Non-periodic quasi-stable nonlinear optical carrier pulses with sliding chirp-free points for transmission at 40 Gbit/s rate

In this paper, we demonstrate the possibility of reaching a quasi-stable nonlinear transmission regime with carrier pulses of 12.5 ps width in multi-channel 40 Gbit/s systems. The quasi-stable pulses that are presented in this work for the first time are not dispersion-managed solitons, and are indeed supported by a large normal span average dispersion and misbalanced optical amplification, and representing a new type of nonlinear carrier.

Interferometric and fibre Bragg grating sensor interrogation using an arrayed waveguide grating

We investigate the use of an arrayed waveguide grating (AWG) to interrogate both fibre Bragg grating (FBG) and interferometric sensors. A broadband light source is used to illuminate both the FBG and interferometric sensors. Reflected spectral information is directed to an AWG with integral photodetectors providing 40 electrical outputs. To interrogate interferometric sensors we investigated the dual wavelength technique to measure the distance of a Fabry-Perot cavity, which produced a maximum unambiguous range of 1440μm with an active sensor. Three methods are described to interrogate FBG sensors. The first technique makes use of the reflected light intensity in an AWG channel passband from a narrow bandwidth grating, giving a usable range of 500με and a dynamic strain resolution of 96nε/√Hz at 30Hz. The second approach utilises wide gratings larger than the channel spacing of the AWG; by monitoring the intensity present in corresponding AWG channels an improved range of 1890με was achieved. The third method improves the dynamic range by utilising a heterodyne approach based on interferometric wavelength shift detection providing a dynamic strain resolution of 17nε/√Hz at 30Hz.

Mode locking of semiconductor laser with curved waveguide and passive mode expander

Active mode locking is reported for a 1.55 μm semiconductor laser with a curved waveguide and passive mode expander, placed in a wavelength tunable external cavity. One facet with a very low reflectivity of 8×10−6 is achieved through a curved active region that tapers into an underlying passive waveguide, thus expanding the mode to give reduced divergence. 10 GHz pulses of 3.1 ps duration have been generated, with a linewidth of 0.81 nm.

Efficient yellow-green light generation at 561 nm by frequency-doubling of a QD-FBG laser diode in a PPLN waveguide

A compact high-power yellow-green continuous wave (CW) laser source based on second-harmonic generation (SHG) in a 5% MgO doped periodically poled congruent lithium niobate (PPLN) waveguide crystal pumped by a quantum-dot fiber Bragg grating (QD-FBG) laser diode is demonstrated. A frequency-doubled power of 90.11 mW at the wavelength of 560.68 nm with a conversion efficiency of 52.4% is reported. To the best of our knowledge, this represents the highest output power and conversion efficiency achieved to date in this spectral region from a diode-pumped PPLN waveguide crystal, which could prove extremely valuable for the deployment of such a source in a wide range of biomedical applications.

Sensing applications of arrayed waveguide grating devices

Progress in optical fibre sensor research has often been achieved by taking advantage of components developed for use in telecommunications, where the greater existing market is able to support the rapid commercialisation of novel devices. In the last few years there has been considerable interest in the telecommunications community in deploying arrayed waveguide gratings (AWGs) produced in a range of technologies in a variety of roles. We feel it is therefore surprising that there have been very few reports of research into using AWGs for sensing. In this paper we consider some possible roles for these devices in interrogation systems for interferometric and fibre Bragg grating (FBG) sensors.

On Finite Element Methods for 2nd order (semi–) periodic Eigenvalue Problems

We deal with a class of elliptic eigenvalue problems (EVPs) on a rectangle Ω ⊂ R^2 , with periodic or semi–periodic boundary conditions (BCs) on ∂Ω. First, for both types of EVPs, we pass to a proper variational formulation which is shown to fit into the general framework of abstract EVPs for symmetric, bounded, strongly coercive bilinear forms in Hilbert spaces, see, e.g., [13, §6.2]. Next, we consider finite element methods (FEMs) without and with numerical quadrature. The aim of the paper is to show that well–known error estimates, established for the finite element approximation of elliptic EVPs with classical BCs, hold for the present types of EVPs too. Some attention is also paid to the computational aspects of the resulting algebraic EVP. Finally, the analysis is illustrated by two non-trivial numerical examples, the exact eigenpairs of which can be determined.

Some Computational Aspects of the Consistent Mass Finite Element Method for a (semi-)periodic Eigenvalue Problem

We consider a model eigenvalue problem (EVP) in 1D, with periodic or semi–periodic boundary conditions (BCs). The discretization of this type of EVP by consistent mass finite element methods (FEMs) leads to the generalized matrix EVP Kc = λ M c, where K and M are real, symmetric matrices, with a certain (skew–)circulant structure. In this paper we fix our attention to the use of a quadratic FE–mesh. Explicit expressions for the eigenvalues of the resulting algebraic EVP are established. This leads to an explicit form for the approximation error in terms of the mesh parameter, which confirms the theoretical error estimates, obtained in [2].

A Periodic Lotka-Volterra System

In this paper periodic time-dependent Lotka-Volterra systems are considered. It is shown that such a system has positive periodic solutions. It is done without constructive conditions over the period and the parameters.

Mean-Periodic Solutions of Retarded Functional Differential Equations

In this paper we present a spectral criterion for existence of mean-periodic solutions of retarded functional differential equations with a time-independent main part.

Numerical solution of parabolic Cauchy problems in planar corner domains

An iterative method for the parabolic Cauchy problem in planar domains having a finite number of corners is implemented based on boundary integral equations. At each iteration, mixed well-posed problems are solved for the same parabolic operator. The presence of corner points renders singularities of the solutions to these mixed problems, and this is handled with the use of weight functions together with, in the numerical implementation, mesh grading near the corners. The mixed problems are reformulated in terms of boundary integrals obtained via discretization of the time-derivative to obtain an elliptic system of partial differential equations. To numerically solve these integral equations a Nyström method with super-algebraic convergence order is employed. Numerical results are presented showing the feasibility of the proposed approach. © 2014 IMACS.

Algorithm BIDIMS for Automated Systematization of Data Array. Case Study: Rediscovering Mendeleev’s Periodic Table of Chemical Elements

The method (algorithm BIDIMS) of multivariate objects display to bidimensional structure in which the sum of differences of objects properties and their nearest neighbors is minimal is being described. The basic regularities on the set of objects at this ordering become evident. Besides, such structures (tables) have high inductive opportunities: many latent properties of objects may be predicted on their coordinates in this table. Opportunities of a method are illustrated on an example of bidimentional ordering of chemical elements. The table received in result practically coincides with the periodic Mendeleev table.

Localized waves in optical systems with periodic dispersion and nonlinearity management

We overview our recent developments in the theory of dispersion-managed (DM) solitons within the context of optical applications. First, we present a class of localized solutions with a period multiple to that of the standard DM soliton in the nonlinear Schrödinger equation with periodic variations of the dispersion. In the framework of a reduced ordinary differential equation-based model, we discuss the key features of these structures, such as a smaller energy compared to traditional DM solitons with the same temporal width. Next, we present new results on dissipative DM solitons, which occur in the context of mode-locked lasers. By means of numerical simulations and a reduced variational model of the complex Ginzburg-Landau equation, we analyze the influence of the different dissipative processes that take place in a laser.

Mean-Periodic Functions Associated with the Jacobi-Dunkl Operator on R

2000 Mathematics Subject Classification: 34K99, 44A15, 44A35, 42A75, 42A63

Hydrothermal saline promoted grafting of periodic mesoporous organic sulfonic acid silicas for sustainable FAME production

Hydrothermal saline promoted grafting of sulfonic acid groups onto SBA-15 and periodic mesoporous organic silica analogues affords solid acid catalysts with high acid site loadings (>2.5 mmol g-1 H+), ordered mesoporosity and tunable hydrophobicity. The resulting catalysts show excellent activity for fatty acid esterification and tripalmitin transesterification to methyl palmitate, with framework phenyl groups promoting fatty acid methyl esters production. (Chemical Equation Presented)