Ideal materials make for perfect invisibility

13 Sep 2007

Swedish researchers have shown that an invisibility cloak must be made from ‘ideal’ materials to hide an object.

If you want to make a perfect invisibility cloak, you’d better use as ideal materials as possible, according to calculations done by physicists in Sweden. The team have scrutinized the mathematics behind invisibility and found that a cloak with “ideal” material parameters would hide an object – but that even the slightest deviation from these parameters would cause significant light scattering that could reveal the cloak to an observer (Phys. Rev. Lett. in publication).

First proposed theoretically in May last year and realized for microwaves five months later, the invisibility cloak has captured the imagination of the public and defence agencies alike. The idea is that metamaterials – artificial materials with exotic electromagnetic properties – can be designed to guide radiation around an object, like water flowing around a smooth stone.

A perfect cloak would need to make the light passing through its interior catch up with the light passing around it to prevent any scattering. Physicists think the only way to do this would be to make the phase velocity of light on the inner lining infinite by using a metamaterial with infinite values of permittivity and permeability, which is impossible. Still, because it is difficult to deal with infinite values numerically, there has been uncertainty over whether a metamaterial with even these ideal parameters would be able to render an object perfectly invisible, and hence how much of a deviation from the ideal parameters would be acceptable in a real device.

Min Qiu and co-workers from the Royal Institute of Technology have got around this problem using an analytical approach. They began by considering a cylindrical cloak, and examined the equations that relate the electric field of the light to the radius of the metamaterial layer. To prevent infinite values occurring at the innermost layer, they added a small perturbation to this radius, but then calculated what happened when they shrunk this perturbation closer to zero.

The team found that the light’s scattering did gradually disappear as the perturbation was reduced. However, they also found that just a tiny perturbation – for example 10^-99 of the inner radius – would still produce significant scattering. To an observer, claims Qiu, this scattering would appear as a thin line at the centre of the cloak that would gradually become more blurred as the perturbation was increased.

Ulf Leonhardt – one of the physicists who came up with the proposal for invisibility cloaks last year – told physicsworld.com that he thinks the theoretical sensitivity to perturbations is very interesting. But he pointed out that the experimental device demonstrated last year by researchers at Duke University in the US worked very well, suggesting that the sensitivity might not be that important in real devices.