Cloaking Devices, Electromagnetic Wormholes and Transformation Optics

Cloaking Devices, Electromagnetic Wormholes and Transformation Optics

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Copyright © by SIAM. Unauthorized reproduction of this article is prohibited. SIAM REVIEW c ° 2009 Society for Industrial and Applied Mathematics Vol. 51, No. 1, pp. 3–33 Cloaking Devices, Electromagnetic Wormholes, and Transformation Optics Allan Greenleaf Yaroslav Kurylev Matti Lassas § Gunther Uhlmann Abstract. We describe recent theoretical and experimental progress on making objects invisible to detection by electromagnetic waves. Ideas for devices that would once have seemed fanciful may now be at least approximately implemented physically using a new class of artiFcially structured materials called metamaterials . Maxwell’s equations have transformation laws that allow for the design of electromagnetic material parameters that steer light around a hidden region, returning it to its original path on the far side. Not only would observers be unaware of the contents of the hidden region, they would not even be aware that something was being hidden. An object contained in the hidden region, which would have no shadow, is said to be cloaked . Proposals for, and even experimental implementations of, such cloaking devices have received the most attention, but other designs having striking e±ects on wave propagation are possible. All of these designs are initially based on the transformation laws of the equations that govern wave propagation but, due to the singular parameters that give rise to the desired e±ects, care needs to be taken in formulating and analyzing physically meaningful solutions. We recount the recent history of the subject and discuss some of the mathematical and physical issues involved. Key words. cloaking, transformation optics, electromagnetic wormholes, invisibility AMS subject classiFcations. 78A40, 35P25, 35R30 DOI. 10.1137/080716827 1. Introduction. Invisibility has been a subject of human fascination for millen- nia, from the Greek legend of Perseus versus Medusa to the more recent The Invisible Man and the Harry Potter series. Over the years, there have been occasional sci- entiFc prescriptions for invisibility in various settings, e.g., [46, 6]. However, since Received by the editors ²ebruary 27, 2008; accepted for publication (in revised form) Septem- ber 5, 2008; published electronically ²ebruary 5, 2009. http://www.siam.org/journals/sirev/51-1/71682.html Department of Mathematics, University of Rochester, Rochester, NY 14627 (allan@math. rochester.edu). The work of this author was partially supported by NS² grant DMS-0551894. Department of Mathematics, University College London, Gower Street, London, WC1E 5BT, UK (ucahyku@ucl.ac.uk). The work of this author was partially supported by EPSRC grant EP/²034016/1. § Helsinki University of Technology, Institute of Mathematics, P.O. Box 1100, ²IN-02015, ²inland (Matti.Lassas@hut.F). The work of this author was partially supported by Academy of ²inland CoE Project 213476.
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Cloaking Devices, Electromagnetic Wormholes and Transformation Optics

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