Collapse of optical vortices

We theoretically and experimentally investigate the self-focusing of optical vortices in Kerr media. We observe collapse to a distinct self-similar profile, which becomes unstable to azimuthal perturbations. We analyze the azimuthal modulational instability for ring-shaped vortices and predict the number of azimuthal maxima solely as a function of power and topological charge. In our experiments, the observed multiple-filamentation patterns are in excellent agreement with our theoretical analysis.     

Bisoxazolines with one and two sidearms: stereodirecting ligands for copper-catalysed asymmetric allylic oxidations of alkenes

A series of sidearm functionalized bisoxazoline ligands has been synthesized by reaction of the monolithiated methyl{bis(oxazolinyl)}methane with the appropriate electrophiles, and tested in the copper catalyzed asymmetric allylic oxidation of cyclohexene ("Kharasch-Sosnovski" reaction). The observed enantioselectivities were higher (up to 85% ee) than for the unfunctionalized bisoxazoline ("BOX") derivatives (ca. 60% ee). Regardless of the functional groups incorporated into the sidearm unit, the ee's obtained for the different derivatives were essentially indistinguishable. This implies that the sidearms do not interfere directly in this reaction and only play an indirect role by virtue of their steric demand. Three of the copper complexes have been characterized by X-ray diffraction, establishing a distorted octahedral coordination geometry around the copper atom in all three cases. In the elongated distorted CuN(2)O(4) octahedra, the two nitrogen atoms of the oxazolines and one oxygen atom of each acetate ligand occupy the 'equatorial' positions whereas the sidearms do not interact with the metal centres.     

Reactivity of styrene and substituted styrenes in the presence of a homogeneous isospecific titanium catalyst

The isospecific polymerization of several para‐substituted styrenes was performed in the presence of the catalyst dichloro[1,4‐dithiabutanediyl‐2,2′‐bis(4,6‐di‐tert‐butyl‐phenoxy)]titanium activated by methylaluminoxane. All the polymers were highly regioregular and isotactic with narrow molecular weight distributions. The presence of electron‐donating substituents on the aromatic ring had a positive effect on the catalyst activity, whereas electron‐withdrawing substituents affected the polymerization activity negatively. Binary copolymerizations of the various substituted styrenes showed an inversion of the reactivity with respect to that observed in the homopolymerization. These results suggested that the last monomer unit of the polymer chain coordinated to the metal center, influencing the reactivity of the catalyst with respect to the incoming monomer. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 1486–1491, 2006     

Resonant optical interactions with molecules confined in photonic band-gap fibers

We investigate resonant nonlinear optical interactions and demonstrate induced transparency in acetylene molecules in a hollow-core photonic-band-gap fiber at 1.5 mum. The induced spectral transmission window is used to demonstrate slow-light effects, and we show that the observed broadening of the spectral features is due to collisions of the molecules with the inner walls of the fiber core. Our results illustrate that such fibers can be used to facilitate strong coherent light-matter interactions even when the optical response of the individual molecules is weak.     

Calogero Conjecture and Hubble Law

Acceptance of the Calogero hypothesis on the cosmic origin of quantizationin the framework of Nelson stochastic mechanics would imply that the age ofuniverse is larger than the standard quantum mechanical interpretation of theredshift measurement implies. This is due to variation of h with the radius of theuniverse and thus with time.     

Nonlinear propagation and continuum generation in microstructured optical fibers

A theoretical investigation of the propagation of femtosecond pulses under conditions similar to those of recent experiments in which a white-light continuum was generated in a microstructured fiber is presented. It is found that higher-order dispersion primarily determines the shape and width of the generated spectrum and that the fine spectral substructure exhibits extreme sensitivity to the initial pulse energy.     

Pulse contrast enhancement of high-energy pulses by use of a gas-filled hollow waveguide

Using nonlinear ellipse rotation in a gas-filled hollow waveguide, we have increased the pulse contrast of a microjoule femtosecond laser pulse by several orders of magnitude. This scheme offers a number of advantages over competing techniques, including a high degree of tunability that allows for a broad range of input pulse parameters, higher throughput, greater stability, and an output pulse with high spatial quality that is compressible to a quarter of the original temporal width.