Modeling, Analysis, and Computation of Diffractive and Nano Optics

该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。本计划所发展的数学建模技术和计算方法将解决应用数学中的关键科学挑战，包括周期性手征或非线性结构中的三维电磁波传播、不适定逆衍射问题的全局唯一性和数值解、求解线性和非线性麦克斯韦方程组的自适应技术、电介质和金属非线性光学介质中的二次谐波产生;和多尺度建模，分析，纳米结构的光学响应计算。性能计算设备和微光刻制造技术已经导致了来自亚波长结构的衍射的应用，建立衍射光学和纳米光学作为两个最迅速发展的领域，目前的研究在光学工程。可能的应用包括：快速光学开关是纯光学计算机的关键元件;等离子体材料和光学超材料，这导致了真正令人惊讶的技术创新，如“隐形衣”和“超级透镜”;近场或超分辨率光学显微镜允许观察小于光波长的物体，衍射光学和纳米光学的重要应用的实质性增长推动了对新的数学模型和数值算法的需求。这些材料中电磁场的精确建模在理论和计算上都提出了具有挑战性的数学问题。我们的计算模型和优化设计工具将为光学器件的设计和制造提供一个廉价且易于控制的结构虚拟原型。研究结果将有利于光学工业和纳米技术。

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). The mathematical modeling techniques and computational methods developed in this project will address key scientific challenges in applied mathematics including three-dimensional electromagnetic wave propagation in periodic chiral or nonlinear structures; global uniqueness and numerical solution of the ill-posed inverse diffraction problems; adaptive techniques for solving linear and nonlinear Maxwell's equations; second harmonic generation in dielectric and metallic nonlinear optical media; and multiscale modeling, analysis, and computation of optical responses of nano structures.The recent enabling technologies of high-performance computing facilities and microlithographic fabrication techniques have led to applications of diffraction from subwavelength structures, establishing diffractive optics and nano optics as two of the most rapidly advancing areas of current research in optical engineering. Possible application include: fast optical switches that are a key element of purely optical computers; plasmonic materials and optical metamaterials, which are leading to really amazing technological innovations, such as "invisibility cloaks" and "superlenses"; near-field or super-resolution optical microscopy that allows to observe objects that a smaller than the light wavelength, etc. The substantial growth of significant applications of diffractive and nano optics has driven the need for novel mathematical models and numerical algorithms. Accurate modeling of electromagnetic fields within these materials presents challenging mathematical questions both in theory and computation. Our computational models and optimal design tools will provide an inexpensive and easily controllable virtual prototype of the structures in the design and fabrication of optical devices. The research results will benefit the optics industry and nano technology.