Abstract
The aim of this paper is to extend the method of Ammari et al. (Commun. Math. Phys., 2012) to scattering problems. We construct very effective near-cloaking structures for the scattering problem at a fixed frequency. These new structures are, before using the transformation optics, layered structures and are designed so that their first scattering coefficients vanish. Inside the cloaking region, any target has near-zero scattering cross section for a band of frequencies. We analytically show that our new construction significantly enhances the cloaking effect for the Helmholtz equation.
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Communicated by S. Zelditch
This work was supported by ERC Advanced Grant Project MULTIMOD–267184 and National Research Foundation through grants No. 2009-0085987, 2010-0017532 and 2010-0004091.
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Ammari, H., Kang, H., Lee, H. et al. Enhancement of Near-Cloaking. Part II: The Helmholtz Equation. Commun. Math. Phys. 317, 485–502 (2013). https://doi.org/10.1007/s00220-012-1620-y
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DOI: https://doi.org/10.1007/s00220-012-1620-y