3 research outputs found
A rigorous analysis of high order electromagnetic invisibility cloaks
There is currently a great deal of interest in the invisibility cloaks
recently proposed by Pendry et al. that are based in the transformation
approach. They obtained their results using first order transformations. In
recent papers Hendi et al. and Cai et al. considered invisibility cloaks with
high order transformations. In this paper we study high order electromagnetic
invisibility cloaks in transformation media obtained by high order
transformations from general anisotropic media. We consider the case where
there is a finite number of spherical cloaks located in different points in
space. We prove that for any incident plane wave, at any frequency, the
scattered wave is identically zero. We also consider the scattering of finite
energy wave packets. We prove that the scattering matrix is the identity, i.e.,
that for any incoming wave packet the outgoing wave packet is the same as the
incoming one. This proves that the invisibility cloaks can not be detected in
any scattering experiment with electromagnetic waves in high order
transformation media, and in particular in the first order transformation media
of Pendry et al. We also prove that the high order invisibility cloaks, as well
as the first order ones, cloak passive and active devices. The cloaked objects
completely decouple from the exterior. Actually, the cloaking outside is
independent of what is inside the cloaked objects. The electromagnetic waves
inside the cloaked objects can not leave the concealed regions and viceversa,
the electromagnetic waves outside the cloaked objects can not go inside the
concealed regions. As we prove our results for media that are obtained by
transformation from general anisotropic materials, we prove that it is possible
to cloak objects inside general crystals.Comment: The final version is now published in Journal of Physics A:
Mathematical and Theoretical, vol 41 (2008) 065207 (21 pp). Included in
IOP-Selec
The Boundary Conditions for Point Transformed Electromagnetic Invisibility Cloaks
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, , and at the
inside, , of the boundary of the cloaked object . Namely, that
the tangential components of the electric and the magnetic fields have to
vanish at -what is always true- and that the normal components
of the curl of the electric and the magnetic fields have to vanish at . These results are proven requiring that energy be conserved. In the case
of one spherical cloak with a spherically stratified and a radial current
at 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.Comment: This final, published, version has been edited, comments have been
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