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

项目名称：衍射光学结构的建模与优化 项目摘要 PI建议对两名数学科学行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培养研究生的技能和经验，使他们在工业环境中成为强有力的竞争者。 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。 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PI与霍尼韦尔公司的长期合作，并与克雷研究公司（Cray Research，Inc.）它将为研究生助理提供机会，从事学术/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。 拟议研究的主要课题如下： --光学薄膜的计算建模。多尺度 有限元法 --衍射光学的逆设计和优化设计问题。 表面增强非线性光学效应。 优化 和非线性光学的设计问题。 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)