study the large time new computational methods and to discuss its convergence error estimate, the existence of approximate attractors etc. In this pape we study the NSE with weakly damped (1.1). We assume,where 0【λ【2 is a constant. If we wish to construct the higher accuracy computational scheme, it will be difficult that staigh from the equation (1.1). Therefore we start with (1. 4) and use fully discrete Fourier spectral method with time difference to

Recent advances in nonlinear optics for bio‐imaging applications

Nonlinear optics,which is a subject for studying the interaction between intense light and materials,has great impact on various research fields.Since many structures in biological tissues exhibit strong nonlinear optical effects,nonlinear optics has been widely applied in biomedical studies.Especially in the aspect of bio-imaging,nonlinear optical techniques can provide rapid,label-free and chemically specific imaging of biological samples,which enable the investigation of biological processes and analysis of samples beyond other microscopy techniques.In this review,we focus on the introduction of nonlinear optical processes and their applications in bio-imaging as well as the recent advances in this filed.Our perspective of this field is also presented.

Global Solution of a Nonlinear Conservation Law with Weak Discontinuous Flux in the Half Space

This paper is concerned with the initial-boundary value problem of a nonlinear conservation law in the half space R+= {x |x > 0} where a>0 , u(x,t) is an unknown function of x ∈ R+ and t>0 , u ± , um are three given constants satisfying um=u+≠u- or um=u-≠u+ , and the flux function f is a given continuous function with a weak discontinuous point ud. The main purpose of our present manuscript is devoted to studying the structure of the global weak entropy solution for the above initial-boundary value problem under the condition of f '-(ud) > f '+(ud). By the characteristic method and the truncation method, we construct the global weak entropy solution of this initial-boundary value problem, and investigate the interaction of elementary waves with the boundary and the boundary behavior of the weak entropy solution.

恒河猴慢性青光眼模型的建立及相关生物学特性

目的建立两种激光光凝的恒河猴慢性高眼压性青光眼模型,评价模型眼的相关生物学特性。方法成年恒河猴15只,分别采用半导体倍频532激光和氩激光,在房角镜下对功能小梁网区行360°光凝。对其中7只恒河猴分别采用A超、视网膜断层成像仪和视网膜血流仪进行模型眼和另侧对照眼的眼球及视盘形态、血流参数的检测。结果两种光凝模式相比,眼压升高后第4周,倍频532激光组平均眼压为48.4±10.3mmHg,氩激光组平均眼压为44.2±7.0mmHg,倍频532激光组与氩激光组的三次光凝成功率的差异无显著性意义。除视盘面积外,恒河猴模型眼的视杯形态指数、杯盘面积比、盘沿面积、视网膜神经纤维层的平均厚度,与对照眼相比差异有极显著性意义。眼轴和前房深度与对照眼相比差异有显著性意义。筛板血流量、血流速度和红细胞移动速率与对照眼相比差异无显著性意义。结论两种激光光凝恒河猴小梁网均可用以建立慢性高眼压性青光眼模型,模型眼出现青光眼眼底特征性的形态学改变。

双管式挫屈束制(屈曲约束)支撑之耐震行为与应用

挫屈束制(屈曲约束)支撑一般是由十字型或一字型钢板构成之核心单元加上钢管混凝土构成之束制(约束)单元所组成。由于单核心断面之挫屈束制支撑在与构架接合时每一端需使用八片续接板及两套的螺栓,造成接合部分较长且易发生挫屈(屈曲),为了改善此种挫屈束制支撑与接合,相关研究已发展出以双T型核心配双钢管或双钢板核心配双钢管而组成之双钢管型挫屈束制支撑构件,并已成功地在台大完成一系列之试验,本研究进一步针对大尺寸之单层挫屈束制支撑构架进行试验。研究目的包括:(1)探讨支撑具不同核心长度比例构架之试验与解析行为;(2)研究挫屈束制支撑核心应变与楼层侧位移角之关系;(3)提供含挫屈束制支撑构架之分析与设计建议。由三组V型双钢板双钢管挫屈束制支撑构架之试验显示,支撑核心之极限应变可利用楼层的最大侧位移角需求,以简单的几何关系及支撑核心长度与工作点间长度之比值计算而得,试验结果亦显示,在构架产生最大侧位移角时支撑之核心拉应变会大于相邻支撑之核心压应变,显示两相邻支撑之轴拉力与轴压力在试体中有互相平衡之趋势,而不会发生最大轴压力显著大于最大轴拉力的现象。

Qualitative Properties and Numerical Solution of the Kolmogorov-Fisher Type Biological Population Task with Double Nonlinear Diffusion

In the present work we study the global solvability of the Kolmogorov-Fisher type biological population task with double nonlinear diffusion and qualitative properties of the solution of the task based on the self-similar analysis. In additional, in this paper we consider the model of two competing population with dual nonlinear cross-diffusion.

Impact of Channel Dynamics, Combined Nonlinearities and ASE Noise on Transmission Performance of all Optical Star WDM Networks

For all optical Wavelength Division Multiplexing (WDM) network based on G.653 fibers, we investigate the quality factor deterioration due to combined nonlinear effects and Amplified spontaneous emission (ASE) noise for system parameters based on ITU-T Recommendation G.692. The investigation: (a) emphasizes on stimulated Raman scattering (SRS) and four wave mixing (FWM) effects which are the dominant nonlinearities known to limit WDM system performance and (b) accounts for beating between nonlinearities and beating between ASE noise and nonlinearities. Using the proposed model, performance of the worst affected channels due to SRS and FWM is compared and the results indicate that the worst affected channel due to SRS performs better and hence must be preferred for reliable and efficient transmission over the worst affected channel due to FWM. Further, the results suggest that to achieve a desired error rate (quality factor);there exists an optimal value of channel spacing for a given number of channels. The proposed theoretical model is also validated through extensive simulations over Rsoft OptSimTM simulator and the two sets of results are found to match, indicating that the proposed model accurately calculates the quality factor of the all optical WDM network.

Nonlinear waves of the Hirota and the Maxwell Bloch equations in nonlinear optics

In this paper, considering the Hirota and the Maxwell–Bloch （H-MB） equations which are governed by femtosecond pulse propagation through a two-level doped fiber system, we construct the Darboux transformation of this system through a linear eigenvalue problem. Using this Daurboux transformation, we generate multi-soliton, positon, and breather solutions （both bright and dark breathers） of the H-MB equations. Finally, we also construct the rogue wave solutions of the above system.

Quantum Computation with Nonlinear Optics

We propose a scheme of quantum computation with nonlinear quantum optics. Polarization states of photons are used for qubits. Photons with different frequencies represent different qubits. Single qubit rotation operation is implemented through optical elements like the Faraday polarization rotator. Photons are separated into different optical paths, or merged into a single optical path using dichromatic mirrors. The controlled-NOT gate between two qubits is implemented by the proper combination of parametric up and down conversions. This scheme has the following features： （1） No auxiliary qubits are required in the controlled-NOT gate operation; （2） No measurement is required in the course of the computation; （3） It is resource efficient and conceptually simple.

AN EPOXY/(METHYL METHACRYLATE)INTERPENETRATING POLYMER NETWORK FOR NONLINEAR OPTICS

An interpenetrating polymer networks (IPN) consisting of an epoxy-based polymer network and a polymethyl methacrylate network were synthesized and characterized. The IPN showed only one T-g, and hence a homogeneous-phase morphology was suggested. The second-order nonlinear optical coefficient (d(33)) of the IPN was measured to be 1.72 X 10(-7) esu. The study of NLO temporal stability at room temperature and elevated temperature (100 degrees C) indicated that the IPN exhibits a high stability in the dipole orientation due to the permanent entanglements of two component networks in the IPN system. Long-term stability of second harmonic coefficients was observed at room temperature for more than 1000 h.

夏季副热带高压北移的非线性机理探讨

文中建立了含22个变量的强迫、耗散、非线性的斜压大气动力系统。该系统包含了超长波、长波和纬向气流三者的相互作用;反映了北半球两大洋、两大陆的“二波型”的纬向和经向非均匀热力强迫;采用相轨线图、流函数图以及Poincar啨图相结合的方法,归纳出若干典型的流动体制和环流型式;用长方形通道中的流动近似地表征北半球环流。结果表明:(1)该系统能很好地刻画斜压大气中7种流动体制及其转换;随着夏季热力强迫的增大,系统状态经历了R1R12V-NVR12的变化。(2)刻画了4种主要的环流型式及其转换;随着夏季热力强迫的增大,环流型从G2转G3,即副高季节性北移西伸。(3)系统的流动体制和环流型式之间的联系表现为:夏季副热带高压北移西伸即G2转G3的变化,对应着流动体制由Rossby流转振荡态(R12V-NV);副热带高压在偏北位置上的南北向和东西向的振荡活动,则对应着系统振荡态的维持。