A Novel Finite Element Method Toolbox for Interface Phenomena in Plasmonic Structures

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The research in this project will lead to the development of an efficient computational platform that will provide valuable insight into this physical problem of light scattering. The overarching goal is to provide a toolbox that can be used by several communities to accurately compute the electromagnetic field, complementing experimental measurements. The research will advance knowledge in several fields by filling a gap in the theory and mathematical modeling of electromagnetic fields in exotic structures. The project is designed to include an interdisciplinary (computer science, physics, mathematics), team-based approach with graduate training. The team will focus on creating applied math research results that directly impact current and future experiments. The project includes activities to organize mini-symposia at conferences to foster discussions with other researchers. This research project will be used as a recruiting tool to further promote women and underrepresented minorities in STEM-fields. The goal of this project is to develop a state-of-the-art computational and mathematical platform that accurately and efficiently capture the multiscale behaviors of the electromagnetic field in plasmonic structures. Plasmonic structures are commonly made of metals and dielectrics, and exhibit at optical frequencies surface electromagnetic waves at the metal-dielectric interfaces, called surface plasmons. Over the past decades there has been a great interest to guide and confine surface plasmons in nanophotonic devices, with applications to antennas, cloaking, and others. Surface plasmons are sub-wavelength, hyper-singular near corners, and consequently highly sensitive to the geometry. Commercial software commonly used by scientists and engineers is based on the finite element method, and poorly approximates the electromagnetic near-field in these exotic structures. There is a need for an adapted mathematical framework to capture the multiple scales, and for numerical approaches for computing the electromagnetic field in plasmonic structures to avoid inaccurate predictions. This project will develop a finite element based approach to address this problem that involves specific treatments near the interface the accurately capture the surface plasmons, and a functional framework to extract the highly oscillatory behaviors of the electromagnetic near-field. Specific work includes: (1) solve plasmonic problems for any 2D geometries in a classical framework, (2) solve plasmonic problems for any 2D geometries when hyper-singular behaviors appear, and (3) extend the framework to 3D plasmonic problems and other plasmonic models. Results from this project will lead to insights into the underlying physics, develop accurate methods, and apply them to realistic problems.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.