Multiscale Modeling and Computation of Nano-Optics

该研究的主要目的是研究用于纳米光学器件多尺度和多物理模型的稳健、高效和精确的数值方法。纳米级的实验和制造技术在生物医学工程和新材料方面已经证明了巨大的成功和潜力。定量的建模和仿真不仅有助于理解这些纳米器件的机理，而且可以通过最小化测试误差和优化性能来大大降低成本。PI将与化学家和材料科学家在光子驱动的纳米设备和属性科学方面进行合作。为纳米光学开发的方法将揭示各种各样的纳米级问题。对自洽多尺度方法的数学分析将为多尺度建模和计算领域带来新的见解。初级合作者和研究生将接受应用数学新前沿的跨学科培训，并将更好地结合建模、分析和计算技能来解决实际问题。为了充分了解光子驱动的纳米和微型设备，PI将结合经典电动力学、含时电流密度泛函理论和Ehrenfest分子动力学，在线性响应区域推导出电磁场、电子激发和分子运动之间相互作用的多尺度模型。采用自洽的多尺度格式对系统进行有效求解。还将对金属增强进行研究。为了准确地模拟包含非线性高阶相互作用的强场过程的长时间传播，PI将采用自适应数值策略。多尺度格式将被设计用于在时间域上同时模拟电动力学和量子力学过程。PI还将从收敛和稳定性方面对算法进行彻底的分析。

The main objective of the proposed research is to study robust, efficient and accurate numerical methods for multiscale and multiphysical models of nanoscale optical devices. Nanoscale experimental and manufacturing technologies have proved huge successes and potentials in biomedical engineering and new materials. Quantitative modeling and simulation will not only help to understand the mechanism of these nano devices but also greatly reduce the cost by minimizing trial errors and optimizing the performance. The PI will collaborate with chemists and material scientists on photon driven nano devices and attosciences. Methods developed for nano-optics will shed light on a wide variety of nanoscale problems. The mathematical analysis of the self-consistent multiscale methods will bring new insights into the field of multiscale modeling and computation. Junior collaborators and graduate students will receive cross disciplinary training on new frontiers of applied mathematics, and will be better prepared to solve realistic problems with a combination of modeling, analytical and computational skills.To fully understand photon driven nano and micro devices, the PI will derive multiscale models for interactions between the electromagnetic field, electronic excitations and molecular motions by combining classical electrodynamics, time dependent current density functional theory and Ehrenfest molecular dynamics in the linear response regime. The self-consistent multiscale scheme will be adopted to solve the system efficiently. Metal enhancement will also be investigated. To accurately simulate long time propagations of strong field processes involving nonlinear higher order interactions, the PI will adopt adaptive numerical strategies. Multiscale schemes will be designed for the concurrent simulation of electrodynamics and quantum mechanical processes on the time domain. The PI will also conduct a thorough analysis of the algorithms in terms of convergence and stability.