Journal
SIAM REVIEW
Volume 52, Issue 2, Pages 359-377Publisher
SIAM PUBLICATIONS
DOI: 10.1137/090757873
Keywords
electrical impedance tomography; cloaking; metamaterial; Dirichlet-to-Neumann map; Laplace's equation; inverse problem
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In this article we provide an accessible account of the essential idea behind cloaking, aimed at nonspecialists and undergraduates who have had some vector calculus, Fourier series, and linear algebra. The goal of cloaking is to render an object invisible to detection from electromagnetic energy by surrounding the object with a specially engineered metamaterial that redirects electromagnetic waves around the object. We show how to cloak an object against detection from impedance tomography, an imaging technique of much recent interest, though the mathematical ideas apply to much more general forms of imaging. We also include some exercises and ideas for undergraduate research projects.
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