Electromagnetic Resonance in Periodic Structures

周期性结构中的电磁共振

• 批准号: 0505833
• 负责人: Stephen Shipman
• 金额: --
• 依托单位: Louisiana State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-06-01 至 2008-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0505833&HistoricalAwards=false
• 关键词: Electromagnetic; Resonance; Periodic; Structures

Award abstract, DMS-0505833, S Shipman, Louisiana State UniversityTitle: Electromagnetic Resonance in Periodic StructuresThe subject is motivated by the abundance of analytical problemsgenerated by interesting phenomena of scattering and resonance ofelectromagnetic fields, which comprise a set of basic tools for thedesign of photo-electronic devices. The driving phenomenon is theexistence of photonic frequency stop-bands for periodically structuredmaterials, called photonic crystals, which is the source of therichness of their resonant behavior. One of the salient problems of currentinterest is anomalous transmission of source fields through periodicslabs near resonant frequencies, corresponding to weakly leaky guidedslab modes. The project addresses the mathematics of this and relatedproblems on several fronts: We use the complex-analytic theory ofboundary-integral operators to obtain asymptotic formulas for thestructure of transmission anomalies near non-robust slab modes; wepursue a development of the spectral theory for general open systems,such as leaky slabs, based on the concept of the unique conservativeextension of a dissipative system; and we investigate the existencetheory of modes and optimization of the associated resonant phenomena,as well as efficient numerical schemes for their simulation.Collaborators include S. Venakides, A. Figotin, D. Volkov, R. Lipton,and O. Bruno.Because of their capacity to block electromagnetic waves at selectedfrequencies and to trap energy, photonic crystals have become asubject of intense research in recent decades. Applications includehigh-efficiency lasers and filters, waveguides, and directionalantennas. Engineering of these devices relies on precise tuning ofresonant frequencies, transmission-vs.-frequency profiles, and theinteraction of open electromagnetic resonators with their surroundingmedium. This project aims to set the theoretical framework of theseresonant phenomena on a solid mathematical footing. The central themeis the frequency-response theory of open resonators, which providesthe framework for the guiding of light and other radiation bystructures, precise computation of the interaction of guided energywith applied sources, and optimization of resonant properties.Numerical computations and experimental results from the literaturewill guide the theoretical investigations. The project involves anundergraduate student and a graduate student as research assistants.The undergraduate has been assisting the PI in numerical simulationsand will be part of a collaboration with the computationalelectromagnetics group at Cal Tech. The graduate student will pursueher Ph.D. on the subject of resonant scattering by periodic pillars.

奖项摘要，DMS-0505833，S Shipman，路易斯安那州立大学题目：周期性结构中的电磁共振这门学科的动机是由电磁场散射和共振的有趣现象所产生的大量分析问题，这些问题包括一套用于设计光电器件的基本工具。 周期性结构材料（光子晶体）中存在的光子频率阻带是其共振行为丰富性的根源。 当前感兴趣的突出问题之一是源场在共振频率附近通过平板的异常传输，对应于弱漏导板模式。 该项目在几个方面解决了这一问题的数学和相关问题：我们使用边界积分算子的复分析理论来获得非鲁棒板模式附近透射异常结构的渐近公式;我们基于耗散系统的唯一保守扩展概念，致力于发展一般开放系统（如漏板）的谱理论;我们研究了模式的存在理论和相关共振现象的优化，以及有效的数值模拟方案。Venakides，A. Figotin，D.沃尔科夫河Lipton和O.由于光子晶体能够阻挡特定频率的电磁波并捕获能量，因此近几十年来，光子晶体已成为研究热点。 应用包括高效激光器和滤波器、波导和定向天线。 这些设备的工程依赖于精确调谐谐振频率，传输与频率分布，以及开放式电磁谐振器与周围介质的相互作用。 这个项目的目的是建立在坚实的数学基础上的理论框架这些共振现象。 中心主题是开放式谐振腔的频率响应理论，它提供了结构对光和其他辐射的引导、引导能量与应用源的相互作用的精确计算以及谐振特性的优化的框架，文献中的数值计算和实验结果将指导理论研究。 该项目涉及一名本科生和一名研究生作为研究助理，本科生一直在协助PI进行数值模拟，并将与加州理工学院的计算电磁学小组合作。 这个研究生将攻读博士学位。关于周期性柱体的共振散射的主题。