Modulation instabilities in two-core optical fibers

Modulation instability (MI) of cw states of a two-core fiber, incorporating the effects of coupling-coefficient dispersion (CCD), is studied by solving a pair of generalized, linearly coupled nonlinear Schrödinger equations. CCD refers to the property that the coupling coefficient depends on the optical wavelength, and earlier studies of MI do not account for this physics. CCD does not seriously affect the symmetric/antisymmetric cw, but can drastically modify the MI of the asymmetric state. Generally, new MI frequency bands are produced, and CCD reduces (enhances) the original MI band in the anomalous (normal) dispersion regime. Another remarkable result is the existence of a critical value for the CCD, where the MI gain spectrum undergoes an abrupt change. In the anomalous dispersion regime, a new low-frequency MI band is generated. In the normal dispersion regime, an MI band vanishes, reappears, and then moves up in frequency on crossing this critical value. In both dispersion regimes, the relative magnitude of the low-frequency band and the high-frequency band depends strongly on the total input power.It is possibleto switch the dominantMI frequency between a low frequency and a high frequency by tuning the total input power, providing a promising scheme to manipulate MI-related nonlinear effects in two-core fibers. The MI bands are independent of the third-order dispersion, but can be shifted significantly by self-steepening at a sufficiently high total input power. The evolution of MI from a cw input is also demonstrated with a wave propagation study. © 2011 Optical Society of America.published_or_final_versio

Switching of ultrashort pulses in nonlinear high-birefringence two-core optical fibers

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Doubly periodic patterns of modulated hydrodynamic waves: Exact solutions of the Davey-Stewartson system

Exact doubly periodic standing wave patterns of the Davey-Stewartson (DS) equations are derived in terms of rational expressions of elliptic functions. In fluid mechanics, DS equations govern the evolution of weakly nonlinear, free surface wave packets when long wavelength modulations in two mutually perpendicular, horizontal directions are incorporated. Elliptic functions with two different moduli (periods) are necessary in the two directions. The relation between the moduli and the wave numbers constitutes the dispersion relation of such waves. In the long wave limit, localized pulses are recovered. © 2011 The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg.postprin

Breathers and 'black' rogue waves of coupled nonlinear Schrödinger equations with dispersion and nonlinearity of opposite signs

Breathers and rogue waves of special coupled nonlinear Schrödinger systems (the Manakov equations) are studied analytically. These systems model the orthogonal polarization modes in an optical fiber with randomly varying birefringence. Studies earlier in the literature had shown that rogue waves can occur in these Manakov systems with dispersion and nonlinearity of opposite signs, and that the criterion for the existence of rogue waves correlates closely with the onset of modulation instability. In the present work the Hirota bilinear transform is employed to calculate the breathers (pulsating modes), and rogue waves are obtained as a long wave limit of such breathers. In terms of wave profiles, a ‘black’ rogue wave (intensity dropping to zero) and the transition to a four-petal configuration are elucidated analytically. Sufficiently strong modulation instabilities of the background may overwhelm or mask the development of the rogue waves, and such thresholds are correlated to actual physical properties of optical fibers. Numerical simulations on the evolution of breathers are performed to verify the prediction of the analytical formulations.postprin

Modulation instabilities in birefringent two-core optical fibers

Previous studies of the modulation instability (MI) of continuous waves (CWs) in a two-core fibre (TCF) did not consider effects caused by co-propagation of the two polarized modes in a TCF that possesses birefringence, such as cross-phase modulation (XPM), polarization-mode dispersion (PMD) and polarization-dependent coupling (PDC) between the cores. This paper reports an analysis of these effects on the MI by considering a linear-birefringence TCF and a circular-birefringence TCF, which feature different XPM coefficients. The analysis focuses on the MI of the asymmetric CW states in the TCFs, which have no counterparts in single-core fibres. We find that the asymmetric CW state exists when its total power exceeds a threshold (minimum) value, which is sensitive to the value of the XPM coefficient. We consider, in particular, a class of asymmetric CW states that admit analytical solutions. In the anomalous dispersion regime, without taking the PMD and PDC into account, the MI gain spectra of the birefringent TCF, if scaled by the threshold power, are almost identical to those of the zero-birefringence TCF. However, in the normal dispersion regime, the power-scaled MI gain spectra of the birefringent TCFs are distinctly different from their zero-birefringence counterparts, and the difference is particularly significant for the circular-birefringence TCF, which takes a larger XPM coefficient. On the other hand, the PMD and PDC only exert weak effects on the MI gain spectra. We also simulate the nonlinear evolution of the MI of the CW inputs in the TCFs and obtain good agreement with the analytical solutions.postprin

Metrics with Prescribed Ricci Curvature near the Boundary of a Manifold

Suppose $M$ is a manifold with boundary. Choose a point $o\in\partial M$. We investigate the prescribed Ricci curvature equation \Ric(G)=T in a neighborhood of $o$ under natural boundary conditions. The unknown $G$ here is a Riemannian metric. The letter $T$ in the right-hand side denotes a (0,2)-tensor. Our main theorems address the questions of the existence and the uniqueness of solutions. We explain, among other things, how these theorems may be used to study rotationally symmetric metrics near the boundary of a solid torus $\mathcal T$. The paper concludes with a brief discussion of the Einstein equation on $\mathcal T$.Comment: 13 page

Simple, Fast and Accurate Implementation of the Diffusion Approximation Algorithm for Stochastic Ion Channels with Multiple States

The phenomena that emerge from the interaction of the stochastic opening and closing of ion channels (channel noise) with the non-linear neural dynamics are essential to our understanding of the operation of the nervous system. The effects that channel noise can have on neural dynamics are generally studied using numerical simulations of stochastic models. Algorithms based on discrete Markov Chains (MC) seem to be the most reliable and trustworthy, but even optimized algorithms come with a non-negligible computational cost. Diffusion Approximation (DA) methods use Stochastic Differential Equations (SDE) to approximate the behavior of a number of MCs, considerably speeding up simulation times. However, model comparisons have suggested that DA methods did not lead to the same results as in MC modeling in terms of channel noise statistics and effects on excitability. Recently, it was shown that the difference arose because MCs were modeled with coupled activation subunits, while the DA was modeled using uncoupled activation subunits. Implementations of DA with coupled subunits, in the context of a specific kinetic scheme, yielded similar results to MC. However, it remained unclear how to generalize these implementations to different kinetic schemes, or whether they were faster than MC algorithms. Additionally, a steady state approximation was used for the stochastic terms, which, as we show here, can introduce significant inaccuracies. We derived the SDE explicitly for any given ion channel kinetic scheme. The resulting generic equations were surprisingly simple and interpretable - allowing an easy and efficient DA implementation. The algorithm was tested in a voltage clamp simulation and in two different current clamp simulations, yielding the same results as MC modeling. Also, the simulation efficiency of this DA method demonstrated considerable superiority over MC methods.Comment: 32 text pages, 10 figures, 1 supplementary text + figur

High-performance predictor for critical unstable generators based on scalable parallelized neural networks

A high-performance predictor for critical unstable generators (CUGs) of power systems is presented in this paper. The predictor is driven by the MapReduce based parallelized neural networks. Specifically, a group of back propagation neural networks (BPNNs), fed by massive response trajectories data, are efficiently organized and concurrently trained in Hadoop to identify dynamic behaviour of individual generator. Rather than simply classifying global stability of power systems, the presented approach is able to distinguish unstable generators accurately with a few cycles of synchronized trajectories after fault clearing, enabling more in-depth emergency awareness based on wide-area implementation. In addition, the technique is of rich scalability due to Hadoop framework, which can be deployed in the control centers as a high-performance computing infrastructure for real-time instability alert. Numerical examples are studied using NPCC 48 machines test system and a realistic power system of China

Diabetes status and post-load plasma glucose concentration in relation to site-specific cancer mortality: findings from the original Whitehall study

ObjectiveWhile several studies have reported on the relation of diabetes status with pancreatic cancer risk, the predictive value of this disorder for other malignancies is unclear. Methods: The Whitehall study, a 25year follow-up for mortality experience of 18,006 men with data on post-challenge blood glucose and self-reported diabetes, allowed us to address these issues. Results: There were 2158 cancer deaths at follow-up. Of the 15 cancer outcomes, diabetes status was positively associated with mortality from carcinoma of the pancreas and liver, while the relationship with lung cancer was inverse, after controlling for a range of potential covariates and mediators which included obesity and socioeconomic position. After excluding deaths occurring in the first 10years of follow-up to examine the effect of reverse causality, the magnitude of the relationships for carcinoma of the pancreas and lung was little altered, while for liver cancer it was markedly attenuated. Conclusions: In the present study, diabetes status was related to pancreatic, liver, and lung cancer risk. Cohorts with serially collected data on blood glucose and covariates are required to further examine this area

Ordering phenomena in quasi one-dimensional organic conductors

Low-dimensional organic conductors could establish themselves as model systems for the investigation of the physics in reduced dimensions. In the metallic state of a one-dimensional solid, Fermi-liquid theory breaks down and spin and charge degrees of freedom become separated. But the metallic phase is not stable in one dimension: as the temperature is reduced, the electronic charge and spin tend to arrange themselves in an ordered fashion due to strong correlations. The competition of the different interactions is responsible for which broken-symmetry ground state is eventually realized in a specific compound and which drives the system towards an insulating state. Here we review the various ordering phenomena and how they can be identified by optic and magnetic measurements. While the final results might look very similar in the case of a charge density wave and a charge-ordered metal, for instance, the physical cause is completely different. When density waves form, a gap opens in the density of states at the Fermi energy due to nesting of the one-dimension Fermi surface sheets. When a one-dimensional metal becomes a charge-ordered Mott insulator, on the other hand, the short-range Coulomb repulsion localizes the charge on the lattice sites and even causes certain charge patterns. We try to point out the similarities and conceptional differences of these phenomena and give an example for each of them. Particular emphasis will be put on collective phenomena which are inherently present as soon as ordering breaks the symmetry of the system.Comment: Review article Naturwissenschaften 200