FRG: Collaborative Research: Modeling, Computation, and Analysis of Optical Responses of Nano Structures

跨学科的FRG团队将在最近的科学和工业应用的推动下，为纳米级结构的光-物质相互作用开发数学技术和计算方法。将研究多物理建模、多尺度模拟以及麦克斯韦和薛定谔耦合方程的数学分析等关键问题。我们提出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，包括多物理建模、多尺度计算、密度泛函理论、麦克斯韦方程的有效数值解以及相关的新的非线性PDE模型的适定性。将开发用于模拟和优化纳米光子结构的计算电磁学方面的先进工具，特别是那些能够实现多物理和多尺度计算的工具。最初的努力将致力于开发能够有效模拟动态调制的光子结构的工具，其中迫切需要克服由于电子和光学过程之间的大时间尺度分离而产生的数值挑战。这里的发展将直接有助于提高光学信息处理应用的速度和降低能耗。FRG的合作伙伴将合作，使多物理模拟应用于传感或能量转换等实用技术中的影响。控制光的能力对现代社会的许多方面至关重要，并在能源、传感和信息技术等关键领域得到应用。纳米结构的使用，其中单个结构是纳米级的，在我们寻求控制光的过程中处于最前沿。纳米光学是一项基础和蓬勃发展的技术，具有广泛的应用前景，包括快速光开关、等离子体材料、光子纳米电路、光学显微镜、拉曼光谱和光学超材料。近年来，高性能计算设备和现代光刻技术的使能技术导致了亚波长和纳米结构的应用激增，使纳米光学成为当前光学科学研究中发展最快的领域之一。当光场遇到纳米结构时遇到的一个巨大挑战是尺度上的根本不匹配，这导致了传统光学中没有遇到的现象，并提出了与这种结构相互作用的挑战。纳米光学的未来发展显然将受益于有效的计算建模工具和数学分析技术的可用性。该计划中开发的计算工具将使我们能够更好地了解和设计这些结构，潜在地导致更快的信息处理设备，这些设备消耗更少的电力，传感器具有更高的灵敏度，太阳能电池具有更好的转换效率。

The interdisciplinary FRG team will develop mathematical techniques and computational methods for the light-matter interactions for nanoscale structures motivated by recent scientic and industrial applications. Critical issues on multi-physics modeling, multi-scale simulations as well as mathematical analysis of the coupled Maxwell and Schrodinger equations will be investigated. Our proposed mathematical modeling techniques and computational methods will address key scientific challenges in applied mathematics including multi-physics modeling, multi-scale computation, density functional theory, efficient numerical solution of Maxwell's equations, and well-posedness of the associated new nonlinear PDE models. Advanced tools in computational electromagnetics for simulations and optimizations of nanophotonic structures will be developed, with a specific focus on those tools that enable multi-physics and multi-scale computations. The initial efforts will be directed towards developing tools that enable efficient simulations of dynamically modulated photonic structures, where there is a critical need to overcome the numerical challenges resulting from the large time-scale separations between the electronic and the optical processes. The development here will contribute directly to increasing speed and reducing energy consumption in optical information processing applications. Partners in this FRG will collaborate to enable the applications of multi-physics simulations towards impacts in practical technologies such as sensing or energy conversion. The capabilities for controlling light are of paramount importances for many aspects of modern society, and have applications in critical areas such as energy, sensing and information technology. The use of nanophotonic structures, where individual structure is at the nanoscale, is at the very forefront in our quest to control light. Nano-optics is a fundamental and vigorously growing technology with diverse applications including fast optical switches, plasmonic materials, photonic nanocircuits, optical microscopy, Ramam spectroscopy, and optical metamaterials. The recent enabling technologies of high-performance computing facilities and modern lithographic techniques have led to a substantial surge of applications of subwavelength and nano structures, establishing nano-optics as one of the most rapidly advancing areas of current research in optical science. A grand challenge encountered when optical fields meet nano structures is a fundamental mismatch in scales, which gives rise to phenomena not encountered in conventional optics and presents a challenge in interacting with such structures. The future development of nano-optics will clearly benefit from the availability of an efficient computational modeling tool and mathematical analysis techniques. The computational tools developed in this program will allow us to better understand and design these structures, potentially leading to faster information processing devices that consume less power, sensors with higher sensitivity, and solar cells with better conversion efficiency.