Beam propagation method for wide-field nonlinear wave mixing microscope

We develop a nonlinear beam propagation method for signal generation in inhomogeneous medium for wide-field nonlinear wave mixing microscope. Experimental results performed in wide-field coherent anti-Stokes Raman imaging have shown good agreement with the developed theory.     

一维非线性声波传播特性

针对一维非线性声波的传播问题进行了有限元仿真和实验研究. 首先推导了一维非线性声波方程的有限元形式, 含有高阶矩阵的非线性项导致声波具有波形畸变、谐波滋生、基频信号能量向高次谐波传递等非线性特性. 编制有限元程序对一维非线性声波进行了计算并对仿真得到的畸变非线性声波信号进行处理, 分析其传播性质和物理意义. 为验证有限元计算结果, 开展了水中的非线性声波传播的实验研究, 得到了不同输入信号幅度激励下和不同传播距离的畸变非线性声波信号. 然后对基波和二次谐波的传播性质进行详细讨论, 分析了二次谐波幅度与传播距离和输入信号幅度的变化关系及其意义, 拟合出二次谐波幅度随传播距离变化的方程并阐述了拟合方程的物理意义. 结果表明, 数值仿真信号及其频谱均与实验结果有较好的一致性, 证实计算方法和结果的正确性, 并提出了具有一定物理意义的二次谐波随传播距离变化的简单数学关系. 最后还对固体中的非线性声波传播性质进行了初步探讨. 本研究工作可为流体介质中的非线性声传播问题提供理论和实验依据.     

A small signal theory of gyro-devices using the concept ofspace-charge waves

The linear theory of the interaction between a thin annular beam of gyrating electrons and a traveling electromagnetic wave is developed. This theory is very close in its methodology to the classical small signal theory of O- and M-type devices. Just this fact makes it possible to consider a number of issues in the theory of gyro-devices, namely, space-charge wave propagation in drifting electron beams, noise and parametric phenomena, effects of input signal suppression (Kompfner dip) in gyro-traveling-wave-tubes, and gyro-backward-wave-amplifiers     

Signal amplification based on the local nonlinear Mach–Zehnder interferometer

Using the phase modulation of spatial solitons, a new scheme for all-optical signal amplification has been proposed in this paper. The considered structure is composed of the nonlinear Mach–Zehnder interferometer (NMZI) with the straight control waveguide (CWG), the uniform nonlinear medium (NLM) and the linear output waveguide. The local NMZI functions like a phase shifter. The light-induced index changes in the local nonlinear MZI are responsible for the input beam routing in the uniform nonlinear medium. The coupling of the input beam to the output waveguide depends on its propagation direction in the NLM. It is shown that the signal launched at CWG can deflect the beam launched at the NMZI (input beam) and a modulated (amplified) output could be obtained at the output waveguide. Further, signal pulse may be reshaped by appropriately increasing the NLM length. In addition, amplification factor may be enhanced by increasing the NLM length and injecting an appropriate continuous wave beam along with the signal beam at CWG.     

Interaction of pulsed laser beams in quadratic nonlinear media

A theory of three-wave cascade interaction of pulsed laser beams in quadratic nonlinear media is developed with regard to diffraction and dispersion. The space-time trajectories of signal motion in a medium with an inhomogeneity induced by high-power low-frequency pumping are analyzed. It is shown that total signal reflection from a moving localized inhomogeneity can be implemented. This reflection is accompanied by a change in the frequency, velocity, and propagation direction of the signal wave.     

All optical self signal processing using chalcogenide nonlinear fiber Bragg grating

In this study, we simulate numerically quasi pulse propagation in a uniform nonlinear fiber Bragg grating (FBG) made of chalcogenide glasses. Because of bistability and nonlinearity behavior of FBG, the shapes of output pulse vary abruptly and strongly according to the input peak intensity. We take Gaussian pulse as input and produce saw-tooth wave and square wave in the output by suitable input amplitude and FBG length also we could reach pulse chopping and pulse compression. These all optical signal processing achieved for a few length, i.e. 6.6 mm and few intensity, i.e. 35 W/m² because of high nonlinearity of chalcogenide glasses.     

Optical gap solitons in nonresonant quadratic media

We demonstrate an important role of the process of optical rectification in the theory of nonlinear wave propagation in quadratically nonlinear [or chi(2)] periodic optical media. We derive a novel physical model for gap solitons in chi(2) nonlinear Bragg gratings.     

Photorefractive deceleration of light pulses

We theoretically study the effect of light deceleration in photorefractive nonlinear media. This includes consideration of different types of the photorefractive nonlinear response, different wave interaction schemes, and an analysis of the influence of the input parameters, such as the input temporal pulse width and the coupling strength, on the output pulse characteristics: the time delay, the propagation velocity, the amplification factor, and the output width. We show that photorefractive light deceleration has numerous advantages over other known techniques. It works already at low intensities, at room temperature, and within wide spectral ranges and offers a vast variety of handles for manipulating light pulses. An analogy with the light deceleration method based on the quantum effect of electromagnetically induced transparency in ultracold resonant gases is also considered. The text was submitted by the authors in English.     

等离子体中电波传播的三波非线性效应

利用等离子体非线性效应的三波法是解决黑障问题的一种可能的解决方案。从三波非线性理论出发,详细介绍了转化效率的计算方法,进而对不同等离子体电子密度模型下的非线性效应进行分析。数值仿真结果表明:存在一个最优的信号入射角度,当信号以该角度入射时转化效率最大;等离子体厚度会对最佳入射角产生一定影响,当厚度减小时,最佳入射角变大;等离子体电子密度变化范围、厚度、入射波及泵源参数都相同时,共振点处电子密度导数值越大,非线性效应越强。     

Two-dimensional modeling of wave propagation in materials with hysteretic nonlinearity

A multiscale model for the two-dimensional nonlinear wave propagation in a locally microdamaged medium is presented, and numerical simulations are analyzed in view of nondestructive testing applications. The multiscale model uses a statistical distribution of hysterons and upscales their microscopic stress-strain relations to a mesoscopic level. Macroscopic observations are then predicted by finite integration techniques. The influence of a small region with hysteretic nonlinearity on the generation of harmonics is investigated, and numerical results for different amplitudes of the input signal and different analysis techniques of the response signal are presented. Second, a study is conducted on the interaction of a Rayleigh wave with a microdamaged zone with hysteretic nonlinearity at the surface of an otherwise linear body, and the influence of the microdamaged zone on the surface wave velocity and on the generation of harmonics is examined. It is found that the effect of hysteresis on the Rayleigh wave propagation can be barely seen in the surface wave velocity measurement, but shows up nicely in the wave spectrum. The potential of a nonlinearity based depth profiling technique is explored by evaluating the nonlinear responses at different frequencies for a vertically stratified medium with spatially varying hysteresis properties.     

光纤放大器中非自治光畸波的传播控制研究

本文采用一个通用的理论,即用相似变换的方法,研究构建了(1+1)维变系数非线性薛定谔方程的精确畸形波解,首先讨论了一阶光畸波在光纤放大器中的传播问题.发现光学畸波的特性,如宽度、振幅和位置,可通过非线性光学介质特性和光脉冲的初始参量进行控制;然后在选择可控参数条件下,讨论了可控光畸波在非线性介质的传播行为,包括延迟激发、抑制、以及保持.这在理论和实际应用上具有启迪价值.     

Propagation dynamics of dipole breathing wave in lossy nonlocal nonlinear media

In the framework of nonlinear wave optics,we report the evolution process of a dipole breathing wave in lossy nonlocal nonlinear media based on the nonlocal nonlinear Schr?dinger equation.The analytical expression of the dipole breathing wave in such a nonlinear system is obtained by using the variational method.Taking advantage of the analytical expression,we analyze the influences of various physical parameters on the breathing wave propagation,including the propagation loss and the input power on the beam width,the beam intensity,and the wavefront curvature.Also,the corresponding analytical solutions are obtained.The validity of the analysis results is verified by numerical simulation.This study provides some new insights for investigating beam propagation in lossy nonlinear media.     

Resonance modes in optical fibres

The weakly nonlinear boundary value problem of wave propagation in an optical fibere(for the transverse electric mode,for example)is formulated and a modified linear solution is obained.It is shown that a self-consistent theory of fibre optics should be weakly nonlinear,The mode of critical refraction that does not exist in the linear theory is obtained,showing that it is a mode consisting of resonance modes,It is shown that the signal carriers in a long fibre are of resonance modes,not normal modes,Some experimental data are given for comparison with the theoretical predictions and the agreement seems satisfactory.     

Understanding Soliton Wave Propagation in Nonlinear Transmission Lines for Millimeter Wave Multiplication

In this paper, soliton propagation in nonlinear transmission lines (NLTLs) periodically loaded with symmetric voltage dependent capacitances is studied. From the lumped element equivalent circuit of the line we have analyzed the influence of nonlinear shunt reactances on soliton propagation characteristics. It is shown that by increasing the non linearity of the C–V characteristic, a faster separation of input signal into solitons is achieved. The fact that frequency multiplication in NLTLs is governed by soliton formation makes the results of this work relevant to understand the influence of nonlinear loading devices on multiplier performance. Since a heterostructure barrier varactor (HBV)-like voltage dependent capacitance has been considered for the nonlinear devices, this study can be of interest for the design of millimeter wave frequency multipliers loaded with HBVs.     

Wave propagation in embedded inhomogeneous nanoscale plates incorporating thermal effects

In this article, an analytical approach is developed to study the effects of thermal loading on the wave propagation characteristics of an embedded functionally graded (FG) nanoplate based on refined four-variable plate theory. The heat conduction equation is solved to derive the nonlinear temperature distribution across the thickness. Temperature-dependent material properties of nanoplate are graded using Mori–Tanaka model. The nonlocal elasticity theory of Eringen is introduced to consider small-scale effects. The governing equations are derived by the means of Hamilton’s principle. Obtained frequencies are validated with those of previously published works. Effects of different parameters such as temperature distribution, foundation parameters, nonlocal parameter, and gradient index on the wave propagation response of size-dependent FG nanoplates have been investigated.     

Use of the application of heterodyne laser interferometer in power ultrasonics

We are particularly interested in the measurement of nonlinear acoustic waves in air, within the range of the Raman-Nath diffraction regime. We used a heterodyne laser interferometric system with a Bragg cell frequency of 80 MHz. A harmonic power acoustic wave with a frequency in the range of 20 kHz was generated, but higher harmonics appear when nonlinear propagation occurs in restricted volumes or waveguides. This topic raises a number of interesting questions. The most complex problem arises when processing an extremely wide-band output signal from a photo-detector, where the signal contains a huge number of high amplitude harmonics in a measured acoustic signal. The wide-band output signal from nonlinear wave measurement was simulated by means of similar wide-band output signals obtained by measuring known dynamic mechanical displacements. Because the frequency band of common analog circuits used for signal processing is too narrow, the output signal from the interferometer was digitalized and processed. This paper discusses the results of these tests and provides estimates of the frequency restrictions of signal processing.     

Nonlinear wave propagation in constrained solids subjected to thermal loads

The classical mathematical treatment governing nonlinear wave propagation in solids relies on finite strain theory. In this scenario, a system of nonlinear partial differential equations can be derived to mathematically describe nonlinear phenomena such as acoustoelasticity (wave speed dependency on quasi-static stress), wave interaction, wave distortion, and higher-harmonic generation. The present work expands the topic of nonlinear wave propagation to the case of a constrained solid subjected to thermal loads. The origin of nonlinear effects in this case is explained on the basis of the anharmonicity of interatomic potentials, and the absorption of the potential energy corresponding to the (prevented) thermal expansion. Such “residual” energy is, at least, cubic as a function of strain, hence leading to a nonlinear wave equation and higher-harmonic generation. Closed-form solutions are given for the longitudinal wave speed and the second-harmonic nonlinear parameter as a function of interatomic potential parameters and temperature increase. The model predicts a decrease in longitudinal wave speed and a corresponding increase in nonlinear parameter with increasing temperature, as a result of the thermal stresses caused by the prevented thermal expansion of the solid. Experimental measurements of the ultrasonic nonlinear parameter on a steel block under constrained thermal expansion confirm this trend. These results suggest the potential of a nonlinear ultrasonic measurement to quantify thermal stresses from prevented thermal expansion. This knowledge can be extremely useful to prevent thermal buckling of various structures, such as continuous-welded rails in hot weather.     

微结构固体中的孤立波及其存在条件

根据Mindlin理论,考虑宏观尺度非线性效应、二次和三次微尺度非线性效应以及微尺度频散效应,建立了描述一维微结构固体中纵波传播的一种新模型.用动力系统定性分析理论,分析了微结构固体中孤立波的存在条件及其几何特征,证明了当介质参数和孤立波传播速度满足适当条件时,在二次微尺度非线性效应的影响下微结构固体中可以形成一种非对称孤立波,在三次微尺度非线性效应的影响下微结构固体中可以形成一种对称孤立波.最后,用数值方法进一步验证了上述结论.     

On the validity of Hertz contact law for granular material acoustics

We discuss the acoustical behavior of a 1D model of granular medium, which is a chain of identical spherical beads. In this geometry, we are able to test quantitatively alternative models to the Hertz theory of contact between elastic solids. We compare the predictions of the different models to experimental results that concern linear sound wave propagation in the chain submitted to a static force, and nonlinear solitary wave propagation in an unconstrained chain. We use elastic, elastic-plastic and brittle materials, the beads roughness extends on one order of magnitude, and we also use oxidized metallic beads. We demonstrate experimentally that at low static forces, for all types of beads, the linear acoustic waves propagate in the system as predicted by Hertz's theory. At larger forces, after onset of permanent plastic deformation at the contacts, the brass beads exhibit non Hertzian behavior, and hysteresis. Except in the case of brass beads, the nonlinear waves follow the predictions of Hertz theory. Revised: 28 May 1998 / Accepted: 27 July 1998     

非线性静磁表面波的传播特性

将文献[4]的理论结果加以推广,用微扰理论导出了微波场作用下铁磁材料的动态非线性磁化强度的各阶近似表达式。严格分析了在波矢k与外偏置磁场H₀成任意角度时非线性静磁表面波的传播特性。证明了静磁表面波在任何传播方向上都不能演化为静磁孤子。 关键词：