非线性高阶效应下光纤中非自治怪波动力学研究

发布时间：2018-06-11 20:13

本文选题：光怪波 + 高阶效应　；参考：《西北大学》2015年硕士论文

【摘要】：怪波(Rogue waves)是海洋中突然出现又突然消失并且具有很高峰值的水波,其强大的破坏性和不可预测性给航海人员带来了巨大的灾难。最近研究表明非线性机制可以解释怪波的形成原因,1983年,Peregrine研究表示非线性薛定谔方程的有理解可以用来描述怪波。事实上,怪波不仅存在于海洋中,也存在于大气、超流体、等离子体、光学、冷原子凝聚体等非线性机制中。光怪波最早由Solli发现于非线性光学实验中,基于此,相关的研究陆续被展开。在非线性光纤中,当超短脉冲入射时,高阶效应对光怪波的影响不能被忽视。高阶效应存在下光怪波的动力学已经被研究,但对五次非线性效应考虑较少。然而,为了产生更短的脉冲而增大入射光强时,五次非线性效应也非常重要。存在五次非线性和非线性色散效应的非线性光学系统中的光场演化可以用Kundu-Eckhaus(KE)方程来描述。基于光纤系统的非自治性以及对怪波“可控”观点的提出,我们研究广义非自治KE方程中怪波的动力学行为。本文利用相似变换的方法求得了广义非自治KE方程的解析怪波解。我们验证了在这两种高阶效应存在的情况下,光怪波依然能够稳定存在。常系数非线性管理下光怪波的波形和标准非线性薛定谔方程怪波解相一致,只是相位分布发生变化。在不同的非线性管理下,怪波的动力学演化能够很好地被操控。指数非线性管理下,怪波波形陡峭性减小,怪波的轨迹发生一定的扭曲；周期非线性管理下,怪波的波峰、波谷、宽度以及轨迹都具有呼吸震荡的动力学行为,但轨迹整体上依然显示“X”形演化分布。此外,我们发现,高阶效应对怪波的波峰、波谷和宽度没有影响,只影响怪波的轨迹。高阶效应的存在使得怪波的轨迹发生一定角度的偏转,偏转程度由高阶效应强度决定。
[Abstract]:Rogue wavesis a water wave that suddenly appears and disappears in the ocean and has a very high peak value. Its powerful destructive and unpredictability has brought great disaster to seafarers. Recent studies have shown that the nonlinear mechanism can explain the formation of strange waves. The 1983 Peregrine study shows that the understanding of the nonlinear Schrodinger equation can be used to describe the strange waves. In fact, strange waves not only exist in the ocean, but also in the atmosphere, superfluid, plasma, optics, cold atomic condensate and other nonlinear mechanisms. Strange light waves were first discovered by Solli in nonlinear optical experiments. When ultrashort pulse is incident in nonlinear fiber, the influence of higher order effect on the optical strange wave can not be ignored. In the presence of higher order effect, the dynamics of the light strange wave has been studied, but the quintic nonlinear effect is less considered. However, in order to generate shorter pulses and increase the intensity of incident light, the fifth order nonlinear effect is also very important. The evolution of light field in a nonlinear optical system with quintic nonlinearity and nonlinear dispersion effect can be described by Kundu-EckhausKe equation. Based on the nonautonomy of optical fiber system and the viewpoint of "controllable" of strange waves, we study the dynamic behavior of strange waves in generalized nonautonomous Ke equations. In this paper, the analytic strange wave solutions of the generalized nonautonomous Ke equation are obtained by using the method of similarity transformation. We verify that the light strange waves can still exist stably in the presence of these two higher order effects. The waveforms of light waves under constant coefficient nonlinear management are consistent with the solution of standard nonlinear Schrodinger equation, but the phase distribution is changed. Under different nonlinear management, the dynamic evolution of strange waves can be well controlled. Under exponential nonlinear management, the waveform of strange wave decreases steepness, and the trajectory of strange wave is distorted to a certain extent, and the wave peak, trough, width and trajectory of strange wave have the dynamic behavior of respiratory oscillation under periodic nonlinear management. But the trajectory still shows the "X" shape evolution distribution on the whole. In addition, we find that the higher order effect has no effect on the peak, trough and width of the strange wave, but only on the track of the strange wave. The existence of higher order effect makes the track of strange wave deflect at certain angle, and the degree of deflection is determined by the intensity of high order effect.
【学位授予单位】：西北大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TN253

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