Few ideas capture the imagination as vividly as cloaking, or rendering objects invisible to electromagnetic radiation. While escaping from long-winded meetings by turning ourselves invisible is not for tomorrow, investigations into this phenomenon are progressing at a rapid pace.

One way in which cloaking could work is by ‘bending’ light around an object: incoming light rays are deflected so that they pass around the object itself, and are then combined again to continue on their original path. Because the light rays appear to originate directly from the source, the object is effectively invisible.

The key here, of course, is precise control over the light path. Fundamentally the trajectory of a light ray is governed by the refractive indices of the media through which it propagates. Carefully controlling the path then, to achieve cloaking, requires a precise refractive index distribution of the material surrounding the object. While we cannot hope to find such materials in nature, the field of artificial metamaterials should be up to the task in the near future.

Yet designing practical metamaterials is only part of the puzzle, as we need to have an idea of what the refractive index distribution should look like in the first place. It is here that a recent breakthrough was reported by Ulf Leonhardt, University of St Andrews, UK, and Tomás Tyc, Masaryk University, Czech Republic [Leonhardt and Tyc, Science (2009) 323, 111]. Their discovery extends a previous approach in which researchers start out with a homogenous, flat medium, with propagating light rays, and determine the mathematical coordinate transforms required to distort this space so that light effectively passes around an empty ‘hole’, where an object could be hidden. Knowing these transforms, the required refractive index distribution can then be determined.

While powerful, this approach results in some points having extreme refractive indices, and fails if the light is not monochromatic. Leonhardt explains: “within these devices, cloaking works only when no new information is transmitted, when nothing changes. So the waves have to be completely stationary - they must oscillate at only one frequency.”

The innovation in their study is in deriving the coordinate transforms from a conceptual medium that is not flat, but can bend parallel light waves so that they meet – thus the ‘non-euclidean’.

“By calculating the refractive index distribution in this way,” Leonhardt continues, “the implementation does not demand extreme optical properties such as infinities or zeros of the speed of light, and should allow broadband invisibility.”