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

提案标题：衍射光结构的建模与优化项目概述该项目建议对两名数学科学实业研究生研究助理的专业发展进行培训。培训活动的第一个目标是为研究生培养技能和经验，使他们在工业环境中成为强大的竞争对手。另一个目标是培养具有资格的研究生，使他们成为学术/工业环境中科学和技术发展的重要贡献者。提出的研究重点是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。这项研究将扩展PI与霍尼韦尔公司的长期合作，并与Cray Research，Inc.发展新的合作。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，并为令人兴奋的应用和工业数学领域做出重要贡献。本文的主要研究内容如下：--光学薄膜的计算模型。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。非线性光学中的优化和设计问题。这些问题都是由工业应用引起的。该项目由公安部多学科活动办公室(OMA)和数学科学司(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)