Direct and Inverse Modeling of Diffractive Optics and Near-Field Optics

这个项目研究数学问题并开发计算方法来解决亚波长结构光学衍射中的重要的正问题和逆问题。这项工作的动机是工业应用，包括线性和非线性双周期结构(交叉光栅)的散射和衍射，衍射光学中的逆和优化设计问题，以及周期和一般结构中的近场光学。这项研究考察了三维电磁波在周期结构中的传播，反问题的不适定性，解线性和非线性麦克斯韦方程的自适应技术，以及近场成像的建模。将开发新的计算方法和数学建模技术来解决近场光学的基本正反问题。将发展新的技术来处理复杂介质和结构中散射的线性和非线性麦克斯韦方程。我们将为相关的优化设计、逆问题和成像问题开发稳健的解决方法，为新型光学设备的创造提供指导。brbr微衍射光学和近场光学是基础和蓬勃发展的技术，应用广泛，包括光学计算、通信、激光技术、近场光学显微镜、生物样品成像和纳米技术。由于微小的结构特征，光在微光学结构中的传输通常是由衍射主导的。这些材料中电磁场的精确建模提出了具有挑战性和重要的数学和计算问题。该项目开发的计算模型和优化设计工具将为新型光学设备设计中涉及的结构和介质提供廉价且易于控制的“虚拟原型”。研究成果将对光学行业产生立竿见影的效果。

This project investigates mathematical issues and develops computational methods for solving important classes of direct and inverse problems in optical diffraction from subwavelength structures. The work is motivated by industrial applications, including scattering and diffraction by linear and nonlinear biperiodic structures (crossed gratings), inverse and optimal design problems in diffractive optics, and near-field optics in periodic and general structures. The research examines three-dimensional electromagnetic wave propagation in periodic structures, ill-posedness for inverse problems, adaptive techniques for solving linear and nonlinear Maxwell equations, and modeling of near-field imaging. New computational methods and mathematical modeling techniques will be developed to solve the underlying direct and inverse problems for near-field optics. New techniques will be developed to deal with the associated linear and nonlinear Maxwell equations for scattering in complex media and structures. We will develop robust solution methods for the associated optimal design, inverse, and imaging problems, to provide guidance for the creation of novel optical devices.brbrMicro diffractive optics and near-field optics are fundamental and vigorously growing technologies with diverse applications, including optical computing, communications, laser technology, near-field optical microscopy, imaging of biological samples, and nanotechnology. Because of the small structural features, light propagation in micro-optical structures is generally dominated by diffraction. Accurate modeling of electromagnetic fields within these materials presents challenging and significant mathematical and computational questions. The computational models and optimal design tools developed by this project will provide inexpensive and easily controllable "virtual prototypes" of the structures and media involved in the design of novel optical devices. The research results will be of immediate benefit to the optics industry.