CBMS Conference: Mathematical Foundations of Transformation Optics

该奖项将支持2014年夏天在华盛顿霍华德大学举行的关于变换光学数学基础的NSF/CBMS区域会议。主讲嘉宾是罗切斯特大学的艾伦·格林利夫教授。讲座将涵盖变换光学设计的理论基础，例如隐形、场旋转器和电磁虫洞，以及在尝试物理实现它们时出现的一些问题。讨论的领域包括不同类型的波传播，控制它们的方程，以及它们如何在变量变化下变换；静电和热静态、标量光学和声学以及电磁波的理想隐身材料；近似隐形;共鸣既是困难也是机遇。除了格林利夫教授的主讲外，魏茨曼研究所的乌尔夫·莱昂哈特教授还将主讲物理界的观点。休斯敦大学的Daniel Onofrei教授将提供进一步的讲座，他将讨论其他的隐形方法和数值方法。在过去的七年里，人们对隐形设备的设计、分析、模拟和实际实现产生了极大的兴趣。物理学和工程学的这一领域适用于对波传播具有根本性影响的材料和设备的更广泛的持续发展，其中所讨论的波可以从电磁（包括可见光）到声波，从热流到量子力学中的物质波。许多隐形和相关装置的设计都是基于描述这些波的方程的变换规则，这一领域现在被称为变换光学。这些设计的物理实现是使用结构复合材料（称为超材料）创建的。使用转换光学设计并使用超材料实现的设备有可能从根本上改变技术操纵波的方式，无论是电磁波、声波、热波还是其他。设计对多种类型的波传播具有根本性影响的设备的能力具有广泛的潜在应用，从军事到工业，从医疗到娱乐。拥有更大范围的设备或性能更好的设备，或者就此而言，对它们的局限性有更清醒的认识，将是很有价值的。这些讲座将讨论使用这些技术设计的器件的理论背景和一些实际限制。

This award will support an NSF/CBMS regional conference to be held at Howard University in Washington, DC in the summer of 2014 on the mathematical foundations of transformation optics. The principal speaker will be Prof. Allan Greenleaf from the University of Rochester. The lectures will cover topics concerning both the theoretical basis for transformation optics designs, such as cloaks, field rotators and electromagnetic wormholes, and some of the issues which arise in trying to physically realize them. Areas to be discussed include different types of wave propagation, the equations that govern them, and how they transform under changes of variables; ideal cloaking for electro- and thermal statics, for scalar optics and acoustics, and for electromagnetic waves; approximate cloaking; and resonances as both difficulties and opportunities. In addition to the main lectures by Prof. Greenleaf, a lecture on the view from the physics community will be given by Prof. Ulf Leonhardt of the Weizmann Institute. Further additional lectures will be presented by Prof. Daniel Onofrei of the University of Houston, who will discuss both other approaches to cloaking and numerical methods.The last seven years have seen an explosion of interest in the design, analysis, simulation and actual implementation of cloaking, or invisibility, devices. This area of physics and engineering fits into a broader ongoing development of materials and devices that have radical effects on wave propagation, where the waves in question can range from electromagnetism (including visible light) to acoustic waves to heat flow to matter waves in quantum mechanics. Many of the designs for cloaking and related devices are based on the transformation rules for the equations that describe these waves, an area that is now referred to as transformation optics. Physical realization of these designs are created using structured composite materials, called metamaterials. Devices designed using transformation optics and implemented using metamaterials have the potential to radically change the way that technology manipulates waves, whether they be electromagnetic, acoustic, thermal or other. The ability to design devices with radical effects on wave propagation of many types has enormously varied potential applications, ranging from military to industrial to medical to entertainment. Having a greater range of devices or better performing ones, or for that matter a more sober view of their limitations, will be of great value. These lectures will address both the theoretical background and some of the practical limitations on devices designed using these techniques.