Impact of Polarization-Mode Dispersion on Fiber Nonlinearities

尽管近年来对偏振模色散（PMD）现象进行了广泛的研究，但大多数对PMD的研究都是在忽略所有光纤非线性的线性近似下进行的。虽然这种方法提供了相当多的物理见解，它不能用于真实的光波系统中的非线性效应，如自和交叉相位调制（SPM和XPM）通常是不可忽略的。由于同样的原因，它不能用于非线性效应用于维持孤子的孤子区域。 我们需要的是一个全面的研究计划，研究PMD对各种非线性效应，如SPM，XPM，四波混频（FWM），受激拉曼散射的影响。 提出的研究的主要目标是开发一个新的理论框架，能够包括PMD对光纤内部发生的几个重要的非线性效应的影响。更具体地说，我们计划研究PMD对SPM，XPM，FWM和受激拉曼散射的影响。PMD问题由于其随机性质而通常相当复杂。到目前为止，大多数关于PMD的研究都忽略了光纤的非线性，因为它分别考虑了脉冲的每个频率分量的偏振状态。这种方法不能用于真实的光波系统，其中的非线性效应通常是不可忽略的。为了弥补这种情况，PI提出了一个研究计划，其中PMD效应将通过求解基本的非线性薛定谔方程与矩量法。这种方法可以使我们得到脉冲位置、宽度、啁啾和能量等重要参数的随机常微分方程，而对于PMD对四波混频和受激拉曼散射的影响，则需要另一种处理方法。这两种非线性效应越来越多地用于制造参量放大器和拉曼放大器。 用于制造这种放大器的光纤长度足够长，使得PMD效应不能被忽略。PI已经开始关注拉曼放大问题，并开发了一个简单的模型，使PI能够找到放大信号中PMD引起的波动的平均值和标准差。他计划将这种技术扩展到参量放大的情况。虽然大多数拟议的研究是理论性的，PI打算与其他实验组合作验证理论预测。

0320816AgrawalEven though the polarization-mode dispersion (PMD) phenomenon has been studied extensively in recent years, most of the research on PMD has been carried out within the linear approximation in which all fiber nonlinearities are neglected. Although this approach has provided considerable physical insight, it cannot be used for real lightwave systems in which nonlinear effects such as self- and cross-phase modulation (SPM and XPM) are not generally negligible. For the same reason, it cannot be used in the soliton regime where the nonlinear effects are used for sustaining solitons. What is needed is a comprehensive research program that studies the impact of PMD on various nonlinear effects such as SPM, XPM, four-wave mixing (FWM), and stimulated Raman scattering. The primary goal of the proposed research is to develop a new theoretical framework that is capable of including the impact of PMD on several important nonlinear effects occurring inside optical fibers. More specifically, we plan to study the impact of PMD on SPM, XPM, FWM, and stimulated Raman scattering. The PMD problem is generally quite complicated because of its stochastic nature. Most of the research so far on PMD has ignored fiber nonlinearities because it considers the state of polarization of each frequency component of the pulse separately. This approach cannot be used for real lightwave systems in which the nonlinear effects are not generally negligible. To remedy this situation, the PI proposes a research program in which the PMD effects will be incorporated by solving the underlying nonlinear Schrodinger equation with the moment method. This technique will allow us to find the stochastic but ordinary differential equations for several important pulse parameters such as the position, width, chirp, and energy.A somewhat different approach is needed for handling the PMD effects on FWM and stimulated Raman scattering. These two nonlinear effects are increasingly being used for making parametric and Raman amplifiers. Fiber lengths used for making such amplifiers are long enough that PMD effects cannot be ignored. The PI has already begun to focus on the Raman-amplification problem and has developed a simple model that allows the PI to find the average and standard deviation of the PMD-induced fluctuations in the amplified signal. He plans to extend this technique to the case of parametric amplification. Although most of the proposed research is of theoretical nature, the PI intends to verify the theoretical predictions in collaboration with other experimental groups.