Efficient and Adaptive Methods for Simulating Multiscale Effects in Optical Metamaterials

该项目的中心是开发新的计算方法来模拟超材料的光学性质。超材料是一种在微观尺度上操纵光的小型光学装置。该项目的一个重要方面是以公开可用的开放源码软件的形式传播开发的数值算法。因此，该项目将促进和促进需要强大计算组件的光学领域的研究方向。除了向科学界传播研究成果外，还将通过研究生课程、学生辅导以及大学内部研究和学生研讨会向学生介绍研究成果。特别是，PI计划开发一门关于光学问题的高级有限元方法的新的研究生水平课程。将努力吸引女性和少数族裔学生，并通过在高年级本科生的数值方法课程中展示和融入令人兴奋的新研究主题来激发他们的兴趣。超材料是专门设计的、周期性排列的微结构，具有不寻常的光学特性。在涉及超材料的散射过程的模拟中表现出的一个主要挑战是，它们具有明显的双尺度特征，这意味着相关的光学过程在非常不同的长度尺度上起作用。这是复杂的事实，现实的实验几何包含一维不连续在2D材料板材的边界。这种不连续会导致边缘效果，由于它们的主导和奇异行为，模拟起来很有挑战性。该项目的中心是开发和分析新的计算方法来模拟复杂光学器件中的散射过程，这些方法能够应对双尺度特性和边缘效应的发生：(1)将面向目标的局部网格加密和区域分解相结合的并行自适应有限元方法用于三维器件模拟，用于MPI并行化和预处理；(2)将开发和分析结合模型自适应策略的异质多尺度方法，以有效地采样有效的超材料参数；(3)将在两个研究方向上特别强调将算法和数字发展与跨学科应用相联系。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

The project centers on the development of novel computational approaches to simulate the optical properties of metamaterials. Metamaterials are small optical devices that manipulate light on a microscopic scale. An important aspect of the project is the dissemination of the developed numerical algorithms in form of publicly available open source software. As such the project will enable and foster research directions in optics that require a strong computational component. In addition to the dissemination of the research to the scientific community, results will be presented to students through graduate courses, mentoring of students, and university-internal research and student seminars. In particular, the PI plans to develop a new graduate-level course about advanced finite element methods for optical problems. Efforts will be made to attract female and minority students and stimulate their interest by presenting and incorporating exciting new research topics in numerical methods courses on upper-division undergraduate level.Metamaterials are specifically engineered, periodically aligned microstructures that exhibit unusual optical properties. A major challenge that manifests in the simulation of scattering processes involving metamaterials is that they are of pronounced two-scale character, meaning that relevant optical processes act on very different length scales. This is complicated by the fact that realistic experimental geometries contain 1D discontinuities at boundaries of the 2D material sheets. Such discontinuities cause edge effects that are challenging to simulate due to their dominant and singular behavior. The project centers around the development and analysis of novel computational approaches for the simulation of scattering processes in complex optical devices, that are able to cope with the two-scale character and the occurrence of edge effects: (1) a parallel and adaptive finite element method for 3D device simulations will be developed and implemented that combines goal-oriented local mesh refinement and domain decomposition for MPI parallelization and preconditioning; (2) a heterogeneous multiscale method will be developed and analyzed that incorporates model-adaptive strategies for an efficient sampling of effective metamaterial parameters; (3) special emphasis will be given in both research directions to connect the algorithmic and numerical development to interdisciplinary applications.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.