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设备。这种光学几何结构允许人们在微观尺度上操纵光。该项目解决了对能够可靠地描述复杂微尺度几何图形的光学响应的健壮和可控的数值格式的迫切需要。该项目将使更广泛的科学界能够对光学设备进行直接的数值模拟，并将有助于弥合物理理论和光学设备工程之间的差距。除了向科学界传播研究成果外，PI还将通过针对德克萨斯A&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展示这项工作：一个以研究为基础的研究生课程，它弥合了数值分析和跨学科研究之间的差距；一个面向本科生的以项目为中心的合作研究计划，突出跨学科研究和应用计算数学；以及伴随而来的暑期班。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。将努力吸引女性和少数族裔学生参加这些本科生活动，并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。现代纳米级光学设备是基于入射电磁波和纳米设备的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方向进行组织，以满足对能够可靠地描述复杂纳米尺度几何图形的光学响应的健壮和可控的数值格式的迫切需要：(I)第一个研究方向涉及用于模拟时间谐和非局部电导率响应的计算方法的开发和分析。(Ii)第二个研究方向将集中于开发和分析高度可伸缩的分布式时间步长方法，该方法将时间相关的麦克斯韦方程与模拟亚尺度电导率响应的二维演化方程相结合。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，这些研究合作涉及用于调制和控制光路的纳米级光学设备的设计和模拟，以及针对最近的实验结果验证电子响应的流体力学模型。所有这些项目都依赖于强大的计算组件，这是目前的方法所不提供的，也是商业上无法获得的。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 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.