Flat broadband wavelength conversion based on cascaded second-harmonic generation and difference frequency generation in segmented quasi-phase matched gratings

Bandwidth enhancement and response flattening of wavelength conversion based on single-pass and double-pass cascaded second harmonic generation and difference frequency generation were investigated in segmented quasi-phase matched (QPM) gratings. It is shown that the signal and pump bandwidths are both efficiently widened by increasing the segment number of the QPM grating and optimising the poling period of each segment. The ripple on the matching response is also very small. The conversion bandwidth in a 3-cm-long three-segment waveguide reaches 150–160?nm, which is over the whole conventional band and long-wavelength band. Larger signal bandwidth can be obtained with a little response flatness penalty and conversion efficiency penalty, which can be compensated by increasing the input pump power. Compared with a sinusoidally chirped optical superlattice device, a wavelength converter based on the segmented gratings has higher conversion efficiency, broader bandwidth and better pump-wavelength tolerance, and is easier to fabricate in practice.     

Quantum travelling-wave analysis of a quasi-phase-matched parametric amplifier

The paper describes a phase-mismatched Fokker–Planck equation formulation for parametric amplification in periodically inverted nonlinear media. An analytical solution of the phase-mismatched Fokker–Planck equation and the amplitude quantum fluctuation after passing through the quasi-phase-matched (QPM) device are obtained. The calculated results for the QPM device conform to that of the Langevin equation in the case of no loss k=0, and give a general solution for k≠0. From this one can derive knowledge of the dependence of squeezing on the loss coefficient k and make a comparison between the QPM device and a phase matched device at the threshold k=ε₀.     

Multi-pulse chaotic dynamics of non-autonomous nonlinear system for a honeycomb sandwich plate

The global bifurcations and multi-pulse chaotic dynamics of a simply supported honeycomb sandwich rectangular plate under combined parametric and transverse excitations are investigated in this paper for the first time. The extended Melnikov method is generalized to investigate the multi-pulse chaotic dynamics of the non-autonomous nonlinear dynamical system. The main theoretical results and the formulas are obtained for the extended Melnikov method of the non-autonomous nonlinear dynamical system. The nonlinear governing equation of the honeycomb sandwich rectangular plate is derived by using the Hamilton’s principle and the Galerkin’s approach. A two-degree-of-freedom non-autonomous nonlinear equation of motion is obtained. It is known that the less simplification processes on the system will result in a better understanding of the behaviors of the multi-pulse chaotic dynamics for high-dimensional nonlinear systems. Therefore, the extended Melnikov method of the non-autonomous nonlinear dynamical system is directly utilized to analyze the global bifurcations and multi-pulse chaotic dynamics of the two-degree-of-freedom non-autonomous nonlinear system for the honeycomb sandwich rectangular plate. The theoretical results obtained here indicate that multi-pulse chaotic motions can occur in the honeycomb sandwich rectangular plate. Numerical simulation is also employed to find the multi-pulse chaotic motions of the honeycomb sandwich rectangular plate. It also demonstrates the validation of the theoretical prediction.     

Effects of Weak Links in the Nonlinear Microwave Response of MgB2 Superconductor

We report experimental results of second-harmonic (SH) response at microwave frequency in several ceramic MgB₂ samples, prepared by different methods. The SH signal has been investigated as a function of the temperature and DC magnetic field. The investigation has been carried out at low magnetic fields, where nonlinear processes arising from motion of Abrikosov fluxons are ineffective. We show that the low-temperature SH emission is ascribable to processes involving weak links. Comparison among the peculiarities of the SH signal radiated by the different samples shows that the presence of weak links strongly depends on the sample preparation method, as well as on the purity and morphology of the components used for the preparation.     

混沌激励下振动系统的非线性参数识别

本文对基于时-频相结合的非线性振动系统的参数识别问题进行了研究。首先建立含非线性参数单自由度振动系统的力学模型,将已知非线性系统产生的混沌响应作为该系统的激励, 假定其响应有若干不稳定的周期轨道组成,从混沌响应的状态空间中提取出近似周期轨道, 采用谐波平衡法识别出系统的参数,然后对识别出的参数进行误差分析。最后通过数值模拟,验证了混沌信号作为激励源对非线性系统进行参数识别的可行性。     

Second harmonic generation using an electrically controlled asymmetric plasmonic waveguide

ABSTRACT

In this study, it was shown that field enhancement in the nonlinear metal-insulator-metal (MIM) plasmonic waveguides can result in a large enhancement of the second harmonic generation (SHG) magnitude as compared with values reported in the literature. The proposed structure has two metals at the top and two metals at the bottom of the crystal. In this structure, a voltage is applied on metals to produce a SHG electrically. Hence, the metals that define the cavity also serve as electrodes capable of generating high direct current electric fields across the nonlinear material. The frequency of a fundamental wave at 458 nm was doubled and modulated in intensity by applying a moderate external voltage to the electrodes, yielding a voltage-dependent nonlinear generation with a higher coupling efficiency. All the simulations here have been calculated by using the finite-element-based commercial COMSOL software.     

Nonlinear vibration of the piezoelectric nanobeams based on the nonlocal theory

This paper investigates the nonlinear vibration of the piezoelectric nanobeams based on the nonlocal theory and Timoshenko beam theory. The piezoelectric nanobeam is subjected to an applied voltage and a uniform temperature change. The nonlinear governing equations and boundary conditions are derived by using the Hamilton principle and discretized by using the differential quadrature (DQ) method. A direct iterative method is employed to determine the nonlinear frequencies and mode shapes of the piezoelectric nanobeams. A detailed parametric study is conducted to study the influences of the nonlocal parameter, temperature change and external electric voltage on the size-dependent nonlinear vibration characteristics of the piezoelectric nanobeams.     

Quasi-phase-matched second harmonic generation device in Mg-doped LiNbO3 and its application to high-density optical disk system

The resistance to photorefractive damage is investigated for several nonlinear crystals. A quasi-phase-matched (QPM) second harmonic generation (SHG) waveguide device is fabricated in 5 mol% Mg-doped LiNbO₃ which has high resistance to optical damage. The SHG blue laser of the QPM-SHG waveguide device and a tunable distributed Bragg reflector (DBR) laser diode is demonstrated, wherein output stability of continuous blue light is measured. The SHG blue laser, using the QPM-SHG waveguide device with broadened flat matching response, shows good modulation characteristics. The pulsed peak power of 23 mW with rectangular modulated waveform is generated. The SHG blue laser is installed to an optical head, and good recording and readout characteristics are demonstrated. Moreover, butt-coupled SHG blue laser is examined to gain a miniature module with volume of 0·8 cc.     

Resource‐Efficient Low‐Temperature Synthesis of Microcrystalline Pb2B5O9X (X = Cl,Br) for Surfaces Studies by Optical Second Harmonic Generation

Optically nonlinear Pb₂B₅O₉X (X = Cl, Br) borate halides are an important group of materials for second harmonic generation (SHG). Additionally, they also possess excellent photocatalytic activity and stability in the process of dechlorination of chlorophenols, which are typical persistent organic pollutants. It would be of great interest to conduct in situ (photo‐) catalysis investigations during the whole photocatalytic process by SHG when considering them as photocatalytic materials. In order to get superior photocatalytic efficiency and maximum surface information, small particles are highly desired. Here, a low‐cost and fast synthesis route that allows growing microcrystalline optically nonlinear Pb₂B₅O₉X borate halides at large quantities is introduced. When applying the ionothermal growth process at temperatures between 130 and 170 °C, microcrystallites with an average size of about 1 µm precipitate with an orthorhombic hilgardite‐like borate halide structure. Thorough examinations using powder X‐ray diffraction and scanning electron microscopy, the Pb₂B₅O₉X microcrystals are indicated to be chemically pure and single‐phased. Besides, the Pb₂B₅O₉X borate halides' SHG efficiencies are confirmed using confocal SHG microscopy. The low‐temperature synthesis route thus makes these borate halides a highly desirable material for surface studies such as monitoring chemical reactions with picosecond time resolution and in situ (photo‐) catalysis investigations.     

Modification of iterative processes for improved convergence characteristics

A method for improving the convergence rate of iterative processes is presented. This method monitors the sequence of approximations produced by an iterative process, and generates a new iterative process, or sequence of processes, each with more rapid convergence characteristics than the previous one. This method of process modification can be applied to many iterative techniques currently in use. Examples of application of the method are given, using both nonlinear and linear systems. In one of these examples it is shown that the method can be applied to a divergent iterative process, producing a convergent one. It is also shown how the technique can be applied to equations of one variable, yielding a method with convergence characteristics similar to those of Newton's method, but without the explicit calculation of derivatives.     

An efficient method for analyzing second harmonic generation with the consideration of pump depletion

We propose a simple method to analyze second harmonic generation (SHG) in general quasi-phase-matching media with the consideration of pump depletion. It allows us to conveniently predict precise result from undepleted pump approximation solution. Based on this method, multi-wavelength generation with arbitrary target efficiency and wavelength spacing is engineered. The effect of pump depletion on the performance of constructed multi-wavelength generator is analyzed. We demonstrate that it is efficient to design nonlinear device for multi-wavelength SHG by proposed method.     

非线性参数结构系统的参数识别

本对基于时域信息的非线性参数系统参数识别问题进行了研究。首先提出了一种非线性参数系统的分类方法。然后对非线性参数系统的参数化问题进行了讨论：本提出用NEWTON RAPHSON方法进行非线性参数系统识别方程的求解，并用埃特金加速法提高迭代收敛的速度。章的最后以剪力墙参数的识别问题为例演示了本所提方法的有效性。数值算例表明，识别结果的精度和识别耗时对参数初值的选取并不敏感。     

Estimation of kinetic model parameters in fluorescence optical diffusion tomography

We present a technique for reconstructing the spatially dependent dynamics of a fluorescent contrast agent in turbid media. The dynamic behavior is described by linear and nonlinear parameters of a compartmental model or some other model with a deterministic functional form. The method extends our previous work in fluorescence optical diffusion tomography by parametrically reconstructing the time-dependent fluorescent yield. The reconstruction uses a Bayesian framework and parametric iterative coordinate descent optimization, which is closely related to Gauss-Seidel methods. We demonstrate the method with a simulation study.     

Hybrid Plasmonic–Ferroelectric Architectures for Lasing and SHG Processes at the Nanoscale

Coherent light sources providing sub‐wavelength confined modes are in ever more demand to face new challenges in a variety of disciplines. Scalability and cost‐effective production of these systems are also highly desired. The use of ferroelectrics in functional optical platforms, on which plasmonic arrangements can be formed, is revealed as a simple and powerful method to develop coherent light sources with improved and novel functionalities at the nanoscale. Two types of sources with sub‐diffraction spatial confinement and improved performances are presented: i) plasmon‐assisted solid‐state nanolasers based on the interaction between metallic nanostructures and optically active rare earth doped ferroelectric crystals and ii) nonlinear radiation sources based on quadratic frequency mixing processes that are enhanced by means of localized surface plasmon (LSP) resonances. The mechanisms responsible for the intensification of the radiation–matter interaction processes by LSP resonances are discussed in each case. The challenges, potential applications, and future perspectives of the field are highlighted.     

基于增量谐波平衡法的含索铰可折展桁架非线性动力学特性

为了揭示含索铰可折展桁架的非线性动力学行为,建立了考虑铰链间隙、刚度和阻尼及索非线性特性的可折展桁架纯弯曲动力学模型。对非线性动力学方程进行一次泰勒展开和参量的多次谐波描述,实现了非线性动力学方程到代数方程的转化,通过迭代进行非线性动力学系统的响应计算。并利用龙格库塔方法对非线性系统进行数值分析,与增量谐波平衡(IHB)法进行对比,验证了IHB法计算的正确性。以激振频率为变化参数,对悬臂支撑的含索铰桁架结构进行解的稳定性分析,得到铰链间隙、铰链刚度、激振力和索对结构响应稳定性的影响。基于IHB法可快速准确的进行多自由度可折展结构动力学求解,为研究大型折展桁架的动力学行为奠定了基础。     

非线性振动方程多重解求解方法

非线性振动方程多重解的求解过程中,迭代初值难以有效确定,不稳定周期解收敛域很小,利用通常的微分方程解法无法直接求解。针对这个问题,引入同伦算法,使得初始值的选取无任何限制;同时利用预测-校正算法对外激励参数变化下的解曲线进行追踪,得到系统的多重解。该方法不但可以计算稳定的周期解,而且不稳定的周期解也可以求出。采用Duffing振子运动方程对该方法进行了计算验证,通过与理论近似解以及龙格-库塔法计算结果的对比,验证了该方法的有效性。     

二阶系统非一致目标跟踪混合自适应迭代学习控制

针对一类含有时变和时不变参数的二阶非线性系统,利用Backstepping方法,提出了一种新的自适应迭代学习控制方法,该方法由微分-差分型自适应律和学习控制律组成,保证对非一致目标的跟踪误差的平方在一个有限区间上的积分收敛于零,克服了传统的迭代学习控制对目标轨线的限制,可以跟踪非一致目标轨线。通过构造复合能量函数,给出了闭环系统收敛的一个充分条件。仿真结果说明了该方法的可行性和有效性。     

Numerical simulation of cascaded third harmonic generation for both phase matched and mismatched schemes

Numerical solutions to the nonlinear coupling-wave equations of second harmonic (SH) and third harmonic (TH) generators are investigated for both phase matched and phase mismatched configurations. For phase mismatched TH generation, several kinds of schemes (the phase mismatch either in second harmonic generation (SHG) or sum-frequency generation (SFG) process) are considered and analyzed. The physical nature corresponding to the different ratios of the coupling coefficients is discussed.     

Stochastic analysis of nonlinear vehicle systems using a generalized harmonic linearization technique

The discrete harmonic linearization method which is applicable to stochastic systems could not provide an equivalent stiffness coefficient for a nonlinear restoring element. In this paper, this technique is generalized to obtain linear representations of both nonlinear restoring and damping elements, based on a principle of energy similarity of dynamic elements. A numerical iterative procedure is presented to compute the local linear coefficients of nonlinear dynamic elements. A nonlinear system is then represented by a set of its complex frequency response function matrices, as functions of the excitation frequency. Stochastic analysis of general multi-DOF nonlinear vehicle systems is established in terms of response PSD characteristics.     

Nonlinear vibration of piezoelectric nanoplates using nonlocal Mindlin plate theory

ABSTRACT

This article investigates the nonlinear vibration of piezoelectric nanoplate with combined thermo-electric loads under various boundary conditions. The piezoelectric nanoplate model is developed by using the Mindlin plate theory and nonlocal theory. The von Karman type nonlinearity and nonlocal constitutive relationships are employed to derive governing equations through Hamilton's principle. The differential quadrature method is used to discretize the governing equations, which are then solved through a direct iterative method. A detailed parametric study is conducted to examine the effects of the nonlocal parameter, external electric voltage, and temperature rise on the nonlinear vibration characteristics of piezoelectric nanoplates.