OP: High Accuracy Modeling of Graphene Plasmonics in Three Dimensional Grating Structures

OP：三维光栅结构中石墨烯等离子体的高精度建模

• 批准号: 1813033
• 负责人: David Nicholls
• 金额: $ 27万
• 依托单位: University of Illinois at Chicago
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-07-15 至 2023-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1813033&HistoricalAwards=false
• 关键词: OP; Accuracy; Modeling; Graphene; Plasmonics

Since it was first isolated experimentally in 2004, graphene (a single layer of carbon atoms in a honeycomb lattice) has transformed the fields of plasmonics and photonics. Graphene has remarkable mechanical, chemical, and electronic properties, and is finding its way into devices of engineering interest from communications and military capabilities to medical sciences and biological sensing. Of particular note is graphene's semi-metallic character which permits one to tune its electrical properties. It is not surprising that extensive investigation of graphene has been conducted in the engineering community, however, there is very little to report in the applied mathematics literature. There is an opportunity to make valuable contributions. The goal of this project is to provide a rigorous mathematical framework for the study of graphene in grating structures and to describe a computational framework for highly accurate simulation of these models. With these, the project aims to guide the design of engineers to deliver devices of interest in a greatly expedited fashion.The family of High-Order Perturbation of Surfaces (HOPS) methods, which the Principal Investigator has developed over the past decade, are an ideal choice for the model at hand. However, further algorithmic enhancements and extensions are required to produce tools which will continue to be useful to practitioners. In particular, the project will advance the state of the art in the modeling, numerical simulation, and design of grating structures featuring two-dimensional materials with the following objectives: (1) While materials such as graphene have been incorporated into the existing models in two-dimensional, scalar configurations, these efforts must be extended to the case of three-dimensional vector electromagnetic simulations; (2) The Method of Transformed Field Expansions (TFE) is a stabilized HOPS algorithm with which one can not only derive rigorous existence, uniqueness, and analyticity results, but also provide highly accurate numerical approximations, and these recursions must be extended to the three-dimensional vector electromagnetic case; (3) The surface formulations advocated by the PI are affected by the choice of surface integral operator relating Dirichlet and Neumann traces, and the project will investigate the performance of Impedance-Impedance Operators which are free of the "Dirichlet Eigenvalues" which plague the straightforward Dirichlet-Neumann Operators used in previous implementations; (4) the PI and collaborators recently studied the statistical properties of scattering by random rough gratings and will include two-dimensional materials in three-dimensional structures into this framework as part of the project; and (5) In addition to using these HOPS methods to identify grating structures featuring graphene, the project also aims to design them for optimal performance.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.

由于它是在2004年首次在实验中分离的，因此石墨烯（蜂窝状晶格中的单层碳原子）改变了等离子体和光子学的场。石墨烯具有非凡的机械，化学和电子特性，并且正在进入工程感兴趣的设备，从通信和军事能力到医学科学和生物传感。特别值得注意的是石墨烯的半金属特征，它允许一个人调整其电气性能。毫不奇怪，在工程界对石墨烯进行了广泛的研究，但是在应用数学文献中几乎没有什么可报告的。有机会做出宝贵的贡献。该项目的目的是为光栅结构中的石墨烯提供严格的数学框架，并描述一个计算框架，以高度准确地模拟这些模型。有了这些，该项目旨在指导工程师的设计以极大的速度交付感兴趣的设备。高级表面扰动（HOP）方法的家族（主要研究人员在过去十年中都开发了）是一种手头模型的理想选择。但是，需要进一步的算法增强功能和扩展，以生产将继续对从业者有用的工具。特别是，该项目将在建模，数值模拟以及具有以下目标的二维材料的光栅结构的设计中推进最新技术：（1）虽然已经将诸如石墨烯之类的材料纳入了现有模型中二维标量配置，这些努力必须扩展到三维矢量电磁模拟的情况。 （2）转化场扩展的方法（TFE）是一种稳定的啤酒花算法，它不仅可以得出严格的存在，独特性和分析性结果，而且还提供了高度准确的数值近似值，并且必须将这些递归扩展到三种递归到这三种递归。 - 维载体电磁病； （3）PI提倡的表面配方受到与Dirichlet和Neumann Traces相关的表面积分操作员的选择，并且该项目将调查不受“ Dirichlet Eigenvalues”的阻抗 - 阻抗操作员的性能，这些算子不受欢迎，这会使直接陷入困境，这使这位痕迹不受欢迎。 Dirichlet-Neumann运营商在先前的实现中使用； （4）PI和合作者最近通过随机粗糙的光栅研究了散射的统计特性，并将在该框架中包括三维结构中的二维材料，作为项目的一部分； （5）除了使用这些啤酒花方法来识别具有石墨烯的光栅结构外，该项目还旨在设计它们以实现最佳性能。该奖项反映了NSF的法定任务，并被认为是通过使用该基金会的知识分子优点和评估来获得支持的更广泛的影响审查标准。

项目成果

Modal explicit filtering for large eddy simulation in discontinuous spectral element method

间断谱元法中大涡模拟的模态显式滤波

• DOI: 10.1016/j.jcpx.2019.100024
• 发表时间: 2019
• 期刊: Journal of Computational Physics: X
• 作者: Ghiasi, Zia;Komperda, Jonathan;Li, Dongru;Peyvan, Ahmad;Nicholls, David;Mashayek, Farzad
• 通讯作者: Mashayek, Farzad

Simulation of Localized Surface Plasmon Resonances in Two Dimensions via Impedance-Impedance Operators

• DOI: 10.1137/20m133066x
• 发表时间: 2021-01
• 期刊: SIAM J. Appl. Math.
• 作者: D. Nicholls;Xin Tong

On the consistent choice of effective permittivity and conductivity for modeling graphene

关于石墨烯建模中有效介电常数和电导率的一致选择

• DOI: 10.1364/josaa.430088
• 发表时间: 2021
• 期刊: Journal of the Optical Society of America A
• 作者: Hong, Youngjoon;Nicholls, David P.
• 通讯作者: Nicholls, David P.

A Rigorous Numerical Analysis of the Transformed Field Expansion Method for Diffraction by Periodic, Layered Structures

• DOI: 10.1137/20m131374x
• 发表时间: 2021-01
• 期刊: SIAM J. Numer. Anal.
• 作者: Youngjoon Hong;D. Nicholls

Periodic corrugations to increase efficiency of thermophotovoltaic emitting structures

周期性波纹可提高热光伏发射结构的效率

• DOI: 10.1063/1.5080548
• 发表时间: 2019
• 期刊: Applied Physics Letters
• 影响因子: 4
• 作者: Hong, Youngjoon;Otten, Matthew;Min, Misun;Gray, Stephen K.;Nicholls, David P.
• 通讯作者: Nicholls, David P.