Pulse Dynamics in Optical Communications

在过去的十年中，在增加光纤通信系统的传输容量方面取得了巨大的进步。实现这种增长的一种技术涉及在波分复用（WDM）中已知的过程中沿单个光纤线路同时传输多个数据流。为了使这种技术发挥作用，不同数据流之间的交互必须最小化。另一个重要的发展是所有光学设备和系统组件的出现，这些设备和系统组件利用光纤中的参数过程以比传统光电组件更快的速率执行数据操作。与WDM系统相比，这些设备依赖于不同频率分量之间的强相互作用才能发挥作用。提出的是一个考虑的问题，信道间的相互作用（以不同频率为中心的数据流的相互作用）在两个限制建议的WDM系统（弱相互作用）和所有的光学设备（强相互作用）。为了实现这一目标，渐近，多尺度和孤子微扰理论，变分方法和对称性约化技术将被用来获得约化方程的光脉冲的动力学在相关的限制。 这些方程将进行分析和数值研究，以确定支持稳定和有效的系统操作的参数制度。在分析的每个阶段将使用数值模拟，以将结果与实验数据进行比较。该大学-行业合作研究（U-ICR）计划项目由MPS多学科活动办公室（OMA）和数学科学部（DMS）联合支持。

Over the past decade, tremendous strides have been made in increasing the transmission capacity of fiber optic communications systems. One technique that has enabled this increase involves transmitting multiple streams of data simultaneously down a single fiber line in a process known at wavelength division multiplexing (WDM). In order for this technique to work, interaction between the different data streams must be minimized. Another important development has been the appearance of all optical devices, system components that exploit parametric processes in optical fiber to perform data manipulation at faster rates than more tradition opto-electronic components. In contrast to WDM systems, these devices depend on strong interaction between different frequency components in order to function. Proposed is a consideration of the problem of interchannel interaction (the interaction of data streams centered at different frequencies) in the two limits suggested by WDM systems (weak interaction) and all optical devices (strong interaction). To meet this goal, asymptotics, multiple scale and soliton perturbation theory, variational methods, and symmetry reduction techniques will be used to obtain reduced equations for the dynamics of optical pulses in the relevant limit. These equations will be studied analytically and numerically in order to identify the parameter regimes that support stable and efficient system operation. Numerical simulations will be used at each stage of the analysis to compare results with experimental data. This University-Industry Cooperative Research (U-ICR)Program project is jointly supported by the MPS Office of Multidisciplinary Activities (OMA) and the Division of Mathematical Sciences (DMS).