Vibration isolation via a scissor-like structured platform

More and more attentions are attracted to the analysis and design of nonlinear vibration control/isolation systems for better isolation performance. In this study, an isolation platform with n-layer scissor-like truss structure is investigated to explore novel design of passive/semi-active/active vibration control/isolation systems and to exploit potential nonlinear benefits in vibration suppression. Due to the special scissor-like structure, the dynamic response of the platform has inherent nonlinearities both in equivalent damping and stiffness characteristics (although only linear components are applied), and demonstrates good loading capacity and excellent equilibrium stability. With the mathematical modeling and analysis of the equivalent stiffness and damping of the system, it is shown that: (a) the structural nonlinearity in the system is very helpful in vibration isolation, (b) both equivalent stiffness and damping characteristics are nonlinear and could be designed/adjusted to a desired nonlinearity by tuning structural parameters, and (c) superior vibration isolation performances (e.g., quasi-zero stiffness characteristics etc.) can be achieved with different structural parameters. This scissor-like truss structure can potentially be employed in different engineering practices for much better vibration isolation or control.     

Comprehensive research on self phase modulation based optical delay systems

This paper comprehensively investigates the properties of self phase modulation based optical delay systems consisting of dispersion compensation fibre and highly nonlinear fibres.It researches into the impacts of power level launched into highly nonlinear fibres,conversion wavelength,dispersion slope,modulation format and optical filter bandwidth on the overall performance of optical delay systems.The results reveal that,if the power launched into highly nonlinear fibres is fixed,the time delay generally varies linearly with the conversion wavelength,but jumps intermittently at some conversion wavelengths.However,the time delay varies semi-periodically with the power launched into highly nonlinear fibres.The dispersion slope of highly nonlinear fibres has significant influence on the time delay,especially for the negative dispersion slope.The time delay differs with modulation formats due to the different combined interaction of nonlinearity and dispersion in fibres.The bandwidth of the optical filters also greatly affects the time delay because it determines the bandwidth of the passed signal in the self phase modulation based time delay systems.The output signal quality of the overall time delay systems depends on the conversion wavelength and input power level.The optimisation of the power level and conversion wavelength to provide the best output signal quality is made at the end of this paper.     

High-order numerical method for the nonlinear Helmholtz equation with material discontinuities in one space dimension

The nonlinear Helmholtz equation (NLH) models the propagation of electromagnetic waves in Kerr media, and describes a range of important phenomena in nonlinear optics and in other areas. In our previous work, we developed a fourth order method for its numerical solution that involved an iterative solver based on freezing the nonlinearity. The method enabled a direct simulation of nonlinear self-focusing in the nonparaxial regime, and a quantitative prediction of backscattering. However, our simulations showed that there is a threshold value for the magnitude of the nonlinearity, above which the iterations diverge.In this study, we numerically solve the one-dimensional NLH using a Newton-type nonlinear solver. Because the Kerr nonlinearity contains absolute values of the field, the NLH has to be recast as a system of two real equations in order to apply Newton’s method. Our numerical simulations show that Newton’s method converges rapidly and, in contradistinction with the iterations based on freezing the nonlinearity, enables computations for very high levels of nonlinearity.In addition, we introduce a novel compact finite-volume fourth order discretization for the NLH with material discontinuities. Our computations corroborate the design fourth order convergence of the method.The one-dimensional results of the current paper create a foundation for the analysis of multidimensional problems in the future.     

Highly nonlinear chalcogenide fibres for all-optical signal processing

Chalcogenide glasses offer many attractive properties for all-optical signal processing including large Kerr nonlinearity (up to 500 × silica glass), an intrinsic ultrafast response time and low to moderate two-photon absorption (TPA). These properties together with the convenience of a fibre format allow us to achieve all-optical signal processing at low peak power and in a very compact form. In this paper, several nonlinear processing functions will be demonstrated including: femto-second pedestal free, pulse compression; all-optic wavelength conversion; and all-optical regenerator. In addition, we show enhanced nonlinearity for more efficient signal processing by tapering the As₂Se₃ fibre. These applications show chalcogenide glass fibres are very promising candidate materials for nonlinear all-optic signal processing.     

Nonlinearity penalties and benefits of light traveling in a fiber optic ring resonator

The nonlinearity properties of light traveling in a fiber optic ring resonator (FORR) are presented. The nonlinearity penalties suffering from Kerr effects and four-wave mixing nonlinear types including bistability, chaos and bifurcation are investigated. The advantages of the nonlinearity penalties including photon correlation, optical switching and information security using chaotic signals are also discussed. The obtained results have shown that the parameters of FORR can be changed, and thus the penalties of the nonlinear effects have shown the potential of using for some applications.     

兼具低非线性和高功率限制的狭缝波导（英文）

利用非线性效应的全矢量模型和狭缝波导的有限元模场求解法,系统地研究了狭缝波导结构和包层材料对其非线性和功率限制特性的影响.研究结果表明,狭缝波导的硅臂宽度、狭缝宽度、硅层高度和包层材料均影响其非线性和功率限制特性.对于空气包层狭缝波导,不同结构参数下的最高功率限制因子对应的非线性系数均高于20 W^-1·m^-1,而最低非线性系数6.5 W^-1·m^-1均出现在模式截止附近,泄露损耗较大,功率限制较弱,故空气包层狭缝波导无法同时实现低非线性和高功率限制;如果在狭缝波导上包覆二氧化硅,则可以同时获得低非线性和高功率限制,非线性系数可低至4.12 W^-1·m^-1,同时功率限制因子可达42%.     

Large-amplitude nonlinear vibrations of a Mooney–Rivlin rectangular membrane

An analysis of the linear and nonlinear vibration response and stability of a pre-stretched hyperelastic rectangular membrane under harmonic lateral pressure and finite initial deformations is presented in this paper. Geometric nonlinearity due to finite deformations and material nonlinearity associated with the hyperelastic constitutive law are taken into account. The membrane is assumed to be made of an isotropic, homogeneous, and incompressible Mooney–Rivlin material. The results for a neo-Hookean material are obtained as a particular case and a comparison of these two constitutive models is carried out. First, the exact solution of the membrane under a biaxial stretch is obtained, being this initial stress state responsible for the membrane stiffness. The equations of motion of the pre-stretched membrane are then derived. From the linearized equations, the natural frequencies and mode shapes of the membrane are analytically obtained for both materials. The natural modes are then used to approximate the nonlinear deformation field using the Galerkin method. A detailed parametric analysis shows the strong influence of the stretching ratios and material parameters on the linear and nonlinear oscillations of the membrane. Frequency–amplitude relations, resonance curves, and bifurcation diagrams, are used to illustrate the nonlinear dynamics of the membrane. The present results are compared favorably with the results evaluated for the same membrane using a nonlinear finite element formulation.     

Frequency domain analysis and identification of block-oriented nonlinear systems

Block-oriented nonlinear models including Wiener models, Hammerstein models and Wiener-Hammerstein models, etc. have been extensively applied in practice for system identification, signal processing and control. In this study, analytical frequency response functions including generalized frequency response functions (GFRFs) and nonlinear output spectrum of block-oriented nonlinear systems are developed, which can demonstrate clearly the relationship between frequency response functions and model parameters, and also the dependence of frequency response functions on the linear part of the model. The nonlinear part of these models can be a more general multivariate polynomial function. These fundamental results provide a significant insight into the analysis and design of block-oriented nonlinear systems. Effective algorithms are therefore proposed for the estimation of nonlinear output spectrum and for parametric or nonparametric identification of nonlinear systems. Compared with some existing frequency domain identification methods, the new estimation algorithms do not necessarily require model structure information, not need the invertibility of the nonlinearity and not restrict to harmonic inputs. Simulation examples are given to illustrate these new results.     

Stable helical solitons in optical media

We present a review of new results which suggest the existence of fully stable spinning solitons (self-supporting localised objects with an internal vorticity) in optical fibres with self-focusing Kerr (cubic) nonlinearity, and in bulk media featuring a combination of the cubic self-defocusing and quadratic nonlinearities. Their distinctive difference from other optical solitons with an internal vorticity, which were recently studied in various optical media, theoretically and also experimentally, is that all the spinning solitons considered thus far have been found to be unstable against azimuthal perturbations. In the first part of the paper, we consider solitons in a nonlinear optical fibre in a region of parameters where the fibre carries exactly two distinct modes, viz., the fundamental one and the first-order helical mode. From the viewpoint of application to communication systems, this opens the way to doubling the number of channels carried by a fibre. Besides that, these solitons are objects of fundamental interest. To fully examine their stability, it is crucially important to consider collisions between them, and their collisions with fundamental solitons, in (ordinary or hollow) optical fibres. We introduce a system of coupled nonlinear Schrödinger equations for the fundamental and helical modes with nonstandard values of the cross-phase-modulation coupling constants, and show, in analytical and numerical forms, results of collisions between solitons carried by the two modes. In the second part of the paper, we demonstrate that the interaction of the fundamental beam with its second harmonic in bulk media, in the presence of self-defocusing Kerr nonlinearity, gives rise to the first ever example of completely stable spatial ring-shaped solitons with intrinsic vorticity. The stability is demonstrated both by direct simulations and by analysis of linearized equations.     

Dynamics of one electron in a nonlinear disordered chain

In this paper we report new numerical results on the disordered Schr?dinger equation with nonlinear hopping. By using a classical harmonic Hamiltonian and the Su-Schrieffer-Heeger approximation we write an effective Schr?dinger equation. This model with off-diagonal nonlinearity allows us to study the interaction of one electron and acoustical phonons. We solve the effective Schr?dinger equation with nonlinear hopping for an initially localized wavepacket by using a predictor-corrector Adams-Bashforth-Moulton method. Our results indicate that the nonlinear off-diagonal term can promote a long-time subdiffusive regime similar to that observed in models with diagonal nonlinearity.     

连续动力系统时间序列的非线性检验

用相位随机化的替代数据方法，研究了连续混沌动力系统时间序列的非线性检验判定.研究发现，在不同的采样情况下，混沌时间序列的非线性特性检验有所差异，尤其对于过采样时间序列，往往会出现虚假的判断结果.针对过采样时间序列，最好采用能够反映非线性特征的参数，作为检验统计量进行检验判断. 关键词： 替代数据 关联维数 连续时间序列 非线性检验     

Analysis of nonlinear oscillators using Volterra series in the frequency domain

The Volterra series representation is a direct generalisation of the linear convolution integral and has been widely applied in the analysis and design of nonlinear systems, both in the time and the frequency domain. The Volterra series is associated with the so-called weakly nonlinear systems, but even within the framework of weak nonlinearity there is a convergence limit for the existence of a valid Volterra series representation for a given nonlinear differential equation. Barrett (1965) [1] proposed a time domain criterion to prove that the Volterra series converges within a given region for a class of nonlinear systems with cubic stiffness nonlinearity. In this paper this time-domain criterion is extended to the frequency domain to accommodate the analysis of nonlinear oscillators subject to harmonic excitation. A common and severe nonlinear phenomenon called jump, a behavior associated with the Duffing oscillator and the multi-valued properties of the response solution, is investigated using the new frequency domain criterion of establishing the upper limits of the nonlinear oscillators, to predict the onset point of the jump, and the Volterra time and frequency domain analysis of this phenomenon are carried out based on graphical and numerical techniques.     

基于高非线性微结构光纤的全光再生研究

提出了利用高非线性微结构光纤自相位调制效应进行全光再生的研究方案。分析了一组微结构光纤的色散和非线性特性。结果显示光纤的非线性系数与光纤结构有密切关系。通过减小有效模面积,可以提高光纤的非线性系数。采用一种高空气填充比的高非线性微结构光纤作为非线性介质,进行了基于自相位调制效应的全光再生研究。结果表明,由于微结构光纤的高非线性,采用较短的光纤长度就可以实现较好的再生效果。同时,输入微结构光纤的峰值功率、滤波器的参量选择对光再生的效果有重要的影响,它们必需满足一定要求,才能实现光再生。此外,对再生器的传输特性进行了研究。通过调整输入峰值功率和滤波器的参量,可以对不同宽度的光脉冲信号进行全光再生。     

基于双芯光子晶体光纤的低非线性宽带色散补偿光纤的设计

采用矢量光束传输法数值模拟了基于模式耦合的双芯光子晶体光纤的色散和非线性与其结构的关系。结果表明:通过在包层中移除一层空气孔以形成外纤芯并调整内外纤芯之间的距离及包层空气孔的占空比,内外纤芯间的模式耦合可以在宽带范围内发生,导致产生大负色散。同时,由于光场分布在两个纤芯内,增大了模场面积,产生低非线性,可以实现低非线性宽带色散补偿。     

Nonlinear optical switching and all-figures of merit in Bi_2S_(3-x)Se_x/PMMA nanocomposite films investigated by Z scan under visible CW laser

Bi2S3-xSex/poly(methyl methacrylate)(PMMA)nanocomposite films were prepared using microwave assisted synthesis with different compositions of x.Crystal structure,surface morphology,and optical properties were investigated to characterize the prepared nanocomposite films.The crystallinity and optical band gap of the prepared Bi2S3-xSex/PMMA were affected by x.The prepared samples showed a blue shift in the absorption edge.The laser power dependent nonlinear refraction and absorption of Bi2S3-xSex/PMMA nanocomposite films were investigated by using the Z-scan technique.The optical nonlinearity of the nanocomposite films exhibited switchover from negative nonlinear refraction to positive nonlinear refraction to negative nonlinear refraction effects,and from saturable absorption to reverse saturable absorption to saturable absorption with an increase and decrease in the composition.An interesting all-optical figure of merit was reported to assess the nanocomposite films for a practical device.It was calculated that the device all-figures of merit were based on the nonlinear response,which is important for the all-optical switching device.The results demonstrate that the optimized all-optical figures of merit can be achieved by adjusting the composition and input laser power,which can be used for the design of different all-photonic devices,and the results of nonlinear switching behavior can open new possibilities for using the nanocomposite films in laser Q-switching and mode-locking.     

Behavior of nonlinear fluid viscous dampers for control of shock vibrations

Fluid viscous dampers have been widely used for suppression of high velocity shocks. While linear fluid viscous dampers have been used for a long time, nonlinear fluid viscous dampers show considerable promise due to their superior energy dissipation characteristics and significant reduction in the damper force compared to a linear fluid viscous damper for the same peak displacement. This paper presents results from experimental study to characterize fluid viscous dampers when subjected to half-cycle sine shock excitation. The mathematical formulation and a numerical study to evaluate the relative performance of structures with fluid viscous dampers subjected to short-duration shock (impulse) loading are also discussed. The influence of damper nonlinearity (α) and the supplemental damping ratio (ξ_sd) on response has been investigated. The supplemental damping ratio of nonlinear fluid viscous dampers when subjected to shock excitation is found by equivalent linearization using the concept of equal energy dissipation. The paper also presents some design charts, which can be used for preliminary decisions on parameters of nonlinear dampers to be used in design.     

Nonlinear directional coupling between plasmonic slot waveguides

A numerical investigation of nonlinear switching in plasmonic directional couplers made of two dielectric slab waveguides with metallic claddings is presented. We assume Kerr-nonlinear dielectric and study the influence of geometrical parameters, metallic losses, and metal nonlinearities on coupler characteristics. We observe a general trade-off between losses and nonlinearity levels required for the switching operation. Underlying physical mechanisms that affect the coupler performance are discussed. The obtained results can be useful in design and optimization of the nonlinear plasmonic couplers.     

Evaluation of two-photon nonlinearity by a semiclassical method

In order to discuss the two-photon nonlinearity theoretically, both photons and nonlinear materials should be treated quantum mechanically, which usually is a heavy theoretical task. Contrarily, nonlinear optics for classical light has been developed well and a detailed analysis is possible for realistic complex nonlinear systems. Here we show that the two-photon nonlinearity can be evaluated from the linear and third-order nonlinear output fields against a classical input pulse, which contains 2(-1/2) photons on average.     

Propagation of local spatial solitons in power-law nonlinear PT-symmetric potentials based on finite difference

We consider the (2+1)-dimensional nonlinear Schrödinger equation with power-law nonlinearity under the parity-time-symmetry potential by using the Crank–Nicolson alternating direction implicit difference scheme, which can also be used to solve general boundary problems under the premise of ensuring accuracy. We use linear Fourier analysis to verify the unconditional stability of the scheme. To demonstrate the effectiveness of the scheme, we compare the numerical results with the exact soliton solutions. Moreover, by using the scheme, we test the stability of the solitons under the small environmental disturbances.     

Nonlinearity management in optics: experiment, theory, and simulation

We conduct an experimental investigation of nonlinearity management in optics using femtosecond pulses and layered Kerr media consisting of glass and air. By examining the propagation properties over several diffraction lengths, we show that wave collapse can be prevented. We corroborate these experimental results with numerical simulations of the (2+1)-dimensional focusing cubic nonlinear Schr?dinger equation with piecewise constant coefficients and a theoretical analysis of this setting using a moment method.