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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.

纳米尺度上周期性结构对光的相互作用和散射是纳米光子学和超材料技术领域中一个具有重要意义的课题。随着这一使能技术的迅速发展，对周期复杂介质或周期超材料的光散射正问题和反问题的新的数学理论和计算算法提出了更高的要求。该项目旨在开发这样的理论和算法。该项目的成果将促进纳米光子学和超材料技术方面的知识、理解和成像技术。例如，为正问题开发的数学理论和计算算法对光学器件的模拟、制造和维护非常有用。为反问题开发的成像技术可用于无损检测，有助于检测和表征光学元件和器件中的离散缺陷。该项目包括两个主要研究领域：直接散射问题的数学和数值分析，以及反散射问题的高效反演算法的发展。更准确地说，对于正问题，Pi和他的同事们将在以下方面开展工作：1)建立周期复杂介质直接散射问题的体积积分方程公式；2)开发基于积分方程的直接散射问题的快速数值求解器；3)研究周期复杂介质的内部传输本征值；4)研究手性超材料散射的适定性。建议的反问题研究包括：1)开发周期性复杂介质成像的采样方法；2)开发检测光子晶体局部缺陷的采样方法；3)开发识别光子晶体材料参数的全局收敛方法。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。