On regularized full- and partial-cloaks in acoustic scattering

TL;DR

This paper provides precise quantitative estimates for the convergence of regularized acoustic cloaks, demonstrating near-perfect cloaking for arbitrary contents and relaxing previous geometric constraints on the cloaking surface.

Contribution

It introduces sharp estimates for regularized full- and partial-acoustic cloaks, extending prior results by removing convexity restrictions on the cloaking set.

Findings

Approximate full-cloak within δ^2 for generic curves.

Approximate partial-cloak within δ for flat surface subsets.

Cloaking devices are effective regardless of cloaked content.

Abstract

The aim of this work is to derive sharp quantitative estimates of the qualitative convergence results developed in [28] for regularized full- and partial-cloaks via the transformation-optics approach. Let $\Gamma_0$ be a compact set in $\mathbb{R}^3$ and $\Gamma_\delta$ be a $\delta$-neighborhood of $\Gamma_0$ for $\delta\in\mathbb{R}_+$. $\Gamma_\delta$ represents the virtual domain used for the blow-up construction. By incorporating suitably designed lossy layers, it is shown that if the generating set $\Gamma_0$ is a generic curve, then one would have an approximate full-cloak within $\delta^2$ to the perfect full-cloak; whereas if $\Gamma_0$ is the closure of an open subset on a flat surface, then one would have an approximate partial-cloak within $\delta$ to its perfect counterpart. The estimates derived are independent of the contents being cloaked; that is, the cloaking devices are capable of nearly cloaking an arbitrary content. Furthermore, as a significant byproduct, our argument allows the relaxation of the convexity requirement on $\Gamma_0$ in [28], which is critical for the Mosco convergence argument therein.