Modeling and Design of Diffractive Optics

本研究的重点是线性和非线性光学介质中光学微结构建模和设计的计算方法和数值分析。这项研究将扩大我们与克雷研究公司的现有合作，并与朗讯科技贝尔实验室展开新的合作。它将为两名研究生助理提供机会，从事大学-工业联合研究计划，并为应用和工业数学的一个令人兴奋的领域做出重要贡献。 本论文的主要研究内容如下：衍射问题的界面最小二乘有限元法：计算与数值分析。 逆绕射与最佳设计问题。新的计算方法。 非线性衍射光学的建模。结构增强非线性光学效应。 这些问题是由工业应用引起的。 培训活动的目标是：（1）培养研究生的技能和经验，使他们成为学术/工业环境中强有力的竞争者;（2）培养研究生，使他们具备在学术/工业环境中为科学和技术发展做出重要贡献的资格。 连同学院，大学将提供第一年总支持的50%。研究助学金或教学助学金将在几年后提供。 克雷研究将支持PI的一名研究生的暑期实习。 Cray的Guangye Li将花时间监督暑期实习生并从事软件开发工作。 克雷还将提供PI和他的学生访问计算机，以及必要的技术支持。 该GOALI项目由MPS多学科活动办公室（OMA）和数学科学部（DMS）联合支持。

The proposed research focuses on computational methods and numerical analysis for modeling and design of optical micro-structures in linear and nonlinear optical media. The research will extend our existing collaboration with Cray Research, Inc., and develop a new collaboration with Lucent Technology, Bell Labs. It will provide opportunities for two graduate assistants to engage in University-Industry joint research programs and make important contributions to an exciting area of applied and industrial mathematics. The main topics of the proposed research are as follows: Interface least-squares finite element methods for diffraction problems: computation and numerical analysis. Inverse diffraction and optimal design problems. A new computational approach. Modeling of nonlinear diffractive optics. Structure enhanced nonlinear optical effects. These problems are motivated by industrial applications. The objectives of the training activities are to (1) prepare the graduate students with skills and experiences that will make them strong competitors in an academic/industrial environment and (2) produce graduate students who have qualifications that will make them important contributors to science and technology developments in an academic/industrial environment. Together with the College, the University will provide 50% of the total support for the first year. Research assistantships or teaching assistantship will be provided in the years after. Cray Research will support a summer internship for one graduate student of the PI. Guangye Li of Cray will devote time in supervising the summer intern and working on the software development. Cray will also provide the PI and his students access to computers, together with necessary technical support. This GOALI project is jointly supported by the MPS Office of Multidisciplinary Activities (OMA) and the Division of Mathematical Sciences (DMS).