Numerical calculation of cutoff frequencies of optical fibers by a variational technique

A numerical method for calculating cutoff frequencies of modes of weakly guiding optical fibers is described. Starting from a properly constructed field representation, the method follows a variational approach to obtain an eigenvalue problem for the cutoff frequencies which can be easily solved by a standard numerical routine. The field representation uses an expansion in terms of the Laguerre–Gauss functions in the fiber core and limiting form for small arguments of modified Bessel functions in the fiber cladding. Fibers with power-law refractive index profiles and fibers with a profile showing a dip on the axis are analyzed. Results obtained for modes of arbitrary order (both azimuthal and radial) show that our method is very efficient and accurate.     

Characterizing abrupt changes in the stock prices using a wavelet decomposition method

Abrupt changes in the stock prices, either upwards or downwards, are usually preceded by an oscillatory behavior with frequencies that tend to increase as the moment of transition becomes closer. The wavelet decomposition methods may be useful for analysis of this oscillations with varying frequencies, because they provide simultaneous information on the frequency (scale) and localization in time (translation). However, in order to use the wavelet decomposition, certain requirements have to be satisfied, so that the linear and cyclic trends are eliminated by standard least squares techniques. The coefficients obtained by the wavelet decomposition can be represented in a graphical form. A threshold can then be established to characterize the likelihood of a short-time abrupt change in the stock prices. Actual data from the São Paulo Stock Exchange (Bolsa de Valores de São Paulo) were used in this work to illustrate the proposed method.     

Spin 3/2 Field Equation: Separation and Solution in a Class of Lema?tre–Tolman–Bondi Cosmologies

The spin 3/2 field equation is studied in the general Lema?tre–Tolman–Bondi (LTB) space-time. The equation is separated by variable separation. The angular dependence factors out at the level of the general LTB metric. Due to spherical symmetry the separated angular equations coincide with those, previously integrated, relative to the Robertson–Walker and Schwarzschild metric. Separation of time and radial dependence is possible within a class of LTB cosmological models for which the physical radius is a product of a time and a radial function, the last one being further selected by the consistency condition of the radial equations. The separated time dependence, that can be integrated by series, results essentially unique. Instead the radial dependence can be reduced to two independent second order ordinary differential equations that still depend on an arbitrary radial function that is an integration function of the cosmological model. The generalization of the scheme to arbitrary spin field equation is suggested.     

Extreme statistics in Raman fiber amplifiers: From analytical description to experiments

In this work, we investigate the emergence of rare and intense events during the Raman fiber amplification of a continuous wave. We highlight how dispersive properties and pump depletion can strongly influence the statistical properties of the amplified signal and its optical spectrum. Under certain conditions, the probability density functions of the amplified signal are calculated analytically and compared with the results of the numerical simulations. The conclusions are qualitatively validated by experiments carried out at telecommunication wavelengths.     

Using permutations to detect dependence between time series

In this paper, we propose an independence test between two time series which is based on permutations. The proposed test can be carried out by means of different common statistics such as Pearson’s chi-square or the likelihood ratio. We also point out why an exact test is necessary. Simulated and real data (return exchange rates between several currencies) reveal the capacity of this test to detect linear and nonlinear dependences.     

Localization of Bose-Einstein condensates in optical lattices

The dynamics of repulsive bosons condensed in an optical lattice is effectively described by the Bose-Hubbard model. The classical limit of this model, reproduces the dynamics of Bose-Einstein condensates, in a periodic potential, and in the superfluid regime. Such dynamics is governed by a discrete nonlinear Schrödinger equation. Several papers, addressing the study of the discrete nonlinear Schrödinger dynamics, have predicted the spontaneous generation of (classical) breathers in coupled condensates. In the present contribute, we shall focus on localized solutions (quantum breathers) of the full Bose-Hubbard model. We will show that solutions exponentially localized in space and periodic in time exist also in absence of randomness. Thus, this kind of states, reproduce a novel quantum localization phenomenon due to the interplay between bounded energy spectrum and non-linearity.     

Frequency down-conversion using cascading arrays of coupled nonlinear oscillators

A novel coupling scheme using M≥2 arrays of coupled nonlinear elements arranged in a specific configuration can produce multifrequency patterns or a frequency down-converting effect on an external (input) signal. In such a configuration, each array contains N≥3 nonlinear elements with similar dynamics and each element is coupled unidirectionally within the array. The subsequent arrays in the cascade are coupled in a similar fashion except that the coupling direction is arranged in the opposite direction with respect to that of the preceding array. Previous theoretical work and numerical results have already been reported in [P. Longhini, A. Palacios, V. In, J. Neff, A. Kho, A. Bulsara, Exploiting dynamical symmetry in coupled nonlinear elements for efficient frequency down-conversion, Phys. Rev. E 76 (2007) 026201]. This paper is focused on results of experiments implemented on two distinct systems: the first system is fabricated using discrete component circuits to approximate an overdamped bistable Duffing oscillator described by a quartic potential system, and the second system is built in a microcircuit, where the nonlinearity is described by a hyperbolic tangent function, with the option of applying an external signal to investigate resonant effects. In particular, the circuit implementations for each case use M=2 arrays, but their voltage oscillations already demonstrate that the frequency relations between each of the successive arrays decrease by a rational factor, conforming to earlier theoretical and numerical results for the general case containing M arrays. This behavior is important for efficient frequency down-converting applications which are essential in many communication systems where heterodyning is typically used and it involves multi-step processes with complicated circuitry.