Investigation of optical nonlinearities in Pd(po)2 by Z-scan technique

With nanosecond scale at a 532 nm wavelength, we firstly measured the nonlinear optical absorption and refraction coefficients of Pd(po)₂ complex by using Z-scan technique, here Hpo=1-hydioxy-2-pyridone. We describe an empirical expression for the case when nonlinear refraction is accompanied by nonlinear absorption to separately evaluate the nonlinear refraction and the nonlinear absorption by performing straightforward measurements with the aperture removed. The nonlinear optical response of Pd(po)₂ was determined by the linear decreasing irradiance-dependence. The nonlinear absorption originates from the near resonant two-photon absorption while the mechanism of the nonlinear refraction is the near resonant two-photon absorption transition enhancement. The linear increasing dependences of the optical nonlinearities on the incident irradiance arise from the population redistribution due to the near resonant two-photon absorption.     

Resonant properties of a nonlinear dissipative layer excited by a vibrating boundary: Q-factor and frequency response

Simplified nonlinear evolution equations describing non-steady-state forced vibrations in an acoustic resonator having one closed end and the other end periodically oscillating are derived. An approach based on a nonlinear functional equation is used. The nonlinear Q-factor and the nonlinear frequency response of the resonator are calculated for steady-state oscillations of both inviscid and dissipative media. The general expression for the mean intensity of the acoustic wave in terms of the characteristic value of a Mathieu function is derived. The process of development of a standing wave is described analytically on the base of exact nonlinear solutions for different laws of periodic motion of the wall. For harmonic excitation the wave profiles are described by Mathieu functions, and their mean energy characteristics by the corresponding eigenvalues. The sawtooth-shaped motion of the boundary leads to a similar process of evolution of the profile, but the solution has a very simple form. Some possibilities to enhance the Q-factor of a nonlinear system by suppression of nonlinear energy losses are discussed.     

The Spectral Density of Nonlinear O-U Noise and the Influence of Nonlinear Fluctuation on the Transition of Bistable System

A stochastic differential equation driven by N-order nonlinear fluctuation is investigated by defining a novel stochastic process Г(t). The spectral densities of Г(t) for N = 1,2,3 and 4 are obtained. We compare the results of the linear fluctuation case with the nonlinear fluctuation case and find that the extremum of the spectral density for linear case is directly proportional to the noise intensity D and independent of the correlation time τ, the extremum of the spectral density for nonlinear case is determined by both D and τ. An approximate Fockker-Planck equation of the N-order nonlinear fluctuation is derived by Hanggi-like ansatz. The infl uences of nonlinear fluct uation on the transition of bistable system are studied. It is found that the area of unimodal region and bimodal region of the stationary probability is independent of D and τ for linear case, however, the area of two regions is related to D and τ for nonlinear case.     

The refractive nonlinearities of InAs/GaAs quantum dots above-bandgap energy

The third-order optical nonlinear refractive properties of InAs/GaAs quantum dots grown by molecular beam epitaxy have been measured using the reflection Z-scan technique at above-bandgap energy. The nonlinear refractive index and nonlinear absorption index of the InAs/GaAs quantum dots were determined for wavelengths from 740 to 777 nm. The measured results are compared with the nonlinear refractive response of several typical III-V group semiconductor materials. The corresponding mechanisms responsible for the large nonlinear response are discussed.     

On the Feynman proof of the exact relation between a class of path sums and the general nonlinear Fokker-Planck equation

A simple sum over paths will be considered for the general nonlinear diffusion process described by complex coordinates. In order to derive the corresponding stochastic differential equation the Feynman method used in quantum mechanics will be generalised for the present case of a coordinate dependent variance or diffusion function by means of a nonlinear coordinate transformation. The resulting equation will be seen to be the general nonlinear Fokker-Planck equation. The relevance of the present formulation for nonequilibrium phenomena, such as for example those occuring in nonlinear quantum optics, will be discussed.     

红外光谱辐射计探测器高阶非线性响应校正方法

针对傅里叶变换红外光谱辐射计辐射定标需要黑体辐射面充满仪器视场的技术特点,分析了由于入射光子流较高导致红外探测器产生非线性响应误差的机理.通过仿真包含非线性误差的黑体辐射数据,研究了非线性误差对光谱产生的影响,并根据卷积和交叉迭代两种校正方法,提出了适合校正高阶非线性响应误差的迭代方法—梯度下降法.利用傅里叶变换红外光谱辐射计进行辐射定标实验,对比卷积、交叉迭代和梯度下降法三种校正方法的效果,结果显示三种校正方法均可有效减小非线性误差,分别使拟合优度提高了0.15%,0.29%和0.39%,梯度下降法校正后的光谱数据更为准确.     

Numerical modelling of TE and TM modes in lossy nonlinear optical waveguides

The intensity-dependent characteristics of nonlinear TE and TM waves in a thin film bounded by lossy nonlinear media are analysed by the finite-element method. In this approach, the power-dependent complex propagation constants and local complex electromagnetic field distributions of lossy nonlinear TE and TM waves are obtained directly from the given lossy nonlinear waveguides, without any approximations. Numerical results for these modes in a lossy nonlinear waveguiding system with different absorption coefficients are given. It is shown that the complex dispersion relations, for both TE and TM modes, are strongly power dependent.     

On the nonlinear normal modes of free vibration of piecewise linear systems

A modification of the Shaw–Pierre nonlinear normal modes is suggested in order to analyze the vibrations of a piecewise linear mechanical systems with finite degrees of freedom. The use of this approach allows one to reduce to twice the dimension of the nonlinear algebraic equations system for nonlinear normal modes calculations in comparison with systems obtained by previous researchers. Two degrees of freedom and fifteen degrees of freedom nonlinear dynamical systems are investigated numerically by using nonlinear normal modes.     

非均匀交换各向异性铁磁介质的非线性表面自旋波

利用Landau-Lifshitz 方程，研究了具有非均匀交换各向异性的半无限大铁磁体的非线性表 面自旋波理论。导出了部分钉扎纯交换铁磁介质的磁化强度所满足的边界条件和非线性表面 自旋波的色散关系，并获得了自旋波振幅沿z方向驻波的一维非线性Schrdinger方程和包 络振幅沿平面传播的二维非线性Schrdinger方程，结果表明铁磁体磁化强度的包络振幅随时空变化的性质是由二维非线性Schrdinger方程决定的。因此预言铁磁介质的表面非线性激发应是二维孤波的形式。对于弱非线性表面自旋波，对非线性Schrdinger方程存在孤子形式解的可能性作了讨论. 关键词： 表面自旋波 Landau-Lifshitz方程 非线性Schrdinger方程 孤子     

Nonlinear quark theory for spin 2 (gravimesons). III

A nonlinear field equation for spin s = 2 is derived on the basis of the nonlinear quark theory by the coalescence method. The octet of gravimesons is analyzed. A nonlinear equation is derived for the neutral gravimeson (strong gravitation).     

Coupled multiwave interactions in aperiodically poled nonlinear optical crystals

A new type of coupled nonlinear optical interactions that can be implemented in crystals with an aperiodic modulation of the nonlinear susceptibility is studied. The quasi-phase matching condition is satisfied simultaneously for several conventional three-frequency processes involved in the interaction due to the aperiodic variation of the nonlinearity in space. A simple method for designing aperiodically poled nonlinear optical crystals is proposed and analyzed. The method is based on the superposition of nonlinearity modulations produced by several periodic functions simultaneously so that each of these functions individually corresponds to its own quasi-phase-matched nonlinear process. The dynamics of energy exchange during interaction of five waves with different frequencies that involves three coupled three-frequency parametric interaction processes is investigated thoroughly. The ratio between the effective nonlinear wave coupling coefficients and the amplitudes of pump waves is determined for the case in which the initial stage of the interaction is characterized by the parametric instability. It is demonstrated that the secondary simplification of the coupled differential equations with spatially modulated nonlinear coefficients, which leads to the system of equations with constant nonlinear coefficients, correctly describes the dynamics of interaction of the waves at distances of the order of 50 characteristic nonlinear lengths.     

弱非线性复合体中的高阶非线性响应

利用谱表示理论和微扰展开法，从理论上给出了适合于一般微结构复合体系的有效非线性响 应的一般表示式，并结合有效媒质近似（EMA），在弱非线性条件下研究了由三阶非线性组 分（体积分数为p）和线性组分构成的非线性复合体系的有效非线性响应，讨论了复合 体系的有效介电常数ε～e=εe+χe|E0|2+ηe|E0| 4中的有效三次非线性响应χe和有效高次非线性响应ηe与体积分数p和 退极化因子L之间的关系，分析了非线性组分的介电常数为复数情形时体系的有效高阶非线 性响应，从理论上说明了组分的高次非线性响应对整个复合体系的有效介电常数的影响.  关键词： 非线性复合介质 有效非线性响应 谱表示理论     

Optical limitation in two-dimensional nonlinear photonic crystal with triangular lattice

Optical limitation in a 2D nonlinear photonic crystal (NPC) has been studied in this Letter. Since the optical limitation is due to Bragg scattering induced by the variation of nonlinear refractive index, it is sure that the optical limitation can be realized in nonlinear photonic crystal. The light propagation characteristics in a two-dimensional nonlinear photonic crystal with triangular lattice has been calculated by using the finite-difference time-domain algorithm, which is constructed by placing certain number of nonlinear dielectric rods in a linear photonic crystal. The optical limiting effects at 1.300 and 0.504 μm have been obviously obtained for TE polarization and TM polarization, respectively.     

多量子阱光波导中非线性TM波的有限元解

本文用有限元法分析了任意非线性介质的多量子阱(MQW)光波导中传输与总光功率有关的TM波性质。用简单的迭代过程得到目洽解。给出了MQW波导具有不同非线性机理时,非线性TM波的色散关系、磁场(Hx)以及二个电场(Ey和Ez)的分布。结果表明:分子取向机理的光波导对非线性TM模存在不同的功率限制作用。     

Stochastic Processes and Mean Field Systems Defined by Nonlinear Markov Chains: An Illustration for a Model of Evolutionary Population Dynamics

In physics, there is a growing interest in studying stochastic processes described by evolution equations such as nonlinear master equations and nonlinear Fokker–Planck equations that define the so-called nonlinear Markov processes and are nonlinear with respect to probability densities. In this context, however, relatively little is known about nonlinear Markov processes defined by nonlinear Markov chains. In the present work, we demonstrate explicitly how the nonlinear Markov chain approach can be carried out by addressing a model for evolutionary population dynamics. In line with the nonlinear Markov chain approach, we derive a measure that tells us how attractive it is for a biological entity to evolve towards a particular biological type. Likewise, a measure for the noise level of the evolutionary process is obtained. Both measures are found to be implicitly time dependent. Finally, a simulation scheme for the many-body system corresponding to the Markov chain model is discussed.     

二维不可压流体Kelvin-Helmholtz不稳定性的弱非线性研究

通过将扰动速度势展至三阶,提出了Kelvin-Helmholtz（KH）不稳定性的弱非线性理论.在模耦合过程中观察到一个重要的共振现象,共振使得模耦合过程变得相当复杂,单模扰动很快进入非线性区,产生大量高次谐波,共振加强了非线性作用.分析了单模扰动中二次和三次谐波产生效应,以及对基模指数增长的非线性校正.模拟结果支持了解析理论.利用该理论,分析了KH不稳定的非线性阈值问题. 关键词： Kelvin-Helmholtz不稳定性 弱非线性理论 非线性阈值     

Beyond the absorption-limited nonlinear phase shift with microring resonators

We show that the nonlinear phase shift produced by a ring resonator constructed from a given nonlinear optical material can be greater than the phase shift produced by a single pass through an infinite length of the same material when linear and nonlinear absorption are taken into consideration. The figure of merit (defined by the phase shift times the throughput) also improves for the ring resonator over that of the native nonlinear absorbing material. We finally show that these benefits of using the ring resonator as a nonlinear phase-shifting element can enhance the switching characteristics of a Mach-Zehnder interferometer.     

振动声调制技术下微裂纹的非线性响应分析

采用非线性弹簧模型对振动声调制技术下微裂纹产生的非线性调制效应进行解释。从理论上分析了振动声调制技术下微裂纹产生非线性调制现象的原理,将微裂纹的开合状态等效为非线性弹簧。利用有限元软件构建并仿真微裂纹非线性弹簧模型,分别观察不同激励下裂纹界面的开合状态及混合声波的传播特性。结果表明,微裂纹界面随低频声波呈周期性开合,使得通过裂纹界面的高频声波与低频声波相互调制而产生非线性现象。在以上研究基础上,开展振动声调制实验研究。对比仿真结果,非线性调制系数R在实验条件下和仿真随低频激励幅值的变化趋势相同,证明了该模型的正确性。该模型为振动声调制技术应用于微裂纹的超声非线性检测提供了理论依据。      

Nonlinear planar asymmetrical optical waveguides for sensing applications

This paper provides a theoretical analysis for TE polarized waves guided by a linear film surrounded by two asymmetrical nonlinear media for sensing applications. The sensitivity of the proposed sensor is derived. The conditions required for the sensor to exhibit its maximum sensitivity are presented. This analysis covers the case when the measurand is homogeneously distributed in the covering medium. We show that nonlinear sensors have sensitivities higher than those of linear sensors. The authors believe that optical sensing can be improved by introducing nonlinear waveguides.     

The equation of state of a microinhomogeneous medium and the frequency dependence of its elastic nonlinearity

In the framework of a rheological model, a nonlinear dynamic equation of state of a microinhomogeneous medium containing nonlinear viscoelastic inclusions is derived. The frequency dependences of the effective nonlinear parameters are determined for the difference frequency and second harmonic generation processes in the case of a quadratic elastic nonlinearity. It is shown that the frequency dependence of the nonlinear elasticity of the medium is governed by the linear relaxation response of the inclusions at the primary excitation frequency, as well as by the relaxation of the inclusions at the nonlinear generation frequencies.