色散缓变光纤对皮秒光孤子的压缩效应

本文从描述超短光脉冲在色散缓变光纤(FSDD)中传输所满足的准非线性Schrodinger(NLS)方程出发,证明该方程与常规光纤中含增益效应时的NLS方程等价,并在此基础上进行了理论分析,讨论了光弧子脉冲在不同FSDD中的传输特性;最后采用数值模拟方法研究了高阶皮秒光孤子在不同FSDD中的压缩效应,发现利用FSDD和弧子压缩效应不但可以获得更高压缩率弧子光脉冲,而且可以有效地缩短所需的光纤长度。     

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.     

强双折射光纤中单一频率传输区域的调制不稳定性

利用光脉冲在光纤中传播时所遵守的相干非线性薛定谔耦合方程,研究了单一频率的线偏振光,且偏振方向沿两个双折射轴的分量强度相等时,在反常色散区和正常色散区所产生的调制不稳定性.结果表明在反常色散区和正常色散区,对应不同的功率区域输入脉冲有不同的增益谱,并且当输入脉冲功率一定时,双折射性质变化导致增益谱表现出明显的不同.     

光孤子在色散缓变光纤中传输时的等价增益

从准非线性Ｓｃｈｒ?ｄｉｎｇｅｒ（ＮＬＳ）方程出发，导出了色散缓变光纤中光孤子脉冲传输所满足的与常规光纤中含增益效应等价的ＮＬＳ方程，给出了该方程的微扰解析解和光孤子脉冲宽度演化表达式。对于阶跃型单模光纤，得到了光纤几何参数与增益系数之间的一般函数关系。最后采用数值模拟方法模拟了不同色散缓变光纤中光孤子脉冲传输特性，指出色散缓变光纤不仅能补偿光纤损耗对孤子脉冲的展宽效应，而且能压缩光孤子脉冲，因而预计它可能有较广泛的应用前景。 关键词：     

Evolution of optical pulses in the presence of third-order dispersion

We model the propagation of femtosecond pulses through optical fibres by a nonlinear Schrödinger (NLS) equation involving a perturbing term arising due to third-order dispersion in the medium. The perturbative effect of this higher-order dispersion causes the usual NLS soliton to emit a radiation field. As a result, the given initial pulse propagating through the fibre exhibits nonsolitonic behaviour. We make use of a variational method to demonstrate how an initial pulse by the interaction with the emitted radiation can evolve into a soliton. We also demonstrate that the effect of interaction between the initial pulse and radiation field can be accounted for by including, in the evolution equation, terms associated with self-steepening and stimulated Raman scattering that characterize the optical medium.     

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.     

双折射光纤中斯托克斯波的增益谱

根据激光脉冲在双折射光纤中传输时的混合模方程,考虑拉曼效应后,得出在受激拉曼散射和参量放大共同作用下的增益。数值模拟了当输入泵浦波沿两双折射轴450附近区域传输时,在不同色散区斯托克斯增益谱随输入功率及群速度失配等相关参数的变化关系;结果表明斯托克斯增益谱在不同色散区表现出明显不同的特性,当满足一定条件下,可利用混合模双折射光纤中传输的泵浦波分解出的脉冲序列来分离和提取T频脉冲。     

保偏光纤中相近频率传输区域的调制不稳定性

利用激光脉冲在光纤中传播时所遵守的相干非线性薛定谔耦合方程,研究了保偏光纤中两相近频率的线偏振光，其偏振方向相互正交且平行于光纤的双折射轴，且偏振方向沿两个双折射轴的分量强度相等时，在同为反常色散区和正常色散区所产生的调制不稳定性.结果表明在反常色散区和正常色散区都能产生调制不稳定性；在正常色散区存在不同的调制不稳定性功率区域，对应不同的功率区域，导致增益谱表现出明显的不同，并且当输入功率一定时，波长差(或频率差)的变化导致增益谱的变化. 关键词： 相近频率传输区域 双折射 保偏光纤 调制不稳定性     

双折射光纤中斯托克斯波的增益谱

根据激光脉冲在双折射光纤中传输时的混合模方程,考虑拉曼效应后,得出在受激拉曼散射和参量放大共同作用下的增益。数值模拟了当输入泵浦波沿两双折射轴450附近区域传输时,在不同色散区斯托克斯增益谱随输入功率及群速度失配等相关参数的变化关系;结果表明斯托克斯增益谱在不同色散区表现出明显不同的特性,当满足一定条件下,可利用混合模双折射光纤中传输的泵浦波分解出的脉冲序列来分离和提取T频脉冲。     

色散补偿及高阶孤子压缩啁啾光脉冲的理论与实验研究

利用半导体激光器的单模速率方程及超短光脉冲在光纤中传输的非线性薛定谔(NLS)方程，从理论及实验上研究了增益开关DFB半导体激光器出射的啁啾光脉冲在色散补偿光纤(DCF)及色散位移光纤(DSF)中的压缩过程与规律.实验上，从1.55μm增益开关DFB半导体激光器出射的重复频率为2.5GHz、脉冲宽度为53.8ps的光脉冲经色散补偿光纤压缩至12ps,而后利用色散位移光纤中的高阶孤子压缩效应将脉冲压缩至2.5ps.改变色散位移光纤参数及入射光功率后获得最窄光脉冲宽度为2.1ps.理论与实验结果符合. 关键词：     

Transformation from the nonautonomous to standard NLS equations

In this paper we show a systematical method to obtain exact solutions of the nonautonomous nonlinear Schrödinger (NLS) equation. An integrable condition is first obtained by the Painlevé analysis, which is shown to be consistent with that obtained by the Lax pair method. Under this condition, we present a general transformation, which can directly convert all allowed exact solutions of the standard NLS equation into the corresponding exact solutions of the nonautonomous NLS equation. The method is quite powerful since the standard NLS equation has been well studied in the past decades and its exact solutions are vast in the literature. The result provides an effective way to control the soliton dynamics. Finally, the fundamental bright and dark solitons are taken as examples to demonstrate its explicit applications.     

高阶色散对高双折射光纤增益谱的影响

根据参量放大和拉曼效应共同作用下的耦合波方程,在考虑高阶色散情况下,当输入泵浦波偏振方向同双折射轴成45时,通过引入拉曼增益的洛伦兹模型,研究了高双折射光纤中,参量放大和拉曼效应共同作用下的增益谱随相关参量的变化关系。结果表明:高双折射光纤中,在不同色散区,不同的输入参量（输入功率、群速度失配等）条件下,参量放大和拉曼效应共同作用下的增益谱受到高阶色散的影响,增益谱的结构、强度和谱宽产生了变化, 高阶色散对增益谱的影响不可忽略;可以利用增益谱在大群速度失配区域远离中心频率偏移的性质,提取T频率脉冲。     

色散渐减光纤中自相似脉冲传输区域的研究

从非线性薛定谔(NLS)方程出发,用分步傅里叶方法结合对数值解的波形分析,确定了色散渐减光纤(DDF)中能实现自相似脉冲传输的区域,并研究了初始脉冲和光纤参数对自相似区域和演化速度的影响。结果表明,初始脉冲能量的减小有利于扩宽自相似区域,但会使自相似演化进程略为减慢;初始脉宽有一个最佳值,在最佳值上自相似区域最宽,演化较快且输出脉冲和啁啾较为稳定;高斯脉冲比双曲正割脉冲更快转化为自相似脉冲,传输区域也更广。选择具有较小非线性参量的DDF可以获得较广的自相似区域,同时非线性参量的增大可以加快自相似演化,而群速度色散参量和增益系数必须选择在最佳值附近,才能获得最大自相似区域和最快演化速度。     

Extended symmetry transformation of (3+1)-dimensional generalized nonlinear Schrdinger equation with variable coefficients

In this paper, the extended symmetry transformation of (3+1)-dimensional (3D) generalized nonlinear Schrdinger (NLS) equations with variable coefficients is investigated by using the extended symmetry approach and symbolic computation. Then based on the extended symmetry, some 3D variable coefficient NLS equations are reduced to other variable coefficient NLS equations or the constant coefficient 3D NLS equation. By using these symmetry transformations, abundant exact solutions of some 3D NLS equations with distributed dispersion, nonlinearity, and gain or loss are obtained from the constant coefficient 3D NLS equation.     

Singularity analysis and integrability for a HNLS equation governing pulse propagation in a generic fiber optics

Taking into account many developments in fiber optics communications, we propose a higher nonlinear Schrödinger equation (HNLS) with variable coefficients, more general than that in [R. Essiambre, G.P. Agrawal, Opt. Commun. 131 (1996) 274], which governs the propagation of ultrashort pulses in a fiber optics with generic variable dispersion. The study of this equation is performed using the Painlevé test and the zero-curvature method. Also, we prove the equivalence between this equation and its anomalous integrable counterpart (the so-called Sasa-Satsuma equation). Finally, in view of its physical relevance, we present a soliton solution which represents the propagation of ultrashort pulses in a dispersion decreasing fiber.     

Noncommutative NLS equation

In the framework of noncommutative field theory we discuss a deformation (ncNLS) of the nonlinear Schrödinger (NLS) equation. In particular, a first order equation in the deformation parameter is obtained which generates a (Seiberg-Witten-type) map from NLS to ncNLS solutions.     

双折射色散阶跃光纤中拉曼效应和参量放大增益谱

在拉曼效应和参量放大共同作用下,当激光脉冲在双折射光纤中传输时,根据所遵循的耦合模方程,通过引入平行拉曼增益的洛伦兹模型,导出了当输入泵浦波偏振方向同双折射轴成45°角时,在双折射色散阶跃光纤中拉曼效应和参量放大共同作用所导致的增益,讨论并分析了在不同色散区增益谱随相关参量的变化。结果表明:由于拉曼效应、参量放大、双折射和色散的相互作用,导致增益谱的斯托克斯波与反斯托克斯波彼此不对称;在反常色散区,产生的增益以反斯托克斯波为主,在正常色散区则以斯托克斯波为主;当表征距离的级数m发生变化时,增益谱也随之发生变化,可以利用色散阶跃光纤在适当的级数m位置提取T频率脉冲。     

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.