Normal Reflection Research Articles

Andreev scattering and Josephson current in a one-dimensional electron liquid

Andreev scattering and the Josephson current through a one-dimensional interacting electron liquid sandwiched between two superconductors are re-examined. We first present some apparently new results on the non-interacting case by studying an exactly solvable tight-binding model rather than the usual continuum model. We show that perfect Andreev scattering (i.e. zero normal scattering) at the Fermi energy can only be achieved by fine-tuning junction parameters. We also obtain exact results for the Josephson current, which is generally a smooth function of the superconducting phase difference except when the junction parameters are adjusted to give perfect Andreev scattering, in which case it becomes a sawtooth function. We then observe that, even when interactions are included, all low energy properties of a junction (E<<\Delta, the superconducting gap) can be obtained by "integrating out" the superconducting electrons to obtain an effective Hamiltonian describing the metallic electrons only with a boundary pairing interaction. This boundary model provides a suitable starting point for bosonization/renormalization group/boundary conformal field theory analysis. We argue that total normal reflection and total Andreev reflection correspond to two fixed points of the boundary renormalization group. For repulsive bulk interactions the Andreev fixed point is unstable and the normal one stable. However, the reverse is true for attractive interactions. This implies that a generic junction Hamiltonian (without fine-tuned junction parameters) will renormalize to the normal fixed point for repulsive interactions but to the Andreev one for attractive interactions. An exact mapping of our tight-binding model to the Hubbard model with a transverse magnetic field is used to help understand this behavior.

Microwave absorption characteristics of chiral materials with Fe3O4-polyaniline composite matrix

Fe3O4-polyaniline composites have been prepared in which the concentrations of Fe3O4 are 10%, 15%, 20%, 30% and 40% by weight. Microwave chiral composites are then prepared employing copper helices as chiral inclusions and the Fe3O4-polyaniline composites as the matrix. The electromagnetic parameters of the chiral Fe3O4-polyaniline composites are measured using a circular waveguide method at 9.5 GHz, and the normal reflectance from a perfect conductor-backed chiral slab is calculated. The microwave absorption characteristics of the chiral Fe3O4- polyaniline composites are studied and compared with those of a non-chiral Fe3O4-polyaniline composite matrix. The results show that the addition of the chiral inclusions to the non-chiral matrix improves both the dielectric and the magnetic losses. As well as this improvement in losses, the chiral materials have higher microwave absorption. The optimal concentration of Fe3O4 in the matrix is about 15% to obtain the lowest reflectance of chiral Fe3O4-polyaniline composites.

Critical current in superconducting quantum point contacts

The quantization of the critical current I c in a quantum point contact is studied on varying the number of free channels (varying the constriction width d0 in 2DEG). It is shown that the shape of the quantum I c is not universal and depends on the parameters of the contact, in particular, on the properties of the 2DEG-S boundaries. Because of the effect of normal reflection from the S-2DEG boundaries, the quantum critical current nonmonotonically depends on d0 and may have a resonance structure. If E F coincides with a quasi-stationary level of the square potential well formed by the contact walls, the critical current has a local maximum (resonance) equal (in the first channel) to the ratio of the electron charge to its time of travel through the contact. The critical current at the maximum is determined by the lowest positive Andreev level (for the phase difference π).

Optical properties of hot-pressed B_4C in the extreme ultraviolet

Hot-pressed B(4)C is found to have a high normal reflectance in the extreme-UV spectral region above 49 nm. This reflectance is comparable with or higher than chemical-vapor-deposited SiC in the spectral region from 49 to 92 nm. Reflectance measurements as a function of the angle of incidence yielded the optical constants of B(4)C in the spectral range 49-121.6 nm.

Attenuated total reflectance infrared microspectroscopy of coal

The measurement of i.r. microspectra utilising an attenuated total reflection (ATR) objective is described. The ATR objective contains a small crystal about 100 μm in diameter which must contact the coal surface. This allows i.r. spectra to be measured from standard polished petrography blocks, without further preparation. The spectra obtained are similar to normal absorption spectra, unlike specular or diffuse reflection spectra. The spectra reflect the changes in coal structure with rank typically seen with macro i.r. methods. A silicon crystal gave better results than a germanium crystal because it has a greater depth of penetration into the sample.

Fast and accurate reflectivity calculations for shaped core optical fibres

A novel scalar (i.e. paraxial) free space radiation mode method is presented for calculating the normal incidence facet reflectivity of the main guided mode of a step-index optical fibre with generally shaped smooth core. Numerical results are presented and discussed for several cases of the Nth order super-elliptical core shape, including the circular, elliptical, rectangular-type and slab limiting cases.

Delineation of a complexly dipping temperate glacier bed using short-pulse radar arrays

AbstractWe have defined the complex bed topography for a section of a small temperate glacier using 50 MHz monostatic short-pulse radar data and a synthetic-aperture array-processing method. The data were collected on a 100 m by 340 m array grid in the upper stem of Gulkana Glacier, central Alaska, U.S.A. The array processing was based on a modified three-dimensional (3-D) Kirchhoff migration integral and implemented with a synthetic-aperture approach that uses sequences of overlapping sub-arrays to generate depth images in vertical planes. Typical sub-array beam patterns are generally &lt;5° at the −6 dB level, giving a flashlight-like searching capability without distorting the wavelet shape. The bed topography was constructed using normal reflections picked from 3-D array depth images. In some instances reflections were imaged outside the data-cover-age area. The bed surface dips steeply, both parallel and transverse to the direction of ice flow. The maximum observed depth is roughly 140 m. The 3-D method resolved bed dips up to 45°. In regions of steepest dip, it improved depth accuracy by 36% compared with raw data, and by 15% compared with standard two-dimensional (2-D) migration. Over 12 dB of signal-to-noise improvement and improved spatial resolution was achieved compared to raw data and 2-D migration. False bottom layering seen in the raw data and in 2-D migrations is not observed in the 3-D array results. Furthermore, loss of bottom reflections is shown by the 3-D migration to be attributable to the dip and curvature of the reflector, and not scattering losses or signal clutter from englacial inclusions.

Point-contact spectroscopy of quasi-1D conductors with CDW

The nature of carrier reflection from a normal metal-Peierls conductor interface is clarified by studying both the characteristics of direct point contacts Au-NbSe 3 (K 0.3 MoO 3 ) oriented along the chains, and point contacts formed with an intermediate metallic layer sputtered onto the K 0.3 MoO 3 crystals. In the Peierls state, for bias voltages eV smaller than the Peierls gap Ap, an excess differential resistance is observed for both experimental configuration. The dominant contribution to the excess resistance for injection along the chains is from normal reflection of carriers without changes in the sign of their charge and a momentum transfer 2p F to the condencate of electron-hole pairs carried away from the interface. For Au-K 0.3 MoO 3 contacts the character of nonlinearity and the observed asymmetric features of the IV characteristics indicate that a substantial shift of the chemical potential occurs near the boundary with the normal metal.

Cuttlefish use polarization sensitivity in predation on silvery fish

Cephalopods are sensitive to the linear polarization characteristics of light. To examine if this polarization sensitivity plays a role in the predatory behavior of cuttlefish, we examined the preference of Sepia officinalis when presented with fish whose polarization reflection was greatly reduced versus fish whose polarization reflection was not affected. Cuttlefish preyed preferably on fish with normal polarization reflection over fish that did not reflect linearly polarized light ( n=24, χ 2=17.3, P<0.0001), implying that polarization sensitivity is used during predation. We suggest that polarization vision is used to break the countershading camouflage of light-reflecting silvery fish.

Orientation measurements from the surfaces of injection moulded plaques of thermotropic liquid crystalline polymer using normal incidence specular reflection

This article reviews the application of FTIR methods (attenuated total reflection, specular reflectance and photoacoustic detection) to orientation measurements of polymers, and to thermotropic liquid crystalline polymers (LCPs) in particular. FTIR specular reflectance dichroism studies are then applied to determine molecular orientation from the surface of injection mouldings (square plaques with dimensions 60×60×2mm, unfilled polymer; 60×60×4mm, filled polymer) of a LC copolyester based on hydroxybenzoic acid, terephthalic acid, 4,4′-oxydibenzoic acid and chlorohydroquinone. The effects of the melt temperature (265–315°C) and of the addition of fillers (mica, silica or glass beads) on the development of orientation are investigated. Scans are presented showing the quality of orientation with respect to orthogonal axes. The orientation profiles are related to the flow behaviour of LCPs during processing (spreading radial flow at the entrance to the mould, converging flow in the first half of the mould and fountain flow). At some positions, orientation minima occur which assume parabolic profiles and are associated with an arc-like band-pattern consisting of dark and brownish white bands at the surface of the mould. The light-coloured arcs correspond to regions in which the chains are not planar and tend to lie with their long axis in the thickness direction.

Comparative analysis of the optical spectra of YBa [formula omitted]Cu [formula omitted]O [formula omitted

New experimental data on the temperature dependence of the optical reflectivity of YBa 2 Cu 3 O 7 films are studied in the framework of strong electron–phonon interaction. It is shown that the normal state reflectivity in the far- and mid-infrared region can be explained using an Eliashberg function α 2(ω)F(ω) typical for this system with a constant of coupling λ=2. The superconducting state data are compared to the theoretical calculations using the usual strong-coupling approach. This leads to the conclusion that some other mechanism, supplementary to electron–phonon interaction, exists in this system.

Wetting phenomena at mercury–sapphire interface under high temperature and pressure

Optical reflectivity experiments on fluid mercury against a sapphire surface under high pressure and temperature reveal the existence of a prewetting transition of mercury on sapphire substrate. In the present work, we performed not only normal reflection measurements but also ellipsometric measurements with 45° reflection geometry to make a quantitative analysis. By using this technique, we determined the bulk complex refractive index, and then, the properties of the wetting layer were determined.

NEAR Photometry of Asteroid 253 Mathilde

NEAR's Multispectral Imager (MSI) recorded over 300 images of asteroid 253 Mathilde during a flyby on June 27, 1997. Images were acquired at 0.70 μm at solar phase angles from 40° to 136°. These data, combined with telescopic observations at phase angles from 1° to 16° were used to derive a photometric model for Mathilde. The photometric properties of Mathilde were then compared with those of similar small bodies. We find that: (1) Mathilde has a geometric albedo of 0.047±0.005 at 0.55 μm, making it the darkest minor planet yet observed by spacecraft. (2) Mathilde is remarkably homogeneous in reflectance across the surface. Normal reflectance ranges from 0.041 to 0.053, a distribution at the low end of the range of reflectance measurements of carbonaceous chondrites (0.03–0.11) and in the middle of the range of albedo measurements of C-type asteroids (0.03–0.06). (3) Typical reflectance contrasts on Mathilde occur at the level of ±6% from the mean, as compared to Phobos which exhibits variation at the level of ±20% from the mean. (4) As a whole, Mathilde is more backscattering than Phobos, and Mathilde may have a less porous regolith or a different distribution of regolith grain sizes than Phobos.

Non-specular reflectivity of spin flipped neutrons

For the first time we observed large intensity non-specular reflection peaks of neutrons incident at small grazing angles on not fully magnetized ferromagnetic samples. In addition to the normal specular reflection spin flipped neutrons are reflected at distinctly higher (lower) angles if the incoming spin down (spin up) neutrons hit the surface at angles near the respective critical angle. The same effect occurs in transmission. The angles at which the non-specular reflection occurs can be calculated by a simple model, which assumes a spin flip without a change of direction and takes into account the different refraction angles of the original and the flipped spin state when the neutrons leave the sample.

Diffraction d'une onde électromagnétique plane par un biréseau métallique plan formé de cavités hémisphéroïdales

The diffraction of an electromagnetic plane wave from a bigrating of prolate spheroid cavities hollowed in a perfectly conducting metallic plate is studied using an exact differential analytic method. The theoretical treatment is carried out for any incidence and direction of polarization, but first, numerical results are given for normal incidence in view of comparison with previous results obtained in same conditions from a bigrating of hemispherical cavities. So, original efficiency curves ɛ ff (0, 0) (or normal reflectance) versus the size of cavities are given.

Angle dependence of Andreev scattering at semiconductor–superconductor interfaces

We study the angle dependence of the Andreev scattering at a semiconductor-superconductor interface, generalizing the one-dimensional theory of Blonder, Tinkham and Klapwijk. An increase of the momentum parallel to the interface leads to suppression of the probability of Andreev reflection and increase of the probability of normal reflection. We show that in the presence of a Fermi velocity mismatch between the semiconductor and the superconductor the angles of incidence and transmission are related according to the well-known Snell's law in optics. As a consequence there is a critical angle of incidence above which only normal reflection exists. For two and three-dimensional interfaces a lower excess current compared to ballistic transport with perpendicular incidence is found. Thus, the one-dimensional BTK model overestimates the barrier strength for two and three-dimensional interfaces.

Phoebe: Albedo Map and Photometric Properties

Using clear-filter images from Voyager 2 (effective wavelength 0.48 μm), we have constructed the first-ever digital albedo map of Saturn's moon Phoebe. Most normal reflectances in this new map are between 0.07 and 0.11; the albedo histogram is largely bimodal, suggesting that the satellite is covered predominantly by two different types of surface materials. The highest albedos are confined to isolated, quasi-circular spots 40 to 100 km across, including three spots of varying albedo in a band immediately south of the equator and one especially bright spot at latitude 60°N (normal reflectance as high as 0.13, ≈50% brighter than the average surface). The bright northern spot and the brightest of the southern spots occur at approximately the same longitude, an alignment that gives Phoebe its significant rotational lightcurve. The low resolution of the Voyager images does not permit interpretation of the bright spots' origin.Phoebe's global-average photometric function was determined by combining the satellite's telescopic near-opposition phase curve (S. Kruseet al.1986,Icarus68, 168–175) with absolute disk-resolved reflectances measured from the Voyager images (triaxial-ellipsoid shape assumed with radii 115, 110, and 105 km). Modeling of the telescopic observations supports the presence of a significant opposition surge, although scatter in the data does not allow unambiguous determination of the surge's exact strength. The derived photometric function is consistent with the idea that Phoebe is a C-type object—probably a primitive, captured body related to Chiron, Pholus, and the inhabitants of the Kuiper Belt. The albedo map and photometric information will aid in the planning of high-resolution Cassini images of Phoebe, which will represent our first close look at this class of primitive outer Solar-System object.

Exciton-polariton reflectance in CuI single crystals

We have measured the normal reflection spectrum of (1 1 0) cleaved faces of single crystals of CuI in the spectral range of the Z 12(3058 meV) and Z 3(3699 meV) exciton lines at the temperature of 95 K. We have fitted the experimental data by computing a non local dielectric function and taken into account various additional boundary conditions (ABC) as well as the dead layer model in a semi-infinite crystal. A quantitative agreement is obtained assuming the following values for the background dielectric constant ε ∞=7.2 and for the effective masses of the excitons M(Z 12)=1.8 m 0, M(Z 3)=0.5 m 0. These results do not depend on the choice of a particular ABC. The longitudinal-transverse exciton splitting energies deduced from the fit are: ω LT (Z 12)=5.9 meV and ω LT (Z 3)=2 meV.

Spatial distribution of hotspot material added to the lithosphere under La Réunion, from wide‐angle seismic data

Wide‐angle seismic lines recorded by ocean bottom and land seismometers provide a pseudo three‐dimensional investigation of the crust and upper mantle structure around the volcanically active hotspot island of La Réunion. The submarine part of the edifice has fairly low seismic velocities, without evidence for intrusives. An upper unit with a velocity‐depth gradient is interpreted as made of material erupted subaerially then transported and compacted downslope. Between this unit and the top of the oceanic plate, imaged by normal incidence seismic reflection, a more homogeneous unit indicated by shadow zones on several wide‐angle sections may correspond to lavas of a different nature, extruded underwater in the earlier phase of volcanism. Coincident wide angle and normal incidence reflections document that the oceanic plate is not generally downwarping toward the island but doming instead toward its southeastern part, with limited evidence for some intracrustal intrusion. Deeper in the lithosphere, the presence of a layer of intermediate velocity between the crust and mantle is firmly established. It is interpreted as resulting from the advection of hotspot magmatic products, possibly partially molten, and of a composition for which the crust is a density barrier. The extensive wide‐angle coverage constrains the extent of this body. It does not show the elongated shape expected from plate drift above a steady hotspot supply. Alternative propositions can hence be considered, for example, that La Réunion is caused by a solitary wave of hotspot material or by a young hotspot. The size of the underplate, 140 km wide and up to 3 km thick, corresponds to less than half the volume of the edifice on top of the plate.

Effects of differing sediment types and structures on normal incident acoustic reflections

Data acquired during a recent survey of coastal Florida and the Bahamas have provided an opportunity to correlate normal and near normal incidence acoustic returns with distinguishing seafloor sediment characteristics. These include physical property measurements (both in situ and laboratory) as well as bottom textural measurements derived from diver observations and from video and stereo photography. Measurements were made with a calibrated 1–3 piezocomposite transducer, which offered a very narrow (∼8 deg) beam width over the 10–50-kHz transmitted chirp. In addition, a roll and pitch sensor mounted on the transducer and 0–5 deg ship motion allowed for a monostatic backscatter experiment. This resulted in quatitative measurements of reflectivity versus angle over a relatively broad frequency band. Interestingly, the measured reflection coefficients were significantly lower (especially at high frequencies) and exhibited a greater range in values than those obtained in laboratory tank measurements with a flat, level interface. Also, the range of reflectivity at any fixed angle and anchor location was greater than the systematic dependence on angle. This suggests that very slight ship motion combined with either bottom roughness or discrete scatterers is responsible for the variable reflectivity. [Work supported by ONR.]