Al satellite transition spectroscopy (SATRAS) of polycrystalline aluminium borate 9Al2O3 · 2B2O3

²⁷Al NMR spectra of polycrystalline aluminium borate 9Al₂O₃ · 2B₂O₃ have been measured at 104, 130 and 156 MHz. The parameters of the quadrupole interaction and the isotropic chemical shifts have been obtained by fitting the CT/MAS pattern and consideration of the inner satellite transitions m = 3/2 ↔ 1/2 and m = −1/2 ↔ −3/2. The gain in spectral resolution concerned with the observation of the MAS lines of the inner satellites leads to complete separation of the signals of AlO₆, AlO₅ and AlO₄ polyhedra. Also signals of structural groups of one and the same coordination number can be distinguished. Experimental and theoretical lineshape calculations are compared.     

Global existence via Ginzburg-Landau formalism and pseudo-orbits of Ginzburg-Landau approximations

The so-called Ginzburg-Landau formalism applies for parabolic systems which are defined on cylindrical domains, which are, close to the threshold of instability, and for which the unstable Fourier modes belong to non-zero wave numbers. This formalism allows to describe an attracting set of solutions by a modulation equation, here the Ginzburg-Landau equation. If the coefficient in front of the cubic term of the formally derived Ginzburg-Landau equation has negative real part the method allows to show global existence in time in the original system of all solutions belonging to small initial conditions, inL . Another aim of this paper is to construct a pseudo-orbit of Ginzburg-Landau approximations which is close to a solution of the original system up tot=. We consider here as an example the socalled Kuramoto-Shivashinsky equation to explain the methods, but it applies also to a wide class of other problems, like e.g. hydrodynamical problems or reaction-diffusion equations, too.     

The shadow of a collapsing dark star

The shadow of a black hole is usually calculated, either analytically or numerically, on the assumption that the black hole is eternal, i.e., that it has existed for all time. Here we ask the question of how this shadow comes about in the course of time when a black hole is formed by gravitational collapse. To that end we consider a star that is spherically symmetric, dark and non-transparent and we assume that it begins, at some instant of time, to collapse in free fall like a ball of dust. We analytically calculate the dependence on time of the angular radius of the shadow, first for a static observer who is watching the collapse from a certain distance and then for an observer who is falling towards the centre following the collapsing star.     

Multiple conversion and optical limiting in a subharmonic-pumped parametric oscillator

We demonstrate that multiple coexisting frequency-conversion processes can occur in an externally resonant second-harmonic generator under suitable conditions. Besides the generation of signal and idler waves by subharmonic-pumped parametric oscillation, sum-frequency mixing among the resonant subharmonic (1064-nm), signal, and idler waves was observed, leading to additional emission wavelengths around the harmonic wavelength (532 nm). The output waves both exhibit high frequency stability, with as long as 4 h of mode-hop-free parametric oscillation, and are continuously tunable over 2 GHz. Near degeneracy the parametric oscillator operates as an optical limiter for the harmonic wave.     

Nanometric Antimony Powder Synthesis by Activated Alkaline Hydride Reduction of Antimony Pentachloride

A novel chemical reduction method using an activated alkaline hydride (LiH or NaH-t-BuONa) in tetrahydrofuran solvent has been applied to antimony salt reduction. X-ray diffraction and transmission electron microscopy studies have been carried out to characterize the morphology and structure of the materials. Alkali hydride nature influence has been proved. In both cases the process allows to prepare antimony particles in nanometer range from few nanometers to about 20nm which could be used as anodic materials for lithium–ion batteries. With lithium hydride well-crystallized particles inclined to agglomeration were observed whereas finely dispersed amorphous particles were pointing out after activated sodium hydride reduction.     

Time-resolved photoemission electron microscopy of magnetic field and magnetisation changes

Owing to its parallel image acquisition, photoemission electron microscopy is well suited for real-time observation of fast processes on surfaces. Pulsed excitation sources like synchrotron radiation or lasers, fast electric pulsers for the study of magnetic switching, and/or time-resolved detection can be utilised. A standard approach also being used in light optical imaging is stroboscopic illumination of a periodic (or quasi-periodic) process. Using this technique, the time dependence of the magnetic field in a pulsed microstrip line has been imaged in real time exploiting Lorentz-type contrast. Similarly, the corresponding field-induced changes in the magnetisation of cobalt microstructures deposited on the microstrip line have been observed exploiting magnetic X-ray circular dichroism as a contrast mechanism. The experiment has been performed at the UE 56/1-PGM at BESSY II (Berlin) in the single-bunch mode. Received: 2 September 2002 / Accepted: 2 September 2002 / Published online: 5 March 2003 RID="*" ID="*"Corresponding author. Fax: +49-6131/392-3807, E-mail: krasyuk@mail.uni-mainz.de     

Examples of Twisted Cyclic Cocycles from Covariant Differential Calculi

For two covariant differential *-calculi, the twisted cyclic cocycle associated with the volume form is represented in terms of commutators for some self-adjoint operator and some *-representation of the underlying *-algebra.     

Time-resolved electron transport studies on InGaAs/GaAs-QWIPs

Due to the short internal response time, quantum-well infrared photodetectors (QWIPs) are interesting for high-speed applications such as heterodyne spectroscopy or laser pulse monitoring. We studied the photocurrent transients of InGaAs/GaAs-QWIPs after irradiation with infrared laser pulses of 250 fs duration. The excitation wavelength of about 9 μm matches the peak wavelength of the QWIP structure. The photocurrent transient consists of two different dynamical components, representing the fast photoionization in the quantum-wells and the slow injection current that compensates the remaining space charge. The investigations of the different components as a function of temperature and bias voltage were performed on a nanosecond time-scale. The experimental separation of the two photocurrent contributions allows us to determine the photoconductive gain. The Fourier transform of the photocurrent transient was compared with other experimental methods including heterodyne detection and microwave rectification. The quantitative agreement between these different measurement techniques is excellent.     

Efficient terahertz coupling lens based on planar photonic crystals on silicon on insulator

We present a promising coupling device, namely, a terahertz (THz) planar photonic crystal (PhC) lens based on the effective refractive-index contrast between the PhC and the surrounding unpatterned area. Three-dimensional finite-difference time-domain calculations show a 90% power transfer from a 100-microm silicon waveguide to a 10-microm waveguide, and 45% coupling efficiency is confirmed experimentally. These results demonstrate the utility of the PhC lens as an effective approach to coupling into PhC THz circuits.