Intermediate Self-similar Solutions of the Nonlinear Schrödinger Equation with an Arbitrary Longitudinal Gain Profile

We study pulse propagation in a normal-dispersion optical fibre amplifier with an arbitrary longitudinal gain profile by self-similarity techniques. We show the functional form of the development of low-amplitude wings on the parabolic pulse, which are associated with the evolution of an arbitrary input pulse to the asymptotic parabolic pulse solution. It is found that for the increasing gain the amplifier output corresponding to the input Gaussian pulse converges to the asymptotic parabolic pulse solution more quickly than the output obtained with the input hyperbolic secant pulse, whereas for the decreasing gain the input pulse profiles have nearly no effect on the speed of convergence to the parabolic pulse solution. These theoretical results are confirmed by numerical simulations.     

色散渐减光纤中Ginzburg-Landau方程的自相似脉冲演化的解析解

采用对称约简的分析方法，得出了变系数Ginzburg-Landau方程的抛物渐近自相似脉冲解析解的一般表达式.给出了二阶色散系数纵向双曲型变化和纵向指数型变化的色散渐减光纤中自相似脉冲的振幅、啁啾以及脉冲宽度的具体形式，并与数值解进行了对比，其结果符合得很好.从而证实了稀土元素掺杂的色散渐减光纤中，在增益色散因子的影响下，脉冲的演化具有抛物型自相似特性.     

高阶色散效应常系数Ginzburg-Landau方程自相似脉冲演化的解析分析

采用自相似分析方法,基于常系数高阶色散的Ginzburg-Landau方程,通过分离变量法得出了高阶色散效应自相似脉冲演化的解析解,给出了自相似脉冲的振幅、相位、啁啾以及脉冲宽度的一般表达式.研究表明,在增益光纤的二阶正常色散区域,同时考虑高阶色散和增益色散双重效应影响下演化的自相似孤子脉冲仍然保持线性啁啾;振幅解析解的三阶色散效应显著.这与数值计算的结果非常一致. 关键词： 三阶色散 Ginzburg-Landau方程 自相似脉冲 二阶正常色散     

Analytical self-similar solutions of the Ginzburg-Landau equation with three-order dispersion effect

Based on the technique of the symmetry reduction, we find the asymptotic self-similarity analytical resolutions from the constant coefficient Ginzburg-Landau equation considering both influences of the thirdorder dispersion and gain dispersion on the evolution of pulses. We have obtained the self-similar pulse amplitude function, phase function, strict linear chirp function, and the effective temporal pulse width. Numerical simulations show qualitative agreement with these theoretical results.     

色散渐减光纤中自相似脉冲传输特性研究

研究了在高阶色散影响下,自相似脉冲在具有正常色散的色散渐减光纤中的演化情况.结果表明:当考虑高阶色散的影响时,脉冲的啁啾仍然具有很强的线性特性,只是中心变得不对称,产生中心漂移.这种啁啾特性使得自相似脉冲在时域中的抛物线形状产生畸形,导致了脉冲峰向一边延迟,并使脉冲的中心位置漂移,同时伴随着脉冲边沿的振荡.但是通过采用色散补偿技术,自相似脉冲强的线性啁啾仍然可以得到高质量的飞秒量级压缩脉冲,与忽略三阶色散影响时得到的压缩脉冲的脉宽近似相等.     

Analytic solutions of self-similar pulse based on Ginzburg-Landau equation with constant coefficients

Based on the constant coefficients of Ginzburg-Landau equation that considers the influence of the doped fiber retarded time on the evolution of self-similar pulse, the parabolic asymptotic self-similar solutions were obtained by the symmetry reduction algorithm. The parabolic asymptotic amplitude function, phase function, strict linear chirp function and the effective temporal pulse width of self-similar pulse are given in this paper. And these theoretical results are consistent with the numerical simulations. Supported by the Natural Science Foundation of Guangdong Province of China (Grant No. 04010397)     

受激喇曼散射对自相似脉冲产生的影响

研究了在受激喇曼散射与三阶色散共同作用下,自相似脉冲在具有正常色散的色散渐减光纤中的演化情况.结果表明:在同一个传输距离上,当考虑受激喇曼散射与三阶色散的共同影响时,脉冲中心的不对称特性相对好转;产生中心漂移与边缘振荡较只有三阶色散作用时要减弱,啁啾仍然具有很强的线性特性,但是线性范围减小,导致频谱的窄化以及对接下来自相似脉冲的压缩产生了不利影响;而且光纤长度的延长并没有起到展宽啁啾线性范围的效果,反而导致严重的啁啾非线性;因此对脉冲进行压缩后,压缩脉冲质量较不考虑受激喇曼散射时要差.     

Distortion of parabolic pulse due to higher-order effects in a dispersion-decreasing fiber

Considering Third-order Dispersion (TOD) and Stimulated Raman Scattering effect (SRS) simultaneously, the properties of the self-similar parabolic pulse evolution in a dispersion-decreasing optical fiber with normal group-velocity dispersion are firstly investigated in our paper. Our results show that parabolic pulses are distorted and the characteristic of exactly self-similarity will be lost due to the High-order effects. When only the TOD is taken into account, the chirp still reveals highly linear but glows into asymmetric which causes the waveform appearing optical wave breaking. When only considering SRS, the pulse still reveals highly linear chirp only linearity range narrow down, resulting in delaying the self-similar evolution. When considering SRS and TOD simultaneously, parabolic pulses are distorted less and the characteristic of exactly self-similarity will be better due to SRS effect than only considering TOD effect. The highly linear chirp in optical pulse still allows for efficient and high-quality pulse compression by use of dispersion compensation technique.     

掺镱光纤放大器中自相似脉冲传输特性研究

研究了高阶色散和增益色散影响下,自相似脉冲在掺镱光纤放大器中的传输特性.从解析求解和数值模拟两方面分别阐述了初始脉冲能量、三阶色散和偶极子驰豫时间对脉冲传输质量的影响.结果表明,当传输考虑三阶色散效应时,伴随着脉冲啁啾非线性区域的扩大,啁啾中心随着色散系数取值的大小和正负前、后移动,脉冲峰向一侧延迟,中心位置发生漂移.增益色散对脉冲放大起到滤波作用,对自相似脉冲具有压窄效应.证实了具有一定驰豫时间的增益介质能够维持自相似孤子波的稳定传输.     

1550 nm飞秒脉冲自相似光纤放大仿真模拟EI北大核心CSCD

针对全光纤的超短脉冲掺铒光纤放大器进行了仿真模拟,对正常色散条件下掺铒光纤自相似脉冲放大过程进行了详细分析。在光纤预放大器中,使用高正色散掺铒光纤对脉冲形状进行预整形,将重复频率43 MHz、脉冲宽度600 fs、平均输出功率1.2 mW的孤子型锁模脉冲预整形为抛物线型脉冲,预整形后的脉冲通过光纤主放大器进行功率放大。经两级光纤放大后,1.2 mW的信号光功率放大为102 mW,放大增益19.3 dB。分析了掺铒光纤长度、放大功率对脉冲自相似演化过程的影响。放大后的脉冲经4.4 m长单模光纤将脉冲宽度压缩至53 fs,峰值功率为44.8 kW。     

光纤放大器中的自相似抛物脉冲

本文研究在含有增益色散、增益饱和、三阶色散、自频移、自陡峭等效应的光纤放大器中自相似抛物脉冲的产生和传输。结果表明,在渐近约束条件下,自相似脉冲的中心区域可用倒置的抛物脉冲来描绘,并且它的有效脉宽和功率都是线性增长的,而峰值振幅和频谱宽度保持常量。数值模拟结果与理论预期符合的非常好,这表明:在光纤放大器中,在适当的条件下初始输入脉冲可自相似地演化为抛物脉冲。     

Chirped soliton-like solutions for nonlinear Schrödinger equation with variable coefficients

The exact chirped bright and dark soliton-like solutions of generalized nonlinear Schrödinger equation including linear and nonlinear gain(loss) with variable coefficients describing dispersion-management or soliton control is obtained detailedly in this paper. To begin our numerical studies of the stability of the solutions, we present a periodically distributed dispersion management or soliton control system as an example. It is found that both the bright and dark soliton-like solutions are stable during propagation in the given system. The numerical results are well in accordance with those obtained by analytical methods.     

Modulational instability in the cubic-quintic nonlinear Schrödinger equation through the variational approach

The dynamics of nonlinear pulse propagation in an average dispersion-managed soliton system is governed by a constant coefficient nonlinear Schrödinger (NLS) equation. For a special set of parameters the constant coefficient NLS equation is completely integrable. The same constant coefficient NLS equation is also applicable to optical fiber systems with phase modulation or pulse compression. We also investigate MI arising in the cubic-quintic nonlinear Schrödinger equation for ultrashort pulse propagation. Within this framework, we derive ordinary differential equations (ODE’s) for the time evolution of the amplitude and phase of modulation perturbations. Analyzing the ensuing ODE’s, we derive the classical modulational instability criterion and identify it numerically. We show that the quintic nonlinearity can be essential for the stability of solutions. The evolutions of modulational instability are numerically investigated and the effects of the quintic nonlinearity on the evolutions are examined. Numerical simulations demonstrate the validity of the analytical predictions.     

Propagation of short soliton pulses through a parabolic index fiber with dispersion decreasing along length

A parabolic index dispersion decreasing fiber (DDF) has been designed and optimized to produce high capacity soliton communication system. Variation of different fiber parameters such as core radius, effective core area and GVD factor along the 25 km of DDF length has been carried out to optimize a best possible DDF which can sustain the propagation of fundamental soliton. The variation of non-linearity with length along with the conventional power and GVD factor variation has been included in the generalized non-linear Schrodinger equation (NLSE). This NLSE has been solved numerically by split step Fourier method for shorter pulse propagation, incorporating the term for third order dispersion and intrapulse Raman scattering. Stable soliton pulses in transmission system have been achieved by our simulation, when a correction factor due to Raman induced soliton mean frequency shift is incorporated to the GVD profile predicted by the fundamental soliton condition. The interaction of neighboring soliton pulse pair through the proposed fiber has also been studied.     

增益色散和双光子吸收对光纤放大器中自相似脉冲的影响

以包含增益色散、增益饱和、三阶色散、自陡峭、自频移等高阶效应的光纤放大器为研究对象,对其产生渐近抛物型自相似脉冲的条件及传输特性进行了详细的讨论.结果表明,合理选择系统参数,在渐近约束条件下,可以获得不同振幅和脉宽大小的自相似脉冲;此外,非线性增益(或吸收)与非线性谱宽限制在自相似脉冲存在的范围内近似成线性比例关系,且脉冲的有效脉宽,功率,峰值振幅及能量的大小及增长速度也将随参数的变化面变化.相关结果将为实验中调节光纤放大器以及系统参数的选择提供一定的理论参考.     

Dependence of parabolic pulse amplification on stimulated Raman scattering and gain bandwidth

An analytical model has been developed and verified by numerical simulations to determine limits induced by stimulated Raman scattering (SRS) on parabolic pulse evolution in high-power, high-energy Yb-fiber amplifiers. Our results show that the maximum achievable parabolic pulse energies are limited by SRS at low amplifier gains and by the finite gain bandwidth at high gains. Therefore, an optimum gain value exists that maximizes the achievable output pulse energy.     

Third-order dispersion role on parabolic pulse propagation in dispersion-decreasing fiber with normal group-velocity dispersion

Parabolic pulse propagation in a dispersion-decreasing fiber with normal group velocity dispersion (ND-DDF) has been studied when the third-order dispersion (TOD) is included. The results show that the characteristic of exact self-similarity and linear chirp will be lost due to the third-order dispersion. However, by using the dispersion compensation technique, one can obtain efficient and high-quality compressed pulses. The analytic results have been confirmed using numerical simulations.     

A Formula of Propagating Beams Driven by Few-Cycle Gaussian Pulse in Dispersive Media

A formula is developed to describe the propagation of beams driven by few-cycle Gaussian pulse in a media with group velocity dispersion （GVD）. With the method, the spatiotemporal evolution of the pulsed beam can be straightforwardly quantified as long as the monochromatic beam solutions in free space, which have been widely investigated in previous works, are known. The method makes it possible to analytically deal with the few-cycle pulsed beams with transverse profiles other than the Gaussian one, which is, to our knowledge, the one mainly investigated previously, in GVD media.     

Three-Wave Resonant Interaction in Optical Fibres on a Continuous-Wave Background

We predict that a three-wave resonant interaction (TWRI) for the excitations created from a continuous-wave background is possible in nonlinear optical fibres with a centro-symmetry. We show that in normal dispersion regime and near the zero-dispersion point of a single-mode optical fibre, the phase-matching condition for the TWRI can be satisfied by suitably choosing the wavevectors and frequencies of the exciting waves. The nonlinear envelope equations for the TWRI are derived by using a method of multiple-scales, and their explicit solutions for sum- and difference-frequency mixing are provided and discussed.     

Interaction between parabolic pulses in a dispersion-decreasing fiber

The properties of the self-similar parabolic pulses interaction in a dispersion-decreasing optical fiber with normal group-velocity dispersion are firstly investigated in our paper. We find that two parabolic pulses separated by a time-delay create oscillation with a sinusoidal fit at the beginning of their overlap, and then further evolve into a train of asymptotic dark solitons. Additionally, outside the overlap regime, the evolution is equal to a single pulse’ propagating behavior. The chirp after interaction in the parabolic pulses still allows for efficient and high-quality pulse compression.