碳纳米管拉曼光谱研究新进展

本文介绍碳纳米管拉曼光谱研究的最新进展。重点介绍金属性和半导体性碳纳米管的共振拉曼效应、表面增强拉曼效应和偏振拉曼效应。同时也介绍了碳纳米管的温度效应、压力效应和杨氏模量的拉曼光谱研究     

“拉曼效应”的发现之路--纪念拉曼逝世50周年

印度物理学家拉曼使用约7美元的“小设备”发现了以他名字命名的“拉曼效应”,荣获1930年诺贝尔物理学奖,是亚洲首位诺贝尔科学奖获得者.回顾了拉曼的生平,通过文献研究还原了他与海水的颜色真实故事,重温了拉曼效应的发现历程,介绍了拉曼效应的内容及意义.     

各向同性光纤中拉曼增益对光脉冲自陡峭的影响

运用数学解析法导出了关于拉曼增益与自陡峭综合效应的光脉冲传输方程,在此基础上引入洛伦兹模型将拉曼增益整合到非线性系数中来研究光脉冲中拉曼增益对自陡峭效应的作用,重点分析了高斯脉冲在各向同性光纤中传播时,拉曼增益对其自陡峭效应具体影响方式,结果表明拉曼增益会减弱自陡峭中后沿偏移程度,减小脉冲展宽,但不会影响其峰值大小.     

饱和非线性效应对负折射材料中孤子自频移的影响

以描述负折射材料中包含拉曼效应的高阶非线性薛定谔方程为模型,采用分步傅里叶算法数值分析了高阶效应,尤其是饱和非线性效应对自聚焦负折射率材料中的孤子拉曼自频移的影响。结果表明,在自聚焦负折射率材料中饱和非线性效应使孤子拉曼自频移速度加快;饱和非线性效应与负的自陡效应共同作用进一步加快孤子自频移的速度;饱和非线性效应同正的自陡效应、三阶色散效应共同作用时孤子拉曼自频移在整体上受到抑制。     

非自治拉曼多色孤子的管理和传输

以变系数的非自治非线性薛定谔方程为模型,考虑了一种色散、非线性和自发拉曼散射效应管理下的非自治系统,通过简单变换显式给出了该系统的精确非自治拉曼多色孤子解。基于精确孤子解,解析研究了该拉曼多色孤子在非自治管理系统中的演化特性,发现孤子的中心位置、波数与色散和非线性以及拉曼效应有关,而孤子频移仅与拉曼效应的参数决定,拉曼效应主导了非自治孤子的自频移,引起了孤子的频移在传输过程中不断的发生变化,导致了孤子的多色性。另外,我们数值讨论了该非自治孤子的传输稳定性,结果表明:该非自治拉曼多色孤子在有限的扰动下具有较好的稳定性。     

Stokes光对频率上移信号光的损耗分析

由于拉曼增益效应,斯托克斯(Stokes)光可以引起频率上移信号光的损耗。通过对描述拉曼效应的耦合功率微分方程组的仿真计算,得到了衰减受传输距离和泵浦光强的影响关系,并从理论上给予了分析说明。同时对前人的实验观察结果进行了验证,理论与实验达到了很好的吻合,提出了利用拉曼增益效应进行光信号处理的可行性。最后指出了利用拉曼效应的优点,并展望了其广阔的应用前景。     

各向同性光纤中拉曼增益对光脉冲自陡峭的影响

运用数学解析法导出了关于拉曼增益与自陡峭综合效应的光脉冲传输方程,在此基础上引入洛伦兹模型将拉曼增益整合到非线性系数中来研究光脉冲中拉曼增益对自陡峭效应的作用,重点分析了高斯脉冲在各向同性光纤中传播时,拉曼增益对其自陡峭效应具体影响方式,结果表明拉曼增益会减弱自陡峭中后沿偏移程度,减小脉冲展宽,但不会影响其峰值大小.     

拉曼激光边带效应对冷原子重力仪测量精度的影响

电光调制技术是产生拉曼光的几种方法之一,其优点是系统简单、易搭建且环境适应性强.然而,这种调制技术会产生额外的边带光,并影响冷原子干涉绝对重力仪的测量精度.本文利用自行研制的可移动冷原子重力仪,研究了边带效应对冷原子重力仪测量精度的影响.详细分析了拉曼反射镜的位置、拉曼脉冲的作用时刻及其间隔、拉曼光的失谐等一系列参数与边带效应之间的关系,实验发现这些参数对冷原子重力仪的精度评估有比较大的影响;此外,我们还发现在有边带效应的情况下,原本不影响重力测量精度的实验参数也会影响最终的重力测量结果.最后,通过研究拉曼边带效应与拉曼光失谐之间的关系,本文提出一种评估拉曼边带效应影响重力仪精度的方法.本文结果为减小拉曼边带效应对冷原子重力仪测量精度的影响提供了依据.     

拉曼效应对低双折射光纤偏振特性的影响

在低双折射光纤中,利用线偏振光满足的包含拉曼效应的非线性耦合模传输方程,通过引入斯托克斯参量,导出了斯托克斯参量所满足的耦合模传输方程.利用庞加莱球图示法,描述了拉曼增益效应作用下光波偏振态的演化,研究分析了拉曼效应对低双折射光纤中光波偏振态演化规律的影响.结果表明,当输入功率与运动常量满足一定关系时,拉曼增益效应改变了光波传输时其偏振态演化周期和偏振态的椭圆率.     

拉曼增益对三类有限背景解传输特性的影响

基于含有拉曼增益效应的自聚焦非线性薛定谔方程,数值研究了拉曼增益分别对Peregrine怪波(PS)、Akhmediev呼吸子(AB)和Kuznetsov-Ma孤子(KMS)传输特性的影响。结果表明:拉曼增益效应会使怪波、AB和KMS在时间方向上发生分裂,且拉曼增益系数越大,分裂速度越快;拉曼增益效应还会使三种孤子解传输距离方向上的峰值功率增大,相邻两最大压缩脉冲之间的距离缩短,且拉曼增益系数越大,最大峰值功率越大,相邻距离越小。     

On the modulation instability development in optical fiber systems

Extensive numerical simulations were performed to investigate all stages of modulation instability development from the initial pulse of pico-second duration in photonic crystal fiber: quasi-solitons and dispersive waves formation, their interaction stage and the further propagation. Comparison between 4 different NLS-like systems was made: the classical NLS equation, NLS system plus higher dispersion terms, NLS plus higher dispersion and self-steepening and also fully generalized NLS equation with Raman scattering taken into account. For the latter case a mechanism of energy transfer from smaller quasi-solitons to the bigger ones is proposed to explain the dramatical increase of rogue waves appearance frequency in comparison to the systems when the Raman scattering is not taken into account.     

Explicit N-Solit on Solution of the Unstable Nonlinear Schrödinger Equation

The unstable nonlinear Schrodinger (NLS) equation is solved by the inverse scattering transform. Based on the constructed Zakharov-Shabat equation, it is shown that the soliton solution of the unstable NLS equation can be known from the soliton solution of the usual NLS equation by simply exchanging the tariables. The explicit N-soliton solution and the position shifts due to the collision are thus calculated.     

Comparisons between sine-Gordon and perturbed nonlinear Schrödinger equations for modeling light bullets beyond critical collapse

The sine-Gordon (SG) equation and perturbed nonlinear Schrödinger (NLS) equations are studied numerically for modeling the propagation of two space dimensional (2D) localized pulses (the so-called light bullets) in nonlinear dispersive optical media. We begin with the (2 + 1) SG equation obtained as an asymptotic reduction in the two level dissipationless Maxwell-Bloch system, followed by the review on the perturbed NLS equation in 2D for SG pulse envelopes, which is globally well posed and has all the relevant higher order terms to regularize the collapse of standard critical (cubic focusing) NLS. The perturbed NLS is approximated by truncating the nonlinearity into finite higher order terms undergoing focusing-defocusing cycles. Efficient semi-implicit sine pseudospectral discretizations for SG and perturbed NLS are proposed with rigorous error estimates. Numerical comparison results between light bullet solutions of SG and perturbed NLS as well as critical NLS are reported, which validate that the solution of the perturbed NLS as well as its finite-term truncations are in qualitative and quantitative agreement with the solution of SG for the light bullets propagation even after the critical collapse of cubic focusing NLS. In contrast, standard critical NLS is in qualitative agreement with SG only before its collapse. As a benefit of such observations, pulse propagations are studied via solving the perturbed NLS truncated by reasonably many nonlinear terms, which is a much cheaper task than solving SG equation directly.     

Solutions of Two Kinds of Non-Isospectral Generalized Nonlinear Schrodinger Equation Related to Bose-Einstein Condensates

Two non-isospectral generalized nonlinear Schrodinger （ONLS） equations, which are two important models of nonlinear excitations of matter waves in Bose-Einstein condensates, are studied. Two novel transformations are constructed such that these two GNLS equations are transformed to the well-known nonlinear Schr6dinger （NLS） equation, which is an isospectral equation. Therefore, once one solution of the NLS equation is provided, we can immediately obtain one solution for two ONLS equations by these transformations. Thus it is unnecessary to solve these two non-isospectral GNLS equations directly. Soliton solutions and periodic solutions are obtained for them by two transformations from the corresponding solutions of the NLS equation, which are generated by Darboux transformation.     

Breathers and solitons for the coupled nonlinear Schr?dinger system in three-spine α-helical protein

We mainly investigate the variable-coefficient 3-coupled nonlinear Schr?dinger(NLS) system, which describes soliton dynamics in the three-spine α-helical protein with inhomogeneous effect. The variable-coefficient NLS equation is transformed into the constant coefficient NLS equation by similarity transformation firstly. The Hirota method is used to solve the constant coefficient NLS equation, and then we get the one-and two-breather solutions of the variable-coefficient NLS equation. The results show that, in the background of plane waves and periodic waves, the breather can be transformed into some forms of combined soliton solutions. The influence of different parameters on the soliton solution and the collision between two solitons are discussed by some graphs in detail. Our results are helpful to study the soliton dynamics inα-helical protein.     

Long-Time Asymptotics for Solutions of the NLS Equation with a Delta Potential and Even Initial Data: Announcement of Results

We consider the one-dimensional focusing nonlinear Schrödinger equation (NLS) with a delta potential and even initial data. The problem is equivalent to the solution of the initial/boundary problem for NLS on a half-line with Robin boundary conditions at the origin. We follow the method of Bikbaev and Tarasov which utilizes a Bäcklund transformation to extend the solution on the half-line to a solution of the NLS equation on the whole line. We study the asymptotic stability of the stationary 1-soliton solution of the equation under perturbation by applying the nonlinear steepest-descent method for Riemann?CHilbert problems introduced by Deift and Zhou. Our work strengthens, and extends, the earlier work on the problem by Holmer and Zworski.     

Rogue Wave Solutions for Nonlinear Schrödinger Equation with Variable Coefficients in Nonlinear Optical Systems

In this paper, the generalized Darboux transformation is constructed to variable coefficient nonlinear Schrödinger (NLS) equation. The N-th order rogue wave solution of this variable coefficient NLS equation is obtained by determinant expression form. In particular, we present rogue waves from first to third-order through some figures and analyze their dynamics.     

On the exact solutions of nonlinear Schrödinger equation with spin current

An integrable nonlinear Schrödinger (NLS) equation driven by spin polarized current governing the magnetization dynamics of a ferromagnetic nanowire is considered. The exact soliton solution of the NLS equation propagating along the direction of wire axis which is also the current direction along which nonuniform magnetization occurs is obtained through the application of exponential function method. The solution of the system admits a class of solitons such as kink and periodic solitons in the nanowire along the direction of the electric current.     

Exact spatial soliton solution for nonlinear Schrödinger equation with a type of transverse nonperiodic modulation

In this paper, we analyze (2 + 1)D nonlinear Schrödinger (NLS) equation based on a type of nonperiodic modulation of linear refractive index in the transverse direction. We obtain an exact solution in explicit form for the (2 + 1)D nonlinear Schrödinger (NLS) equation with the nonperiodic modulation. Finally, the stability of the solution is discussed numerically, and the results reveal that the solution is stable to the finite initial perturbations.     

On a kinetic approach to the modulational stability of envelope solitons in a relativistic plasma in an external electric field

Summary The formation of envelope solitons is discussed in a relativistic plasma under the influence of a fluctuating electric field. We use the kinetic-theory approach for our analysis. Due to the larger inertia, only the electrons are considered to be relativistic and the ions to be nonrelativistic. A NLS equation is derived describing the motion of the solitary wave. This NLS equation actually comes from an approximation of a pair of equations which can be considered to be a relativistic generalisation of the Zakharov equation. We next discuss the exact form of the envelope solitary-wave solution of the NLS equation and the modulation stability of such a wave. When the density, momentum and energy of such wave packets are fixeda priori, conditions are derived for the parameters of the problem from such stability consideration.