Samenvatting
In this thesis, we study emergent structures in spatially extended systems.
We restrict our attention to systems that are internally dissipative and
externally driven, also referred to as systems out of thermodynamical
equilibrium. We investigate a
particular type of emergent structures, called
localized structures (LSs). As their name indicates, LSs are confined in
time and/or space. LSs can develop instabilities that make them move,
deform or oscillate. Oscillations can also lie at the origin of a
dynamical,
neuron
-
like phenomenon called "excitability".
Although LSs, and their various instabilities, can be observed in a wide
range of physical systems, we focus on the field of optics, where LSs can
be observed in nonlinear optical cavities. In this
context, LSs are also
called cavity solitons. To study this type of cavities we use the Lugiato
-
Lefever (LL) model, a partial differential equation first proposed in 1987 to
describe transversal electric field in a passive optical cavity filled with a
non
linear medium. In the last decade, this model has sparked new interest
as it was found to also describe the formation and dynamics of Kerr
frequency combs in microresonators.
A frequency comb consists in a
broad optical spectrum of sharp comb lines with a
n equidistant frequency
spacing that can be used to perform ultra
-
precise measurements of optical
frequencies, and has numerous other applications in spectroscopy, optical
clocks and waveform synthesis. The interesting and essential point here is
that such
coherent frequency combs correspond to the frequency
spectrum of cavity solitons and patterns circulating inside the cavity.
Therefore, by studying LSs in the LL model we obtain crucial information
about the dynamics and stability of Kerr frequency combs.
In the first chapters of the thesis we provide a detailed study of LSs in the
LL model in its two main regimes of operation, namely the region with
anomalous group velocity dispersion (GVD) and the one with normal GVD.
For anomalous GVD, we focus on patt
erned solutions and bright solitons
and characterize their bifurcation structure and instabilities leading to
oscillations in time and/or space. In contrast, in the normal GVD regime,
we show that the main LSs are dark solitons, which have a very different
origin and bifurcation structure, but undergo similar instabilities. Next, we
focus on how higher order dispersion effects modify the soliton dynamics
in both regimes, showing that a various LSs can be stabilized by the higher
order dispersion. Another qu
estion that we address is how bound states of
solitons can form, where interaction between solitons is largely determined
by the oscillatory tails in the soliton's profile. Finally, we focus on how
defects and advection can modify the dynamics of LSs, show
ing the
combination of defects and advection can induce excitability.
| Datum prijs | 3 mrt 2017 |
|---|---|
| Originele taal | English |
| Prijsuitreikende instantie |
|
| Begeleider | Jan Danckaert (Promotor), Lendert Gelens (Promotor), Damia Gomila (Promotor), Alexandre Sevrin (Jury), Guy Van Der Sande (Jury), P. Colet (Jury), Alan Champneys (Jury), Giovanna Tissoni (Jury), Marc Haelterman (Promotor), Edgar Knobloch (Promotor) & Leo François (Promotor) |