CBMS Conference: Mathematical Foundations of Transformation Optics

Howard University, Washington DC

Investigators

Abstract

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.