Opaque perfect lenses

The response of the ``perfect lens'', consisting of a slab of lossless material of thickness $d$ with $\epsilon=\mu=-1$ at one frequency $\omega_0$ is investigated. It is shown that as time progresses the lens becomes increasingly opaque to any physical TM line dipole source located a distance $d_0<d/2$ from the lens and which has been turned on at time $t=0$. Here a physical source is defined as one which supplies a bounded amount of energy per unit time. In fact the lens cloaks the source so that it is not visible from behind the lens either. For sources which are turned on exponentially slowly there is an exact correspondence between the response of the perfect lens in the long time constant limit and the response of lossy lenses in the low loss limit. Contrary to the usual picture where the field intensity has a minimum at the front interface we find that the field diverges to infinity there in the long time constant limit.Comment: The 7th International Conference on the Electrical transport and Optical Properties of Inhomogenous Media (ETOPIM7

A metamaterial frequency-selective super-absorber that has absorbing cross section significantly bigger than the geometric cross section

Using the idea of transformation optics, we propose a metamaterial device that serves as a frequency-selective super-absorber, which consists of an absorbing core material coated with a shell of isotropic double negative metamaterial. For a fixed volume, the absorption cross section of the super-absorber can be made arbitrarily large at one frequency. The double negative shell serves to amplify the evanescent tail of the high order incident cylindrical waves, which induces strong scattering and absorption. Our conclusion is supported by both analytical Mie theory and numerical finite element simulation. Interesting applications of such a device are discussed.Comment: 16 pages, 5 figure

Superscatterer: Enhancement of scattering with complementary media

Based on the concept of complementary media, we propose a novel design which can enhance the electromagnetic wave scattering cross section of an object so that it looks like a scatterer bigger than the scale of the device. Such a ``superscatterer'' is realized by coating a negative refractive material shell on a perfect electrical conductor cylinder. The scattering field is analytically obtained by Mie scattering theory, and confirmed by full-wave simulations numerically. Such a device can be regarded as a cylindrical concave mirror for all angles.Comment: 9 pages, 4 figure

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

Conductance of photons and Anderson localization of light

Conductance properties of photons in disordered two-dimensional photonic crystals is calculated using exact multipole expansions technique. The Landauers two-terminal formula is used to calculate average of the conductance, its variance and the probability density distribution

Finite elements modelling of scattering problems for flexural waves in thin plates: Application to elliptic invisibility cloaks, rotators and the mirage effect

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 deal with the infinite extent of the plates. These are deduced from a geometric transform in the biharmonic equation. To numerically illustrate the power of elastodynamic transformations, we analyse the elastic response of an elliptic invisibility cloak surrounding a clamped obstacle in the presence of a cylindrical excitation i.e. a concentrated point force. Elliptic cloaking for flexural waves involves a density and an orthotropic Young's modulus which depend on the radial and azimuthal positions, as deduced from a coordinates transformation for circular cloaks in the spirit of Pendry et al. [Science {\bf 312}, 1780 (2006)], but with a further stretch of a coordinate axis. We find that a wave radiated by a concentrated point force located a couple of wavelengths away from the cloak is almost unperturbed in magnitude and in phase. However, when the point force lies within the coating, it seems to radiate from a shifted location. Finally, we emphasize the versatility of transformation elastodynamics with the design of an elliptic cloak which rotates the polarization of a flexural wave within its core.Comment: 14 pages, 5 figure

Finite wavelength cloaking by plasmonic resonance

We consider cloaking by a coated cylindrical system using plasmonic resonance, and extend previous quasistatic treatments to include the effect of finite wavelength. We show that a probe cylinder can still be cloaked at finite wavelengths, but the cloaking cylinder develops a non-zero scattering cross-section. We show that this latter effect is dominated by a monopole term in the case of an ideal (lossless) cloaking material, and by a dipole term in the case of a realistic (lossy) material. It can be reduced but not eliminated by variations of geometric or dielectric parameters of the cloaking cylinder