Modeling of CW Yb-doped fiber lasers with highly nonlinear cavity dynamics

We develop a theoretical framework for modeling of continuous wave Yb-doped fiber lasers with highly nonlinear cavity dynamics. The developed approach has shown good agreement between theoretical predictions and experimental results for particular scheme of Yb-doped laser with large spectral broadening during single round trip. The model is capable to accurately describe main features of the experimentally measured laser outputs such as power efficiency slope, power leakage through fibre Bragg gratings, spectral broadening and spectral shape of generated radiation. © 2011 Optical Society of America.

Mode-locking intracavity dynamics:modeling nonlinear power and energy fluctuations

Modern high-power, pulsed lasers are driven by strong intracavity fluctuations. Critical in driving the intracavity dynamics is the nontrivial phase profiles generated and their periodic modification from either nonlinear mode-coupling, spectral filtering or dispersion management. Understanding the theoretical origins of the intracavity fluctuations helps guide the design, optimization and construction of efficient, high-power and high-energy pulsed laser cavities. Three specific mode-locking component are presented for enhancing laser energy: waveguide arrays, spectral filtering and dispersion management. Each component drives a strong intracavity dynamics that is captured through various modeling and analytic techniques.

Interaction dynamics in small networks of nonlinear elements

We study a small circuit of coupled nonlinear elements to investigate general features of signal transmission through networks. The small circuit itself is perceived as building block for larger networks. Individual dynamics and coupling are motivated by neuronal systems: We consider two types of dynamical modes for an individual element, regular spiking and chattering and each individual element can receive excitatory and/or inhibitory inputs and is subjected to different feedback types (excitatory and inhibitory; forward and recurrent). Both, deterministic and stochastic simulations are carried out to study the input-output relationships of these networks. Major results for regular spiking elements include frequency locking, spike rate amplification for strong synaptic coupling, and inhibition-induced spike rate control which can be interpreted as a output frequency rectification. For chattering elements, spike rate amplification for low frequencies and silencing for large frequencies is characteristic

Nonlinear Optics and Carrier Dynamics in Nanostructured and Two-Dimensional Materials

Understanding and measuring the interaction of light with sub-wavelength structures and atomically thin materials is of critical importance for the development of next generation photonic devices.  One approach to achieve the desired optical properties in a material is to manipulate its mesoscopic structure or its composition in order to affect the properties of the light-matter interaction.  There has been tremendous recent interest in so called two-dimensional materials, consisting of only a single to a few layers of atoms arranged in a planar sheet.  These materials have demonstrated great promise as a platform for studying unique phenomena arising from the low-dimensionality of the material and for developing new types of devices based on these effects.  A thorough investigation of the optical and electronic properties of these new materials is essential to realizing their potential.  In this work we present studies that explore the nonlinear optical properties and carrier dynamics in nanoporous silicon waveguides, two-dimensional graphite (graphene), and atomically thin black phosphorus. We first present an investigation of the nonlinear response of nanoporous silicon optical waveguides using a novel pump-probe method. A two-frequency heterodyne technique is developed in order to measure the pump-induced transient change in phase and intensity in a single measurement. The experimental data reveal a characteristic material response time and temporally resolved intensity and phase behavior matching a physical model dominated by free-carrier effects that are significantly stronger and faster than those observed in traditional silicon-based waveguides.  These results shed light on the large optical nonlinearity observed in nanoporous silicon and demonstrate a new measurement technique for heterodyne pump-probe spectroscopy. Next we explore the optical properties of low-doped graphene in the terahertz spectral regime, where both intraband and interband effects play a significant role. Probing the graphene at intermediate photon energies enables the investigation of the nonlinear optical properties in the graphene as its electron system is heated by the intense pump pulse. By simultaneously measuring the reflected and transmitted terahertz light, a precise determination of the pump-induced change in absorption can be made. We observe that as the intensity of the terahertz radiation is increased, the optical properties of the graphene change from interband, semiconductor-like absorption, to a more metallic behavior with increased intraband processes. This transition reveals itself in our measurements as an increase in the terahertz transmission through the graphene at low fluence, followed by a decrease in transmission and the onset of a large, photo-induced reflection as fluence is increased.  A hybrid optical-thermodynamic model successfully describes our observations and predicts this transition will persist across mid- and far-infrared frequencies.  This study further demonstrates the important role that reflection plays since the absorption saturation intensity (an important figure of merit for graphene-based saturable absorbers) can be underestimated if only the transmitted light is considered. These findings are expected to contribute to the development of new optoelectronic devices designed to operate in the mid- and far-infrared frequency range.  Lastly we discuss recent work with black phosphorus, a two-dimensional material that has recently attracted interest due to its high mobility and direct, configurable band gap (300 meV to 2eV), depending on the number of atomic layers comprising the sample. In this work we examine the pump-induced change in optical transmission of mechanically exfoliated black phosphorus flakes using a two-color optical pump-probe measurement. The time-resolved data reveal a fast pump-induced transparency accompanied by a slower absorption that we attribute to Pauli blocking and free-carrier absorption, respectively. Polarization studies show that these effects are also highly anisotropic - underscoring the importance of crystal orientation in the design of optical devices based on this material. We conclude our discussion of black phosphorus with a study that employs this material as the active element in a photoconductive detector capable of gigahertz class detection at room temperature for mid-infrared frequencies.

Interaction Between Fiscal And Monetary Policy In A Dynamic Nonlinear Model.

The objective of this study is to verify the dynamics between fiscal policy, measured by public debt, and monetary policy, measured by a reaction function of a central bank. Changes in monetary policies due to deviations from their targets always generate fiscal impacts. We examine two policy reaction functions: the first related to inflation targets and the second related to economic growth targets. We find that the condition for stable equilibrium is more restrictive in the first case than in the second. We then apply our simulation model to Brazil and United Kingdom and find that the equilibrium is unstable in the Brazilian case but stable in the UK case.

Effects of Variations in Nonlinear Damping Coefficients on the Parametric Vibration of a Cantilever Beam with a Lumped Mass

Uncertainties in damping estimates can significantly affect the dynamic response of a given flexible structure. A common practice in linear structural dynamics is to consider a linear viscous damping model as the major energy dissipation mechanism. However, it is well known that different forms of energy dissipation can affect the structure's dynamic response. The major goal of this paper is to address the effects of the turbulent frictional damping force, also known as drag force on the dynamic behavior of a typical flexible structure composed of a slender cantilever beam carrying a lumped-mass on the tip. First, the system's analytical equation is obtained and solved by employing a perturbation technique. The solution process considers variations of the drag force coefficient and its effects on the system's response. Then, experimental results are presented to demonstrate the effects of the nonlinear quadratic damping due to the turbulent frictional force on the system's dynamic response. In particular, the effects of the quadratic damping on the frequency-response and amplitude-response curves are investigated. Numerically simulated as well as experimental results indicate that variations on the drag force coefficient significantly alter the dynamics of the structure under investigation. Copyright (c) 2008 D. G. Silva and P. S. Varoto.

Matter-wave two-dimensional solitons in crossed linear and nonlinear optical lattices

The existence of multidimensional matter-wave solitons in a crossed optical lattice (OL) with a linear optical lattice (LOL) in the x direction and a nonlinear optical lattice (NOL) in the y direction, where the NOL can be generated by a periodic spatial modulation of the scattering length using an optically induced Feshbach resonance is demonstrated. In particular, we show that such crossed LOLs and NOLs allow for stabilizing two-dimensional solitons against decay or collapse for both attractive and repulsive interactions. The solutions for the soliton stability are investigated analytically, by using a multi-Gaussian variational approach, with the Vakhitov-Kolokolov necessary criterion for stability; and numerically, by using the relaxation method and direct numerical time integrations of the Gross-Pitaevskii equation. Very good agreement of the results corresponding to both treatments is observed.

Two-dimensional supersonic nonlinear Schrodinger flow past an extended obstacle

Supersonic flow of a superfluid past a slender impenetrable macroscopic obstacle is studied in the framework of the two-dimensional (2D) defocusing nonlinear Schroumldinger (NLS) equation. This problem is of fundamental importance as a dispersive analog of the corresponding classical gas-dynamics problem. Assuming the oncoming flow speed is sufficiently high, we asymptotically reduce the original boundary-value problem for a steady flow past a slender body to the one-dimensional dispersive piston problem described by the nonstationary NLS equation, in which the role of time is played by the stretched x coordinate and the piston motion curve is defined by the spatial body profile. Two steady oblique spatial dispersive shock waves (DSWs) spreading from the pointed ends of the body are generated in both half planes. These are described analytically by constructing appropriate exact solutions of the Whitham modulation equations for the front DSW and by using a generalized Bohr-Sommerfeld quantization rule for the oblique dark soliton fan in the rear DSW. We propose an extension of the traditional modulation description of DSWs to include the linear ""ship-wave"" pattern forming outside the nonlinear modulation region of the front DSW. Our analytic results are supported by direct 2D unsteady numerical simulations and are relevant to recent experiments on Bose-Einstein condensates freely expanding past obstacles.

Localized modes of binary mixtures of Bose-Einstein condensates in nonlinear optical lattices

The properties of the localized states of a two-component Bose-Einstein condensate confined in a nonlinear periodic potential (nonlinear optical lattice) are investigated. We discuss the existence of different types of solitons and study their stability by means of analytical and numerical approaches. The symmetry properties of the localized states with respect to nonlinear optical lattices are also investigated. We show that nonlinear optical lattices allow the existence of bright soliton modes with equal symmetry in both components and bright localized modes of mixed symmetry type, as well as dark-bright bound states and bright modes on periodic backgrounds. In spite of the quasi-one-dimensional nature of the problem, the fundamental symmetric localized modes undergo a delocalizing transition when the strength of the nonlinear optical lattice is varied. This transition is associated with the existence of an unstable solution, which exhibits a shrinking (decaying) behavior for slightly overcritical (undercritical) variations in the number of atoms.

Investigation of Normal Force and Moment Coefficients for an AUV at Nonlinear Angle of Attack and Sideslip Range

This paper presents a comparative study of computational fluid dynamics (CFD) and analytical and semiempirical (ASE) methods applied to the prediction of the normal force and moment coefficients of an autonomous underwater vehicle (AUV). Both methods are applied to the. bare hull of the vehicle and to the body-hydroplane combination. The results are validated through experiments in a towing tank. It is shown that the CFD approach allows for a good prediction of the coefficients over the range of angles of attack considered. In contrast with the traditional ASE formulations used in naval and aircraft fields, an improved methodology is introduced that takes advantage of the qualitative information obtained from CFD flow visualizations.

Dependence of transient dynamics in a class-C laser upon variation of inversion with time

The transient statistics of a gain-switched coherently pumped class-C laser displays a linear correlation between the first passage time and subsequent peak intensity. Measurements are reported showing a positive or negative sign of this linear correlation, controlled through the switching time and the laser detuning. Further measurements of the small-signal laser gain combined with calculations involving a three-level laser model indicate that this sign fundamentally depends upon the way the laser inversion varies during the gain switching, despite the added dynamics of the laser polarization in the class-C laser. [S1050-2947(97)07112-6].

Semiquantum versus semiclassical mechanics for simple nonlinear systems

Quantum mechanics has been formulated in phase space, with the Wigner function as the representative of the quantum density operator, and classical mechanics has been formulated in Hilbert space, with the Groenewold operator as the representative of the classical Liouville density function. Semiclassical approximations to the quantum evolution of the Wigner function have been defined, enabling the quantum evolution to be approached from a classical starting point. Now analogous semiquantum approximations to the classical evolution of the Groenewold operator are defined, enabling the classical evolution to be approached from a quantum starting point. Simple nonlinear systems with one degree of freedom are considered, whose Hamiltonians are polynomials in the Hamiltonian of the simple harmonic oscillator. The behavior of expectation values of simple observables and of eigenvalues of the Groenewold operator are calculated numerically and compared for the various semiclassical and semiquantum approximations.

Quantum signatures of chaos in the dynamics of a trapped ion

We show how a nonlinear chaotic system, the parametrically kicked nonlinear oscillator, may be realized in the dynamics of a trapped, laser-cooled ion, interacting with a sequence of standing-wave pulses. Unlike the original optical scheme [G. J. Milburn and C.A. Holmes, Phys. Rev. A 44, 4704 (1991)], the trapped ion enables strongly quantum dynamics with minimal dissipation. This should permit an experimental test of one of the quantum signatures of chaos: irregular collapse and revival dynamics of the average vibrational energy.

Fractional dynamics in DNA

This paper addresses the DNA code analysis in the perspective of dynamics and fractional calculus. Several mathematical tools are selected to establish a quantitative method without distorting the alphabet represented by the sequence of DNA bases. The association of Gray code, Fourier transform and fractional calculus leads to a categorical representation of species and chromosomes.

Analysis of temperature time-series: embedding dynamics into the MDS method

Global warming and the associated climate changes are being the subject of intensive research due to their major impact on social, economic and health aspects of the human life. Surface temperature time-series characterise Earth as a slow dynamics spatiotemporal system, evidencing long memory behaviour, typical of fractional order systems. Such phenomena are difficult to model and analyse, demanding for alternative approaches. This paper studies the complex correlations between global temperature time-series using the Multidimensional scaling (MDS) approach. MDS provides a graphical representation of the pattern of climatic similarities between regions around the globe. The similarities are quantified through two mathematical indices that correlate the monthly average temperatures observed in meteorological stations, over a given period of time. Furthermore, time dynamics is analysed by performing the MDS analysis over slices sampling the time series. MDS generates maps describing the stations’ locus in the perspective that, if they are perceived to be similar to each other, then they are placed on the map forming clusters. We show that MDS provides an intuitive and useful visual representation of the complex relationships that are present among temperature time-series, which are not perceived on traditional geographic maps. Moreover, MDS avoids sensitivity to the irregular distribution density of the meteorological stations.