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Please use this identifier to cite or link to this item: http://hdl.handle.net/10261/46753
Title: Spatial structures and Information Processing in Nonlinear Optical Cavities
Authors: Jacobo, Adrián; Colet, Pere; Gomila, Damià
Issue Date: Feb-2008
Publisher: CSIC-UIB - Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC)
Abstract: Nonlinear optics is the study of phenomena that occur as a consequence of the modification of the optical properties of a material by the presence of light. Such nonlinear e ects usually occur with high intensities of light, that can only be achieved with lasers. In fact, the beginning of nonlinear optics is often considered to be the experiment of Second Harmonic Generation by Franken and coworkers in 1961, shortly after the demonstration of the first working laser by Maiman in 1960. To enhance the interaction between the light and the nonlinear material, it is usually placed inside an optical cavity. This nonlinear optical cavities exhibit various kinds of interesting phenomena such as bistability, pattern formation, localized structures (also called cavity solitons) and chaos. The study of some of those e ects in nonlinear optical cavities and its possible application to information processing is the main topic of this thesis. We will focus in two di erent types of nonlinear optical systems: the Second Harmonic Generation and the Kerr cavity, which constitute two of the most relevant nonlinear optical systems. Thus, in Sections 1.6 and 1.7 respectively, we will derive the equations that describe this two systems.
In the first part of the thesis we will give an introduction to the most relevant concepts that we will encounter along the rest of the thesis. We will first give a brief introduction to the subject of image processing which is then studied in relation with the process of second harmonic generation in Chapter 2. One of this image processing operations is the enhancement of an image’s contrast, this procedure is based in the bistability displayed by the equations for the Second Harmonic Generation process. In Chapter 3 we will introduce a technique based on the contrast enhancement process, and use it to filter data from ecological time series and detect changes on its mean value. Therefore, in Sec. 1.2 we will give a brief summary of methods available in the literature to detect such changes. In Chapter 4 we will apply the same filtering method to decode chaos encrypted messages.
In Sec. 1.3 we will introduce the concept of localized structures which is the main topic of Part II. There we will study the dynamics of localized structures in a Kerr cavity. In particular, in Chapters 5, 6 and 8 we will study the bifurcations that give rise to the di erent dynamical behaviors displayed by these structures. That is why, in Sect. 1.4 we give a brief summary of the bifurcations that we will encounter, and its main properties. The most interesting dynamical behavior of these localized structures is excitability, this concept will be introduced in Sect. 5.4. Once we have characterized the excitable localized structures we will show, in Chapter 7, how they can be used to construct logic gates by coupling several of them. This gates perform basic logic operations and constitute the primary units of information processing, as they can be coupled to perform more complicated operations. In Chapter 8 we will study oscillatory localized structures. In particular we will focus in the study of the interaction of such structures as a model of interacting nonlocal oscillators. Finally in Chapter 9 we will summarize the obtained results, and give some concluding remarks
Description: Tesis leída en febrero de 2008 en la Universidad de Palma de Mallorca para obtener el grado de doctor en Física
URI: http://hdl.handle.net/10261/46753
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