Modeling and Optimal Design of Photonic Structures

NSF奖摘要-DMS-0072439数学科学：光子结构的建模和优化设计这个项目致力于研究和开发新的计算方法和分析技术，用于光子晶体和相关结构的建模和优化设计。该项目的目标是将二维光子晶体的方法扩展到三维结构的情况，开发光子带隙结构中缺陷模的优化方法，模拟和分析色散介质对周期结构中波传播的影响，并研究相关的优化设计问题。最终目标是对平面几何结构中的截断光子晶体进行建模，并开发优化此类结构的散射和共振特性的方法。本项目研究的结构是光学材料的周期性排列，旨在展示与电磁波传播有关的有用特性。利用这种结构是一项基本技术，预计将在激光、传感器、光存储、光通信和高密度光互连等应用中产生重大影响。该项目旨在开发建模和设计能力，这将提高对这些结构特性的理解，并促进它们融入有用的设备。

NSF Award Abstract - DMS-0072439Mathematical Sciences: Modeling and Optimal Design of Photonic StructuresAbstract0072439 DobsonThis project focuses on the investigation and development of new computational methods and analytical techniques for the modeling and optimal design of photonic crystals and related structures. The objectives of the project are to extend methods developed for two-dimensional photonic crystals to the case of three-dimensional structures, to develop methods for the optimization of defect modes in photonic band gap structures, and to model and analyze the effects of dispersive media on wave propagation in periodic structures and study associated optimal design problems. The final objective is to model truncated photonic crystals in planar geometries and develop methods to optimize the scattering and resonance properties of such structures. The structures studied in this project are periodic arrangements of optical materials, designed to exhibit useful properties with respect to electromagnetic wave propagation. Making use of such structures is a fundamental technology, expected to have a significant impact in applications including lasers, sensors, optical storage, optical communications, and high-density optical interconnects. This project aims to develop modeling and design capabilities, which will improve understanding of the properties of these structures and facilitate their incorporation into useful devices.