Two-dimensional dipolar Bose-Einstein condensate bright and vortex solitons on a one-dimensional optical lattice

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Gap solitons in a model of a superfluid fermion gas in optical lattices

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Gap solitons in a dipolar Bose-Einstein condensate on a three-dimensional optical lattice

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Bright solitons in quasi-one-dimensional dipolar condensates with spatially modulated interactions

We introduce a model for the condensate of dipolar atoms or molecules, in which the dipole-dipole interaction (DDI) is periodically modulated in space due to a periodic change of the local orientation of the permanent dipoles, imposed by the corresponding structure of an external field (the necessary field can be created, in particular, by means of magnetic lattices, which are available to the experiment). The system represents a realization of a nonlocal nonlinear lattice, which has a potential to support various spatial modes. By means of numerical methods and variational approximation (VA), we construct bright one-dimensional solitons in this system and study their stability. In most cases, the VA provides good accuracy and correctly predicts the stability by means of the Vakhitov-Kolokolov criterion. It is found that the periodic modulation may destroy some solitons, which exist in the usual setting with unmodulated DDI and can create stable solitons in other cases, not verified in the absence of modulations. Unstable solitons typically transform into persistent localized breathers. The solitons are often mobile, with inelastic collisions between them leading to oscillating localized modes. © 2013 American Physical Society.

Stable and mobile excited two-dimensional dipolar Bose-Einstein condensate solitons

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

The effects of hypocalcemia on spatial alternans and ventricular fibrillation studied with the optical mapping technique

The heart is a wonderful but complex organ: it uses electrochemical mechanisms in order to produce mechanical energy to pump the blood throughout the body and allow the life of humans and animals. This organ can be subject to several diseases and sudden cardiac death (SCD) is the most catastrophic manifestation of these diseases, responsible for the death of a large number of people throughout the world. It is estimated that 325000 Americans annually die for SCD. SCD most commonly occurs as a result of reentrant tachyarrhythmias (ventricular tachycardia (VT) and ventricular fibrillation (VF)) and the identification of those patients at higher risk for the development of SCD has been a difficult clinical challenge. Nowadays, a particular electrocardiogram (ECG) abnormality, “T-wave alternans” (TWA), is considered a precursor of lethal cardiac arrhythmias and sudden death, a sensitive indicator of risk for SCD. TWA is defined as a beat-to-beat alternation in the shape, amplitude, or timing of the T-wave on the ECG, indicative of the underlying repolarization of cardiac cells [5]. In other words TWA is the macroscopic effect of subcellular and celluar mechanisms involving ionic kinetics and the consequent depolarization and repolarization of the myocytes. Experimental activities have shown that TWA on the ECG is a manifestation of an underlying alternation of long and short action potential durations (APDs), the so called APD-alternans, of cardiac myocytes in the myocardium. Understanding the mechanism of APDs-alternans is the first step for preventing them to occur. In order to investigate these mechanisms it’s very important to understand that the biological systems are complex systems and their macroscopic properties arise from the nonlinear interactions among the parts. The whole is greater than the sum of the parts, and it cannot be understood only by studying the single parts. In this sense the heart is a complex nonlinear system and its way of working follows nonlinear dynamics; alternans also, they are a manifestation of a phenomenon typical in nonlinear dynamical systems, called “period-dubling bifurcation”. Over the past decade, it has been demonstrated that electrical alternans in cardiac tissue is an important marker for the development of ventricular fibrillation and a significant predictor for mortality. It has been observed that acute exposure to low concentration of calcium does not decrease the magnitude of alternans and sustained ventricular Fibrillation (VF) is still easily induced under these condition. However with prolonged exposure to low concentration of calcium, alternans disappears, but VF is still inducible. This work is based on this observation and tries to make it clearer. The aim of this thesis is investigate the effect of hypocalcemia spatial alternans and VF doing experiments with canine hearts and perfusing them with a solution with physiological ionic concentration and with a solution with low calcium concentration (hypocalcemia); in order to investigate the so called memory effect, the experimental activity was modified during the way. The experiments were performed with the optical mapping technique, using voltage-sensitive dye, and a custom made Java code was used in post-processing. Finding the Nolasco and Dahlen’s criterion [8] inadequate for the prediction of alternans, and takin into account the experimental results, another criterion, which consider the memory effect, has been implemented. The implementation of this criterion could be the first step in the creation of a method, AP-based, discriminating who is at risk if developing VF. This work is divided into four chapters: the first is a brief presentation of the physiology of the heart; the second is a review of the major theories and discovers in the study of cardiac dynamics; the third chapter presents an overview on the experimental activity and the optical mapping technique; the forth chapter contains the presentation of the results and the conclusions.

Influence of ice crystal habit and cirrus spatial inhomogeneities on the retrieval of cirrus optical thickness and effective radius

Diese Dissertation untersucht den Einfluss von Eiskristallform und räumlicher Inhomogenität von Zirren auf das Retrieval von optischer Wolkendicke und effektivem Eispartikelradius. Zu diesem Zweck werden flugzeuggetragene spektrale Messungen solarer Strahlung sowie solare und langwellige Strahlungstransfersimulationen durchgeführt. Flugzeuggetragene spektrale aufwärtsgerichtete Radianzen (Strahldichten) sind mit dem SMART-Albedometer (Spectral Modular Airborne Radiation measurement sysTem) während des CIRCLE-2 (CIRrus CLoud Experiment-2) Feldexperiments im Mai 2007 gemessen worden. Basierend auf diesen Radianzdaten werden mittels eines Wolkenretrievalalgorithmus optische Wolkendicken und effektive Eispartikelradien anhand von eindimensionalen Strahlungstransferrechnungen bestimmt. Die Auswirkung der Annahme unterschiedlicher Eiskristallformen auf die retrievten Parameter wird durch Variation der Einfachstreueigenschaften der Eispartikel untersucht. Darüber hinaus wird mittels Strahlungstransferrechnungen auch der Einfluss der Eiskristallform auf den Strahlungsantrieb von Eiswolken ermittelt. Die Frage nach dem relativen Einfluss von räumlicher Wolkeninhomogenität und Eiskristallform wird anhand von dreidimensionalen und independent pixel approximation (IPA) Strahlungssimulationen untersucht. Die Analyse basiert auf einer Modelleiswolke, die aus Daten des NASA (National Aeronautics and Space Administration) TC4 (Tropical Composition, Cloud, and Climate Coupling) Feldexperiments im Sommer 2007 in Costa Rica erzeugt wurde. Lokal gesehen können beide Effekte - Eiskristallform und räumliche Eiswolkeninhomogenität - die gleiche Grössenordnung haben und zu einer Unter- bzw. Überschätzung der retrievten Parameter um 40 – 60% führen. Gemittelt über die ganze Wolke ist jedoch der Einfluss der Eiskristallform viel bedeutender als der von räumlichen Inhomogenitäten.

Single-shot electron bunch length measurements using a spatial electro-optical autocorrelation interferometer

A spatial, electro-optical autocorrelation (EOA) interferometer using the vertically polarized lobes of coherent transition radiation (CTR) has been developed as a single-shot electron bunch length monitor at an optical beam port downstream the 100 MeV preinjector LINAC of the Swiss Light Source. This EOA monitor combines the advantages of step-scan interferometers (high temporal resolution) [D. Mihalcea et al., Phys. Rev. ST Accel. Beams 9, 082801 (2006) and T. Takahashi and K. Takami, Infrared Phys. Technol. 51, 363 (2008)] and terahertz-gating technologies [U. Schmidhammer et al., Appl. Phys. B: Lasers Opt. 94, 95 (2009) and B. Steffen et al., Phys. Rev. ST Accel. Beams 12, 032802 (2009)] (fast response), providing the possibility to tune the accelerator with an online bunch length diagnostics. While a proof of principle of the spatial interferometer was achieved by step-scan measurements with far-infrared detectors, the single-shot capability of the monitor has been demonstrated by electro-optical correlation of the spatial CTR interference pattern with fairly long (500 ps) neodymium-doped yttrium aluminum garnet (Nd:YAG) laser pulses in a ZnTe crystal. In single-shot operation, variations of the bunch length between 1.5 and 4 ps due to different phase settings of the LINAC bunching cavities have been measured with subpicosecond time resolution.

Mathematical and numerical modelling of dispersion-managed solitons, autosolitons and self-similar optical pulses

This thesis presents theoretical investigation of three topics concerned with nonlinear optical pulse propagation in optical fibres. The techniques used are mathematical analysis and numerical modelling. Firstly, dispersion-managed (DM) solitons in fibre lines employing a weak dispersion map are analysed by means of a perturbation approach. In the case of small dispersion map strengths the average pulse dynamics is described by a perturbation approach (NLS) equation. Applying a perturbation theory, based on the Inverse Scattering Transform method, an analytic expression for the envelope of the DM soliton is derived. This expression correctly predicts the power enhancement arising from the dispersion management.Secondly, autosoliton transmission in DM fibre systems with periodical in-line deployment of nonlinear optical loop mirrors (NOLMs) is investigated. The use of in-line NOLMs is addressed as a general technique for all-optical passive 2R regeneration of return-to-zero data in high speed transmission system with strong dispersion management. By system optimisation, the feasibility of ultra-long single-channel and wavelength-division multiplexed data transmission at bit-rates ³ 40 Gbit s-1 in standard fibre-based systems is demonstrated. The tolerance limits of the results are defined.Thirdly, solutions of the NLS equation with gain and normal dispersion, that describes optical pulse propagation in an amplifying medium, are examined. A self-similar parabolic solution in the energy-containing core of the pulse is matched through Painlevé functions to the linear low-amplitude tails. The analysis provides a full description of the features of high-power pulses generated in an amplifying medium.

Dark solitons in optical communication systems

This thesis presents experimental and theoretical work on the use of dark optical solitons as data carriers in communications systems. The background chapters provide an introduction to nonlinear optics, and to dark solitons, described as intensity dips in a bright background, with an asymmetrical phase profile. The motivation for the work is explained, considering both the superior stability of dark solitons and the need for a soliton solution suitable for the normal, rather than the anomalous (bright soliton) dispersion regime. The first chapters present two generation techniques, producing packets of dark solitons via bright pulse interaction, and generating continuous trains of dark pulses using a fibre laser. The latter were not dark solitons, but were suitable for imposition of the required phase shift by virtue of their extreme stability. The later chapters focus on the propagation and control of dark solitons. Their response to periodic loss and gain is shown to result in the exponential growth of spectral sidebands. This may be suppressed by reducing the periodicity of the loss/gain cycle or using periodic filtering. A general study of the response of dark solitons to spectral filtering is undertaken, showing dramatic differences in the behaviour of black and 99.9% grey solitons. The importance of this result is highlighted by simulations of propagation in noisy systems, where the timing jitter resulting from random noise is actually enhanced by filtering. The results of using sinusoidal phase modulation to control pulse position are presented, showing that the control is at the expense of serious modulation of the bright background. It is concluded that in almost every case, dark and bright solitons have very different properties, and to continue to make comparisons would not be so productive as to develop a deeper understanding of the interactions between the dark soliton and its bright background.

Spatial contrast sensitivity and external noise: applications to optical and neural modulation transfer functions

The thesis will show how to equalise the effect of quantal noise across spatial frequencies by keeping the retinal flux (If-2) constant. In addition, quantal noise is used to study the effect of grating area and spatial frequency on contrast sensitivity resulting in the extension of the new contrast detection model describing the human contrast detection system as a simple image processor. According to the model the human contrast detection system comprises low-pass filtering due to ocular optics, addition of light dependent noise at the event of quantal absorption, high-pass filtering due to the neural visual pathways, addition of internal neural noise, after which detection takes place by a local matched filter, whose sampling efficiency decreases as grating area is increased. Furthermore, this work will demonstrate how to extract both the optical and neural modulation transfer functions of the human eye. The neural transfer function is found to be proportional to spatial frequency up to the local cut-off frequency at eccentricities of 0 - 37 deg across the visual field. The optical transfer function of the human eye is proposed to be more affected by the Stiles-Crawford -effect than generally assumed in the literature. Similarly, this work questions the prevailing ideas about the factors limiting peripheral vision by showing that peripheral optical acts as a low-pass filter in normal viewing conditions, and therefore the effect of peripheral optics is worse than generally assumed.

Dissipative nonlinear structures in optical fiber systems I : dissipative dispersion managed solitons in mode-locked lasers

In this first talk on dissipative structures in fiber applications, we extend theory of dispersion-managed solitons to dissipative systems with a focus on mode-locked fibre lasers. Dissipative structures exist at high map strengths leading to the generation of stable, short pulses with high energy. Two types of intra-map pulse evolutions are observed depending on the net cavity dispersion. These are characterized by a reduced model and semi-analytical solutions are obtained.

Dissipative nonlinear structures in optical fiber systems III : dissipative solitons via nonlinear mapping

In the third and final talk on dissipative structures in fiber applications, we discuss mathematical techniques that can be used to characterize modern laser systems that consist of several discrete elements. In particular, we use a nonlinear mapping technique to evaluate high power laser systems where significant changes in the pulse evolution per cavity round trip is observed. We demonstrate that dissipative soliton solutions might be effectively described using this Poincaré mapping approach.