Enhanced Near-cloak by FSH Lining

TL;DR

This paper introduces a new cloaking scheme with a lossy layer that significantly improves near-cloaking performance for the Helmholtz equation, achieving optimal cloaking in any dimension with general geometries.

Contribution

The authors develop a cloaking method with a specially designed lossy layer that enhances near-cloaking performance to an optimal level across multiple dimensions.

Findings

Achieves near-cloaking with error of order  ho^N in  ext{N} dimensions

The lossy layer limit corresponds to a sound-hard layer

Works with general geometries and arbitrary cloaked contents

Abstract

We consider regularized approximate cloaking for the Helmholtz equation. Various cloaking schemes have been recently proposed and extensively investigated. The existing cloaking schemes in literature are (optimally) within $|\ln\rho|^{-1}$ in 2D and $\rho$ in 3D of the perfect cloaking, where $\rho$ denotes the regularization parameter. In this work, we develop a cloaking scheme with a well-designed lossy layer right outside the cloaked region that can produce significantly enhanced near-cloaking performance. In fact, it is proved that the proposed cloaking scheme could (optimally) achieve $\rho^N$ in $\mathbb{R}^N$, $N\geq 2$, within the perfect cloaking. It is also shown that the limit of the proposed lossy layer corresponds to a sound-hard layer. We work with general geometry and arbitrary cloaked contents of the proposed cloaking device.