FDTD analysis of nonlinear Bragg grating based optical devices

In this paper, several nonlinear media with different instantaneous third-order nonlinearity responses are analysed. A Finite-Difference-Time-Domain method (FDTD), developed for nonlinear structures, is used to analyse the nonlinear waveguides and periodic nonlinear structures that exhibit attractive properties that make them suitable for novel devices with wavelength tuneable characteristics.     

1D Solitons in Saturable Nonlinear Media with Space Fractional Derivatives

Two decades ago, standard quantum mechanics entered into a new territory called space-fractional quantum mechanics, in which wave dynamics and effects are described by the fractional Schrödinger equation. Such territory is now a key and hot topic in diverse branches of physics, particularly in optics driven by the recent theoretical proposal for emulating the fractional Schrödinger equation. However, the light-wave propagation in saturable nonlinear media with space fractional derivatives is yet to be clearly disclosed. Here, such nonlinear optics phenomenon is theoretically investigated based on the nonlinear fractional Schrödinger equation with nonlinear lattices—periodic distributions of either focusing cubic (Kerr) or quintic saturable nonlinearities—and the existence and evolution of localized wave structures allowed by the model are addressed. The model upholds two kinds of one-dimensional soliton families, including fundamental solitons (single peak) and higher-order solitonic structures consisting of two-hump solitons (in-phase) and dipole ones (anti-phase). Notably, the dipole solitons can be robust stable physical objects localized merely within a single well of the nonlinear lattices—previously thought impossible. Linear-stability analysis and direct simulations are executed for both soliton families, and their stability regions are acquired. The predicted solutions can be readily observed in optical experiments and beyond.     

Size-dependent nonlinear absorption and refraction of Ag nanoparticles excited by femtosecond lasers

Silver (Ag) nanoparticles with different average sizes are prepared, and the nonlinear absorption and refraction of these nanoparticles are investigated with femtosecond laser pulses at 800 nm. The smallest Ag nanoparticles show insignificant nonlinear absorption, whereas the larger ones show saturable absorption. By considering the previously reported positive nonlinear absorption of 9 nm Ag nanoparticles, the nonlinear absorptions of Ag nanoparticles are found to be size-dependent. All these nonlinear absorptions can be compatibly explained from the viewpoints of electronic transitions, energy bands and electronic structures in the conduction band of Ag nanoparticles. The nonlinear refraction is attributed to the effect of hot electrons arising from the intraband transition in the s–p conduction band of Ag nanoparticles.     

有机大分子三阶非线性光学材料的研究进展

根据分子结构特征评述了各类有机大分子三阶非线性光学材料结构与性能的关系。概述了三阶非线性光学性能的计算。分析了材料分子设计原理和展望了应用前景。     

被动锁模光纤激光器多孤子脉冲形成机理

基于非线性耦合薛定谔方程,在非线性偏振技术锁模的掺铒环形光纤激光器中,理论研究多孤子脉冲的形成和演化规律。研究结果表明:随着小信号增益不断增加,光纤激光器的锁模透过率函数影响多脉冲输出,多脉冲产生受色散波和脉冲分裂形成的峰值功率的限制效应和孤子能量量子化的影响,这是增益竞争和非线性偏振旋转引起的损耗之间动态平衡的最终结果。     

Nonlinear integrable couplings of a nonlinear Schrdinger-modified Korteweg de Vries hierarchy with self-consistent sources

By means of the Lie algebra B 2,a new extended Lie algebra F is constructed.Based on the Lie algebras B 2 and F,the nonlinear Schro¨dinger-modified Korteweg de Vries(NLS-mKdV) hierarchy with self-consistent sources as well as its nonlinear integrable couplings are derived.With the help of the variational identity,their Hamiltonian structures are generated.     

Nonlinear wave interactions in patterned Silica and AlGaAs waveguides

We study nonlinear interactions between discrete optical solitons that propagate in different regimes of diffraction, and the nonlinear scattering of dispersive waves by local optical potentials. It is well known in optics that when linear coherent waves meet, they interfere without interactions. Linear waves also scatter through local optical structures not exchanging any power with the guided modes of these structures. As a focusing Kerr nonlinearity is present, such linearly-inhibited phenomena can exist. Our studies are performed in silica and AlGaAs nonlinear waveguides, excited by ultra-short pulses in the near infrared. Presented at 9-th International Workshop on Nonlinear Optics Applications, NOA 2007, May 17–20, 2007, Świnoujście, Poland     

双层非线性耦合反应扩散系统中复杂Turing斑图

采用双层耦合的Brusselator模型, 研究了两个子系统非线性耦合时Turing 模对斑图的影响, 发现两子系统Turing 模的波数比和耦合系数的大小对斑图的形成起着重要作用. 模拟结果表明: 斑图类型随波数比值的增加, 从简单斑图发展到复杂斑图; 非线性耦合项系数在0–0.1时, 系统1中短波模在系统2失稳模的影响下不仅可形成简单六边形、四边形和条纹斑图, 两模共振耦合还可以形成蜂窝六边形、超六边形和复杂的黑眼斑图等超点阵图形, 首次在一定范围内调整控制参量观察到由简单正四边形向超六边形斑图的转化过程; 耦合系数在0.1–1时, 系统1中短波模与系统2失稳模未发生共振耦合仅观察到与系统2相同形状的简单六边形、四边形和条纹斑图. 关键词： Brusselator模型 非线性耦合 Turing模     

Investigation of self-action effects of magnetostatic waves in ferromagnetic structures in terms of the system of Schr?dinger equations with coherent or incoherent coupling

The effect of coupling on the nonlinear dynamics of magnetostatic wave pulses in layered ferromagnetic structures consisting of two ferromagnetic films has been investigated using the numerical solution to the systems of coherent and incoherent nonlinear Schr?dinger equations. The conditions of formation and the possibility of controlling such effects as nonlinear beats, instability of fast solitons, trapping, and tracking have been discussed. The main features of these effects have been analyzed and the applicability of coupled structures to control the formation of nonlinear pulses of magnetostatic waves has been considered.     

Nonlinear control of spacecraft formation flying with disturbance rejection and collision avoidance

A nonlinear controller for disturbances rejection and collision avoidance is proposed for spacecraft formation flying.The formation flying is described by a nonlinear model with the J_2 perturbation and atmospheric drag. Based on the theory of the state-dependent Riccati equation(SDRE), a finite time nonlinear control law is developed for the nonlinear dynamics involved in formation flying. Then, a compensative internal mode(IM) control law is added to eliminate disturbances.These two control laws compose a finite time nonlinear tracking controller with disturbances rejection. Moreover, taking safety requirements into account, the repulsive control law is incorporated in the composite controller to perform collision avoidance manoeuvres. A numerical simulation is presented to demonstrate the effectiveness of the proposed method.Compared to the conventional control method, the proposed method provides better performance in the presence of the obstacles and external disturbances.     

Nonlinear integrable couplings of a nonlinear Schrödinger—modified Korteweg de Vries hierarchy with self-consistent sources

By means of the Lie algebra B₂, a new extended Lie algebra F is constructed. Based on the Lie algebras B₂ and F, the nonlinear Schrödinger-modified Korteweg de Vries (NLS-mKdV) hierarchy with self-consistent sources as well as its nonlinear integrable couplings are derived. With the help of the variational identity, their Hamiltonian structures are generated.     

氢键对2-(N-甲基)氨基-5-硝基吡啶分子非线性光学性质的影响

本文在杂化密度泛函理论水平上研究了溶剂对2-(N-甲基)氨基-5-硝基吡啶分子非线性光学性质的影响.在溶剂中,构造了包括氢键作用的超分子体系,在优化结构的基础上分别研究了由极化连续模型模拟的溶剂与该分子的长程相互作用、溶剂与该分子的氢键相互作用以及溶剂与包括氢键作用的超分子体系整体的相互作用对分子的几何结构、非线性光学性质、紫外吸收光谱和电荷分布等特性的影响.结果表明,溶剂中分子电偶极矩、线性极化率和第一超极化率都增大,而溶剂与溶质分子通过氢键形成的超分子结构与单体有着明显区别.因此,氢键对分子结构和性质的影响较大,从而将明显的影响该类分子的非线性光学性质.     

有损耗介质中非线性光导波的数值模拟

发展了一种以有限元法为基础的数值方法，用它分析由损耗任意大小材料构成的平面非线性波导结构所传导的非线性有损耗光波。在这种方法中，从给出的非线性有损耗波导直接得到ＴＥ和ＴＭ波与功率有关的复传播常数和局域电磁场分布。     

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     

Nonlinear Waves in Nonuniform Complex Astrocloud

The global nonlinear gravito‐electrostatic eigen‐fluctuation behaviors in large‐scale non‐uniform complex astroclouds in quasi‐neutral hydrodynamic equilibrium are methodologically analyzed. Its composition includes warm lighter electrons, ions; and massive bi‐polar multi‐dust grains (inertial) with partial ionization sourced, via plasma‐contact electrification, in the cloud plasma background. The multi‐fluidic viscous drag effects are conjointly encompassed. The naturalistic equilibrium inhomogeneities, gradient forces and nonlinear convective dynamics are considered without any recourse to the Jeans swindle against the traditional perspective. An inho‐mogeneous multiscale analytical method is meticulously applied to derive a new conjugated non‐integrable coupled (via zeroth‐order factors) pair of variable‐coefficient inhomogeneous Korteweg de‐Vries Burger (i ‐KdVB) equations containing unique form of non‐uniform linear self‐consistent gradient‐driven sinks. A numerical illustrative scheme is procedurally constructed to examine the canonical fluctuations. It is seen that the eigenspectrum coevolves as electrostatic rarefactive damped oscillatory shock‐like structures and self‐gravitational compressive damped oscillatory shock‐like patterns . The irregular damping nature is attributable to the i ‐KdVB sinks. The aperiodicity in the hybrid rapid small downstream wavetrains is speculated to be deep‐rooted in the quasi‐linear gravito‐electrostatic interplay. The phase‐evolutionary dynamics grow as atypical non‐chaotic fixed‐point attractors . We, finally, indicate tentative astronomical applications relevant in large‐scale cosmic structure formation aboard facts and faults. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Theoretical study on static (hyper)polarizabilities for polyimide by the elongation finite-field method

The elongation finite-field method is applied to calculate (hyper)polarizabilities of polyimides PMDA/DMDB, PMDA/ODA, and PMDA/TFDB. The nonlinear optical (NLO) properties of planar structures of three polyimides are compared to those of their twist structures. It is found that all α and γ values of the planar structures are larger than the corresponding values of the twist structures, which may be attributed to the fact that π-conjugation of twist structures is decreased compared with the planar structures. All β values of planar and twist structures oscillate regularly along with elongating the chain. Moreover, effect of two side-groups –CH₃ and –CF₃ on the NLO properties of PMDA/DMDB and PMDA/TFDB is investigated.     

密度矩阵重正化群的异构并行优化

密度矩阵重正化群方法（DMRG）在求解一维强关联格点模型的基态时可以获得较高的精度,在应用于二维或准二维问题时,要达到类似的精度通常需要较大的计算量与存储空间.本文提出一种新的DMRG异构并行策略,可以同时发挥计算机中央处理器（CPU）和图形处理器（GPU）的计算性能.针对最耗时的哈密顿量对角化部分,实现了数据的分布式存储,并且给出了CPU和GPU之间的负载平衡策略.以费米Hubbard模型为例,测试了异构并行程序在不同DMRG保留状态数下的运行表现,并给出了相应的性能基准.应用于4腿梯子时,观测到了高温超导中常见的电荷密度条纹,此时保留状态数达到10⁴,使用的GPU显存小于12 GB.     

Some discussions about the variable separating method for solving nonlinear models

Through analysing the exact solution of some nonlinear models, the role of the variable separating method in solving nonlinear equations is discussed. We find that rich solution structures of some special fields of these equations come from the nonzero seed solution. However, these nonzero seed solutions is likely to result in the divergent phenomena for the other field component of the same equation. The convergence and the signification of all field components should be discussed when someone solves the nonlinear equation using the variable separating method.     

共振、混沌与束晕形成

研究强流束中的非线性共振、混沌与束晕形成的关系.给出强流束中非线性共振范围的表达式及其随束流空间电荷效应变化的数值结果和图表曲线,提出由非线性共振而激发的束晕形成的空间电荷效应极限,并分析束晕形成的过程.