Modeling and Design of Diffractive Optics

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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).