CBMS Conference: Mathematical Foundations of Transformation Optics

该奖项将支持将于2014年夏天在华盛顿的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。主讲人是来自罗切斯特大学的艾伦·格林利夫教授。讲座将涵盖有关变换光学设计的理论基础的主题，如斗篷，场旋转器和电磁虫洞，以及在试图物理实现它们时出现的一些问题。要讨论的领域包括不同类型的波的传播，方程，支配他们，以及他们如何变换下的变量的变化;理想的隐形电和热静力学，标量光学和声学，以及电磁波;近似隐形;和共振既是困难和机遇。除了Greenleaf教授的主要演讲外，魏茨曼研究所的Ulf Leonhardt教授将发表关于物理学界观点的演讲。休斯顿大学的丹尼尔·奥诺弗雷教授将作进一步的讲座，他将讨论隐身的其他方法和数值方法。在过去的七年里，人们对隐身装置的设计、分析、模拟和实际应用产生了极大的兴趣。物理学和工程学的这一领域适合于对波传播有根本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）到声波到热流到量子力学中的物质波。许多隐身和相关设备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化的复合材料，称为超材料。使用变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、热波还是其他波。设计对许多类型的波传播具有根本影响的设备的能力具有巨大的潜在应用，从军事到工业到医疗到娱乐。拥有更大范围的设备或性能更好的设备，或者对它们的局限性有更清醒的认识，将具有很大的价值。这些讲座将解决的理论背景和使用这些技术设计的设备的一些实际限制。

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.