Reflection of plane waves from the boundary of a pre-stressed compressible elastic half-space

The effect of pre-stress on the propagation and reflection ofplane waves in an incompressible isotropic elastic half-spacehas been examined recently by the authors (Ogden & Sotiropoulos,1997). In the present paper the corresponding analysis for compressiblematerials is detailed. In the two-dimensional context consideredfor incompressible materials the (homogeneous) plane waves werenecessarily shear waves. By contrast, in the compressible contextpure shear waves can propagate only in specific directions inthe considered principal plane and, in a general direction,a quasi-shear wave may be accompanied by a quasi-longitudinalwave, as is the case in the anisotropic linear theory. The dependenceof the (in-plane) slowness section on the pre-stress (and finitedeformation) and on the choice of constitutive law is elucidated.This information is used to determine the reflection coefficientsfor reflection of either a (quasi-) shear wave or a (quasi-)longitudinal wave from the boundary of the half-space and tocharacterize the different cases which arise depending on thegeometry of the slowness section. The theoretical results are illustrated by numerical calculationsfor the range of possible types of behaviour with referenceforms of strain-energy function and different states of finitedeformation and to the question of stability of the half-space.     

Calculation of the temperature dependence of the negative thermal expansion of polyethylene chains by means of the self-consistent harmonic approximation

A parameter-free model based on molecular mechanics with zero Kelvin potentials is developed to describe quantitatively the shortening of the unit cell of polyethylene crystals in chain direction with increasing temperature. Based on the well-known conception that an increase of the amplitudes of the torsional vibrations will cause the thermal shrinkage, we introduce a self-consistent phonon approach to calculate the temperature dependence of the angular displacement correlation function taking into account the anharmonicity of the potential. By means of these functions, we calculate the mean value of the length of a representative chain segment and compare the results with those obtained from x-ray diffraction measurements. © 1996 John Wiley & Sons, Inc.     

Experimental realization of highly efficient broadband coupling of single quantum dots to a photonic crystal waveguide

We present time-resolved spontaneous emission measurements of single quantum dots embedded in photonic crystal waveguides. Quantum dots that couple to a photonic crystal waveguide are found to decay up to 27 times faster than uncoupled quantum dots. From these measurements beta-factors of up to 0.89 are derived, and an unprecedented large bandwidth of 20 nm is demonstrated. This shows the promising potential of photonic crystal waveguides for efficient single-photon sources. The scaled frequency range over which the enhancement is observed is in excellent agreement with recent theoretical proposals taking into account that the light-matter coupling is strongly enhanced due to the significant slow-down of light in the photonic crystal waveguides.     

Mapping the local density of optical states of a photonic crystal with single quantum dots

We use single self-assembled InGaAs quantum dots as internal probes to map the local density of optical states of photonic crystal membranes. The employed technique separates contributions from nonradiative recombination and spin-flip processes by properly accounting for the role of the exciton fine structure. We observe inhibition factors as high as 70 and compare our results to local density of optical states calculations available from the literature, thereby establishing a quantitative understanding of photon emission in photonic crystal membranes.     

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