Invisibility cloak, part six

I’ve done plenty of blogging on cloak of invisibility tech, and here’s the latest news from PhysOrg.

From the second link:

A paper published in the March 2009 issue of SIAM Review, “Cloaking Devices, Electromagnetic Wormholes, and Transformation Optics,” presents an overview of the theoretical developments in cloaking from a mathematical perspective.

One method involves light waves bending around a region or object and emerging on the other side as if the waves had passed through empty space, creating an “invisible” region which is cloaked. For this to happen, however, the object or region has to be concealed using a cloaking device, which must be undetectable to electromagnetic waves. Manmade devices called metamaterials use structures having cellular architectures designed to create combinations of material parameters not available in nature.

Mathematics is essential in designing the parameters needed to create metamaterials and to show that the material ensures invisibility. The mathematics comes primarily from the field of partial differential equations, in particular from the study of equations for electromagnetic waves described by the Scottish mathematician and physicist James Maxwell in the 1860s.

One of the “wrinkles” in the mathematical model of cloaking is that the transformations that define the required material parameters have singularities, that is, points at which the transformations fail to exist or fail to have properties such as smoothness or boundness that are required to demonstrate cloaking. However, the singularities are removable; that is, the transformations can be redefined over the singularities to obtain the desired results.