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.     

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.     

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.     

On the two dimensional effective electron mass in quantum wells,inversion layers and NIPI superlattices of Kane type semiconductors in the presence of strong light waves: Simplified theory and relative comparison

An attempt is made to study the two dimensional (2D) effective electron mass (EEM) in quantum wells (Qws), inversion layers (ILs) and NIPI superlattices of Kane type semiconductors in the presence of strong external photoexcitation on the basis of a newly formulated electron dispersion laws within the framework of k.p. formalism. It has been found, taking InAs and InSb as examples, that the EEM in Qws, ILs and superlattices increases with increasing concentration, light intensity and wavelength of the incident light waves, respectively and the numerical magnitudes in each case is band structure dependent. The EEM in ILs is quantum number dependent exhibiting quantum jumps for specified values of the surface electric field and in NIPI superlattices; the same is the function of Fermi energy and the subband index characterizing such 2D structures. The appearance of the humps of the respective curves is due to the redistribution of the electrons among the quantized energy levels when the quantum numbers corresponding to the highest occupied level changes from one fixed value to the others. Although the EEM varies in various manners with all the variables as evident from all the curves, the rates of variations totally depend on the specific dispersion relation of the particular 2D structure. Under certain limiting conditions, all the results as derived in this paper get transformed into well known formulas of the EEM and the electron statistics in the absence of external photo-excitation and thus confirming the compatibility test. The results of this paper find three applications in the field of microstructures.