Direct and Inverse Electromagnetic Scattering Problems for Complex Periodic Media

复杂周期性介质的正向和逆向电磁散射问题

基本信息

批准号：
1812693
负责人：
Dinh-Liem Nguyen
金额：
$ 13万
依托单位：
Kansas State University
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：
2018-08-01 至 2022-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1812693&HistoricalAwards=false
关键词：
Direct Inverse Electromagnetic Scattering Problems

项目摘要

The interaction and scattering of light by periodic structures at the nanoscale is a topic of great significance in the area of nanophotonics and metamaterials technology. With the current rapid development of this enabling technology, there is a high demand on new mathematical theories and computational algorithms for both direct and inverse problems of the light scattering by periodic complex media or periodic metamaterials. This project aims to develop such theories and algorithms. Results from this project will advance knowledge, understanding and imaging techniques in the technology of nanophotonics and metamaterials. For instance, the mathematical theories and the computational algorithms developed for the direct problems are extremely useful for the simulation, fabrication and maintaining of optical devices. The imaging techniques developed for the inverse problems can be potentially of practical use for non-destructive tests, which help to detect and characterize discrete flaws in optical components and devices.The project contains two main areas of study: the mathematical and numerical analysis for direct scattering problems, and the development of efficient inversion algorithms for inverse scattering problems. More precisely, for the direct problem, the PI and his colleagues will work on the following topics: 1) develop volume integral equation formulations for direct scattering problems for periodic complex media; 2) develop fast integral equation-based numerical solvers for the direct scattering problems; 3) study interior transmission eigenvalues for periodic complex media; 4) study well-posedness of the scattering by chiral metamaterials. The proposed research for the inverse problem includes the topics: 1) develop sampling methods for imaging of periodic complex media; 2) develop sampling methods for the detection of local defects in photonic crystals; 3) develop globally convergent methods for the identification of material parameters for photonic crystals.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.

纳米级的周期性结构通过周期性结构对光的相互作用和散射是一个在纳米素和超材料技术领域具有重要意义的话题。随着这项有利技术的当前快速发展，对周期复杂媒体或周期性超材料的光散射直接和反向问题的新数学理论和计算算法的需求很高。该项目旨在开发此类理论和算法。该项目的结果将推进纳米素技术和超材料技术中的知识，理解和成像技术。例如，针对直接问题开发的数学理论和计算算法对于光学设备的仿真，制造和维护非常有用。为反问题开发的成像技术可能是用于非破坏性测试的实际用途，这有助于检测和表征光学组件和设备中的离散缺陷。该项目包含两个主要研究领域：用于直接散射问题的数学和数值分析，以及有效的逆转障碍问题的有效逆转差异散射问题。更确切地说，对于直接问题，PI及其同事将在以下主题上致力于：1）为定期复杂媒体的直接散射问题开发体积积分方程式公式； 2）为直接散射问题开发基于快速积分方程的数值求解器； 3）研究周期性复杂介质的内部传播特征值； 4）学习手性超材料散射的良好性。提议的反问题研究包括：1）开发用于成像周期性复杂介质的抽样方法； 2）开发采样方法，以检测光子晶体中的局部缺陷； 3）开发用于识别光子晶体的材料参数的全球收敛方法。该奖项反映了NSF的法定任务，并且使用基金会的知识分子优点和更广泛的影响审查标准，被认为值得通过评估来获得支持。