Modal properties of circular and noncircular optical waveguides

We give a review and a comparison of recent methods of analyzing circular and noncircular optical waveguides. Comparison among competing methodologies is made as follows: Galerkin's method is used with Laguerre-Gauss basis functions in circular geometry to examine the modal solution in a step index fiber, and comparison with the exact solution is made. A W-fiber, which has no exact solution, is then examined. Rectangular geometry is considered, and discussion centers on the use of Galerkin's method using trigonometric basis functions and Hermite-Gauss basis functions. Re difficulty arising from the use of basis functions that do not decay exponentially for large argument (trigonometric functions) is illustrated. Finally, a square step index waveguide is used to illustrate a comparison between a variational method that uses the Gaussian approximation as the starting point, and Galerkin's method using Hermite-Gauss basis functions. We conclude that the variational method does well in predicting the propagation constant β but does not do well in predicting the modal field.     

Optical waveguide analysis using modified Airy functions

We review a little-used but powerful method of solving the scalar wave equation. It uses a modification of the well-known Airy functions, which are easily calculated on desktop computers. The techniques are reminiscent of the WKBJ methodology, but the solution, although approximate, is much more useful than the traditional WKBJ solution and can be used with almost as much ease. Re method is extremely powerful but, to our knowledge, is not used in the optics community. It is useful in analyzing integrated optical waveguide components.     

A comparison of spin relaxation and local motion between symmetrically and asymmetrically ring-substituted bisphenol units in dissolved polycarbonates

Carbon-13 and proton spin-lattice relaxation times were measured at two field strengths on solutions 10% by weight of two polycarbonates in C₂D₂Cl₄ from ?20 to +120°C. The first polycarbonate is an asymmetrically substituted form with one chlorine on one of the two phenylene aromatic rings of the bisphenol unit, whereas the second polycarbonate is symmetrically substituted with two chlorines on each of the two rings. The nuclear spin relaxation data are interpreted in terms of several local motions likely in these polymers. Segmental motion was described by the Hall–Helfand correlation function. Segmental motion in the monosubstituted polycarbonate is somewhat slower than in unsubstituted polycarbonate, whereas segmental motion in the tetrasubstituted polycarbonate is considerably slower. Phenylene ring rotation is observed in unsubstituted polycarbonate and in the monosubstituted polycarbonate above 40°C. Below 40°C in the monosubstituted species, and at all temperatures in the tetrasubstituted species, ring rotation is replaced by ring libration as the predominant motion contributing to spin lattice relaxation. In addition, the rotational motion of the two types of rings in the asymmetric monosubstituted form are very similar although not identical. The substituted ring is slightly less mobile than the rings of unsubstituted polycarbonate. This indicates a strong coupling of ring motion, although the coupling leads to less than synchronous motion. Methyl group rotation is present in both polymers and is little affected by the various structural modifications.     

Measuring the work of adhesion between a soft confined film and a flexible plate

We present a theoretical and experimental study of a method for the determination of the adhesion strength between a thin elastomeric film bonded to a rigid substrate and a flexible plate in a geometry common in the peel test. In particular, we characterize the work of adhesion in terms of the length of an equilibrium crack, generated by a spacer of known thickness wedged between the flexible plate and adhesive film, and the elastic and geometric properties of the film and the plate. We treat both the limit of perfect bonding and that of perfect slippage at the interface of the adhesive film and the flexible plate. A series of experiments allow us to verify the theory quantitatively and thus validate our method, which ought to be of value in many technological situations.     

Enhanced glucose production from cellulose using coimmobilized cellulase and β-glucosidase

β-Glucosidase was covalently immobilized alone and coimmobilized with cellulase using a hydrophilic polyurethane foam (Hypol®FHP 2002). Immobilization improved the functional properties of the enzymes. When immobilized alone, the K_m for cellobiose of β-glucosidase was decreased by 33% and the pH optimum shifted to a slightly more basic value, compared to the free enzyme. Immobilized β-glucosidase was extremely stable (95% of activity remained after 1000 h of continuous use). Coimmobilization of cellulase and β-glucosidase produced a cellulose-hydrolyzing complex with a 2.5-fold greater rate of glucose production for soluble cellulose and a four-fold greater increase for insoluble cellulose, compared to immobilized cellulase alone. The immobilized enzymes showed a broader acceptance of various types of insoluble cellulose substrates than did the free enzymes and showed a long-term (at least 24 h) linear rate of glucose production from microcrystalline cellulose. The pH optimum for the coimmobilized enzymes was 6.0. This method for enzyme immobilization is fast, irreversible, and does not require harsh conditions. The enhanced glucose yields obtained indicate that this method may prove useful for commercial cellulose hydrolysis.     

Extending Coggia–Couvreur attack on Loidreau’s rank-metric cryptosystem

Designs, Codes and Cryptography - A recent paper by Coggia and Couvreur presents a polynomial time key-recovery attack on Loidreau’s encryption scheme, based on rank-metric codes, for some...     

Hydroarylation of alkynes and alkenes through alumina-sulfuric acid catalyzed regioselective CC bond formation

A highly atom-efficient synthetic protocol for hydroarylation of terminal-aryl alkynes and styrene through the regioselective CC bond formation via the electrophilic addition of naphthols and substituted phenols has been developed using alumina-sulfuric acid as a heterogeneous supported solid acid catalyst. This methodology shows excellent regioselectivity and affords the desired product in good to excellent yield. The heterogeneous catalyst can also be recycled efficiently without much loss of activity.     

Synthesis of 1-p-Methoxyphenyl and 1-p-Methoxyphenyl-4-methylbicyclo-[2.2.1]heptan-7-one. The Oxidation of 7-Hydroxy-1-p-methoxyphenyl-4-methylbicyclo[2.2.1]heptan-7-carboxylic Acid with Lead Tetraacetate

A simple synthetic route to 1-p-methoxyphenyl and 1-p-methoxyphenyl-4-methylbicyclo [2.2.1]heptan-7-one 6b,a has been developed through benzilic acid rearrangement of the bicyclo[2.2.1]octandiones 2b,a. The oxidation of 7-hydroxy-1-p-methoxyphenyl-4-methylbicyclo[2.2.1]heptan-7-carboxylic acid 3a with lead tetraacetate gives the carbolactone 7a which is also formed by the reaction of the ketone 6a with m-chloroperbenzoic acid.     

Synthesis, characterization and electron transfer properties of some picolinate complexes of ruthenium

In aqueous solution ruthenium trichloride reacted with picolinic acid (Hpic) in the presence of a base to afford [Ru(pic)₃]. In solution it shows intense ligand-to-metal charge transfer transitions near 310 and 370 nm, together with a low-intensity absorption near 2000 nm. [Ru(pic)₃] is one-electron paramagnetic and shows a rhombic ESR spectrum in 1:1 dimethylsulphoxide-methanol solution at 77 K. The distortions from octahedral symmetry have been calculated by ESR data analysis. The axial distortion is larger than the rhombic one. In acetonitrile solution it shows a reversible ruthenium(III)-ruthenium(II) reduction at −0.09 V vs. SCE and a reversible ruthenium(III)-ruthenium(IV) oxidation at 1.52 V vs. SCE. Chemical or electrochemical reduction of [Ru^III(pic)₃] gives [Ru^II(pic)₃]⁻, which in solution shows intense MLCT transitions near 360, 410 and 490 nm, and is converted back to [Ru(pic)₃] by exposure to air. Reaction of [Ru(pic)₃] with 8-quinolinol (HQ) in dimethylsulphoxide solution affords [RuQ₃]. [Ru(bpy)(pic)₂] (bpy = 2,2′-bipyridine) has been prepared by the reaction of Hpic with [Ru(bpy)(acac)₂]Cl (acac = acetylacetonate ion) in ethyleneglycol. It is diamagnetic and in solution shows intense MLCT transitions near 370, 410 and 530 nm. In acetonitrile solution it shows a reversible ruthenium(II)-ruthernium(III) oxidation at 0.44 V vs. SCE and a reversible one-electron reduction of bpy at − 1.64V vs. SCE.