(15) David Schurig
North Carolina State University, USA.

Title:Transformation Design for Imaging and Communications

Abstract:

Transformation design, the use of coordinate transforms and differential topology to obtain a material specification, is best known for its connection to invisibility cloaks. However, it is a general tool that allows one to find (often complex) material specifications that exert unprecedented and intuitive control over fields. Often it is straightforward to imagine a distorted spatial topology wherein the embedded field excitations behave in a useful or interesting manner. Recording this topology in a coordinate transform, one is then able to directly calculate a set of material properties which provide the same effect on the fields. Though complex (i.e.
inhomogeneous and anisotropic) these material specifications can often be realized, at least in principle, using metamaterials.

The application to invisibility cloaking has certainly captured the imagination of both the scientific and lay community. However, the method will likely make its biggest impact in the commercially important application areas of imaging and communications.

I will discuss some mathematical concepts of the method that are perhaps somewhat fuzzily understood, including: tensor densities and coordinate versus non-coordinate bases. Applications to imaging will be discussed and used to highlight these mathematical concepts and the generality of the method.