Method of producing apparatus comprising a low-reflection optical fiber connection

It has been discovered that tilted optical fiber endfaces useful in low-reflection optical fiber joints can be produced by cleaving, provided the fiber is twisted through an appropriate twist angle. By way of example, for a particular, commercially available single mode fiber, the normalized twist angle typically is in the range of 5-15 degrees/cm, resulting in a nominal tilt angle of the fiber endface in the approximate range 5-20 degrees.Published versio

Directional tunnelling spectroscopy of a normal metal-s+gs+g-wave superconductor junction

We calculate the normal metal-$s+g$-wave superconductor tunnelling spectrum for various junction orientations and for two forms of the superconducting gap, one which allows for point nodes and the other which allows for line nodes. For a junction oriented with its normal parallel to the ab plane of the tetragonal superconductor, we find that the tunnelling spectrum is strongly dependent on orientation in the plane. The spectrum contains two peaks at energies equivalent to the magnitudes of the gap function in the direction parallel to the interface normal and in the direction making a $\pi/4$ angle with the normal. These two peaks appear in both superconductors with point nodes and line nodes, but are more prominent in the latter. For the tunnelling along the c axis, we find a sharp peak at the gap maximum in the conductance spectrum of the superconductor with line nodes, whereas with point nodes we find a peak occurring at the value of the gap function along the c axis. We discuss the relevance of our result to borocarbide systems.Comment: 16 pages, 10 figure

Spin polarized tunneling in ferromagnet/unconventional superconductor junctions

We study tunneling in ferromagnet/unconventional superconductor (F/S) junctions. We include the effects of spin polarization, interfacial resistance, and Fermi wavevector mismatch (FWM) between the F and S regions. Andreev reflection (AR) at the F/S interface, governing tunneling at low bias voltage, is strongly modified by these parameters. The conductance exhibits a very wide variety of features as a function of applied voltage.Comment: Revision includes new figures with angular averages and correction of minor error

Methods for making mirrors

A turning mirror in an optical waveguide structure is made by etching in the upper surface of the structure a cavity (18) that intercepts the path of light propagated by the waveguide (15, 16, 13). Preferably, the cavity is made to be asymmetric with the side (25) of the cavity remote from the waveguide sloping at typically a forty-five degree angle. The asymmetry can be introduced by using mask and etch techniques and treating the surface of the structure such that the etchant undercuts the mask on the side of the cavity remote from the waveguide to a greater extent than it undercuts the mask on the side of the cavity adjacent the waveguide.Published versio

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.Comment: 8 pages including 3 figures (revised, 6 references added

Functional diversity metrics using kernel density n-dimensional hypervolumes

The use ofn-dimensional hypervolumes in trait-based ecology is rapidly increasing. By representing the functional space of a species or community as a Hutchinsonian niche, the abstract Euclidean space defined by a set of independent axes corresponding to individuals or species traits, these multidimensional techniques show great potential for the advance of functional ecology theory. In the panorama of existing methods for delineating multidimensional spaces, therpackagehypervolume(Global Ecology and Biogeography, 23, 2014, 595-609) is currently the most used. However, functions for calculating the standard set of functional diversity (FD) indices-richness, divergence and regularity-have not been developed within thehypervolumeframework yet. This gap is delaying its full exploitation in functional ecology, meanwhile preventing the possibility to compare its performance with that of other methods. We develop a set of functions to calculate FD indices based onn-dimensional hypervolumes, including alpha (richness), beta (and respective components), dispersion, evenness, contribution and originality. Altogether, these indices provide a coherent framework to explore the primary mathematical components of FD within a multidimensional setting. These new functions can work either with hypervolume objects or with raw data (species presence or abundance and their traits) as input data, and are versatile in terms of input parameters and options. These functions are implemented withinbat(Biodiversity Assessment Tools), anrpackage for biodiversity assessments. As a coherent corpus of functional indices based on a common algorithm, it opens the possibility to fully explore the strengths of the Hutchinsonian niche concept in community ecology research.Peer reviewe

Tunnelling spectroscopy of the interface between Sr2RuO4 and a single Ru micro-inclusion in eutectic crystals

The understanding of the zero bias conductance peak (ZBCP) in the tunnelling spectra of S/N junctions involving d-wave cuprate superconductors has been important in the determination of the phase structure of the superconducting order parameter. In this context, the involvement of a p-wave superconductor such as Sr2RuO4 in tunnelling studies is indeed of great importance. We have recently succeeded in fabricating devices that enable S/N junctions forming at interfaces between Sr2RuO4 and Ru micro-inclusions in eutectic crystals to be investigated.3 We have observed a ZBCP and have interpreted it as due to the Andreev bound state, commonly seen in unconventional superconductors. Also we have proposed that the onset of the ZBCP may be used to delineate the phase boundary for the onset of a time reversal symmetry broken (TRSB) state within the superconducting state, which does not always coincide with the onset of the superconducting state. However, these measurements always involved two interfaces between Sr2RuO4 and Ru. In the present study, we have extended the previous measurements to obtain a deeper insight into the properties of a single interface between Sr2RuO4 and Ru.Comment: To appear in J. Phys. Soc. Jpn. Vol. 75 No.12 issu

Mesoscopic Ferromagnet/Superconductor Junctions and the Proximity Effect

We have measured the electrical transport of submicron ferromagnets (Ni) in contact with a mesoscopic superconductor (Al) for a range of interface resistances. In the geometry measured, the interface and the ferromagnet are measured separately. The ferromagnet itself shows no appreciable superconducting proximity effect, but the ferromagnet/superconductor interface exhibits strong temperature, field and current bias dependences. These effects are dependent on the local magnetic field distribution near the interface arising from the ferromagnet. We find that the temperature dependences may be fit to a modified version of the Blonder-Tinkham-Klapwijk theory for normal-superconductor transport.Comment: 4 eps fig

Nonlinear Transport through NS Junctions due to Imperfect Andreev Reflection

We investigate a normal metal -- superconductor (point) contact in the limit where the number of conducting channels in the metallic wire is reduced to few channels. As the effective Fermi energy drops below the gap energy, a conducting band with a width twice the Fermi energy is formed. Depending on the mode of operation, the conduction band can be further squeezed, leading to various non-linear effects in the current-voltage characteristics such as current saturation, a N-shaped negative differential resistance, bistability, and hysteresis.Comment: 4 pages, RevTeX, three postscript figure

Thouless energy of a superconductor from non local conductance fluctuations

We show that a spin-up electron from a normal metal entering a superconductor propagates as a composite object consisting of a spin-down hole and a pair in the condensate. This leads to a factorization of the non local conductance as two local Andreev reflections at both interfaces and one propagation in the superconductor, which is tested numerically within a one dimensional toy model of reflectionless tunneling. Small area junctions are characterized by non local conductance fluctuations. A treatment ignoring weak localization leads to a Thouless energy inverse proportional to the sample size, as observed in the numerical simulations. We show that weak localization can have a strong effect, and leads to a coupling between evanescent quasiparticles and the condensate by Andreev reflections ``internal'' to the superconductor.Comment: 11 pages, 12 figures, revised manuscrip