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

跨学科的FRG团队将开发用于纳米级结构的光物质相互作用的数学技术和计算方法，这些技术和计算方法受到最近科学和工业应用的推动。在多物理场建模，多尺度模拟以及耦合麦克斯韦和薛定谔方程的数学分析的关键问题将进行研究。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，包括多物理场建模、多尺度计算、密度泛函理论、麦克斯韦方程组的有效数值解以及相关的新型非线性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高级工具，特别关注那些能够实现多物理场和多尺度计算的工具。最初的努力将指向开发工具，使动态调制光子结构的有效模拟，这是一个迫切需要克服的数值挑战，造成的大时间尺度分离之间的电子和光学过程。这一发展将直接有助于提高光信息处理应用的速度和降低能耗。该研究小组的合作伙伴将开展合作，使多物理场模拟应用于传感或能量转换等实际技术的影响。控制光的能力对于现代社会的许多方面都是至关重要的，并且在能源、传感和信息技术等关键领域都有应用。纳米光子结构的使用，其中单个结构是纳米级的，是我们追求控制光的最前沿。纳米光学是一项基础和蓬勃发展的技术，具有多种应用，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发展使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。当光场与纳米结构相遇时，遇到的一个重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，并给与这些结构的相互作用带来了挑战。纳米光学的未来发展将明显受益于有效的计算建模工具和数学分析技术的可用性。在这个项目中开发的计算工具将使我们能够更好地理解和设计这些结构，有可能导致消耗更少功率的更快的信息处理设备，具有更高灵敏度的传感器和具有更好转换效率的太阳能电池。

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.