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On the efficiency of different numerical methods for the calculation of intrapulse Raman scattering of optical solitons

机译：关于光学孤子的脉冲内拉曼散射计算的不同数值方法的效率

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摘要

In this paper we compare the performance of different numerical methods for the calculation of the asymptotic evolution of soliton self-frequency shift in the presence of intrapulse Raman scattering (IRS) in optical fibers. First we have calculated the order of global accuracy for the fundamental soliton and the second-order bound state of the unperturbed nonlinear Schrodinger equation for the following numerical methods: the simple split step (SS) method, the full SS method, the reduced SS method, the reduced SS method with fourth order Runge-Kutta (RK4), the Blow-Wood method, the fourth order Runge-Kutta in the interaction picture (RK4IP) method and the Agrawal SS method with one and two iterations. We have shown that the asymptotic evolution of soliton self-frequency shift in the presence of IRS in optical fiber can be best described by the Agrawal SS method (compared to the Blow-Wood method and the RK4IP method). The obtained numerical results for the soliton position and frequency are in agreement with the predictions for these parameters according to the perturbation theory. We have shown that in the presence of IRS the fundamental soliton quickly develops an oscillating tail on its left. The generated tail hardly influences the soliton propagation at large distances. At large distances the form of the soliton gradually becomes asymmetric. The increase of the frequency resolution leads to a notable increase of the maximum propagation distance of the numerical soliton under the influence of IRS.
机译：在本文中，我们比较了在光纤中存在脉冲内拉曼散射（IRS）的情况下，不同数值方法用于计算孤子自频移的渐近演化的性能。首先，我们针对以下数值方法计算了基本孤子的全局精度和无扰动非线性Schrodinger方程的二阶结合状态的阶数：简单分裂步骤（SS）方法，完全SS方法，简化SS方法，具有四阶Runge-Kutta（RK4）的简化SS方法，Blow-Wood方法，交互图片中的四阶Runge-Kutta（RK4IP）方法以及具有一两次迭代的Agrawal SS方法。我们已经表明，通过Agrawal SS方法（与Blow-Wood方法和RK4IP方法相比）可以最好地描述光纤中存在IRS时孤子自频移的渐近演化。所获得的孤子位置和频率的数值结果与根据扰动理论对这些参数的预测一致。我们已经证明，在存在IRS的情况下，基本孤子会在其左侧快速产生振荡的尾巴。产生的尾巴几乎不会影响孤子在远距离的传播。在大距离处，孤子的形式逐渐变得不对称。频率分辨率的提高导致在IRS的影响下数值孤子的最大传播距离显着增加。

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