Invisibility-cloak design doesn't require faster-than-light propagation

St. Andrews, Scotland--An undergraduate physics student at the University of St. Andrews has figured out how to design an optical invisibility cloak that does not require superluminal (faster-than-light) propagation within it.¹

An invisibility cloak works by diverting light within it so that the light avoids a certain volume within which an object could be placed. In addition, the cloak also must reshape the exiting light so that it would be identical to what would be seen if the cloak weren't there. These two qualities would ideally make the object inside the cloak invisible.

In reality, such cloaks are very difficult to make operable at optical frequencies, because the ideal optical materials do not exist (although metamaterials have allowed certain small, less-than-perfect cloaks to be made). But because design is not necessarily constrained by practicality, all sorts of theoretical approaches to cloaking have been taken.

The faster-than-light problem

To design a cloak, the usual approach (based on metamaterials) is to use coordinate transformation to create hidden volumes where light can't reach. The most straightforward way to do this is to take a point in a Euclidean grid and expand it into a sphere, also transforming the space around it in a smooth way. The result is that things could be utterly hidden within the sphere. However, there's one big problem: light that skims the edge of the sphere would have to travel infinitely fast, which is impossible.

Another approach relies on non-Euclidean geometries: in this case, the light does not have to travel infinitely fast. However, the phase velocity of the light skimming the hidden volume would still have to travel a bit faster than the speed of light. This is possible, but just barely, for a narrow band of frequencies (note: the group velocity of this light is still subluminal; if that were not the case, then the laws of relativity would be broken). Such restrictions would make for a poorly operating cloak.

Maxwell's fish eye

The St. Andrews student, Janos Perczel, figured out how to make the entire light path within a cloak subluminal without losing its cloaking ability. He did this by inserting a transformed and mirrored Maxwell's fish-eye lens into the depths of the cloak; in the 2D model, this left an almond-shaped cavity into which things could be hidden. Perczel, who is part of Ulf Leonhardt's group, notes that although the model is 2D, a 3D version could be created as well. The optical properties of the metamaterial are still difficult to achieve, but tweaking the design could ease these constraints.

REFERENCE:

1. Janos Perczel et al., New Journal of Physics 13 (2011) 083007; doi:10.1088/1367-2630/13/8/083007.