Evaluation of optical propagation and radiation in optical waveguide using a numerical method

We introduce a mathematical model based on a concept of intrinsic mode in order to analyse and synthesise optical wave propagation and radiation occurring in a non-uniform optical waveguide used in integrated optics as optical coupler. The model is based on numerical evaluation of electromagnetic wave by applying an intrinsic field integral to evaluate the field behaviour inside the optical waveguide. To analyse the field distribution inside the non-uniform waveguide and predict the beam propagation of optical energy involved in the propagation process, it is necessary to track the motion of any observation point along the tapered waveguide itself. Physically, the rays of the spectrum undergo reflections on the waveguide boundaries until the cut-off occurs and the phenomena of radiation begin. The numerical results show good agreement with those obtained by classical methods of evaluation used bv other works.     

Characterization of the current-induced resistive spots in superconducting \hbox {YBa}_{2} \hbox {Cu}_{3} \hbox {O}_{7} strips

For over a decade, ultrathin superconducting films have been developed for the detection of single photons at optical or near infrared frequencies, with competitive performances in terms of quantum efficiency, speed, and low dark count rate. In order to avoid the requirement of helium refrigeration, we consider here the use of high temperature materials, known to achieve very fast responsiveness to laser irradiation. We excite thin filaments of the cuprate \(\hbox {YBa}_{2} \hbox {Cu}_{3} \hbox {O}_{7}\) by rectangular pulses of supercritical current so as to produce either a phase-slip centre (PSC) or a normal hot spot (HS), according to the temperature and the current amplitude selected. That procedure provides information about the maximum bias current to be used in a particle detector, about the return current back to the quiescent state after excitation, and about the rate of growth and decay of a HS. We also measure the time of PSC nucleation. A unique feature of that approach is to provide the rate of heat transfer between the film and its substrate at whatever temperature, in the superconducting state, in the practical conditions of operation.     

Effects of the van der Waals force,squeeze-film damping,and contact bounce on the dynamics of electrostatic microcantilevers before and after pull-in

The operational range of microcantilever beams under electrostatic force can be extended beyond pull-in in the presence of an intermediate dielectric layer. In this paper, a systematic method for deriving dynamic equation of microcantilevers under electrostatic force is presented. This model covers the behavior of the microcantilevers before and after the pull-in including the effects of van der Waals force, squeeze-film damping, and contact bounce. First, a polynomial approximate shape function with a time-dependent variable for each configuration is defined. Using Hamilton’s principle, dynamic equations of microcantilever in all configurations have been derived. Comparison between modeling results and previous experimental data that have been used for validation of the model shows a good agreement.     

A general two-term recurrence and its solution

We find a general explicit formula for all sequences satisfying a two-term recurrence of a certain kind. This generalizes familiar formulas for the Stirling and Lah numbers.     

On the Stirling numbers associated with the meromorphic Weyl algebra

The generalized Stirling numbers introduced recently (Mansour and Schork, 2011 [5], Mansour et al., 2011 [6]) are considered in detail for the particular case $s=2$ corresponding to the meromorphic Weyl algebra. A combinatorial interpretation in terms of perfect matchings is given for these meromorphic Stirling numbers and the connection to Bessel functions is discussed. Furthermore, two related $q$-polynomial identities are derived.     

Optical properties of nanostructure boron doped NiO thin films

Boron doped NiO films were prepared by sol–gel method. The effects of B content on the morphological and optical properties of NiO films were studied with atomic force microscopy, and optical characterization method. The average transmittance at the visible region is reached to 75 % for lower doped films (0.1 and 0.2 % B), whereas, the recorded average value of transmittance was about 62 % for doped film with 1 % B throughout the region. The optical energy gap value for pure NiO film was found to be 3.73 eV. These values were affected by B doping with non-monotonic variation and reached to 3.64 eV for 0.1 % B doped NiO. Also, the refractive index dispersion and dielectric constants of the NiO films were studied throughout the investigated range of wavelengths. The obtained results indicate that the optical parameters of the NiO film are controlled with boron doping.     

dc and ac characterizations of electrical conducting nanoporous carbon structures based on resorcinol-formaldehyde

Structural, electrical and morphological properties of electrical conducting nanoporous carbon structures, prepared at different pyrolysis temperatures by sol–gel method, were investigated. The effect of the measurement temperature on the electrical properties of the obtained sample pyrolysed at 675 °C was studied. The imaginary and real parts of the sample impedance versus frequency, in the range of 40 Hz–100 MHz, are investigated. The Nyquist diagrams were used to identify an equivalent circuit and the fundamental parameters of the circuit are determined at different temperatures with the aim to study the contributions of the grains and boundary grains to the conductivity.     

On the hyperchaotic complex Lü system

The aim of this paper is to introduce the new hyperchaotic complex Lü system. This system has complex nonlinear behavior which is studied and investigated in this work. Numerically the range of parameter values of the system at which hyperchaotic attractors exist is calculated. This new system has a whole circle of equilibria and three isolated fixed points, while the real counterpart has only three isolated ones. The stability analysis of the trivial fixed point is studied. Its dynamics is more rich in the sense that our system exhibits both chaotic and hyperchaotic attractors, as well as periodic and quasi-periodic solutions and solutions that approach fixed points. The nonlinear control method based on Lyapunov function is used to synchronize the hyperchaotic attractors. The control of these attractors is studied. Different forms of hyperchaotic complex Lü systems are constructed using the state feedback controller and complex periodic forcing.