Theory of power coupling between multimode optical fibres

In this paper power coupling between two multimode optical fibres is investigated. A formalism (based on a geometrical approach) suitable for analysing any coupling configuration between fibres with any index profile and any radiance distribution is presented. The model is applied to obtain coupling losses both in uniformly excited parabolic- and step-index fibres, in the presence of all kinds of coupling errors. Numerical results of extensive utility are shown and useful asymptotic expressions of coupling efficiency, valid for small values of coupling error parameters, are derived together with some practical rules for error combination. Mention is also made of some experimental results we have obtained, which corroborate some previous assertions. The work can supply a useful tool in the design of joints and connectors between single fibres or optical cables.     

AB initio calculations of the electronic properties of N4− in KN3

The energies of the ground state and low-lying excited states of the N₄^? defect in KN₃ have been calculated using ab initio techniques. A rectangular equilibrium geometry with dimensions X = 2.76 and Z = 2.47 a.u. and ground state symmetry of Γ₄⁺ was determined by calculating N₄^? as a free radical. For this ground state the unpaired electron is in a π orbital which is consistent with the experimental hyperfine tensor only if one edge of the N₄^? radical is parallel to the c axis in KN₃. These results were used to calculate the X²Γ₄⁺ state of N₄^? in the crystal field of KN₃, yielding an energy of ?217.899 Hartrees. The isotropic hyperfine constant was calculated to be a = 2.1 G and the components of the anisotropic hyperfine tensor as B_xx = ?3.4 G, B_yy = 7.0 G and B_zz = ?3.6 G, in good agreement with experimental and INDO results. Several excited states were calculated for the N₄^? defect in KN₃. When an estimate was made of the correlation energy, the transition energy of the X²Γ₄⁺→A²Γ₃^? transition agreed well with the peak energy of the 780 nm absorption band which has been attributed to N₄^?.     

Multiple returns for some regular and mixing maps

We study the distributions of the number of visits for some noteworthy dynamical systems, considering whether limit laws exist by taking domains that shrink around points of the phase space. It is well known that for highly mixing systems such limit distributions exhibit a Poissonian behavior. We analyze instead a skew integrable map defined on a cylinder that models a shear flow. Since almost all fibers are given by irrational rotations, we at first investigate the distributions of the number of visits for irrational rotations on the circle. In this last case the numerical results strongly suggest the existence of limit laws when the shrinking domain is chosen in a descending chain of renormalization intervals. On the other hand, the numerical analysis performed for the skew map shows that limit distributions exist even if we take domains shrinking in an arbitrary way around a point, and these distributions appear to follow a power law decay of which we propose a theoretical explanation. It is interesting to note that we observe a similar behavior for domains wholly contained in the integrable region of the standard map. We also consider the case of two or more systems coupled together, proving that the distributions of the number of visits for domains intersecting the boundary between different regions are a linear superposition of the distributions characteristic of each region. Using this result we show that the real limit distributions can be hidden by some finite-size effects. In particular, when a chaotic and a regular region are glued together, the limit distributions follow a Poisson-like law, but as long as the measure of the shrinking domain is not zero, the polynomial behavior of the regular component dominates for large times. Such an analysis seems helpful to understand the dynamics in the regions where ergodic and regular motions are intertwined, as it may occur for the standard map. Finally, we study the distributions of the number of visits around generic and periodic points of the dissipative Henon map. Although this map is not uniformly hyperbolic, the distributions computed for generic points show a Poissonian behavior, as usually occurs for systems with highly mixing dynamics, whereas for periodic points the distributions follow a different law that is obtained from the statistics of first return times by assuming that subsequent returns are independent. These results are consistent with a possible rapid decay of the correlations for the Henon map.     

Comparative Regge analysis of Λ,ΣΛ(1520) and Θ<Superscript>+</Superscript> production in γp,πp and pp reactions

Using the Quark-Gluon Strings Model --combined with Regge phenomenology-- we perform a comparative analysis of Λ, Σ⁰, Λ(1520) and Θ⁺ production in binary reactions induced by photon, pion and proton beams on the nucleon. We find that the existing experimental data on the γp↦K⁺Λ differential and total cross-sections can be described very well by the model for photon energies 1-16 GeV and - t < 2 GeV² assuming a dominant contribution of the K^* Regge trajectory. Moreover, using the same parameters we also reproduce the total γp↦K⁺Σ⁰ and γp↦K⁺Λ(1520) cross-sections suggesting a “universality” of the Regge model. In order to check the consistency of the approach we evaluate the differential and total cross-sections for the reaction π^-p↦K⁰Λ which is also found to be dominated by the K^* Regge trajectory. Using the apparent “universality” of the Regge model we extend our scheme to the analysis of the binary reactions γp↦¯⁰Θ⁺, π^-p↦K^-Θ⁺ and pp↦Σ⁺Θ⁺ as well as the exclusive and inclusive Θ⁺ production in the reactions pp↦p¯⁰Θ⁺ and pp↦Θ⁺X. Our detailed studies demonstrate that Θ⁺ production does not follow the “universality” principle, thus suggesting an essentially different internal structure of the exotic baryon relative to conventional hyperons or hyperon resonances.     

Zirconium complexes having a chiral phosphanylamide in the co-ordination sphere

The chiral phosphanylamido ligand, (N(CHMePh)(PPh2))-, has been introduced into co-ordination chemistry. As starting material the oily amines HN(R-*CHMePh)(PPh2)(1a) and HN(S-*CHMePh)(PPh2)(1b) were used. To reconfirm their absolute structure, 1b was oxidized with H2O2 in air to obtain HN(S-*CHMePh)(P(O)Ph2)(2) as a solid compound. The solid-state structure of 2 was established by single-crystal X-ray diffraction. The lithium salts of both enantiomers Li(N(R-*CHMePh)(PPh2))(3a) and Li(N(S-*CHMePh)(PPh2))(3b) were prepared by deprotonation reaction of 1a,b. Compounds 3a,b were further reacted with zirconocen dichloride to give the chiral metallocenes [(eta5-C5H5)2Zr(Cl)(eta2-N(R-*CHMePh)(PPh2))](4a) and [(eta5-C5H5)2Zr(Cl)(eta2-N(S-*CHMePh)(PPh2))](4b). In an alternative approach to give chiral zirconium compounds, the neutral amine 1b was reacted with [(PhCH2)4Zr] to give the enantiomeric pure complex [(PhCH2)3Zr(eta2-N(S-*CHMePh)(PPh2))](5). The solid-state structures of all zirconium complexes were determined by single-crystal X-ray diffraction.     

Body-centered-cubic Ni and its magnetic properties

The body-centered-cubic (bcc) phase of Ni, which does not exist in nature, has been achieved as a thin film on GaAs(001) at 170 K via molecular beam epitaxy. The bcc Ni is ferromagnetic with a Curie temperature of 456 K and possesses a magnetic moment of 0.52+/-0.08 micro(B)/atom. The cubic magnetocrystalline anisotropy of bcc Ni is determined to be +4.0x10(5) ergs x cm(-3), as opposed to -5.7x10(4) ergs x cm(-3) for the naturally occurring face-centered-cubic (fcc) Ni. This sharp contrast in the magnetic anisotropy is attributed to the different electronic band structures between bcc Ni and fcc Ni, which are determined using angle-resolved photoemission with synchrotron radiation.