色散管理的Ginzburg-Landau方程及其在飞秒激光中的应用
The dispersion-managed Ginzburg-Landau equation and its application to femtosecond lasers
摘要：
复杂的Ginzburg-Landau方程已被广泛用于描述各种非平衡现象。在激光器的背景下，它通过对腔内发生的效应进行平均来模拟脉冲的动力学。然而，钛：蓝宝石飞秒激光器产生的脉冲在每次往返过程中在腔的不同部分发生显著变化。因此，不考虑这种变化的平均模型不能充分描述这种脉冲的动态。这项工作的目的有几个方面。首先，我们介绍了色散管理的金兹伯格-朗道方程（DMGLE）作为一个平均模型，它描述了系统的长期动力学特征的色散，非线性和增益的快速变化，在一般设置，我们研究了方程的属性。然后，我们解释如何特别是DMGLE产生钛：蓝宝石飞秒激光器，我们表征其解决方案。特别是，我们表明，对于中等值的增益/损耗参数，DMGLE的解决方案很好地近似的色散管理的非线性薛定谔方程（DMNLSE），增益和损耗动态的主要影响是简单地选择一个DMNLSE的单参数家庭的解决方案。
英文摘要：
The complex Ginzburg-Landau equation has been used extensively to describe various non-equilibrium phenomena. In the context of lasers, it models the dynamics of a pulse by averaging over the effects that take place inside the cavity. Ti:sapphire femtosecond lasers, however, produce pulses that undergo significant changes in different parts of the cavity during each round-trip. The dynamics of such pulses is therefore not adequately described by an average model that does not take such changes into account. The purpose of this work is severalfold. First we introduce the dispersion-managed Ginzburg-Landau equation (DMGLE) as an average model that describes the long-term dynamics of systems characterized by rapid variations of dispersion, nonlinearity and gain in a general setting, and we study the properties of the equation. We then explain how in particular the DMGLE arises for Ti:sapphire femtosecond lasers and we characterize its solutions. In particular, we show that, for moderate values of the gain/loss parameters, the solutions of the DMGLE are well approximated by those of the dispersion-managed nonlinear Schrodinger equation (DMNLSE), and the main effect of gain and loss dynamics is simply to select one among the one-parameter family of solutions of the DMNLSE.
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