Causality-based criteria for a negative refractive index must be used with care

Using the principle of causality as expressed in the Kramers-Kronig relations, we derive a generalized criterion for a negative refractive index that admits imperfect transparency at an observation frequency $\omega$. It also allows us to relate the global properties of the loss (i.e. its frequency response) to its local behaviour at $\omega$. However, causality-based criteria rely the on the group velocity, not the Poynting vector. Since the two are not equivalent, we provide some simple examples to compare the two criteria.Comment: slightly longer version of published PR

The Effect of Polymethylmethacrylate Bone Cement Vibration on the Bone-Cement Interface

Low frequency vibration of polymethylmethacrylate (PMMA) bone cement reduces the viscosity of the cement by shear thinning. The effect of this low frequency vibration on the bone-cement interface was studied using microfocal radiography (MFR) and scanning electron microscopy (SEM). Effects were studied in-vitro and in-vivo. In-vitro, samples of Palacos low viscosity PMMA were placed on blocks of Kiel bone and vibrated. MFR and SEM demonstrated an improvement in the appearance of the bone-cement interface. In-vivo, PMMA was injected into the upper tibia of the dog. An assessment of the effect of high and low pressure injection, and the effect of added low frequency vibration of the cement was made. The effect on cement penetration was studied using MFR and SEM. It was found that vibration produced an improved bone-cement interface compared to low pressure injection, and an interface comparable to that obtained with high pressure injection

Counterposition and negative phase velocity in uniformly moving dissipative materials

The Lorentz transformations of electric and magnetic fields were implemented to study (i) the refraction of linearly polarized plane waves into a half-space occupied by a uniformly moving material, and (ii) the traversal of linearly polarized Gaussian beams through a uniformly moving slab. Motion was taken to occur tangentially to the interface(s) and in the plane of incidence. The moving materials were assumed to be isotropic, homogeneous, dissipative dielectric materials from the perspective of a co-moving observer. Two different moving materials were considered: from the perspective of a co-moving observer, material A supports planewave propagation with only positive phase velocity, whereas material B supports planewave propagation with both positive and negative phase velocity, depending on the polarization state. For both materials A and B, the sense of the phase velocity and whether or not counterposition occurred, as perceived by a nonco-moving observer, could be altered by varying the observer's velocity. Furthermore, the lateral position of a beam upon propagating through a uniformly moving slab made of material A, as perceived by a nonco-moving observer, could be controlled by varying the observer's velocity. In particular, at certain velocities, the transmitted beam emerged from the slab laterally displaced in the direction opposite to the direction of incident beam. The transmittances of a uniformly moving slab made of material B were very small and the energy density of the transmitted beam was largely concentrated in the direction normal to the slab, regardless of the observer's velocity

H3+ in Diffuse Interstellar Clouds: a Tracer for the Cosmic-Ray Ionization Rate

Using high resolution infrared spectroscopy we have surveyed twenty sightlines for H3+ absorption. H3+ is detected in eight diffuse cloud sightlines with column densities varying from 0.6x10^14 cm^-2 to 3.9x10^14 cm^-2. This brings to fourteen the total number of diffuse cloud sightlines where H3+ has been detected. These detections are mostly along sightlines concentrated in the Galactic plane, but well dispersed in Galactic longitude. The results imply that abundant H3+ is common in the diffuse interstellar medium. Because of the simple chemistry associated with H3+ production and destruction, these column density measurements can be used in concert with various other data to infer the primary cosmic-ray ionization rate, zeta_p. Values range from 0.5x10^-16 s^-1 to 3x10^-16 s^-1 with an average of 2x10^-16 s^-1. Where H3+ is not detected the upper limits on the ionization rate are consistent with this range. The average value of zeta_p is about an order of magnitude larger than both the canonical rate and rates previously reported by other groups using measurements of OH and HD. The discrepancy is most likely due to inaccurate measurements of rate constants and the omission of effects which were unknown when those studies were performed. We believe that the observed column density of H3+ is the most direct tracer for the cosmic-ray ionization rate due to its simple chemistry. Recent models of diffuse cloud chemistry require cosmic-ray ionization rates on the order of 10^-16 s^-1 to reproduce observed abundances of various atomic and molecular species, in rough accord with our observational findings.Comment: Accepted to ApJ, 35 pages, 5 figures, 5 table

General Relativity in Electrical Engineering

In electrical engineering metamaterials have been developed that offer unprecedented control over electromagnetic fields. Here we show that general relativity lends the theoretical tools for designing devices made of such versatile materials. Given a desired device function, the theory describes the electromagnetic properties that turn this function into fact. We consider media that facilitate space-time transformations and include negative refraction. Our theory unifies the concepts operating behind the scenes of perfect invisibility devices, perfect lenses, the optical Aharonov-Bohm effect and electromagnetic analogs of the event horizon, and may lead to further applications

Observations of H3+ in the Diffuse Interstellar Medium

Surprisingly large column densities of H3+ have been detected using infrared absorption spectroscopy in seven diffuse cloud sightlines (Cygnus OB2 12, Cygnus OB2 5, HD 183143, HD 20041, WR 104, WR 118, and WR 121), demonstrating that H3+ is ubiquitous in the diffuse interstellar medium. Using the standard model of diffuse cloud chemistry, our H3+ column densities imply unreasonably long path lengths (~1 kpc) and low densities (~3 cm^-3). Complimentary millimeter-wave, infrared, and visible observations of related species suggest that the chemical model is incorrect and that the number density of H3+ must be increased by one to two orders of magnitude. Possible solutions include a reduced electron fraction, an enhanced rate of H2 ionization, and/or a smaller value of the H3+ dissociative recombination rate constant than implied by laboratory experiments.Comment: To be published in Astrophysical Journal, March 200

General Relativistic Contributions in Transformation Optics

One potentially realistic specification for devices designed with transformation optics is that they operate with high precision in curved space-time, such as Earth orbit. This raises the question of what, if any, role does space-time curvature play in determining transformation media? Transformation optics has been based on a three-vector representation of Maxwell's equations in flat Minkowski space-time. I discuss a completely covariant, manifestly four-dimensional approach that enables transformations in arbitrary space-times, and demonstrate this approach for stable circular orbits in the spherically symmetric Schwarzschild geometry. Finally, I estimate the magnitude of curvature induced contributions to satellite-borne transformation media in Earth orbit and comment on the level of precision required for metamaterial fabrication before such contributions become important.Comment: 14 pages, 3 figures. Latest version has expanded analysis, corresponds to published versio

Experimental Verification of 3D Plasmonic Cloaking in Free-Space

We report the experimental verification of metamaterial cloaking for a 3D object in free space. We apply the plasmonic cloaking technique, based on scattering cancellation, to suppress microwave scattering from a finite-length dielectric cylinder. We verify that scattering suppression is obtained all around the object in the near- and far-field and for different incidence angles, validating our measurements with analytical results and full-wave simulations. Our near-field and far-field measurements confirm that realistic and robust plasmonic metamaterial cloaks may be realized for elongated 3D objects with moderate transverse cross-section at microwave frequencies.Comment: 12 pages, 8 figures, published in NJ