Inverse Diffraction Problems in Optics

点击翻译按钮获取中文摘要

9803604 Bao This project will support research on the mathematical issues and computational methods for solving the following classes of direct and inverse problems motivated by industrial applications: inverse problems in diffractive optics, modeling of structure enhanced nonlinear optical effects, and optimal design problems in nonlinear optics. The main topics of the proposed work include: Uniqueness, stability, and regularity properties for inverse problems in optics. Numerical computation of inverse and optimal design problems in diffractive optics. Modeling of nonlinear second harmonic generation in periodic structures. Structure enhanced nonlinear optical effects. Well-posedness of a partial differential equation model in nonlinear optics. Interface least-squares finite element methods for solving the model problem. Computational methods for design and optimization in nonlinear optics. These problems arise naturally in modeling and design of micro diffractive optics. Micro diffractive optics is a fundamental, emerging technology in which optical devices are micromachined with very small structural features. Exploiting diffraction effects, diffractive structures perform functions unattainable with conventional optics. Examples of current and potential application areas include corrective lenses, electronic displays, microsensors, lasers, optical storage systems, optical communication components, and integrated opto-electronic semiconductor devices. The practical applications and scientific developments have driven the need for rigorous mathematical models, mathematical analysis, and numerical algorithms to accurately describe the diffraction of complicated diffractive structures, to compute electromagnetic vector fields and thus to predict the performance of a given diffractive structure in linear and nonlinear optical media, as well as to carry out optimal design of new structures. The research has significant potential for evo lving new science and providing industry with guidance to design and fabricate new optical devices.