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Electromagnetic Metamaterials
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Electromagnetic Metamaterials and their
Approximations:
Practical and Theoretical Aspects
CSIC Building (#406),
Seminar Room 4122.
Directions: home.cscamm.umd.edu/directions
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Near-cloaking by
Change of Variables at Finite Frequency I:
an Approach using Lossy Layers
Professor
Robert Kohn
New York University
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Abstract:
We say a region of space is "cloaked" with respect
to electromagnetic measurements if its contents --
and even the existence of the cloak -- are
inaccessible to such measurements. One recent
proposal for such cloaking takes advantage of the
coordinate-invariance of Maxwell's equations. As
usually presented, this scheme uses a singular
change of variables. That makes the mathematical
analysis subtle, and the practical implementation
difficult.
This talk examines the correctness and robustness of
the change-of-variable-based scheme, for scalar
waves modelled by Helmholtz's equation, drawing on
joint work with Onofrei, Shen, Vogelius, and
Weinstein. The central idea is to use a
less-singular change of variables. The quality of
the resulting "approximate cloak" can be assessed by
studying the detectability of a small inclusion in
an otherwise uniform medium.
We show that a small inclusion can be made nearly
undetectable (regardless of its contents) by
surrounding it with a suitable lossy layer. The
corresponding approximate cloak has an anisotropic
lossy layer just outside the cloaked region.
Our results suggest that effective cloaking at
finite frequency may require the use of a lossy
layer. They also indicate that effective cloaking at
finite frequency should be easier in 3D than in 2D. |
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