Photorefractive two-beam coupling equations with multiple spatial–temporal features: an SVD approach

We analyze the evolution of multi-feature two-beam coupling, wherein each beam contains several spatial–temporal features (spatial patterns modulated by different signals), using a one-dimensional plane wave model to describe the evolution of paired components. This general scenario is of interest for analyzing signal-processing applications of photorefractives, such as source-separation by orthogonalization of source-modulated spatial patterns. We use singular-value decomposition (SVD) to express each beam as a simple superposition of modes that are both temporally uncorrelated and spatially orthogonal. We find a solution that is a natural matrix generalization of the scalar solution for simple two-beam coupling, and a test for its validity: the two operators that give the spatial overlap associated with the temporal basis signals in the two beams must commute. Equivalently, this means that the same set of signals must be modulating the SVD modes in the two beams. Then the SVD modes are preserved in the two-beam coupling evolution, with only their amplitudes changing. Dedicated to Prof. Dr. Eckard Kr?tzig on the occasion of his 60th birthday. Received: 10 November 1998 / Revised version: 13 January 1999 / Published online: 7 April 1999     

Cochlear compression wave: an implication of the Allen-Fahey experiment

In order to measure the gain of the cochlear amplifier, de Boer and co-workers recently extended the Allen-Fahey experiment by measuring otoacoustic emissions and basilar membrane vibration [J. Acoust. Soc. Am. 117, 1260-1266 (2005)]. Although this new experiment overcame the limitation of the original Allen-Fahey experiment for using a low-frequency ratio, it confirmed the previous finding that there is no detectable cochlear amplification. This result was attributed to destructive interference of the otoacoustic emission over its generation site. The present letter provides an alternative interpretation of the results of the Allen-Fahey experiment based on the cochlear fluid compression-wave theory.     

Spectroscopic studies of the metal complexes of ethylenediaminetetra-acetic acid in aqueous solution

Aqueous solutions of the metal complexes of ethylenediaminetetra-acetic acid (EDTA) are widely used in analysis; though X-ray diffraction methods cannot be directly used for structural determination in solution, ultraviolet-visible region, vibrational and NMR spectroscopy studies demonstrate that the species in solution adopt a similar range of stereochemistries to those determined for the solid state. Thus a review of the spectroscopic properties of the solutions suggests that chelates are formed in which the denticity of EDTA varies from one to six and the co-ordination number about the metal from four to nine.     

Asymptotics of Hermite-Padé polynomials for a set of functions with different branch points

For an example where the functions have different branch points we derive the asymptotics of diagonal Hermite-Padé polynomials of type I. The method uses an integral equation obtained by approximating a reproducing kernel. The results are consistent with a new conjecture on the asymptotics of the polynomials associated with more general functions with different branch points.     

Solid state broadening in Auger spectra

Some Auger spectra in the gas phase show extremely sharp lines and a great deal of fine structure while the Auger spectra of solids, even at high resolution, lack this detailed fine structure and generally have much broader peaks. In an effort to understand the broadening processes which occur on condensation of a gas or vapour to the solid phase, several solids for which high resolution gas phase data exists have been studied. The result of measurements of the M₄₅N₄₅N₄₅ Auger spectrum of cadmium are reported and comparison is made with the vapour phase data. Although the solid data contains considerable quasi-atomic fine structure the lines are broader than the vapour phase and by matching computer broadened vapour phase data to the experimental data an estimate of the individual line widths may be made. The relative intensities of the lines in the simulation agree closely with the solid data if loss processes are considered. Measurements have also been made on the same Cd transition in CdS and in this material the Auger lines are much broader than in Cd metal and the fine structure has almost disappeared. Results are also reported of measurements of the Auger spectra of solid rare gases made with the aid of a UHV cryostat capable of operating at temperatures down to 10 K. The gases studied were Xe, Ar and Kr and again comparison with computer broadened gas data enable the broadening of individual Auger lines to be estimated. Measurements of the line breadths have been made at various temperatures and the results of these experiments will be discussed in terms of lifetime and lattice vibrational broadening.     

Solid state broadening effects in the Auger spectrum of xenon

The M_4,5N_4,5 Auger spectrum has been measured at high resolution from solid xenon. Comparison with the gas phase data shows that considerable broadening of the Auger lines occurs in the solid. Electron energy loss data is also reported for solid xenon.     

Two hydrogenic trapped-hole species in α-quartz

EPR studies of single crystal α-quartz at ca. 25 K, which had been X-irradiated, have revealed the presence of two new trapped-hole impurity centers. One of these is thought to be formed by trapping of an electron hole at an oxygen ion adjacent to a silicon 4+ ion vacancy occupied by four protons. The second center is similar with only three protons present. The Zeeman splitting (g) matrices for the two species have been determined and are compared to those for analogous aluminum hole species.