Communications in Mathematical Physics

, Volume 317, Issue 2, pp 485–502

Enhancement of Near-Cloaking. Part II: The Helmholtz Equation


    • Department of Mathematics and ApplicationsEcole Normale Supérieure
  • Hyeonbae Kang
    • Department of MathematicsInha University
  • Hyundae Lee
    • Department of MathematicsInha University
  • Mikyoung Lim
    • Department of Mathematical SciencesKorean Advanced Institute of Science and Technology

DOI: 10.1007/s00220-012-1620-y

Cite this article as:
Ammari, H., Kang, H., Lee, H. et al. Commun. Math. Phys. (2013) 317: 485. doi:10.1007/s00220-012-1620-y


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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© Springer-Verlag Berlin Heidelberg 2012