Efficient and Adaptive Methods for Simulating Multiscale Effects in Optical Metamaterials
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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.