Evolution of optical pulses in fiber lines with lumped nonlinear devices as a mapping problem

We analyze the steady-state propagation of optical pulses in fiber transmission systems with lumped nonlinear optical devices (NODs) placed periodically in the line. For the first time to our knowledge, a theoretical model is developed to describe the transmission regime with a quasilinear pulse evolution along the transmission line and the point action of NODs. We formulate the mapping problem for pulse propagation in a unit cell of the line and show that in the particular application to nonlinear optical loop mirrors, the steady-state pulse characteristics predicted by the theory accurately reproduce the results of direct numerical simulations. © 2005 Springer Science+Business Media, Inc.

Local Bifurcations in a Nonlinear Model of a Bioreactor

This paper is partially supported by the Bulgarian Science Fund under grant Nr. DO 02– 359/2008.

Integral Manifolds and Perturbations of the Nonlinear Part of Systems of Autonomous Differential Equations with Impulses at Fixed Moments

* This investigation was supported by the Bulgarian Ministry of Science and Education under Grant MM-7.

Nonlinear pulse shaping in fibres for pulse generation and optical processing

The development of new all-optical technologies for data processing and signal manipulation is a field of growing importance with a strong potential for numerous applications in diverse areas of modern science. Nonlinear phenomena occurring in optical fibres have many attractive features and great, but not yet fully explored, potential in signal processing. Here, we review recent progress on the use of fibre nonlinearities for the generation and shaping of optical pulses and on the applications of advanced pulse shapes in all-optical signal processing. Amongst other topics, we will discuss ultrahigh repetition rate pulse sources, the generation of parabolic shaped pulses in active and passive fibres, the generation of pulses with triangular temporal profiles, and coherent supercontinuum sources. The signal processing applications will span optical regeneration, linear distortion compensation, optical decision at the receiver in optical communication systems, spectral and temporal signal doubling, and frequency conversion. © Copyright 2012 Sonia Boscolo and Christophe Finot.

Kerr nonlinear switching in a core-shell microspherical resonator fabricated from the silicon fiber platform

We investigate the Kerr nonlinearity in a core-shell microspherical resonator fabricated from a silicon fiber. By exploiting the ultrafast wavelength shifting, sub-picosecond modulation is demonstrated. © OSA 2015.

Hyperspectral Image Classification with Nonlinear Methods

This thesis introduces two related lines of study on classification of hyperspectral images with nonlinear methods. First, it describes a quantitative and systematic evaluation, by the author, of each major component in a pipeline for classifying hyperspectral images (HSI) developed earlier in a joint collaboration [23]. The pipeline, with novel use of nonlinear classification methods, has reached beyond the state of the art in classification accuracy on commonly used benchmarking HSI data [6], [13]. More importantly, it provides a clutter map, with respect to a predetermined set of classes, toward the real application situations where the image pixels not necessarily fall into a predetermined set of classes to be identified, detected or classified with.

The particular components evaluated are a) band selection with band-wise entropy spread, b) feature transformation with spatial filters and spectral expansion with derivatives c) graph spectral transformation via locally linear embedding for dimension reduction, and d) statistical ensemble for clutter detection. The quantitative evaluation of the pipeline verifies that these components are indispensable to high-accuracy classification.

Secondly, the work extends the HSI classification pipeline with a single HSI data cube to multiple HSI data cubes. Each cube, with feature variation, is to be classified of multiple classes. The main challenge is deriving the cube-wise classification from pixel-wise classification. The thesis presents the initial attempt to circumvent it, and discuss the potential for further improvement.

Nonlinear optics with cold Rb atoms using tapered optical nanofibres

Optical nanofibres (ONFs) are very thin optical waveguides with sub-wavelength diameters. ONFs have very high evanescent fields and the guided light is confined strongly in the transverse direction. These fibres can be used to achieve strong light-matter interactions. Atoms around the waist of an ONF can be probed by collecting the atomic fluorescence coupling or by measuring the transmission (or the polarisation) of the probe beam sent through it. This thesis presents experiments using ONFs for probing and manipulating laser-cooled 87Rb atoms. As an initial experiment, a single mode ONF was integrated into a magneto-optical trap (MOT) and used for measuring the characteristics of the MOT, such as the loading time and the average temperature of the atom cloud. The effect of a near-resonant probe beam on the local temperature of the cold atoms has been studied. Next, the ONF was used for manipulating the atoms in the evanescent fields region in order to generate nonlinear optical effects. Four-wave mixing, ac Stark effect (Autler-Townes splitting) and electromagnetically induced transparency have been observed at unprecedented ultralow power levels. In another experiment, a few-mode ONF, supporting only the fundamental mode and the first higher order mode group, has been used for studying cold atoms. A higher pumping rate of the atomic fluorescence into the higher order fibreguided modes and more interactions with the surrounding atoms for higher order mode evanescent light, when compared to signals for the fundamental mode, have been identified. The results obtained in the thesis are particularly for a fundamental understanding of light-atom interactions when atoms are near a dielectric surface and also for the development of fibre-based quantum information technologies. Atoms coupled to ONFs could be used for preparing intrinsically fibre-coupled quantum nodes for quantum computing and the studies presented here are significant for a detailed understanding of such a system.

Filamentation in Air and Water and Nonlinear Optical Characterization of Biopolymer Using Ultrashort Laser Pulses

Important issues related to femtosecond (fs) pulses and its relevance to this thesis are discussed. A fundamental characteristic, like the timebandwidth product for fs pulses is decribed in detail. A brief review of generation of ultrashort pulses and its propagation through an optically transparent media are presented. Interaction of strong pulses with matter and different ionization processes are also described. An overview of the thesis is presented at the end

Addressing surprise and uncertain futures in marine science, marine governance, and society

On an increasingly populated planet, with decreasing biodiversity and limited new opportunities to tap unexploited natural resources, there is a clear need to adjust aspects of marine management and governance. Although sectarian management has succeeded in addressing and managing some important threats to marine ecosystems, unintended consequences are often associated with overlooking nonlinear interactions and cumulative impacts that increase the risk of surprises in social-ecological systems. In this paper, we begin to untangle science-governance-society (SGS) interdependencies in marine systems by considering how to recognize the risk of surprise in social and ecological dynamics. Equally important is drawing attention to our state of preparedness, adaptation, and timeliness of response in ecosystem governance and society, which involve fostering transformations away from rigid and nonintegrated structures of governance. More inclusive decision-making processes, deeper understanding of complexity, and colearning across SGS can help to build constructive solutions that are likely to benefit multiple stakeholders and build capacity to understand and respond to change.

Nonlinear Dynamics Near the Cell Membrane of Chara Corallina

The phenomenon of patterned distribution of pH near the cell membrane of the algae Chara corallina upon illumination is well-known. In this paper, we develop a mathematical model, based on the detailed kinetic analysis of proton fluxes across the cell membrane, to explain this phenomenon. The model yields two coupled nonlinear partial differential equations which describe the spatial dynamics of proton concentration changes and transmembrane potential generation. The experimental observation of pH pattern formation, its period and amplitude of oscillation, and also its hysteresis in response to changing illumination, are all reproduced by our model. A comparison of experimental results and predictions of our theory is made. Finally, a mechanism for pattern formation in Chara corallina is proposed.

The Helmholtzian Equation: Stabilizing Mechanisms for Quadratic Nonlinear Fields

Hexagonal Resonant Triad patterns are shown to exist as stable solutions of a particular type of nonlinear field where no cubic field nonlinearity is present. The zero ‘dc’ Fourier mode is shown to stabilize these patterns produced by a pure quadratic field nonlinearity. Closed form solutions and stability results are obtained near the critical point, complimented by numerical studies far from the critical point. These results are obtained using a neural field based on the Helmholtzian operator. Constraints on structure and parameters for a general pure quadratic neural field which supports hexagonal patterns are obtained.

An identification procedure of multi-input Wiener models for the distortion analysis of nonlinear circuits

In this contribution, a system identification procedure of a two-input Wiener model suitable for the analysis of the disturbance behavior of integrated nonlinear circuits is presented. The identified block model is comprised of two linear dynamic and one static nonlinear block, which are determined using an parameterized approach. In order to characterize the linear blocks, an correlation analysis using a white noise input in combination with a model reduction scheme is adopted. After having characterized the linear blocks, from the output spectrum under single tone excitation at each input a linear set of equations will be set up, whose solution gives the coefficients of the nonlinear block. By this data based black box approach, the distortion behavior of a nonlinear circuit under the influence of an interfering signal at an arbitrary input port can be determined. Such an interfering signal can be, for example, an electromagnetic interference signal which conductively couples into the port of consideration. © 2011 Author(s).

Systems of coupled clamped beams equations with full nonlinear terms: Existence and location results

This work gives sufficient conditions for the solvability of the fourth order coupled system┊ u⁽⁴⁾(t)=f(t,u(t),u′(t),u′′(t),u′′′(t),v(t),v′(t),v′′(t),v′′′(t)) v⁽⁴⁾(t)=h(t,u(t),u′(t),u′′(t),u′′′(t),v(t),v′(t),v′′(t),v′′′(t)) with f,h: [0,1]×ℝ⁸→ℝ some L¹- Carathéodory functions, and the boundary conditions {┊ u(0)=u′(0)=u′′(0)=u′′(1)=0 v(0)=v′(0)=v′′(0)=v′′(1)=0. To the best of our knowledge, it is the first time in the literature where two beam equations are considered with full nonlinearities, that is, with dependence on all derivatives of u and v. An application to the study of the bending of two elastic coupled campled beams is considered.