2019-06-26T06:27:14Z
https://digital.csic.es/dspace-oai/request
oai:digital.csic.es:10261/46753
2018-09-13T06:57:57Z
com_10261_2855
com_10261_4
col_10261_2866
Jacobo, Adrián
Colet, Pere
Gomila, Damià
2012-03-08T10:45:49Z
2012-03-08T10:45:49Z
2008-02
http://hdl.handle.net/10261/46753
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
eng
openAccess
Spatial structures and Information Processing in Nonlinear Optical Cavities
Tesis