On the Green's Function of the almost-Mathieu Operator

The square tight-binding model in a magnetic field leads to the almost-Mathieu operator which, for rational fields, reduces to a $q\times q$ matrix depending on the components $\mu$, $\nu$ of the wave vector in the magnetic Brillouinzone. We calculate the corresponding Green's function without explicit knowledge of eigenvalues and eigenfunctions and obtain analytical expressions for the diagonal and the first off-diagonal elements; the results which are consistent with the zero magnetic field case can be used to calculate several quantities of physical interest (e. g. the density of states over the entire spectrum, impurity levels in a magnetic field).Comment: 9 pages, 3 figures corrected some minor errors and typo

Entangled Photon Holes

Most experimental demonstrations of entanglement require nonclassical states and correlated measurements of single-photon detection events. It is shown here that entanglement can produce a large decrease in the rate of two-photon absorption for a classical input state that can be observed using classical detectors. These effects can be interpreted as being due to the creation of entangled photon holes that are somewhat analogous to the holes of semiconductor theory.Comment: 4 pages, 3 figures. Additional discussion of Bell's inequalit

Quantum versus classical descriptions of sub-Poissonian light generation in three-wave mixing

Sub-Poissonian light generation in the non-degenerate three-wave mixing is studied numerically and analytically within quantum and classical approaches. Husimi Q-functions and their classical trajectory simulations are analysed to reveal a special regime corresponding to the time-stable sub-Poissonian photocount statistics of the sum-frequency mode. Conditions for observation of this regime are discussed. Theoretical predictions of the Fano factor and explanation of the extraordinary stabilization of the sub-Poissonian photocount behavior are obtained analytically by applying the classical trajectories. Scaling laws for the maximum sub-Poissonian behavior are found. Noise suppression levels in the non-degenerate vs degenerate three-wave mixing are discussed on different time scales compared to the revival times. It is shown that the non-degenerate conversion offers much better stabilization of the suppressed noise in comparison to that of degenerate process.Comment: 9 pages, 12 figures, to be published in J. Optics

Effect of Inorganic (Nano)fillers on the UV Barrier Properties, Photo and Thermal Degradation of Polypropylene Fibres. FIBRES & TEXTILES in Eastern Europe

Abstract Barrier properties against ultraviolet radiation and the light stability of polypropylene (PP) n Introduction The UV barrier properties and light stability of PP composite fibres are extremely important for textile products, light-weight summer fabric and leisure and sports wear. Furthermore, the thermal stability of PP composites is required in the spinning process as well as in the thermal treatment of fibres and fabric. Many papers have also dealt with the photo (light -induced) and thermooxidation of nanocomposites, but relatively poor information related to the effect of sunlight and elevated temperature on nanocomposite fibres and fabrics appears in periodic literature. The UV radiation of sunlight can be divided into UV-C (100 -280 nm), UV-B (280 -315 nm) and UV-A (315-400 nm) components, which denote the effect on living organisms. The human skin has to be protected against UV-B type radiation only, while the most dangerous UV-C type is absorbed by the atmosphere. UV-A radiation is essentially less dangerous than the other two However, the improvement of the UV barrier properties of textile fibres with solid nano particles incorporated into the matrix of the PP fibres also requires them to be environmentally durable in their processing and utilisation. Photo and thermal degradation, especially of PP nanocomposites and composite fibres, has been a very attractive area of research in recent years [6 -10]. The papers most often deal with the effect of UV irradiation on the photostability of PP/organoclay composites as well as with the role of pristine montmorillonite (MMT), compatibilisers and organic ammonium compounds in the oxidative degradation of polymers. The main negative effect on the photo degradation of PP was found for pristine MMT (catalytic active sites), PP grafted with a maleic anhydride compatibiliser (photoresponsive carboxylic and anhydride groups) and for alkyl ammonium compounds (the decomposition of ammonium ion leads to catalytic acidic sites) Furthermore, an organically untreated inorganic boehmite filler decreases the photostability of PP/boehmite composites due to the absorption of stabilisers on the hydrophilic surface, which prevents their antioxidant action Inorganic nanoparticles in polymer composites can also affect their thermal stability and fire retardancy. The improved thermal stability and fire retardancy of PP/organoclay composites (5 wt% of organoclay) were found. The suppression of the thermooxidation of PP composites is explained by the diffusion barrier and reduction in mass loss In this paper the effect of inorganic nanofillers, such as organoclays, boehmites (aluminas) multiwall carbon nanotubes (MWCNT) and nano-sized TiO 2, on the UV barrier properties, photooxidation and thermal stability of PP composite fibres was studied. Correlations between the UV barrier properties, light stability and thermal stability of PP composite fibres are discussed. n Multi-Wall Carbon Nanotubes -Nanocyl® 7000, (MWCNT), average diameter 10 nm, length 0.1 -10 μm, surface area 250 -300 m 2 /g, carbon content 90%, metal oxide impurity 10%, (from Nanocyl S.A., Belgium) Nano TiO 2 fillers: Hombitec S 100, (TiO 2 S100), TiO 2 content 89.0 wt%, particle size 15 nm, specific surface 68 m 2 /g, (from Sachtleben, Inc., Duisburg, Germany), and UV Titan P160 (TiO 2 P160), content 80.0 wt%, particle size 17 nm, specific surface 59 m 2 /g (from Kemira Pigments Oy, Helsinki, Finland). Compatibilisers: n Slovacid 44P (S44P), ester of stearic acid and polypropylene glycol, (from Sasol Co), Preparation of polypropylene nanocomposite fibres The following two-step method was used for the preparation of PP nanocomposite fibres. Preparation of masterbatches of nanofillers in PP (flakes, powder): The PP HP, nanofiller and compatibiliser were mixed in a mixer of high r.p.m. for 3 min. The powder mixture was melted and kneaded using a twin screw corotating extruder (φ 28 mm). The temperatures of the extruder zones from the feedstock to the head were 80, 150, 220, 225, 225, 225 and 232 °C. The temperature of the extrudated melt was 229 °C. The extrudate was then cooled and cut. The concentration of the nanofiller in the PP HP was 10.0 wt%. The content of the compatibiliser was 4.0 wt%. Melt mixing of PP nanocomposite: C-spinning: Chips of the PP and PP/nanofiller masterbatch were mixed and spun using a single screw extruder (φ 15 mm) and spinneret with 13 orifices. The spinning temperature was 250 -280 °C, the metering of the melt 11 g/min, the spinning speed 150 m/min, and the fineness of the as-spun multifilament was about 680 dtex. Fibres were drawn using a laboratory drawing machine at various drawing ratios, λ, at a drawing temperature of 120 °C. D-spinning: The chips of the PP and PP/ nanofiller masterbatch were mixed and spun using a single screw extruder (φ 30 mm) and spinneret with 40 orifices. The spinning temperature was 250 -280 °C, the metering of the melt 30 g/min, the spinning speed 360 m/min, and the fineness of the asspun multifilament was 840 dtex. Fibres were drawn using the laboratory drawing machine at various drawing ratios, λ, at a drawing temperature of 120 °C. Methods used Mechanical properties of the nanocomposite fibres An Instron (Type 3343) was used for measurements of the tensile strength (T) and elongation at break (E), according to Standard ISO 2062:1993, as well as the Young's modulus (YM), according to Instron 3343 software. Barrier against the UV radiation of PP nanocomposite fibres The barrier properties of PP fibres modified with nanofillers were measured using a "Libra S12" spectrophotometer and evaluated on the basis of modified Standard STN EN 13758-1:2001 . The modification of the method was in the preparation of the sample for measurement. Before the measurement the nanocomposite PP fibres were wound on small metallic windows with cuts. The distance between cuts was 0.75 mm. Afterwards the transmittance through the layer of fibres was measured in the UV range. Consequently, the UPF was calculated by standard specification using the following equation: where: UPF -ultraviolet protection factor, E(λ) -relative erythermal spectral effectiveness in W/m 2. nm), S(λ) -solar UVR spectral irradiance (Melbourne), T(λ) -spectral transmittance of the sample, (λ) -bandwidth in nm, λ -wavelength Light stability of the PP nanocomposite fibres The light stability of the PP nanocomposite fibres was investigated by two methods. The measurements consisted of the UV exposure of the fibres using two types of standard devices and the evaluation of changes in the basic mechanical properties of the fibres. The tenacity, elongation and Young's modulus of the fibres in dependence on the UV exposure time were evaluated according to ISO norms. CAROUSEL TEST apparatus (the merry-go-round type set up) -method A and Xenotest 450 -method B were used for the irradiation of fibres Photo-oxidation of the PP nanocomposite films PP composite films were prepared from masterbatch chips in an electrically heated laboratory press (Fontune, The Netherlands) at 190 °C for 1 min. The thickness of the films was ca. 0.1 mm. Photooxidation was performed on a merry-goround type setup. λ > 310 nm. The temperature of photooxidation was 30ºC. The progress of chemical changes was followed by FTIR spectroscopy (NICOLET-400 Germany). The shape of the carbonyl band was broad, since it indicated the presence of several carbonyl products. The course of degradation is represented as the dependence of the degree of carbonyl absorption (measured as the area of CO absorption bands divided by the film thickness) on the irradiation time. Thermal stability of PP nanocomposite fibres The thermal stability of nanocomposite polypropylene fibres was evaluated by DTA using Derivatograf Q-1500D apparatus according to the following procedure: A sample of the fibre was heated to 600 °C at a rate of 10 K . min -1 under air atmosphere. The temperature of the halfweight loss T 1 as well as the destruction temperature T d could be obtained from thermograms according to Standard STN EN ISO 11358. n Results and discussion Characterisation of the PP composite fibres and their mechanical properties The PP composite fibres were prepared at laboratory scale. The difference in spinning conditions (methods C or D), methods of evaluation of the photo-oxidation (methods A or B) and mechanical characteristics of the fibres are presented i

Photo-induced second-order nonlinearity in stoichiometric silicon nitride waveguides

We report the observation of second-harmonic generation in stoichiometric silicon nitride waveguides grown via low-pressure chemical vapour deposition. Quasi-rectangular waveguides with a large cross section were used, with a height of 1 {\mu}m and various different widths, from 0.6 to 1.2 {\mu}m, and with various lengths from 22 to 74 mm. Using a mode-locked laser delivering 6-ps pulses at 1064 nm wavelength with a repetition rate of 20 MHz, 15% of the incoming power was coupled through the waveguide, making maximum average powers of up to 15 mW available in the waveguide. Second-harmonic output was observed with a delay of minutes to several hours after the initial turn-on of pump radiation, showing a fast growth rate between 10$^{-4}$ to 10$^{-2}$ s$^{-1}$, with the shortest delay and highest growth rate at the highest input power. After this first, initial build-up, the second-harmonic became generated instantly with each new turn-on of the pump laser power. Phase matching was found to be present independent of the used waveguide width, although the latter changes the fundamental and second-harmonic phase velocities. We address the presence of a second-order nonlinearity and phase matching, involving an initial, power-dependent build-up, to the coherent photogalvanic effect. The effect, via the third-order nonlinearity and multiphoton absorption leads to a spatially patterned charge separation, which generates a spatially periodic, semi-permanent, DC-field-induced second-order susceptibility with a period that is appropriate for quasi-phase matching. The maximum measured second-harmonic conversion efficiency amounts to 0.4% in a waveguide with 0.9 x 1 {\mu}m$^2$ cross section and 36 mm length, corresponding to 53 {\mu}W at 532 nm with 13 mW of IR input coupled into the waveguide. The according $\chi^{(2)}$ amounts to 3.7 pm/V, as retrieved from the measured conversion efficiency.Comment: 20 pages, 10 figure

The Behaviour of χ(2)\text{}^{(2)} Grating Encoding Function

A new phenomenological model of self-organized second-harmonic generation is proposed describing the photoinduced χ$\text{}^{(2)}$ grating formation as a cumulative third-order nonlinearity via a complex χ$\text{}^{(2)}$ encoding function being dependent upon the light intensities of fundamental and second-harmonic writing radiations. The theoretical results attained are confronted with recent experimental measurements by Lambelet and Feinberg and the χ$\text{}^{(2)}$ encoding function is constructed for this special case

The oxidation kinetics of depleted uranium and its low-alloy molybdenum alloys in moist air

The oxidation kinetics of depleted uranium and its low-alloy molybdenum alloys (U-2wt.%Mo, U-5wt.%Mo) were measured in a moist air (75% relative humidity) at 60 and 75 ° C. Coefficients of reaction rate equations were determined for linear oxidation kinetics. In the oxidation of depleted uranium at 75 ° C, a change in reaction kinetics from linear to exponential behaviour was observed after about 2500 hours

First Experimentally Observed Self-Organized Parametric down Conversion in Optical Fibers

The theoretically predicted self-organized parametric down conversion (the amplification of fundamental radiation on account of the energy of second-harmonic radiation) in doped optical fibers was experimentally demonstrated for the first time and a weak permanent second-order susceptibility grating in the conditioned fiber was identified