Enhancement of near-cloaking. II: The Helmholtz equation. (English) Zbl 1260.35095
Summary: The aim of this paper is to extend the method of [the authors, Commun. Math. Phys. 317, No. 1, 253–266 (2013; Zbl 1303.35108)] 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.
MSC:
| 35P25 | Scattering theory for PDEs |
| 35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
| 35Q60 | PDEs in connection with optics and electromagnetic theory |
Citations:
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