CAREER: Robust and High-Performance Computational Methods for Simulating Metamaterial-Based Optical Devices

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The project centers around the development of novel computational approaches to simulate metamaterial-based optical devices. Such optical geometries allow one to manipulate light on a microscopic scale. The project addresses a critical need for robust and controllable numerical schemes that can reliably describe the optical response of complex microscale geometries. The project will enable a broader scientific community to perform direct numerical simulations of optical devices and will help to bridge the gap between physical theory and optical device engineering. In addition to the dissemination of the research to the scientific community, the PI will present the work to students through the proposed educational agenda targeting the graduate and undergraduate curriculum offered in the Department of Mathematics at Texas A&M University: a research-integrated, project-based graduate-level course that bridges the gap between numerical analysis and interdisciplinary research; a project-centered collaborative research program for undergraduate students that highlights interdisciplinary research and applied computational mathematics; and an accompanying summer school. The educational program will teach core competences in computational sciences highlighting collaborative research and the multidisciplinary character of the computational sciences. Efforts will be made to attract female and minority students to these undergraduate activities and stimulate their interest in exciting new research topics in scientific computing and optics.Modern nanoscale optical devices are based on an intricate interplay of incident electromagnetic waves and the electron structure of the nanodevice. The research component of the proposal is organized around two complementary directions addressing a critical need for robust and controllable numerical schemes that can reliably describe the optical response of complex nanoscale geometries: (i) The first research direction is concerned with the development and analysis of computational methods for simulating time-harmonic non-local conductivity responses. (ii) The second research direction will focus on the development and analysis of highly scalable and distributed time-stepping methods that couple time-dependent Maxwell's equations with 2D evolution equations modeling a subscale conductivity response. In both directions the PI will connect the algorithmic and numerical development to interdisciplinary applications. The numerical and algorithmic development will be carried out alongside a number of research collaborations that are concerned about the design and simulation of nanoscale optical devices for modulation and control of the path of light, and the validation of fluid mechanical models for electron response against recent experimental results. All these projects depend on a strong computational component which current methods do not provide and which is not available commercially.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.