Nonlinear Optics in Photonic Micro and Nanostructures

该项目涉及光子微纳米结构中飞行传播的数学和计算模型。在一个例子中，一个新的和改进的模型将被提出并用于描述新的光脉冲在光子晶体光纤中的传播，例如最近观测到的超连续统产生现象，这些现象不能用现有的慢变包络近似很好地理解。该项目的第二个组成部分是研究光纤阵列中的光定位和转向，特别是在制造这种设备时的不完善在增强或抑制光定位方面的作用。这里考虑的模型是一组耦合的随机微分方程。最后，我们将开始解决在微器件中观察到的光学现象在纳米器件中也可能发生的问题。在所有情况下，数学和计算结果将呈现并与领先的实验成果进行比较。这项研究工作具有跨学科性质，数学建模的使用将有助于提高医疗应用中使用的光学设备的性能，例如相干断层扫描和旨在产生多千瓦功率的先进光纤激光器。最先进的激光器基于这里研究的模型，可能会被证明与国土安全有关。该项目将支持两名女性（一名博士生和一名初级教师）作为应用数学专业人员的职业发展。

This project deals with the mathematical and computational modeling oflight as it propagates in photonic micro and nanostructures. In one example,a new and improved model will be proposed and used to describe novel opticalpulse propagation in photonic crystal fibers such as the recently observed phenomena of supercontinuum generation which cannot be well understood with the existing slowly varying envelope approximation. A second component of this project studies light localization and steering in optical fiber arrays and in particular the role imperfections in the manufacturing of such devices have in enhancing or suppressing light localization. The model considered here is a set of coupled stochastic differential equations. Finally, we will begin to address the question of which optical phenomena that has been observed in micro-devices can also happen in the nano-devices. In all instances, the mathematical and computational outcomes will be presented to and compared with leading experimentalist efforts.This research effort is of interdisciplinary nature and the use of mathematical modeling will help improve performance of optical devicesused in medical applications such as coherent tomography and in advanced fiberlasers aimed at producing powers in the multi-kilowatt regime. State of the art lasers based on the model studied here, will likely prove to be relevant for homeland security. This project will support the advancement of two women (a PhD student and a junior faculty) in their careers as Applied Mathematics professionals.