Enhanced Approximate Cloaking by SH and FSH Lining

Abstract

We consider approximate cloaking from a regularization viewpoint introduced in [13] for EIT and further investigated in [12] [17] for the Helmholtz equation. The cloaking schemes in [12] and [17] are shown to be (optimally) within $|\ln \rho {|}^{-1}$ in 2D and $\rho$ in 3D of perfect cloaking, where $\rho$ denotes the regularization parameter. In this paper, we show that by employing a sound-hard layer right outside the cloaked region, one could (optimally) achieve ${\rho }^N$ in ${\mathbb{R}}^N,N\ge 2$, which significantly enhances the near-cloak. We then develop a cloaking scheme by making use of a lossy layer with well-chosen parameters. The lossy-layer cloaking scheme is shown to possess the same cloaking performance as the one with a sound-hard layer. Moreover, it is shown that the lossy layer could be taken as a finite realization of the sound-hard layer. Numerical experiments are also presented to assess the cloaking performances of all the cloaking schemes for comparisons.

References in corpus (6)

• Achieving transparency with plasmonic coatings
• Acoustic cloaking theory
• Confirmation of Cylindrical Perfect Invisibility Cloak Using Fourier-Bessel Analysis
• Full-wave invisibility of active devices at all frequencies
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Cited by in corpus (2)

• Regularized Transformation-Optics Cloaking for the Helmholtz Equation: From Partial Cloak to Full Cloak
• Approximate Isotropic Cloak for the Maxwell equations