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Communications in Mathematical Physics

, Volume 281, Issue 2, pp 369–385 | Cite as

Electromagnetic Wormholes via Handlebody Constructions

  • Allan Greenleaf
  • Yaroslav Kurylev
  • Matti Lassas
  • Gunther UhlmannEmail author
Article

Abstract

Cloaking devices are prescriptions of electrostatic, optical or electromagnetic parameter fields (conductivity \({\sigma(x)}\) , index of refraction n(x), or electric permittivity \({\epsilon(x)}\) and magnetic permeability \({\mu(x)}\)) which are piecewise smooth on \({\mathbb{R}^3}\) and singular on a hypersurface \({\Sigma}\) , and such that objects in the region enclosed by \({\Sigma}\) are not detectable to external observation by waves. Here, we give related constructions of invisible tunnels, which allow electromagnetic waves to pass between possibly distant points, but with only the ends of the tunnels visible to electromagnetic imaging. Effectively, these change the topology of space with respect to solutions of Maxwell’s equations, corresponding to attaching a handlebody to \({\mathbb{R}^3}\) . The resulting devices thus function as electromagnetic wormholes.

Keywords

Electrical Impedance Tomography Energy Solution North Pole Selfadjoint Extension Single Coating 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Allan Greenleaf
    • 1
  • Yaroslav Kurylev
    • 2
  • Matti Lassas
    • 3
  • Gunther Uhlmann
    • 4
    Email author
  1. 1.Department of MathematicsUniversity of RochesterRochesterUSA
  2. 2.Department of Mathematical SciencesLoughborough Univ.LoughboroughUK
  3. 3.Helsinki University of Technology, Institute of MathematicsHelsinkiFinland
  4. 4.Department of MathematicsUniversity of WashingtonSeattleUSA

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