Waves and Resonance in Photonic Structures

该奖项支持的研究将发展驱动光子设备功能的物理现象的数学基础。具体目标包括开发(1)模型，例如在平板结构中，允许根据设备的某些可测量数据预测共振电磁散射行为的详细结果，(2)用于优化设备的某些输出的算法，如光子状态的能量传输或密度，以及(3)探索新的方向，尤其是具有负折射率成分的复合材料中的波。这些问题将用严格的数学方法来解决，包括微扰理论、偏微分方程组理论、齐次化理论和复变函数理论。该奖项资助的研究是受到现有和未来光电设备(包括成像设备、激光和天线)的工程和制造中出现的热点问题和挑战的启发。许多问题涉及已知了一百多年的物理现象，但由于最近人们认识到光子晶体和相关结构控制光路的潜力，这些现象以新的、基本上未被探索的方式显现出来。其他问题与新材料或超材料的开发有关，这种材料具有以自然材料无法实现的方式操纵电和磁的能力。研究生参与研究议程是该项目不可或缺的一部分。三名学生将作为研究助理得到支持，因为他们接受了数学研究职业的培训。由PI指导的一名本科生也参与了与超材料有关的调查。通过与路易斯安那州立大学物理系和电气工程系的科学家以及路易斯安那州立大学计算与技术中心的同事合作，国际和平研究所将加强和丰富这些研究。

The research supported with this award will develop the mathematical foundations of the physical phenomena that drive the functionality of photonic devices. Specific objectives include the development of (1) models, for example in slab structures, that allow a prediction of detailed outcomes of resonant electromagnetic scattering behavior based on certain measurable data for the device, (2) algorithms for optimization of certain output of devices, as the energy transmission or density of photonic states, and (3) exploration of new directions, in particular, waves in composite materials with negative-index components. These problems will be approached with rigorous mathematical methods, including perturbation theory, the theory of partial differential equations, homogenization, and complex function theory.The research funded by this award is inspired by topical problems and challenges arising in the engineering and fabrication of existing and future opto-electronic devices, including imaging devices, lasers, and antennas. Many of the problems deal with physical phenomena that have been known for over a hundred years but which, because of recent recognition of the potential of photonic crystals and related structures to control the path of light, manifest themselves in new and largely unexplored ways. Other problems are concerned with the development of novel materials, or meta-materials, which have the capacity to maneuver electricity and magnetism in ways that cannot be achieved using naturally-occuring materials. The involvement of graduate students in the research agenda is an integral part of the project. Three students will be supported as research assistants as they are trained for careers in mathematical research. An undergraduate student mentored by the PI is involved as well in the investigations pertaining to meta-materials. The investigations will be strengthened and enriched through the PI's collaboration with scientists in the Physics and Electrical Engineering Departments at LSU, as well as with colleagues affiliated with the Center for Computation and Technology at LSU.