Passively mode-locked Yb:KLu(WO4)2 thin-disk oscillator operated in the positive and negative dispersion regime

We demonstrate a passively mode-locked femtosecond Yb:KLu(WO(4))(2) thin-disk laser oscillator. Chirped-pulse operation in the positive dispersion regime as well as solitary operation have been realized, and the laser performance of both configurations are compared. In the solitary mode-locking regime the output power exceeds 25 W in a diffraction-limited beam, and pulse durations as short as 440 fs at a 34.7 MHz repetition rate have been generated. For the first time we present a chirped-pulse operation of a thin-disk oscillator that yields a maximum average output power of 9.5 W with a Fourier limit of 450 fs.     

Kirsti Andersen: Optical Illusions in Rome – A Mathematical Travel Guide

Mathematische Semesterberichte -     

A numerical study of a rotationally degenerate hyperbolic system. Part I. The Riemann problem

We study numerically the Riemann problem for a 2 x 2 system of conservation laws with a cubic flux function, a particular case of the class of models introduced by Keyfitz and Kranzer. The system is not strictly hyperbolic, and the classical Lax theory for hyperbolic systems is not directly applicable. Correspondingly, some numerical schemes which are accurate for strictly hyperbolic systems are not well behaved for this example. When they do work, different schemes yield markedly different results for certain data. We explain this effect by observing that, near these data, viscous regularization is non-uniform as the viscosity tends to zero. This fact does not contradict the well-posedness of the hyperbolic model; it does imply that precise control of the viscosity introduced into a computational method is crucial for generating the correct numerical solutions. We examine all of these issues and comment on their implications for similar systems which arise in continuum mechanics.     

Effects of annealing on properties of ZnO thin films prepared by electrochemical deposition in chloride medium

The development of cost-effective and low-temperature synthesis techniques for the growth of high-quality zinc oxide thin films is paramount for fabrication of ZnO-based optoelectronic devices, especially ultraviolet (UV)-light-emitting diodes, lasers and detectors. We demonstrate that the properties, especially UV emission, observed at room temperature, of electrodeposited ZnO thin films from chloride medium (at 70 °C) on fluor-doped tin oxide (FTO) substrates is strongly influenced by the post-growth thermal annealing treatments. X-ray diffraction (XRD) measurements show that the films have preferably grown along (0 0 2) direction. Thermal annealing in the temperature range of 150-400 °C in air has been carried out for these ZnO thin films. The as-grown films contain chlorine which is partially removed after annealing at 400 °C. Morphological changes upon annealing are discussed in the light of compositional changes observed in the ZnO crystals that constitute the film. The optical quality of ZnO thin films was improved after post-deposition thermal treatment at 150 °C and 400 °C in our experiments due to the reducing of defects levels and of chlorine content. The transmission and absorption spectra become steeper and the optical bandgap red shifted to the single-crystal value. These findings demonstrate that electrodeposition have potential for the growth of high-quality ZnO thin films with reduced defects for device applications.     

On a new condition distinguishing Weyl and Lorentz space-times

The paper is concerned with the derivability of a Lorentz instead of only a Weyl manifold as space-time structure from postulates about free fall and light propagation. For this purpose it identifies a property distinguishing both kinds of space-times. The property is one of a particular metric of the conformal class of the Weyl manifold. viz. that in suitably chosen locally geodesic coordinates theg _i4 components,i=1, 2, 3 vanish along the time axis. Although seemingly somewhat hidden, one is led to this property in looking for a metric which can play a distinguished role. We demonstrate that for a Lorentzian manifold such a condition is always given; thus it is a necessary one. It is sufficient since for a Weyl space it has the consequence that the metric connection of the selectedg is projectively equivalent to the Weyl connection. Thus, if a Weyl space-time complies with it, it is a reducible one. The results of this paper lay the ground for deriving in a second step this condition from a simple, empirically testable postulate about free-fall worldlines and “radar” measurements by light signals.     

Parallel information-based complexity

We develop the theory of information-based complexity from a parallel point of view. For a model of computation with p processors, each being capable of arithmetic operations and decisions, we analyze the complexity of function approximation, numerical integration, and solution of Fredholm integral equations. We obtain tight bounds on the complexity, considered as a function of three variables simultaneously: the number of processors, the required precision, and (in the case of approximation and integral equations) the number of points, in which the approximate solution is to be determined.     

Hermitian quadratic eigenvalue problems of restricted rank

We consider a quadratic eigenvalue problem such that the second order term is a Hermitian matrix of rank r, the linear term is the identity matrix, and the constant term is an arbitrary Hermitian matrix . Of the n+r solutions that this problem admits, we show at least n-r to be real and located in specific intervals defined by the eigenvalues of A, whence at most 2r are nonreal occuring in possibly repeated conjugate pairs.     

Numerical computation of viscous profiles for hyperbolic conservation laws

Viscous profiles of shock waves in systems of conservation laws can be viewed as heteroclinic orbits in associated systems of ordinary differential equations (ODE). In the case of overcompressive shock waves, these orbits occur in multi-parameter families. We propose a numerical method to compute families of heteroclinic orbits in general systems of ODE. The key point is a special parameterization of the heteroclinic manifold which can be understood as a generalized phase condition; in the case of shock profiles, this phase condition has a natural interpretation regarding their stability. We prove that our method converges and present numerical results for several systems of conservation laws. These examples include traveling waves for the Navier-Stokes equations for compressible viscous, heat-conductive fluids and for the magnetohydrodynamics equations for viscous, heat-conductive, electrically resistive fluids that correspond to shock wave solutions of the associated ideal models, i.e., the Euler, resp. Lundquist, equations.

     

Towards molecular-scale electronics and biomolecular self-assembly

This paper provides an overview of recent research developments in the field of nanoelectronics with organic materials such as carbon nanotubes and DNA-templated nanowires. Carbon nanotubes and gold electrodes are chemically functionalized in order to contact carbon nanotubes by self-assembly. The transport properties of these nanotubes are dominated by charging effects and display clear Coulomb blockade behaviour. A different approach towards nanoscale electronics is based on the molecular recognition properties of biomolecules such as DNA. As an example, DNA is stretched between electrodes using a molecular combing technique. A two-step metallization procedure leads to the formation of highly conductive gold nanowires.