A complete closed form vectorial solution to the Kepler problem

The paper gives an exact vectorial solution to the Kepler problem. A vectorial regularization that linearizes the Kepler problem is given using a Sundman transformation. Closed form expressions describing the Keplerian motion are deduced. A unified approach to the classic Kepler problem is offered, by studying both rectilinear and non-rectilinear Keplerian motions with the same instrument. The approach is an elementary one and only simple vectorial computations are involved.     

Fabrication of buried waveguides in planar silica films using a direct CW laser writing technique

A CW CO₂ laser ablation technique is used to form buried waveguides in planar silica films. It is shown that the refractive index of a silica thin film is reduced sufficiently adjacent to the laser processed region to allow the fabrication of low loss waveguides. The refractive index distribution of these structures is measured using the reflectance of a focussed spot from the surface of the films. The change in refractive index is measured to be of the order of the core cladding refractive index difference of typical single mode waveguides. The spatial resolution of the reflectance technique is 1.3 μm with a refractive index resolution of ±5 × 10^?4. Devices such as 1 × 2 and 1 × 4 multi-mode interference (MMI) splitters have also been demonstrated and shown to exhibit low transmission losses.     

Reactivity of 1-chloro-3-phenyldiazirines

p-Substituted 1-chloro-3-phenyldiazirines (5), the putative intermediates of the reaction of N,N,N'-trichlorobenzamidines (10) with excess of bromide ions, react further to afford mixtures of 3-bromo- (4) and 3-chloro-3-phenyldiazirines (6). The 6:4 ratios inversely correlate with the Hammett sigma(p) and sigma(p)+ constants of the p-substituents. The formation of 4, proposed to proceed by anti-S(N)2' mechanism, is predominant with electron-withdrawing p-substituents. Compounds 6, the major products with electron-donating p-substituents, may arise from 5 by a [1,3]-sigmatropic shift of chlorine proceeding via polar transition structures 12. The results of a gas-phase DFT (B3LYP/6-31+G*) study on the two mechanisms are consistent with experiment.     

Synthesis of carboalkoxychloro- and bromodiazirines

The first known 3H-diazirines bearing a carbonyl group and a halogen atom on C-3 have been prepared by a novel synthetic method. Carboalkoxychloro- and bromodiazirines 1a-d are formed in up to 45% yields by reductive dechlorination of carboalkoxy-N,N,N'-trichloroformamidines 9a,b using chloride or bromide ion. This method constitutes the first example of the use of N,N,N'-trichloroamidines as starting materials in organic synthesis.     

An Investigation of Plasma-Polymer Interactions by Mass Spectrometry

Surface modification of polymers by low-pressure plasmas has gained scientific and industrial importance for controlling adhesion of coatings, wettability, printability, bio-compatibility and other surface-related properties. However, more is to be learned about the complex interactions at the plasma-polymer interface. The present study is designed to investigate these plasma-polymer surface interactions by means of mass spectrometry. Various polymer specimens (polyethylene, polypropylene, polyethylene terephthalate, and polyimide) were placed directly on an electrode which contains the sampling aperture into a quadrupole mass spectrometer. We have identified various molecular fragments from these polymers, which were liberated by chain scissions provoked by various energetic plasma constituents, in particular, bombarding ions and vacuum ultraviolet (VUV) photons.     

Anisotropic nonlinear optical absorption of gold nanorods in a silica matrix

Nanocomposite films consisting of gold nanospheres or gold nanorods embedded in a silica matrix have been prepared using a hybrid deposition technique consisting of plasma-enhanced chemical vapor deposition of SiO₂ and co-sputtering of gold, followed by annealing at 900 °C. Subsequent irradiation with 30 MeV heavy ions (Cu⁵⁺) was used to form gold nanorods. Linear and nonlinear optical properties of this material are closely related with the surface plasmon resonance in the visible. The nonlinear absorption coefficient (α₂@532 nm) for the films containing gold nanospheres was measured by Z-scan and P-scan techniques, and it was found to be isotropic and equal to −4.8 × 10⁻² cm/W. On the contrary, gold nanorods films exhibited two distinct surface plasmon resonance absorption bands giving rise to a strong anisotropic behavior, namely a polarization-dependent linear absorption and saturable absorption. Z-scan and P-scan measurements using various light polarization directions yielded nonlinear absorption coefficient (α₂@532 nm) values varying from −0.9 × 10⁻² cm/W up to −3.0 × 10⁻² cm/W. Linearity of the P-scan method in the context of nanocomposite saturable absorption is also discussed.     

Plasma Surface Modification of Fluoropolymers Studied by ToF-SIMS

Surface modification by plasma treatment is an efficient way of improving metal adhesion to polymers. Here, Time-of-Flight Secondary Ion Mass Spectrometry (ToF-SIMS) is used to characterize the surfaces of Teflon PFA and Teflon AF1600 films, following plasma treatments in H₂, O₂ and N₂ gases. This work is complementary to our previous study using XPS, and is particularly directed toward the identification of incorporated hydrocarbons which could seriously affect metal adhesion. Plasma treatments strongly modify the surfaces of fluoropolymers, causing the ablation of a part of the fluorocarbon structure, with H₂ being the most effective gas. The hydrocarbon content of such surfaces is not negligible, and a comparison with hydrocarbon levels on untreated surfaces suggests that a substantial fraction of this material was incorporated on plasma treatment; this is particularly so in the case of H₂ plasma treatment. Due to expected strong matrix effects caused by significant changes in surface chemistry and structure following the various plasma treatments, the use of SIMS absolute intensity values is discussed in terms of data treatment artifacts. Moreover, due to the differences in secondary ion yields between characteristic hydrocarbon and fluorocarbon SIMS peaks, the use of peaks normalized to the total intensity is also impractical. Here, positive mode absolute intensities and negative mode peak intensity values, when normalized to I_tot - I(H^–) - I(F^–), give valuable information, as in the comparison of hydrocarbon and N incorporations.