Lie-symmetry vector fields for linear and nonlinear wave equations

We derive the Lie symmetry vector fields for the linear wave equation u=0 and nonlinear wave equation u=u ³. The conformal vector fields for the underlying metric tensor fieldg are also given. We construct the conservation laws and derive similarity solutions. Furthermore, we perform a Painlevé test for the nonlinear wave equation and discuss whether Lie-Bäcklund vector fields exist.     

Continuous wave 1.6 μm laser action in Er doped garnets at room temperature⋆

We report on room-temperature cw laser action of Er³⁺: Yttrium-aluminum-garnet (YAG) and Er³⁺: Yttrium-gallium-garnet (YGG) crystals at 1.64 m. The laser operates from the metastable⁴ I _13/2 manifold into an upper Stark level of the⁴ I _15/2 ground-state manifold of Er³⁺. Due to reabsorption losses, the Er³⁺ concentration of the laser crystals must be low. Laser pumping at a wavelength of 647.1 nm yields lowest thresholds around 30 mW and slope efficiencies up to 12.7% for Er:YAG. Laser operation in Er:YGG is achieved with higher thresholds of about 200 mW and smaller slope efficiencies of 0.9%. The effective emission cross section in YAG is estimated to be _e5×10^–21 cm².Dedicated to Prof. Dr. Herbert Welling on the occasion of his 60th birthday     

Influence of end reflectivity on gain saturation in a planar distributed feedback laser

An approximate method for the analysis of planar-waveguide distributed-feedback lasers is extended to include a nonvanishing reflectivity at the ends of the structure. An index grating structure with parasitic losses is investigated. An expression for the small-signal gain coefficient ^0MN as a function of the output power P ^MNout normalized to the saturation power P ^s , coupling coefficient K, complex reflectivity R of end reflectors, and waveguide parameters is presented.     

Conductivity relaxation in glass: Compositional contributions to non-exponentiality

That ionic conductivity in glass is a non-exponential process and has been known for many years. The amorphous structure of glass and hence a distribution of cation sites has often been thought to be the cause for the non-exponentiality. Almost completely unresearched, however, has been the effect of glass composition on the nature of the relaxation process. In this paper, we review the observations that have been made of the relationships between glass composition and the non-exponential character of the conductivity relaxation as well combine our recent wide composition range studies of sodium aluminoborate and lithium phosphate glasses to delineate the major features of the correlation. By examining glass compositions ranging from 0.02 to 60 mole% alkalioxide, it is observed that the rapid development of non-exponentiality within 1% Na₂O is accompanied by a similar rapid decrease in the average cation-cation separation distance, this being calculated using the composition and density. Other quantities such as the dc conductivity or activation energy are observed to vary too slowly with composition to produce a linear correlation with the extent of non-exponentiality as monitored in the parameter of the stretched exponentialkww function.     

The influence of hydrogen on the atomic distribution function and electrical resistance of amorphous chromium films

Electrical resistivity of amorphous chromium films (20–37 nm thick) deposited in a hydrogen atmosphere (P _{H 2}=8·10^–6–2·10^–4 hPa) onto a substrate cooled by liquid helium down to 2 K is measured, and electron-diffraction studies have been performed immediately after the quench condensation and after annealing to different temperatures up to 300 K. The preparation method employed permits a considerable hydrogen enrichment of the films to be reached. The maximum hydrogen concentration corresponds approximately to a stoichiometric composition of CrH. It is found that as the maximum concentration is approached the atomic distribution functionG(r) changes remarkably. The interatomic distances increase considerably (by 10%) and the atomic densities decrease. It is quite possible that amorphous chromium hydride is a final state with the maximum hydrogen concentration. For films with intermediate concentration,G(r) is found to vary substantially under annealing up to 90 K. The electron-diffraction and electronmicroscopic data, as well as the variations in resistivity due to annealing, suggest that with annealing up to 90 K, a hydrogen redistribution occurs in the amorphous films, initially homogenous in concentration. We observe also distinct indications of separation into phases with increased and reduced hydrogen contents.     

Dispersive anisotropic ballistic phonon propagation in [100] GaAs

We report experimental observations of the phonon focusing pattern in [100] GaAs using low temperature electron beam scanning for phonon generation. The typical dispersive effects for high-frequency phonons expected from the calculations by Tamura have clearly been observed using PbIn tunnel junctions for phonon detection. The quantitative comparison of our experimental results with the frequency dependent calculations by Tamura allowed to determine the dominant phonon frequencies contributing to the detector signal in our different experiments. Above the temperature of the -point the dominant phonon frequencies appear to be shifted considerably to lower values, which could be explained by a heating effect in the liquid-He layer adjacent to the tunnel junction detector. By comparing the observed magnitude of the detector signal with different theoretical treatments of the detector response, we have found satisfactory agreement for a model where the perturbation due to the high-frequency phonons is restricted to the base electrode of the detector reached first by the phonons following their passage through the crystal.