Related papers: Cloaking using complementary media for the Helmhol…
Cloaking using complementary media was suggested by Lai et al. in [8]. The study of this problem faces two difficulties. Firstly, this problem is unstable since the equations describing the phenomenon have sign changing coefficients, hence…
The aim of this paper is to extend the method of improving cloaking structures in the conductivity to scattering problems. We construct very effective near-cloaking structures for the scattering problem at a fixed frequency. These new…
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…
Transformation optics constructions have allowed the design of cloaking devices that steer electromagnetic, acoustic and quantum waves around a region without penetrating it, so that this region is hidden from external observations. The…
Base on the concept of complementary media, a scheme to achieve cloak an object outside the shell is proposed by Yun lai et al [PRL 102, 093901].We generalize the concept in acoustic waves and demonstrate numerically how to achieve the…
We develop a very general theory on the regularized approximate invisibility cloaking for the wave scattering governed by the Helmholtz equation in any space dimensions via the approach of transformation optics.
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 $|\ln\rho|^{-1}$…
We study approximate cloaking using transformation optics for electromagnetic waves in the time domain. Our approach is based on estimates of the degree of visibility in the frequency domain for all frequencies in which the frequency…
In this paper, we study approximate cloaking of active devices for the Helmholtz equation in the whole space of dimension 2 or 3 using the scheme introduced by Kohn, Shen, Vogelius, and Weinstein in \cite{KohnShenVogeliusWeinstein}. More…
We design sources for the two-dimensional Helmholtz equation that can cloak an object by cancelling out the incident field in a region, without the sources completely surrounding the object to hide. As in previous work for real positive…
Based on the concept of complementary media, we propose an invisibility cloak operating at a finite frequency that can cloak an object with a pre-specified shape and size within a certain distance outside the shell. The cloak comprises of a…
Transformation optics constructions have allowed the design of electromagnetic, acoustic and quantum parameters that steer waves around a region without penetrating it, so that the region is hidden from external observations. The material…
In this paper, we consider near cloaking for the full Maxwell equations. We extend the recent results, where the quasi-static limit case and the Helmholtz equation are considered, to electromagnetic scattering problems. We construct very…
In this paper, we present a multiscale framework for solving the Helmholtz equation in heterogeneous media without scale separation and in the high frequency regime where the wavenumber $k$ can be large. The main innovation is that our…
We give a comprehensive study on regularized approximate electromagnetic cloaking via the transformation optics approach. The following aspects are investigated: (i) near-invisibility cloaking of passive media as well as active/radiating…
We investigate cloaking property of negative-index metamaterials in the time-harmonic electromagnetic setting for the so-called doubly complementary media. These are media consisting of negative-index metamaterials in a shell (plasmonic…
In this article we consider cloaking for a quasi-linear elliptic partial differential equation of divergence type defined on a bounded domain in $\mathbb{R}^N$ for $N=2,3$. We show that a perfect cloak can be obtained via a singular change…
There has recently been considerable interest in the possibility, both theoretical and practical, of invisibility (or "cloaking") from observation by electromagnetic (EM) waves. Here, we prove invisibility, with respect to solutions of the…
Cloaking a source via anomalous localized resonance (ALR) was discovered by Milton and Nicorovici in \cite{MiltonNicorovici}. A general setting in which cloaking a source via ALR takes place is the settting of doubly complementary media.…
This paper concerns the analysis of a passive, broadband approximate cloaking scheme for the Helmholtz equation in ${\mathbb R}^d$ for $d=2$ or $d=3$. Using ideas from transformation optics, we construct an approximate cloak by ``blowing…