Communications in Mathematical Physics

, Volume 317, Issue 2, pp 485-502

First online:

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

  • Habib AmmariAffiliated withDepartment of Mathematics and Applications, Ecole Normale Supérieure Email author 
  • , Hyeonbae KangAffiliated withDepartment of Mathematics, Inha University
  • , Hyundae LeeAffiliated withDepartment of Mathematics, Inha University
  • , Mikyoung LimAffiliated withDepartment of Mathematical Sciences, Korean Advanced Institute of Science and Technology

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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.