The Boundary Conditions for Point Transformed Electromagnetic Invisibility Cloaks

Abstract

In this paper we study point transformed electromagnetic invisibility cloaks in transformation media that are obtained by transformation from general anisotropic media. We assume that there are several cloaks located in different points in space. Our results apply in particular to the first order invisibility cloaks introduced by Pendry et al. and to the high order invisibility cloaks introduced by Hendi et al. and by Cai et al.. We identify the appropriate {\it cloaking boundary conditions} that the solutions of Maxwell equations have to satisfy at the outside, $\partial K_{+}$, and at the inside, $\partial K_{-}$, of the boundary of the cloaked object $K$. Namely, that the tangential components of the electric and the magnetic fields have to vanish at $\partial K_{+}$ -what is always true- and that the normal components of the curl of the electric and the magnetic fields have to vanish at $\partial K_{-}$. These results are proven requiring that energy be conserved. In the case of one spherical cloak with a spherically stratified $K$ and a radial current at $\partial K$ we verify by an explicit calculation that our {\it cloaking boundary conditions} are satisfied and that cloaking of active devices holds even if the current is at the boundary of the cloaked object. As we prove our results for media that are obtained by transformation from general anisotropic media, our results apply to the cloaking of objects with active and passive devices contained in general anisotropic media, in particular to objects with active and passive devices contained inside general crystals.

This final, published, version has been edited, comments have been added

References in corpus (6)

• Confirmation of Cylindrical Perfect Invisibility Cloak Using Fourier-Bessel Analysis
• Full-wave invisibility of active devices at all frequencies
• Extraordinary surface voltage effect in the invisibility cloak with an active device inside
• Effectiveness and improvement of cylindrical cloaking with the SHS lining
• Coordinate transformation makes perfect invisibility cloak with arbitrary shape
• A rigorous analysis of high order electromagnetic invisibility cloaks

Cited by in corpus (2)

• Silicon nanostructure cloak operating at optical frequencies
• Ground-Plane Quasi-Cloaking for Free Space