SGER: Stimulated Raman Scattering in the Transient Limit

描述受激拉曼的方程 瞬态极限中的散射是非线性的， 可积的 然而，这种物质的物理行为 系统传播后，长距离是相当 不同于其他可积系统如光 光纤中的脉冲。 在光纤中， 脉冲分裂成许多孤子， 色散波的贡献，而在瞬态 受激拉曼散射的机制，解决方案 倾向于相似性解决方案，其取决于 （距离）x（时间）。 最后一个结果虽然是可推断的， 从以前的数值结果来看， 它的许多后果仍然有待证实， 阐明。 第一个值得关注的问题是 第二代斯托克斯和有限的T2 对自我的实验观察 类似的解决方案。 我们会调查的 现象 我们还将探讨 限制转换的瞬态拉曼效应 拉曼降频器的效率 与钛宝石激光器配合使用。 我们将 也探索了类似的技术 可应用于光纤光栅、二能级系统 光折射材料和其它系统 要么已经被证明表现出自我， 相似性或有希望的候选人，因为他们 有长期记忆。 最后在 在数学方面，我们将与汤姆 Seidman在研究这些解决方案的稳定性 和其他数学家一起 自相似情形的渐近公式， 频率是失谐的。

The equations which describe stimulated Raman scattering in the transient limit are nonlinear and integrable. However, the physical behavior of this system after propagating, long distances is quite different from other integrable systems such as light pulses in optical fibers. In optical fibers, the light pulses break up into a number of solitons and a dispersive wave contribution, while in the transient regime of stimulated Raman scattering, the solutions tend toward a similarity solution which depends on (distance) x (time). This last result, while inferrable from previous numerical results, was only recently proved, and many of its consequences remain to be elucidated. The first issue of concern is the limitation which second Stokes generation and finite T2 impose on possible experimental observation of the self- similar solution. We will investigate this phenomenon. We will also explore the impact of the transient Raman effect on limiting the conversion efficiency of Raman frequency downshifters which are used in conjunction with Ti:Sapphire lasers. We will also explore the extent to which similar techniques can be applied to fiber gratings, two-level systems, photorefractive materials, and other systems which have either already been shown to exhibit self- similarity or are promising candidates because they have long-term memory. Finally, on the mathematical front, we will collaborate with Tom Seidman in studying the stability of these solutions and with other mathematicians in obtaining asymptotic formulae for the self-similar case when the frequencies are detuned.