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

该项目的中心是开发新的计算方法来模拟基于超材料的光学器件。这种光学几何形状允许人们在微观尺度上操纵光。该项目解决了一个强大的和可控的数值方案，可以可靠地描述复杂的微尺度几何形状的光学响应的关键需求。该项目将使更广泛的科学界能够对光学器件进行直接的数值模拟，并将有助于弥合物理理论和光学器件工程之间的差距。除了向科学界传播研究成果外，PI还将通过针对德克萨斯州A M大学数学系提供的研究生和本科生课程的拟议教育议程向学生介绍这项工作&：一个研究综合的，基于项目的研究生课程，弥合数值分析和跨学科研究之间的差距;一个以项目为中心的合作研究计划，为本科生，突出跨学科研究和应用计算数学;和一个伴随的暑期学校。该教育计划将教授计算科学的核心能力，突出合作研究和计算科学的多学科特征。将努力吸引女生和少数民族学生参加这些本科生活动，激发他们对科学计算和光学领域令人兴奋的新研究课题的兴趣。现代纳米级光学器件是基于入射电磁波和纳米器件电子结构的复杂相互作用。该提案的研究部分围绕两个互补的方向组织，解决对能够可靠地描述复杂纳米级几何结构的光学响应的稳健和可控数值方案的关键需求：㈠第一个研究方向涉及模拟时谐非局部电导率响应的计算方法的开发和分析。(ii)第二个研究方向将侧重于高度可扩展和分布式时间步进方法的开发和分析，该方法将时间相关的麦克斯韦方程与模拟子尺度电导率响应的2D演化方程相结合。在这两个方向上，PI将把算法和数值开发与跨学科应用联系起来。数值和算法的开发将与一些研究合作一起进行，这些合作涉及用于调制和控制光路的纳米级光学器件的设计和模拟，以及针对最近实验结果的电子响应的流体力学模型的验证。所有这些项目都依赖于一个强大的计算组件，目前的方法不提供，这是不可商业化的。这个奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

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.