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.     

An extension of the Borel-Weil construction to the quantum groupU q (n)

The Borel-Weil (BW) construction for unitary irreps of a compact Lie group is extended to a construction of all unitary irreps of the quantum groupU _q(n). Thisq-BW construction uses a recursion procedure forU _q(n) in which the fiber of the bundle carries an irrep ofU _q(n–1)×U _q(1) with sections that are holomorphic functions in the homogeneous spaceU _q(n)/U _q(n–1)×U _q(1). Explicit results are obtained for theU _q(n) irreps and for the related isomorphism of quantum group algebras.Supported in part by the National Science Foundation, No. PHY-9008007     

Observation of sharp resistance anomalies near Tc in granular superconductors

Granular films prepared from well-defined In clusters embedded in Kr (? 10-40 at % Kr) show sharp resistance anomalies very close to the superconducting transition temperature. The observed resistance peak(s), which go(es) above the normal state resistance R_N and which can be as high as ? 1.5 R_N, can be explained by a “mesoscopic” effect: Superconducting percolation aggregates of size ξ_ρ, larger than the superconducting coherence length ξ_S, but smaller than the quasiparticle relaxation length λ_Q*, have a superconducting gap, but are not yet able to carry a supercurrent.     

The force on a lattice defect in an elastic body

It is shown that the force on a lattice defect in an elastic body is, like the force on a disclination in a nematic liquid crystal, a real force which, for equilibrium, must be balanced by an external force applied to the closed surface enclosing the defect.     

Measurements and simulations of particle dispersion in a turbulent flow

A particle imaging technique has been used to collect droplet displacement statistics in a round turbulent jet of air. Droplets are injected on the jet axis, and a laser sheet and position-sensitive photomultiplier tube are used to track their radial displacement and time-of-flight. Dispersion statistics can be computed which are Lagrangian or Eulerian in nature. The experiments have been simulated numerically using a second-order closure scheme for the jet and a stochastic simulation for the particle trajectories. Results are presented for non-vaporizing droplets of sizes from 35 to 160 μm. The simulations have underscored the importance of initial conditions and early droplet displacement history on the droplet trajectory for droplets with large inertia relative to the turbulence. Estimates of initial conditions have been made and their effect on dispersion is quantified.     

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.     

Serial magnetic resonance imaging in patients following acute myocardial infarction.

The detection of serial changes in magnetic resonance (MR) signal intensity of the heart following acute myocardial infarction may provide a useful method of characterizing tissue healing. Fourteen patients with acute Q-wave infarction underwent T2-weighted, spin-echo cardiac imaging during hospitalization, followed by one or more additional MR studies (total 31) over a 6- to 27-wk period (mean: 3 mo). Visual assessment of the images demonstrated a gradual reduction in signal intensity and localization of the bright signal to the subendocardium of the infarction region over the three-mo study period. A quantitative measurement of signal intensity (infarction/normal myocardium) fell from 1.81 +/- 0.42 on the initial study to 1.34 +/- 0.37 (p less than 0.05) at a mean of 14 wk. Two patients had an increase in signal intensity on the follow-up study and both patients had been readmitted with acute coronary syndromes. In summary, characterization of changes in signal intensity may provide a useful method of assessing myocardial healing following acute myocardial infarction. Further studies are indicated to determine the prognostic significance of these parameters.     

The 3-D FEL pulse propagation equation: An analytical treatment in the low-gain and small-signal regime

Summary In this paper we show that the transverse mode evolution of a FEL operating with short pulses can be treated, in the small-signal and low-gain regime, using a relatively simple mathematical technique leading to a potentially fast numerical algorithm. We also point out that analytical solutions can be obtained for the cases where the slippage length is small compared to the longitudinal bunch length.     

Characterization of carbide phases in high speed tool steels

A study is reported on carbides electrolytically extracted from two different types of high speed tool steels as quenched and after tempering. According to X-ray diffraction analysis and EDS microanalysis, Mössbauer spectra show the presence of MC and M₆C in every analysed sample. Only a few substitutional Fe atoms should be present in MC and they give a minor contribution to the Mössbauer spectrum. A model for evaluating the Mössbauer spectrum of M₆C is proposed which is based on the symmetry of lattice sites occupied by Fe atoms and partially substituted by other metallic atoms. The proposed model also allows to get information on the amount of this substitution.