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.Â
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.
