Shape of things to comeA simpler route to invisibility

Two years ago researchers at Duke University unveiled the first invisibility cloak — a device that can make objects vanish from sight, at least when viewed using a narrow band of microwave frequencies (see 4 September 2008 HS Daily Wire). Such cloaks work by causing electromagnetic waves to flow smoothly around the object and recombine on the other side, making it appear that the waves traveled straight through the object unhindered.

PhysicsToday’s Hamish Johnston writes that since then physicists have struggled to create cloaks that work across a wider range of frequencies and could be used, for example, to hide an object from radar. Now, Ulf Leonhardt of St. Andrew’s University in the United Kingdom and Tomás Tyc of Masaryk University in the Czech Republic have come up with a new way of using mathematics to describe a invisibility cloak — a breakthrough that the physicists say could lead to the development of broadband invisibility cloaks.

Johnston notes that, from a mathematical point of view, an invisibility cloak can be described as a transformation of flat space that makes the light follow a curved path around the object. “The idea is to make a coordinate transformation that takes a point in space and expands it into a sphere, the interior of which is invisible to an observer on the outside.” For this to work light must traverse the surface of the sphere in the same, infinitesimally short time it would take to pass the original point. As a result, the light must travel at an infinitely high speed on the surface of the sphere.

Now, the phase velocity of light can approach infinity in some materials and metamaterials (without, Johnston hastens to add, violating the special theory of relativity because the “signal velocity” remains the speed of light). This has allowed the Duke team and others to actually build invisibility cloaks. The problem, however, is this only occurs for light at certain resonant frequencies.

Leonhardt and Tyc made their theoretical breakthrough by using non-Euclidean geometry to describe the workings of their cloak. Non-Euclidean geometry could be used to define the index of refraction at a specific point in the cloak — and for light traveling in a specific direction. It will be a challenge actually to engineer a material to have an index of refraction that varies just so, but Leonhardt told physicsworld.com “I’m sure it can be done, technical challenges certainly need to be overcome, but no longer principal problems.”

-read more in Ulf Leonhardt and Tomás Tyc, “Broadband Invisibility by Non-Euclidean Cloaking, Science (20 November 2008) (DOI: 10.1126/science.1166332)