Abstract.We make progress towards a 3D finite-element model for the magnetization of a high temperature superconductor (HTS): We suggest a method that takes into account demagnetisation effects and flux creep, while it neglects the effects associated with currents that are not perpendicular to the local magnetic induction. We consider samples that are subjected to a uniform magnetic field varying linearly with time.

Magnetic shielding efficiency was measured on high-T c superconducting hollow cylinders subjected to either an axial or a transverse magnetic field in a large range of field sweep rates, dB app /dt. The behaviour of the superconductor was modelled in order to reproduce the main features of the field penetration curves by using a minimum number of free parameters suitable for both magnetic field orientations. The field penetration measurements were carried out on Pb-doped Bi-2223 tubes at 77 K by applying linearly increasing magnetic fields with a constant sweep rate ranging between 10 µT/s and 10 mT/s for both directions of the applied magnetic field. The experimental curves of the internal field vs. the applied field, B in (B app), show that, at a given sweep rate, the magnetic field for which the penetration occurs, B lim , is lower for the transverse configuration than for the axial configuration. A power law dependence with large exponent, n', is found between B lim and dB app /dt. The values of n' are nearly the same for both configurations. We show that the main features of the curves B in (B app) can be reproduced using a simple 2-D model based on the method of Brandt involving a E(J) power law with an n-exponent and a field-dependent critical current density, J c (B), (following the Kim model: J c = J c0 (1+B/B 1)-1). In particular, a linear relationship between the measured n'-exponents and the nexponent of the E(J) power law is suggested by taking into account the field dependence of the critical current density. Differences between the axial and the transverse shielding properties can be simply attributed to demagnetizing fields.

Abstract. Drilling holes in a bulk high-Tc superconductor enhances the oxygen annealing and the heat exchange with the cooling liquid. However, drilling holes also reduces the amount of magnetic flux that can be trapped in the sample. In this paper, we use the Bean model to study the magnetization and the current line distribution in drilled samples, as a function of the hole positions. A single hole perturbs the critical current flow over an extended region that is bounded by a discontinuity line, where the direction of the current density changes abruptly. We demonstrate that the trapped magnetic flux is maximized if the center of each hole is positioned on one of the discontinuity lines produced by the neighbouring holes. For a cylindrical sample, we construct a polar triangular hole pattern that exploits this principle; in such a lattice, the trapped field is ∼ 20% higher than in a squared lattice, for which the holes do not lie on discontinuity lines. This result indicates that one can simultaneously enhance the oxygen annealing, the heat transfer, and maximize the trapped field.

Abstract-We study the magnetic shielding properties of hybrid ferromagnetic/superconductor (F/S) structures consisting of two coaxial cylinders, with one of each material. We use an axisymmetric finite-element model in which the electrical properties of the superconducting tube are modeled by a nonlinear E-J power law with a magnetic-field-dependent critical current density whereas the magnetic properties of the ferromagnetic material take saturation into account. We study and compare the penetration of a uniform axial magnetic field in two cases: 1) a ferromagnetic tube placed inside a larger superconducting tube (Ferro-In configuration) and 2) a ferromagnetic tube placed outside the superconducting one (Ferro-Out configuration). In both cases, we assess how the ferromagnetic tube improves the shielding properties of the sole superconducting tube. The influence of the geometrical parameters of the ferromagnetic tube is also studied: It is shown that, upon an optimal choice of the geometrical parameters, the range of magnetic fields that are efficiently shielded by the hightemperature superconductor tube alone can be increased by a factor of up to 7 (2) in a Ferro-Out (Ferro-In) configuration. The optimal configuration uses a 1020 carbon steel with a thickness of 2 mm and a height that is half that of the superconducting cylinder (80 mm).Index Terms-Ferromagnetic/high-temperature superconductors (HTSs) hybrid structure, finite element, magnetic shield.

The spatial coherence and the optical phase distribution across a two-dimensional ͑2D͒ photonic crystal implemented with coupled arrays of vertical cavity surface emitting lasers ͑VCSELs͒ are experimentally characterized. This is achieved by performing Young's interference experiments between pairs of array elements using a spatial light modulator arrangement. In contrast to far-field measurements that provide information only on the global spatial coherence, this approach can yield full mapping of the complex degree of spatial coherence. Examples of such analysis are presented for nominally uniform one-dimensional and 2D arrays of coupled VCSELs and possible mechanisms of the observed coherence degradation are discussed. © 2007 American Institute of Physics. ͓DOI: 10.1063/1.2431474͔The output power of single-mode vertical cavity surface emitting lasers ͑VCSELs͒ is typically limited to a few milliwatts because of their small aperture area required for higher-order spatial mode suppression.1 Increasing the aperture size leads to poor selection between spatial modes and, above a certain size, results in uncontrolled filamentation, which limits the output power and degrades the spatial coherence and beam quality of the device. The problem of filamentation can be overcome by coupling a large number of single-mode VCSEL, forming two-dimensional ͑2D͒ arrays of phase-locked emitters. [2][3][4][5] In addition, these arrays exhibit a high degree of spatial coherence, as inferred from their nearly diffraction limited, four-lobed far-field patterns, which indicate that they oscillate predominantly at the lowest loss out-of-phase supermode. 2-5Evaluating the features of spatial coherence of coupled-VCSEL arrays is important not only for optimizing their coupling but also for developing functionalities that rely on such coherence. An example of such application is beam steering, where control over the mutual phase of the emitters is necessary.The spatial coherence in phase-locked VCSEL arrays has traditionally been evaluated using measurements of their far-field patterns 2,3 complemented by model calculations of their supermodes. 4,5 However, this approach yields information only on the global coherence properties of the array, in particular, the deviation of the beam pattern from the expected diffraction limited distribution. Moreover, such analysis generally cannot give direct indications on the mechanisms of coherence degradation. Spectral analysis of such arrays, e.g., using spectrally resolved far-field patterns or spatially resolved emission spectra, could give more indications on spatial coherence, but is difficult due to the small spectral splitting of the supermodes in large arrays.A more complete evaluation of the spatial coherence across a VCSEL array would be to measure the complex degree of spatial coherence ␥͑x , y ; xЈ , yЈ͒ between pairs of points in the array plane ͑x , y͒. This can be accomplished by performing Young's interference experiments, in which the interference pattern corresponding to two selected...