Interchanging Space and Time in Nonlinear Optics Modeling and Dispersion Management Models
Interchanging Space and Time in Nonlinear Optics Modeling and Dispersion Management Models
复制标题
非线性光学建模和色散管理模型中空间和时间的互换
DOI：
10.1007/s00332-022-09788-8
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发表时间：
2022
影响因子：
3
通讯作者：
Schneider Guido
中科院分区：
文献类型：
--
作者：
Fukuizumi Reika;Schneider Guido
在非线性光学中，时间和空间的相互作用被广泛用于模拟光脉冲在玻璃纤维中的演化。在这种装置中，具有周期结构的玻璃纤维中光脉冲的数学描述的唯象模型是所谓的色散管理方程。本文的目的是回答在这种情况下，色散管理方程或其他调制方程是否比唯象模型更多的问题。利用弗洛奎理论，我们证明了在相当强的稳定性和非共振条件成立的假设下，在光的波长和光纤周期相同的情况下，可以推导出常系数的NLS方程和类NLS调制方程，并通过误差估计加以证明。这是关于时间周期色散系统的第一个NLS近似结果。我们解释说，这些条件的失败使我们能够证明这些调制方程通常做出错误的预测。这种失效的原因和系统对于远大于光波长的光纤周期的行为表明，具有周期结构的玻璃纤维的空间和时间的互换作用导致了不想要的现象。
Interchanging the role of space and time is widely used in nonlinear optics for modeling the evolution of light pulses in glass fibers. A phenomenological model for the mathematical description of light pulses in glass fibers with a periodic structure in this set-up is the so-called dispersion management equation. It is the purpose of this paper to answer the question whether the dispersion management equation or other modulation equations are more than phenomenological models in this situation. Using Floquet theory we prove that in case of comparable wave lengths of the light and of the fiber periodicity the NLS equation and NLS like modulation equations with constant coefficients can be derived and justified through error estimates under the assumption that rather strong stability and non-resonance conditions hold. This is the first NLS approximation result documented for time-periodic dispersive systems. We explain that the failure of these conditions allows us to prove that these modulation equations in general make wrong predictions. The reasons for this failure and the behavior of the system for a fiber periodicity much larger than the wave length of light shows that interchanging the role of space and time for glass fibers with a periodic structure leads to unwanted phenomena.