Electromagnetic wormholes via handlebody constructions

Cloaking devices are prescriptions of electrostatic, optical or electromagnetic parameter fields (conductivity $\sigma(x)$, index of refraction $n(x)$, or electric permittivity $\epsilon(x)$ and magnetic permeability $\mu(x)$) which are piecewise smooth on $\mathbb R^3$ and singular on a hypersurface $\Sigma$, and such that objects in the region enclosed by $\Sigma$ are not detectable to external observation by waves. Here, we give related constructions of invisible tunnels, which allow electromagnetic waves to pass between possibly distant points, but with only the ends of the tunnels visible to electromagnetic imaging. Effectively, these change the topology of space with respect to solutions of Maxwell's equations, corresponding to attaching a handlebody to $\mathbb R^3$. The resulting devices thus function as electromagnetic wormholes.Comment: 25 pages, 6 figures (some color

Electromagnetic wormholes and virtual magnetic monopoles

We describe new configurations of electromagnetic (EM) material parameters, the electric permittivity $\epsilon$ and magnetic permeability $\mu$, that allow one to construct from metamaterials objects that function as invisible tunnels. These allow EM wave propagation between two points, but the tunnels and the regions they enclose are not detectable to EM observations. Such devices function as wormholes with respect to Maxwell's equations and effectively change the topology of space vis-a-vis EM wave propagation. We suggest several applications, including devices behaving as virtual magnetic monopoles.Comment: 4 pages, 3 figure

Enhancement of near-cloaking. Part II: the Helmholtz equation

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 structures are, before using the transformation optics, layered structures and are designed so that their first scattering coefficients vanish. Inside the cloaking region, any target has near-zero scattering cross section for a band of frequencies. We analytically show that our new construction significantly enhances the cloaking effect for the Helmholtz equation.Comment: 16pages, 12 fugure

Human acclimation and acclimatization to heat: A compendium of research, 1968-1978

Abstracts and annotations of the majority of scientific works that elucidate the mechanisms of short-term acclimation to heat in men and women are presented. The compendium includes material from 1968 through 1977. Subject and author indexes are provided and additional references of preliminary research findings or work of a peripheral nature are included in a bibliography

Superantenna made of transformation media

We show how transformation media can make a superantenna that is either completely invisible or focuses incoming light into a needle-sharp beam. Our idea is based on representating three-dimensional space as a foliage of sheets and performing two-dimensional conformal maps on each shee

Numerical Analysis of Three-dimensional Acoustic Cloaks and Carpets

We start by a review of the chronology of mathematical results on the Dirichlet-to-Neumann map which paved the way towards the physics of transformational acoustics. We then rederive the expression for the (anisotropic) density and bulk modulus appearing in the pressure wave equation written in the transformed coordinates. A spherical acoustic cloak consisting of an alternation of homogeneous isotropic concentric layers is further proposed based on the effective medium theory. This cloak is characterised by a low reflection and good efficiency over a large bandwidth for both near and far fields, which approximates the ideal cloak with a inhomogeneous and anisotropic distribution of material parameters. The latter suffers from singular material parameters on its inner surface. This singularity depends upon the sharpness of corners, if the cloak has an irregular boundary, e.g. a polyhedron cloak becomes more and more singular when the number of vertices increases if it is star shaped. We thus analyse the acoustic response of a non-singular spherical cloak designed by blowing up a small ball instead of a point, as proposed in [Kohn, Shen, Vogelius, Weinstein, Inverse Problems 24, 015016, 2008]. The multilayered approximation of this cloak requires less extreme densities (especially for the lowest bound). Finally, we investigate another type of non-singular cloaks, known as invisibility carpets [Li and Pendry, Phys. Rev. Lett. 101, 203901, 2008], which mimic the reflection by a flat ground.Comment: Latex, 21 pages, 7 Figures, last version submitted to Wave Motion. OCIS Codes: (000.3860) Mathematical methods in physics; (260.2110) Electromagnetic theory; (160.3918) Metamaterials; (160.1190) Anisotropic optical materials; (350.7420) Waves; (230.1040) Acousto-optical devices; (160.1050) Acousto-optical materials; (290.5839) Scattering,invisibility; (230.3205) Invisibility cloak

Full-wave invisibility of active devices at all frequencies

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 Helmholtz and Maxwell's equations, for several constructions of cloaking devices. Previous results have either been on the level of ray tracing [Le,PSS] or at zero frequency [GLU2,GLU3], but recent numerical [CPSSP] and experimental [SMJCPSS] work has provided evidence for invisibility at frequency $k\ne 0$. We give two basic constructions for cloaking a region $D$ contained in a domain $\Omega$ from measurements of Cauchy data of waves at \p \Omega; we pay particular attention to cloaking not just a passive object, but an active device within $D$, interpreted as a collection of sources and sinks or an internal current.Comment: Final revision; to appear in Commun. in Math. Physic

Inverse problems with partial data for a magnetic Schr\"odinger operator in an infinite slab and on a bounded domain

In this paper we study inverse boundary value problems with partial data for the magnetic Schr\"odinger operator. In the case of an infinite slab in $R^n$, $n\ge 3$, we establish that the magnetic field and the electric potential can be determined uniquely, when the Dirichlet and Neumann data are given either on the different boundary hyperplanes of the slab or on the same hyperplane. This is a generalization of the results of [41], obtained for the Schr\"odinger operator without magnetic potentials. In the case of a bounded domain in $R^n$, $n\ge 3$, extending the results of [2], we show the unique determination of the magnetic field and electric potential from the Dirichlet and Neumann data, given on two arbitrary open subsets of the boundary, provided that the magnetic and electric potentials are known in a neighborhood of the boundary. Generalizing the results of [31], we also obtain uniqueness results for the magnetic Schr\"odinger operator, when the Dirichlet and Neumann data are known on the same part of the boundary, assuming that the inaccessible part of the boundary is a part of a hyperplane

Focusing: coming to the point in metamaterials

The point of the paper is to show some limitations of geometrical optics in the analysis of subwavelength focusing. We analyze the resolution of the image of a line source radiating in the Maxwell fisheye and the Veselago-Pendry slab lens. The former optical medium is deduced from the stereographic projection of a virtual sphere and displays a heterogeneous refractive index n(r) which is proportional to the inverse of 1+r^2. The latter is described by a homogeneous, but negative, refractive index. It has been suggested that the fisheye makes a perfect lens without negative refraction [Leonhardt, Philbin arxiv:0805.4778v2]. However, we point out that the definition of super-resolution in such a heterogeneous medium should be computed with respect to the wavelength in a homogenized medium, and it is perhaps more adequate to talk about a conjugate image rather than a perfect image (the former does not necessarily contains the evanescent components of the source). We numerically find that both the Maxwell fisheye and a thick silver slab lens lead to a resolution close to lambda/3 in transverse magnetic polarization (electric field pointing orthogonal to the plane). We note a shift of the image plane in the latter lens. We also observe that two sources lead to multiple secondary images in the former lens, as confirmed from light rays travelling along geodesics of the virtual sphere. We further observe resolutions ranging from lambda/2 to nearly lambda/4 for magnetic dipoles of varying orientations of dipole moments within the fisheye in transverse electric polarization (magnetic field pointing orthogonal to the plane). Finally, we analyse the Eaton lens for which the source and its image are either located within a unit disc of air, or within a corona 1<r<2 with refractive index $n(r)=\sqrt{2/r-1}$. In both cases, the image resolution is about lambda/2.Comment: Version 2: 22 pages, 11 figures. More figures added, additional cases discussed. Misprints corrected. Keywords: Maxwell fisheye, Eaton lens; Non-Euclidean geometry; Stereographic projection; Transformation optics; Metamaterials; Perfect lens. The last version appears at J. Modern Opt. 57 (2010), no. 7, 511-52

Exterior optical cloaking and illusions by using active sources: a boundary element perspective

Recently, it was demonstrated that active sources can be used to cloak any objects that lie outside the cloaking devices [Phys. Rev. Lett. \textbf{103}, 073901 (2009)]. Here, we propose that active sources can create illusion effects, so that an object outside the cloaking device can be made to look like another object. invisibility is a special case in which the concealed object is transformed to a volume of air. From a boundary element perspective, we show that active sources can create a nearly "silent" domain which can conceal any objects inside and at the same time make the whole system look like an illusion of our choice outside a virtual boundary. The boundary element method gives the fields and field gradients (which can be related to monopoles and dipoles) on continuous curves which define the boundary of the active devices. Both the cloaking and illusion effects are confirmed by numerical simulations