Related papers: Nearly Cloaking the Full Maxwell Equations
We consider the time-harmonic Maxwell equations in a complex geometry. We are interested in geometries that model polarization filters or Faraday cages. We study the situation that the underlying domain contains perfectly conducting…
Transformation optics (TO) is a powerful tool for the design of artiffcial materials with unprecedented optical properties. Here, we propose the approximation of TO structures of arbitrary shape by faceting, in which curved surfaces are…
We investigate the electromagnetic field concentration between two nearly-touching inclusions that possess high-contrast electric permittivities in the quasi-static regime. By using layer potential techniques and asymptotic analysis in the…
The goal of this work is to study the electromagnetic scattering problem of time-domain Maxwell's equations in an unbounded structure. An exact transparent boundary condition is developed to reformulate the scattering problem into an…
Coordinate-transformation cloaking is based on the design of a metamaterial shell made of an anisotropic, spatially inhomogeneous "transformation medium" that allows rerouting the impinging wave around a given region of space. In its…
Cloaking of static magnetic fields by a finite thickness type-II superconductor tube surrounded by a coaxial paramagnet shell is studied. On the basis of exact solutions to the London and Maxwell equations, it is shown that perfect cloaking…
Non-Euclidean geometry combined with transformation optics has recently led to the proposal of an invisibility cloak that avoids optical singularities and therefore can work, in principle, in a broad band of the spectrum [U. Leonhardt and…
In elasticity, the design of a cloaking for an inclusion or a void to leave a vibrational field unperturbed by its presence, so to achieve its invisibility, is a thoroughly analyzed, but still unchallenged, mechanical problem. The 'cloaking…
We consider time-harmonic Maxwell's equations set in an heterogeneous medium with perfectly conducting boundary conditions. Given a divergence-free right-hand side lying in $L^2$, we provide a frequency-explicit approximability estimate…
The coordinate transformation offers a remarkable way to design cloaks that can steer electromagnetic fields so as to prevent waves from penetrating into the {\em cloaked region} (denoted by $\Omega_0$, where the objects inside are…
$\delta$-Covering, for some covering range $\delta>0$, is a continuous facility location problem on undirected graphs where all edges have unit length. The facilities may be positioned on the vertices as well as on the interior of the…
We design a device that generates fields canceling out a known probing field inside a region to be cloaked while generating very small fields far away from the device. The fields we consider satisfy the Laplace equation, but the approach…
We consider here several aspects of the following challenging question: is it possible to use a passive cloak to make invisible a dielectric inclusion on a finite frequency interval in the quasistatic regime of Maxwell's equations for an…
Near-field scanning optical microscopy is a powerful technique for imaging below the diffraction limit, which has been extensively used in bio-medical imaging and nanophotonics. However, when the electromagnetic fields under measurement are…
We propose a finite elements algorithm to solve a fourth order partial differential equation governing the propagation of time-harmonic bending waves in thin elastic plates. Specially designed perfectly matched layers are implemented to…
We propose a realization of a transformation-based acoustic temporal cloak using an active closed-loop control approach to an equivalent electromagnetic problem. Unlike the more common spatial cloaks the goal of which is hiding fixed…
Invisibility or cloaking has captured human's imagination for many years. With the recent advancement of metamaterials, several theoretical proposals show cloaking of objects is possible, however, so far there is a lack of an experimental…
In the past years quasi-conformal mapping has been typically used to design broadband electromagnetic cloaks. However, this technique has some inherit practical limitations such as the lateral beam shift, rendering the device visible or…
In this paper, we present analytic formulas of the temporal convolution kernel functions involved in the time-domain non-reflecting boundary condition (NRBC) for the electromagnetic scattering problems. Such exact formulas themselves lead…
The invariance under co-ordinate transformations of a set of partial differential equations can lead to the possibility of invisibility cloaking, whereby an anomaly in the interior of a body is shielded from an external observer. The form…