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，但大多数关于偏振模色散的研究都是在线性近似范围内进行的，其中忽略了所有光纤非线性。虽然这种方法提供了相当大的物理洞察力，但它不能用于实际的光波系统，其中非线性效应，如自相位和交叉相位调制（SPM和XPM）通常不可忽略。由于同样的原因，它不能用于用非线性效应维持孤子的孤子区。需要的是一个综合的研究计划，研究PMD对各种非线性效应的影响，如SPM， XPM，四波混频（FWM）和受激拉曼散射。本研究的主要目标是建立一个新的理论框架，该框架能够包括PMD对光纤内部发生的几种重要非线性效应的影响。具体来说，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，通常是相当复杂的。目前对PMD的研究大多是单独考虑脉冲各频率分量的偏振状态，忽略了光纤的非线性特性。这种方法不能用于非线性效应不可忽略的实际光波系统。为了纠正这种情况，PI提出了一个研究计划，其中PMD效应将通过用矩量法求解潜在的非线性薛定谔方程来纳入。这种技术将使我们能够找到几个重要脉冲参数的随机常微分方程，如位置、宽度、啁啾和能量。处理PMD对FWM和受激拉曼散射的影响需要一种不同的方法。这两种非线性效应越来越多地用于制作参数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，因此PMD效应不容忽视。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。他计划将这项技术扩展到参数放大的情况。虽然大多数提出的研究都是理论性的，但PI打算与其他实验小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.