tripping the light–fantastic · tripping the light–fantastic invisibility is no longer confined...

MM/61 The Mathematical Moments program promotes appreciation and understanding of the role mathematics plays in science, nature, technology, and human culture. www.ams.org/mathmoments Tripping the Light–Fantastic Invisibility 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. 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. We'll finish with this: For More Information: “Metamaterial Electromagnetic Cloak at Microwave Frequencies,” D. Schurig et al, Science, November 10, 2006. Image courtesy of Michael Bozec AMS Podcast Series Gunther Uhlmann, University of Washington

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Page 1: Tripping the Light–Fantastic · Tripping the Light–Fantastic Invisibility is no longer confined to fiction. In a recent experiment, microwaves were bent around a cylinder and

MM61

The Mathematical Moments program promotes appreciation and understanding of the role mathematics plays in science nature technology and human culture

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Tripping the LightndashFantastic

Invisibility 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 doesnt mean that were ready for invisible humans (or spaceships) but by using Maxwells equations which are partial differential equations fundamental to electromagnetics mathematicians have demonstrated that in some simple cases not seeing is believing too

Part of this successful demonstration of invisibility is due to metamaterialsndashelectromagnetic 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

Well finish with this

For More Information ldquoMetamaterial Electromagnetic Cloak at Microwave Frequenciesrdquo D Schurig et al Science November 10 2006

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AMS Podcast Series

Gunther Uhlmann University of Washington