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Mathematical Moments: Tripping the Light-Fantastic

Half-cloaked spaceshipInvisibility is no longer confined to fiction. In a recent experiment, microwaves were bent around a cylinder and returned to their original trajectories, rendering the cylinder almost invisible at those wavelengths. This doesn't mean that we're ready for invisible humans (or spaceships), but by using Maxwell's equations, which are partial differential equations fundamental to electromagnetics, mathematicians have demonstrated that in some simple cases not seeing is believing, too. Image courtesy of Michael Bozec.

Part of this successful demonstration of invisibility is due to metamaterials– electromagnetic materials that can be made to have highly unusual properties. Another ingredient is a mathematical transformation that stretches a point into a ball, "cloaking" whatever is inside. This transformation was discovered while researchers were pondering how a tumor could escape detection. Their attempts to improve visibility eventually led to the development of equations for invisibility. A more recent transformation creates an optical "wormhole," which tricks electromagnetic waves into behaving as if the topology of space has changed.

Gunther Uhlmann
Gunther Uhlmann
University of Washington

Listen to Gunther Uhlmann speak about mathematics and invisibility.

For More Information: “Metamaterial Electromagnetic Cloak at Microwave Frequencies,” D. Schurig et al, Science, November 10, 2006.