A split-step finite difference method for nonparaxial nonlinear Schrödinger equation at critical dimension

The critical nonlinear Schrödinger equation (NLS) is the model equation for propagation of laser beam in bulk Kerr medium. One of the final stages in the derivation of NLS from the nonlinear Helmholtz equation (NLH) is to apply paraxial approximation. However, there is numerical evidence suggesting nonparaxiality prevents singularity formation in the solutions of NLS. Therefore, it is important to develop numerical methods for solving nonparaxial NLS. Split-step methods are widely used for finding numerical solutions of NLS equation. Nevertheless, these methods cannot be applied to nonparaxial NLS directly. In this study, we extend the applicability of split-step methods to nonparaxial NLS by using Padé approximant operators. In particular, split-step Crank-Nicolson (SSCN) method is used in conjunction with Padé approximants to provide examples of numerical solutions of nonparaxial NLS.     

Mode-locked 1.93 microm thulium fiber laser with a carbon nanotube absorber

We report a ring-cavity thulium fiber laser mode locked with a single-wall carbon nanotube absorber used in transmission. A carboxymethyl cellulose polymer film with incorporated carbon nanotubes synthesized by the arc discharge method has an absorption coinciding with in the amplification bandwidth of a Tm-doped fiber. This laser is pumped by an erbium fiber laser at 1.57 microm wavelength and produces a 37 MHz train of mode-locked 1.32 ps pulses at 1.93 microm wavelength with an average output power of 3.4 mW.     

In situ XPS investigation of Pt(Sn)/Mg(Al)O catalysts during ethane dehydrogenation experiments

Calcined hydrotalcite with or without added metal (Mg(Al)O, Pt/Mg(Al)O and Pt,Sn/Mg(Al)O) have been investigated with in situ X-ray photoelectron spectroscopy (XPS) during ethane dehydrogenation experiments. The temperature in the analysis chamber was 450 °C and the gas pressure was in the range 0.3-1 mbar. Depth profiling of calcined hydrotalcite and platinum catalysts under reaction, oxidation and in hydrogen-water mixture was performed by varying the photon energy, covering an analysis depth of 10-21 Å. It was observed that the Mg/Al ratio in the Mg(Al)O crystallites does not vary significantly in the analysis depth range studied. This result indicates that Mg and Al are homogeneously distributed in the Mg(Al)O crystallites. Catalytic tests have shown that the initial activity of a Pt,Sn/Mg(Al)O catalyst increases during an activation period consisting of several cycles of reduction-dehydrogenation-oxidation. The Sn/Mg ratio in a Pt,Sn/Mg(Al)O catalyst was followed during several such cycles, and was found to increase during the activation period, probably due to a process where tin spreads over the carrier material and covers an increasing fraction of the Mg(Al)O surface. The results further indicate that spreading of tin occurs under reduction conditions.A PtSn₂ alloy was studied separately. The surface of the alloy was enriched in Sn during reduction and reaction conditions at 450 °C. Binding energies were determined and indicated that Sn on the particle surface is predominantly in an oxidised state under reaction conditions, while Pt and a fraction of Sn is present as a reduced Pt-Sn alloy.     

The role of cloud-scale resolution on radiative properties of oceanic cumulus clouds

Both individual and combined effects of the horizontal and vertical variability of cumulus clouds on solar radiative transfer are investigated using a two-dimensional (x- and z-directions) cloud radar dataset. This high-resolution dataset of typical fair-weather marine cumulus is derived from ground-based cloud radar observations. The domain-averaged (along x-direction) radiative properties are computed by a Monte Carlo method. It is shown that (i) different cloud-scale resolutions can be used for accurate calculations of the mean absorption, upward and downward fluxes; (ii) the resolution effects can depend strongly on the solar zenith angle; and (iii) a few cloud statistics can be successfully applied for calculating the averaged radiative properties.     

Density functional theory simulations of amorphous high-κ oxides on a compound semiconductor alloy: a-Al2O3/InGaAs(100)-(4×2), a-HfO2/InGaAs(100)-(4×2), and a-ZrO2/InGaAs(100)-(4×2)

The structural properties of a-Al(2)O(3)∕In(0.5)Ga(0.5)As, a-HfO(2)∕In(0.5)Ga(0.5)As, and a-ZrO(2)∕In(0.5)Ga(0.5)As interfaces were investigated by density-functional theory (DFT) molecular dynamics (MD) simulations. Realistic amorphous a-Al(2)O(3), a-HfO(2), and a-ZrO(2) samples were generated using a hybrid classical-DFT MD "melt-and-quench" approach and tested against the experimental properties. For each stack type, two systems with different initial oxide cuts at the interfaces were investigated. All stacks were free of midgap states, but some had band-edge states which decreased the bandgaps by 0%-40%. The band-edge states were mainly produced by deformation, intermixing, and bond-breaking, thereby creating improperly bonded semiconductor atoms. The interfaces were dominated by metal-As and O-In∕Ga bonds which passivated the clean surface dangling bonds. The valence band-edge states were mainly localized at improperly bonded As atoms, while conduction band-edge states were mainly localized at improperly bonded In and Ga atoms. The DFT-MD simulations show that electronically passive interfaces can be formed between high-κ oxides dielectrics and InGaAs if the processing does not induce defects because on a short time scale the interface spontaneously forms electrically passive bonds as opposed to bonds with midgap states.     

Exploring electronic versus steric effects in stereoselective ring-opening polymerization of lactide and β-butyrolactone with amino-alkoxy-bis(phenolate)-yttrium complexes

A series of methoxy‐amino‐bis(phenol)s (ONOO)H₂ possessing on the phenol rings R¹ ortho substituents with variable steric and electronic properties (R¹=CMe₂Ph, 1 ; CMe₂tBu, 3 ; CMe₂(4‐CF₃C₆H₄), 5 ; CPh₃, 9 ; Cl, 10 ) has been synthesized and further reacted with [Y{N(SiHMe₂)₂}₃](THF)₂ to give cleanly the corresponding yttrium compounds [Y(ONOO){N(SiHMe₂)₂}(thf)_n] ( Y‐x ); the solid‐state structures of Y‐3 and Y‐10 have been determined. These amido complexes have been used as initiators for the ring‐opening polymerization (ROP) of rac‐lactide (LA) and rac‐β‐butyrolactone (BBL) to provide heterotactically enriched poly(lactic acid)s (PLAs) and syndiotactically enriched poly(3‐hydroxybutyrate)s (PHBs), respectively, by means of a chain‐end control mechanism. Most of these polymerizations proceeded in a controlled fashion, giving polymers with narrow polydispersities and experimental molecular weights in good agreement with calculated values. The nature of the R¹ ortho substituents has a profound impact on the rates and, more spectacularly, on the stereocontrol of the polymerizations. The heterotactic stereocontrol in the ROP of rac‐LA appears to be governed essentially by steric considerations; the larger the substituent, the higher the heterotacticity: R¹=Cl (P_r=0.56)?CMe₃ (P_r=0.80)?CMe₂Ph (P_r=0.90)2(4 CF₃‐Ph) (P_r=0.93–0.94)≤CMe₂tBu (P_r=0.94–0.95)≤CPh₃ (P_r=0.95–0.96). On the other hand, the syndiotactic stereocontrol in the polymerization of rac‐BBL follows a quite different trend: R¹=Cl (P_r=0.42–0.45)?CMe₂tBu (P_r=0.62–0.70)3 (P_r=0.80)≤CMe₂(4 CF₃? Ph) (P_r=0.82–0.84)2Ph (P_r=0.89)3 (P_r=0.94), which suggests the involvement of electronic interactions. DFT computations on model intermediates confirmed a stabilizing C? H ??? π interaction between a methylene C? H of the ring‐opened BBL unit and the π system of one of the ortho‐aryl substituents of the ONOO ligand; by contrast, for model intermediates in the ROP of LA, no such C? H ??? π interaction involving the methyl group of lactate was observed.     

Group 3 and 4 single-site catalysts for stereospecific polymerization of styrene

The present review aims at a comprehensive survey of controlled stereospecific styrene polymerization by single-site catalysts to give syndiotactic and isotactic polystyrene. The early transition metals (groups 3 and 4) complexes that were successfully applied as catalyst precursors are reviewed. Catalytic performances and mechanistic insights, in particular in the stereoregulation phenomenon, are discussed.