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.     

The double duals and gauges of the Lanczos tensor

It is shown that: i) the Weyl tensor can be expressed in terms of the sum of a tensor and its double dual, where the tensor is constructed from the covariant derivatives of the Lanczos tensor, ii) a similar expression does not exist for the Riemann tensor in electromagnetic theory, iii) the electromagnetic field cannot be identified with the differential gauge freedom of the Lanczos tensor, iv) the symmetries of Einstein Maxwell theory and the Lanczos tensor do not prohibit the identification of the electromagnetic field with the algebraic gauge freedom of the Lanczos tensor, these symmetries require a differential equation relating the electromagnetic field tensor to the algebraic gauge vector and this is given.     

Temperature dependence of magnetization in nanocrystalline FeCoZr alloy

The temperature dependence of magnetization of a nanocrystalline Fe₆₀Co₃₀Zr₁₀ alloy annealed at various temperatures to varying crystal sizes was investigated down to 5 K in the field range up to 5 T. The fitting procedure gave T^3/2 as the leading term irrespective of the crystal size. We suggest that the increase of the coefficient by this term for smaller crystals may be connected to an increased relative volume of their surface.     

The effect of crystallinity on chain mobility and free volume in the amorphous regions of a miscible polycarbonate/polyester blend

Homopolymers and blends of polycarbonate/ThermX have been investigated by differential scanning calorimetry, dynamic mechanical analysis, density measurements, and positron annihilation lifetime spectroscopy. The study focuses on the chain mobility and free volume in the amorphous miscible regions of the blends and how this mobility and free volume are affected by increasing crystallinity. It is proposed that judicious annealing, which results in increasing crystallinity (while avoiding ageing or transesterification), induces a constraint on the amorphous region leading to an increase in T_g and coalescence of free volume sites. © 1994 John Wiley & Sons, Inc.     

A note on the growth of topological Sidon sets

We give an estimate for the number of elements in the intersection of topological Sidon sets inR ⁿ with compact convex subsets and deduce a necessary and sufficient conditions for an orbit of a linear transformation ofR ⁿ to be a topological Sidon set.