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Center for Scientific Computation and Mathematical Modeling

Research Activities > Programs > Electromagnetic Metamaterials

Electromagnetic Metamaterials and their Approximations:
Practical and Theoretical Aspects

CSIC Building (#406), Seminar Room 4122.
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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

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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