Facão M, Carvalho M I, Parker D F
Departamento de Física, Universidade de Aveiro, Campus Universitário de Santiago, 3810-193 Aveiro, Portugal.
Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Apr;81(4 Pt 2):046604. doi: 10.1103/PhysRevE.81.046604. Epub 2010 Apr 20.
Ultrashort pulse propagation in fibers is affected by intrapulse Raman scattering (IRS) which causes both a linear frequency downshift and a quadratic displacement of the peak pulse, as functions of the propagation distance. This effect has been known and treated by perturbation methods applied to the nonlinear Schrödinger equation since the period of intense research on soliton propagation. Here, we find solutions of the model equation using an accelerating self-similarity variable and study their stability. These solutions have Airy function asymptotics which give them infinite energy. For small IRS, the algebraically decaying tail is negligible and these solutions are a very good approximation of the profiles observed in the full equation simulations. For strong IRS (but beyond the regime in which the evolution equation is valid for silica fibers), the self-similar pulses have noticeable left tails exhibiting Airy oscillations. Whenever their truncated forms are used as initial conditions of the full equation, they experience amplitude decay and show left tails that are consistent with radiation escaping from the central pulse. These observations are interpreted as being the effects of a continuum constitution of the infinite left tail.
光纤中的超短脉冲传播受到脉冲内拉曼散射（IRS）的影响，这会导致峰值脉冲出现线性频率下移和二次位移，它们都是传播距离的函数。自对孤子传播进行深入研究以来，这种效应就已为人所知，并通过应用于非线性薛定谔方程的微扰方法进行处理。在此，我们使用加速自相似变量找到模型方程的解，并研究其稳定性。这些解具有艾里函数渐近线，这使得它们具有无限能量。对于小的IRS，代数衰减尾部可忽略不计，并且这些解是全方程模拟中观察到的脉冲形状的很好近似。对于强IRS（但超出了演化方程对石英光纤有效的范围），自相似脉冲具有明显的左尾部，呈现出艾里振荡。每当将其截断形式用作全方程的初始条件时，它们会经历幅度衰减，并显示出与从中心脉冲逸出的辐射一致的左尾部。这些观察结果被解释为无限左尾部连续体构成的效应。
