Numerical Methods for Multiscale Modeling of Nano-Optics

该研究的主要目标是研究纳米级光学器件的多尺度和多物理模型的鲁棒，高效和准确的数值方法。纳米尺度的实验和制造技术已被证明是非常成功的，在生物医学工程和新材料工程中具有巨大的潜力。定量建模和仿真不仅有助于理解纳米器件的机理，而且还可以通过最小化试验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合作，研究光子驱动的纳米器件和原子科学。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，并将更好地准备使用建模，分析和计算的组合来解决现实问题。为了充分理解光子驱动的纳米和微型器件，PI将通过结合经典电动力学，推导电磁场，电子激发和分子运动之间相互作用的多尺度模型，含时电流密度泛函理论和线性响应区域中的Escherichfest分子动力学。采用自洽的多尺度格式对系统进行有效求解。还将研究金属增强。为了精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将采用自适应的数值策略。多尺度方案将被设计用于电动力学和量子力学过程在时域中的并行模拟。PI还将在收敛性和稳定性方面对算法进行彻底分析。

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 proven very successful with huge potentials in biomedical engineering and engineering of new materials. Quantitative modeling and simulation will not only help to understand the mechanism of nano devices, but will also greatly reduce the costs by minimizing trial errors and optimizing 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 using a combination of modeling, analysis and computations.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 in the time domain. The PI will also conduct a thorough analysis of the algorithms in terms of convergence and stability.