Modeling, Analysis, and Simulation of Photonic Microstructures

提案：DMS-0313890 （GOALI）学术PI: Robert V. Kohn，纽约大学工业Co-PI: Michael I. Weinstein，朗讯科技estitle：光子微结构的建模，分析和模拟摘要***********使用本行以下的文字*******************光子微结构是异质光学介质。技术上重要的例子包括(a)光子晶体光纤，(b)有缺陷的周期性平面结构；应用范围从通信系统中的传输介质和设备到光学计算机。这种结构的光学性质以复杂的方式取决于微观结构的细节。目前，直接数值模拟是分析光子结构性能的主要手段。这个工具是不够的，因为虽然模拟可以应用于特定的结构，但它并没有提供指导更好的结构设计的一般原则。纽约和朗讯科技之间的研究将开发和分析新的、基于均质化的方法，以理解光子结构的特征。这些方法将提供关于结构几何如何决定其整体光学性质（群速度，色散，共振，辐射率等）的改进直觉，它们也将导致改进的数值方案来计算光子结构的光谱性质。有大量关于光子微结构及其应用的物理和工程文献，其中包括用于数据传输和计算的光纤和设备。这种结构的设计和分析主要依靠直觉、实验和计算机模拟。纽约大学和朗讯科技公司之间的研究将采用数学分析来提供新的直觉来源和改进的模拟技术——我们希望，这将导致改进的光子微结构和器件的设计。纽约大学和朗讯科技的这一GOALI合作活动将提供一名具有宝贵工业经验的博士后研究员。

Proposal: DMS-0313890 (GOALI)Academic PI: Robert V. Kohn, New York UniversityIndustrial Co-PI: Michael I. Weinstein, Lucent TechnologiesTitle: Modeling, Analysis, and Simulation of Photonic MicrostructuresABSTRACT *********** Use text below this line *******************Photonic microstructures are heterogeneous optical media. Technologically important examples include (a) photonic crystal fibers, and (b) periodic planar structures with defects; applications range from transmission media and devices in telecommunication systems to optical computers. The optical properties of such structures depend in complex ways on the details of the microstructure. At present, direct numerical simulation is the main tool for analyzing the performance of a photonic structure. This tool is inadequate, because while simulation can be applied to specific structures, it does not provide general principles to guide the design of better structures. The research between New York and Lucent Technologies will develop and analyze new, homogenization-based methods for understanding the characteristics of photonic structures. These methods will provide improved intuition about how a structure's geometry determines its overall optical properties (group velocity, dispersion, resonances, radiation rates, etc.) They will also lead to improved numerical schemes for computing the spectral properties of photonic structures.There is a large physics and engineering literature on photonic microstructures and their applications -- which include optical fibers and devices for use in data transmission and computing. The design and analysis of such structures relies mainly on intuition, experimentation, and computer simulation. The research between New York and Lucent Technologies will employ mathematical analysis to provide new sources of intuition and improved techniques for simulation -- leading, we hope, to the design of improved photonic microstructures and devices. This GOALI cooperative activitybetween New York University and Lucent Technologies will provide a postdoctoral researcher with valuable industrial experience.