US-China-Germany Planning Visits: Direct and Inverse Scattering Methods for Periodic Structures with Arbitrary Profiles and Defects

美中德规划访问：具有任意轮廓和缺陷的周期性结构的直接和逆散射方法

• 批准号: 1427665
• 负责人: Jiguang Sun
• 金额: $ 3.67万
• 依托单位: Michigan Technological University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-07-01 至 2016-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1427665&HistoricalAwards=false
• 关键词: US; China; Germany; Planning; Visits

AbstractDirect and Inverse Scattering Methods for Periodic Structures with Arbitrary Profiles and DefectsPeriodic structures have many applications, such as solar energy, semiconductors, photonic crystals, medical imaging, and diffraction gratings. In solar energy, the solar thermal collectors are periodic arrays.The surface of a diffraction grating is made up with a periodic array of grooves. Optical waveguides have many cells of the same structure. The main subject of the proposed international collaboration is to develop fast and rigorous numerical simulations and inverse scattering techniques for periodic structures with arbitrary profiles and defects. The research is important to the analysis, design, and optimization of periodic structures and has been an active area for many mathematicians, scientists and engineers. The proposed research activities will lead to important progress for computational methods and mathematical theory for direct and inverse scattering problems for periodic structures with arbitrary profiles and imbedded defects. The research outcome will provide physicists and engineers useful tools to treat practical problemssuch as effect of incidence angle and the shadowing phenomenon of diffraction gratings. The first goal of the proposed research is to develop efficient and accurate numerical methods for wave propagation in periodic structures and bi-periodic structures with local defects. Due to the induced perturbed part of the scattered field by the defects, classic methods, such as the differential method, do not work in general. Based on the Limiting Absorption Principle, i.e., the solution for the periodic structure without absorption is the unique limit of the solutions as the absorption parameter tends to zero, the PI and his collaborators propose to employ an effective recursive doubling technique. Since the method can be further accelerated using super computers, it is realistic for practical industry applications with legions of identical cells for periodic structures.Detection of a compact inhomogeneity in a periodic structure has been a challenging problem, which is of interest by many engineers. For example, defects in memory chips and LCD electrodes have been a serious problem for years. Efficient and effective inverse scattering algorithms to detect/reconstruct defects are of great practical value. As the second goal, the PI plans to develop effective qualitative methods for the reconstruction of defects embedded in periodic structures.The qualitative methods avoid incorrect model assumptions and can provide extremely fast reconstruction. To the PI's knowledge, the proposed research is one the first attempts in the inverse scattering communityto effectively reconstruct defects in periodic structures with arbitrary geometric profiles and physical properties.

具有任意曲线和缺陷结构的周期结构的摘要直接和反向散射方法具有许多应用，例如太阳能，半导体，光子晶体，医学成像和衍射片段。在太阳能中，太阳能热收集器是周期性阵列。衍射光栅的表面由周期性的凹槽组成。光学波导具有许多相同结构的细胞。拟议的国际合作的主要主题是为具有任意特征和缺陷的周期性结构开发快速，严格的数值模拟和逆散射技术。这项研究对于周期性结构的分析，设计和优化至关重要，对于许多数学家，科学家和工程师来说，这是一个活跃的领域。提出的研究活动将为计算方法和数学理论带来重要的进展，以实现具有任意概况和嵌入缺陷的周期性结构的直接和反向散射问题。研究结果将为物理学家和工程师提供有用的工具来处理实际问题，以作为入射角的影响和衍射光栅的阴影现象。 拟议的研究的第一个目标是开发具有局部缺陷的周期性结构和双周期结构中的波浪传播的有效，准确的数值方法。由于缺陷诱发了散射场的扰动部分，因此经典方法（例如差异方法）通常不起作用。基于限制吸收原理，即无吸收的周期结构的溶液是溶液的独特限制，因为吸收参数趋于零，PI及其合作者建议采用有效的递归加倍技术。由于可以使用超级计算机进一步加速该方法，因此对于具有周期性结构的相同细胞的实用行业应用是现实的。定期结构中紧凑的不均匀性的检测是一个具有挑战性的问题，这是一个具有挑战性的问题，这是许多工程师的意义。例如，多年来，记忆芯片和LCD电极中的缺陷一直是一个严重的问题。有效且有效的逆散射算法检测/重建缺陷具有巨大的实用价值。作为第二个目标，PI计划开发有效的定性方法来重建嵌入周期性结构中的缺陷。定性方法避免了错误的模型假设，并可以提供非常快速的重建。据PI所知，拟议的研究是反向散射社区中的首次尝试，可以有效地重建具有任意几何谱和物理特性的周期性结构中的缺陷。