University - Industry Cooperative Research Programs in the Mathematical Sciences- Modeling and Optimization of Diffractive Optical Structures

方案题目：衍射光学结构的建模与优化项目摘要：PI提出对两名数学科学产业型研究生研究助理进行专业发展培训。培训活动的首要目标是为研究生提供技能和经验，使他们在工业环境中成为强有力的竞争对手。另一个目标是培养具有资格的研究生，使他们在学术/工业环境中对科学和技术发展作出重要贡献。本文主要研究线性和非线性光学介质中光学微结构的建模和设计的计算方法和数值分析。该研究将扩展PI与霍尼韦尔公司的长期合作，并与克雷研究公司建立新的合作关系。它将为研究生助理提供参与学术/工业联合研究项目的机会，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。本课题主要研究方向如下：光学镀膜的计算建模。多尺度有限元方法。衍射光学中的逆设计和优化设计问题。——表面增强的非线性光学效应。非线性光学的优化与设计问题。这些问题是由工业应用引起的。该项目由MPS多学科活动办公室（OMA）和数学科学部（DMS）联合支持。

Title of Proposal: Modeling and optimization of diffractive optical structures Project Summary The PI proposes training on the professional development of two Mathematical Sciences Industry-Based Graduate Research Assistants. The first objective of the training activities is to prepare the graduate students with skills and experiences that will make them strong competitors in an industrial environment. Another objective is to produce the graduate students who have qualifications that will make them important contributors to science and technology developments in a academic/industrial environment. 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 the PI's long term collaboration with Honeywell, Inc., and develop a new collaboration with Cray Research, Inc. It will provide opportunities for the graduate assistants to engage in academic/industrial 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: -- Computational modeling of optical coatings. Multiscale finite element methods. -- Inverse and optimal design problems in diffractive optics. -- Surface enhanced nonlinear optical effects. Optimization and design problems in nonlinear optics. These problems are motivated by industrial applications. This project is jointly supported by the MPS Office of Multidisciplinary Activities (OMA) and the Division of Mathematical Sciences (DMS)