超短脉冲倍频中三阶非线性效应的影响及补偿

 为了提高超短脉冲二倍频的转换效率和改善出射倍频光的脉冲形状,对超短脉冲倍频中三阶非线性效应的影响进行了理论分析和数值模拟,并采用初始相位失配的方法来补偿三阶非线性效应的影响。结果表明：用KDP晶体二倍频中心波长为800 nm的超短脉冲,当入射功率密度大于100 GW/cm²时,三阶非线性效应是倍频转换效率的主要影响因素。对脉宽为50 fs,入射功率密度为250 GW/cm²的超短脉冲在KDP晶体（2 mm）中的二次谐波变换,当初始相位失谐0.9 mrad时,转换效率提高了10%,同时由三阶非线性效应引起的强度调制得到明显抑制,出射基频光和倍频光的脉冲形状得到明显改善。     

梯度折射率介质中高斯光束的非线性传输特性

 利用无像差自聚焦理论研究了梯度折射率非线性Kerr介质中高斯光束的传输特性,得到了高斯光束光斑半径和波面曲率半径的表达式。解析结果清楚地表明了衍射、自聚焦以及梯度折射率效应之间的竞争对高斯光束传输行为的影响。梯度折射率效应使光束自聚焦的距离缩短。     

On nonlinear effects in magnetic chains

The effect of phonon unharmonism and nonlinearity in exchange integrals on soliton excitations in ferromagnetic chains in the classical and long-wave limit are studied. It has been first shown that the unharmonic effect leads to a system of coupled Boussinesque and nonlinear Schrödinger equations allowing two types of soliton solutions. The nonlinear effect on the other hand results nonlinear Schrödinger equation with saturable nonlinearity admitting stable solitons in higher dimensional models.     

减小外差干涉一次谐波非线性误差的方法

为了补偿激光外差干涉纳米测量中的非线性误差,提出了一种减小非线性误差的一次谐波方法。基于全反射理论分析了镀膜实体角锥棱镜反射光偏振特性,并由此推导出角锥棱镜反射光偏振特性及测量角锥棱镜以其运动方向为轴线的轴向旋转对激光外差干涉非线性误差一次谐波的影响模型。理论分析表明,测量角锥棱镜以其运动方向为轴线的轴向旋转会减小非线性误差一次谐波,当测量角锥棱镜轴向旋转97°时,可使非线性误差一次谐波达到最小,约为原有非线性误差一次谐波分量的1/20倍。当激光器出射的两束线偏振光存在6°非正交误差时,镀膜实体测量角锥棱镜轴向旋转角度从0°增加到97°,非线性误差一次谐波由5.30 nm减小到0.30 nm。     

Rosen--Zener Transition in a Nonlinear System for Two-Component Bose--Einstein Condensates in Optical Lattices

We study the Rosen-Zener transition （RZT） in a nonlinear system for two-component Bose-Einstein condensates in optical lattices. It is found that the percentage of the components could affect the quantum transition dramatically. For the component with large percentage it is equivalent that the effect of the nonlinearity is stronger, whereas for the component with small percentage the effect is weaker. We also find that the nonlinearity c11 can affect the quantum transition dramatically. This is similar to that reported from Ref. [14]. Compared with one-component systems, however, the effect of the nonlinearity is decreased due to the two components of the BEGs in optical lattices. Furthermore, the effect of the coupling nonlinearity between two components c12 is studied. The component with large percentage is more affected by the nonlinearity than that with small-percentage component.     

Light-induced thermomechanical effect as a new mechanism of orientational optical nonlinearity in liquid crystals

A laser-induced thermomechanical effect in twist-aligned nematic liquid crystals has been revealed and experimentally studied. It has been proved that the nature of this phenomenon is orientational rather than diffraction. It has been shown that the orientational optical nonlinearity resulting from this effect can be as strong as the well-known giant optical nonlinearity. Moreover, giant optical nonlinearity does not exist at normal incidence of the laser beam, whereas thermomechanical nonlinearity remains of the same order of magnitude at any angle of incidence of the beam.     

Dynamics of a two-wave packet in a nonlinear optical fiber at detuning from phase matching

The effect of detuning from phase matching on the dynamics of a wave packet consisting of two unidirectional strongly interacting modes in a fiber with Kerr nonlinearity is considered. The effective parameters of dispersion and nonlinearity are analyzed for a wave packet that can be represented by a single partial pulse.     

Laser-induced orientational nonlinear phenomena and new vortex structures

Theoretical study of the third-type thermomechanical effect in a twist cell of nematic liquid crystal is presented. The solution of director equation is obtained and optical nonlinearity is evaluated. It is proved that the nonlinearity is of the same order as in case of the direct orientational optical nonlinearity. Possibility of observing thermomechanical effect in non-uniform vortex structures is also discussed.     

数值模拟高阶色散和非线性对光孤子传输的影响

光孤子传输中的高阶色散以及高次非线性效应是光纤通讯发展的重要制约因素。从光孤子在光纤中的一般传输方程出发, 在较大的入纤功率的前提下, 综合考虑了高阶色散、五次非线性和损耗因素, 得到其具体传输方程, 并据此从理论上分析了高阶色散和非线性对光孤子传输性能的影响。本文采用分步傅里叶方法, 以MATLAB为实现工具, 实现高阶色散和非线性对光孤子传输影响的模拟计算, 并深入分析了高阶色散和非线性导致的孤子脉冲频移现象。计算结果表明: 在入射功率较大的时候, 高阶色散效应不可忽略。当五次非线性γ2>0时,孤子脉冲主峰发生微小频移; 而当五次非线性γ2<0时, 孤子脉冲主峰基座产生微小频移; 当高阶色散β3>0时频率出现红移, 而当β3<0时, 频率出现蓝移。     

The characteristics of a nonlinear vibration neutralizer

This paper concerns an investigation into the use of cubic nonlinearity in a vibration neutralizer to improve its effectiveness. It is assumed that the frequency of the harmonic excitation is well above the resonance frequency of the machine to which the neutralizer is attached, and that the machine acts as a simple mass. It is also assumed that the response of the system is predominantly at the harmonic excitation frequency of the machine. The harmonic balance method is used to analyze the system. It is shown how the nonlinearity has the effect of shifting the resonant peak to a higher frequency away from the tuned frequency of the neutralizer so that the device is robust to mistune. In a linear neutralizer this can only be achieved by adding mass to the neutralizer, so the nonlinearity has a similar effect to that of adding mass. Some characteristic features are highlighted, and the effects of the system parameters on the performance are discussed. It is shown that, for a particular combination of the system parameters, the effect of the nonlinearity is also to increase the bandwidth of the device compared to the linear neutralizer with similar mass and damping. Some approximate expressions are derived, which facilitate insight into the parameters which influence the dynamics of the system. The results are validated by some experimental work.     

Effect of diffusion nonlinearity and an external electric field on the formation of ion-exchange diffraction gratings in glass

The formation of gratings in glass by the ion exchange technique is analyzed. The ion exchange is modeled, and the effect of diffusion nonlinearity and the external electric field on the diffusant concentration profile and diffraction characteristics of gratings are studied. It is shown that the character of diffusion nonlinearity has a substantial effect on the diffraction efficiency of the gratings produced by thermal ion exchange. It is also shown that the diffraction efficiency can be considerably increased by using an external electric field.     

Enhancement of Kerr nonlinearity via spontaneously generated coherence in a four-level N-type atomic system

A theoretical investigation is carried out into the effect of spontaneously generated coherence (SGC) on Kerr nonlinearity of a four-level N-type system. It’s found that the Kerr nonlinearity can be obviously enhanced with SGC present. We attribute the enhancement of Kerr nonlinearity mainly to the generation of extra coherences induced by the superposition of the two SGC channels, and when the superposition is controlled by the interference between two SGC channels properly, the maximal Kerr nonlinearity does not only enter the electromagnetically induced transparency window as the spontaneous generated coherences intensify, but also gets enhanced about 10 times with very large SGC coefficients than that with no SGC effect.     

Thermal nonlinearity in a photoacoustic cell

The effect of the thermal nonlinearity caused by the temperature dependence of the specific heat and thermal conductivity of a sample, substrate, and air on the temperature field in a photoacoustic cell is stud-ied theoretically. Exact solutions are obtained for a steady temperature field with allowance for thermal nonlin-earity and for a nonsteady field without allowance for this nonlinearity. The nonsteady nonlinear problem was solved numerically. It is shown that, due to thermal nonlinearity, the linear dependence of the temperature of the irradiated surface on the heating beam intensity gradually transforms into a power-law dependence as the beam intensity increases.     

Enhancing Kerr nonlinearity via quantum interference from incoherent pumping

The effect of quantum interference from incoherent pump field on the Kerr nonlinearity of V- and Lambda-type three-level systems is investigated. It is found that enhanced Kerr nonlinearity can be obtained via quantum interference of incoherent pump field. It is also demonstrated that the enhanced Kerr nonlinearity is located in the reduced-absorption region. The enhancement of Kerr nonlinearity is attributed mainly to the presence of extra atomic coherence induced by quantum interference from incoherent pump field.     

Irreversibility in an Optical Parametric Driven Optomechanical System

This study investigates the role of nonlinearity via optical parametric oscillator on the entropy production rate and quantum correlations in a hybrid optomechanical system. Specifically, the modified entropy production rate of an optical parametric oscillator placed in the optomechanical cavity is derived, which is well described by the two-mode Gaussian state. The irreversibility and quantum mutual information associated with the driving the system far from equilibrium are found to be controlled by the phase and strength of nonlinearity. This analysis shows that the system entropy flow, heating, or cooling, are determined by choosing the appropriate phase of the self-induced nonlinearity. It is further demonstrated that this effect persists for a reasonable range of cavity decay rate.     

Control of Group Velocity via Spontaneous Generated Coherence and Kerr Nonlinearity

A four-level N-type atomic medium is considered to study the effect of spontaneous generated coherence(SGC) and Kerr nonlinearity on light pulse propagation. A light pulse is propagating inside the medium where each atom follows four-level N-type atom-field configuration of rubidium(85Rb) atom. The atom-field interaction leads to electromagnetically induced transparency(EIT) process. The atom-field interaction is accompanied by normal dispersion and in the presence of SGC and Kerr nonlinearity the dispersion property of the proposed atomic medium is modified,which leads to enhancement of positive group index of the medium. The enhancement of positive group index then leads to slow group velocity inside the medium. A more slow group velocity is also investigated by incorporated the collective effect of SGC and Kerr nonlinearity. The control of group velocity inside a four-level N-type atomic medium via collective effect of SGC and Kerr nonlinearity is the major part of this work.     

交叉克尔非线性对二阶非线性诱导透明的影响

考虑耦合介质存在交叉克尔非线性的情形下,研究了交叉克尔效应对耦合双谐振腔中二阶非线性诱导透明的影响.首先给出了描述体系理论模型的哈密顿量,再通过对海森堡-朗之万方程进行线性化,得到了探测场的透射率,进而得出系统的吸收和色散关系.研究结果表明,在交叉克尔非线性强度较小时,可忽略其对诱导透明的影响;随着交叉克尔非线性强度的增大,诱导透明窗口宽度随之快速变窄.此外,吸收曲线中还出现了双吸收峰.进一步增强交叉克尔非线性,导致原本出现的诱导透明消失,并在新吸收峰处产生了新的诱导透明,新的诱导透明的吸收零点位置随着交叉克尔非线性增加而向左偏移.这些结果可能在不透明介质的窄窗口光传输和提高光学腔的性能方面提供一些参考.     

转镜式傅里叶变换光谱仪光程差非线性的研究

转镜式傅里叶光谱仪中,转镜的转动形成光程差的非线性。光程差非线性是转镜材料和工作角选择时要考虑的重要因素,通过对它的研究,可以为工程实践提供指导,为进一步研究奠定基础。通过输入单色光时的情况对干涉图进行研究,发现光程差非线性使干涉图的周期发生变化;通过和光程差线性系统的仪器函数比较对复原光谱进行研究,发现非线性给复原光谱带来了噪声和波数漂移。由于光程差的变化是已知的,在光谱复原时,用非线性的光程差代替傅里叶变换中的光程差,就可以对光程差非线性进行补偿。计算机仿真实验的结果表明,这种方法效果明显,经补偿后复原光谱中光程差非线性带来的噪声基本消失。     

The role of nonlinearity in computing graph-theoretical properties of resting-state functional magnetic resonance imaging brain networks

In recent years, there has been an increasing interest in the study of large-scale brain activity interaction structure from the perspective of complex networks, based on functional magnetic resonance imaging (fMRI) measurements. To assess the strength of interaction (functional connectivity, FC) between two brain regions, the linear (Pearson) correlation coefficient of the respective time series is most commonly used. Since a potential use of nonlinear FC measures has recently been discussed in this and other fields, the question arises whether particular nonlinear FC measures would be more informative for the graph analysis than linear ones. We present a comparison of network analysis results obtained from the brain connectivity graphs capturing either full (both linear and nonlinear) or only linear connectivity using 24 sessions of human resting-state fMRI. For each session, a matrix of full connectivity between 90 anatomical parcel time series is computed using mutual information. For comparison, connectivity matrices obtained for multivariate linear Gaussian surrogate data that preserve the correlations, but remove any nonlinearity are generated. Binarizing these matrices using multiple thresholds, we generate graphs corresponding to linear and full nonlinear interaction structures. The effect of neglecting nonlinearity is then assessed by comparing the values of a range of graph-theoretical measures evaluated for both types of graphs. Statistical comparisons suggest a potential effect of nonlinearity on the local measures-clustering coefficient and betweenness centrality. Nevertheless, subsequent quantitative comparison shows that the nonlinearity effect is practically negligible when compared to the intersubject variability of the graph measures. Further, on the group-average graph level, the nonlinearity effect is unnoticeable.     

Modeling and identification of freeplay nonlinearity

A nonlinear analysis is performed for the purpose of identification of the pitch freeplay nonlinearity and its effect on the type of bifurcation of a two degree-of-freedom aeroelastic system. The databases for the identification are generated from experimental investigations of a pitch-plunge rigid airfoil supported by a nonlinear torsional spring. Experimental data and linear analysis are performed to validate the parameters of the linearized equations. Based on the periodic responses of the experimental data which included the flutter frequency and its third harmonics, the freeplay nonlinearity is approximated by a polynomial expansion up to the third order. This representation allows us to use the normal form of the Hopf bifurcation to characterize the type of instability. Based on numerical integrations, the coefficients of the polynomial expansion representing the freeplay nonlinearity are identified.