We study nonlinear wave dynamics in coherently driven cavities with a parabolic potential. Different states including high-order solitons, high-order breathers, and chaoticons are characterized in terms of a phase diagram.
Since its first demonstration, spatial beam self-cleaning has been targeted as a breakthrough nonlinear effect, for its potential of extending to multimode fibers different technologies based on single-mode fibers, such as fiber lasers and endoscopes. To date, most of the theoretical descriptions of beam self-cleaning are based on scalar models. Whereas, in experiments the analysis of the polarization state of self-cleaned beams is often neglected. Here, we fill this gap between theory and experiments, by demonstrating that a self-cleaned beam eventually loses its degree of polarization, as long as linearly polarized light of enough power is injected at the fiber input. Our results are cast in the framework of a thermodynamic description of nonlinear beam propagation in multimode fibers, providing the first experimental proof of the applicability of scalar theories for the description of the spatial beam self-cleaning effect.
We present a theoretical model for describing dissipative solitons and optical frequency combs formation in a dispersive and nonlinear χ(3)-based cavity system that is phase-matched for third-harmonic generation. We consider the importance of the stability properties of the homogeneous solution in generating various types of multi-frequency combs, and demonstrate a novel type of bistable cavity solitons.
We unveil the existence of stable high-order dissipative spatiotemporal stationary solitons (i.e., light bullets) and breathers in the externally driven multimode nonlinear systems with a three-dimensional confining parabolic potential. Specifically, we focus on the externally driven multimode Kerr cavities. We show that the potential is responsible for stabilization of these three-dimensional states, and that it dictates their rich internal structure.
In this work we present a detailed analysis of bifurcation structures of cavity solitons (CSs) and determine the different dynamical regimes in the Lugiato-Lefever (LL) equation in the presence of anomalous and normal chromatic dispersion regimes. Such an analysis has been shown to also increase our understanding of frequency combs (FCs). A FC consists in a set of equidistant spectral lines that can be used to measure light frequencies and time intervals more easily and precisely than ever before. Due to the duality between CSs in microcavities and FCs, we can gain information about the behavior of FCs by analyzing the dynamics of CSs. In the anomalous dispersion case bright CSs are organized in what is known as a homoclinic snaking bifurcation structure. In contrast, in the normal dispersion regime dark CSs are organized differently, in a structure known as collapsing snaking. Despite the differences in bifurcation scenarios, both types of CSs present similar temporal instabilities.
The Lugiato-Lefever equation (LLE) has been extensively studied since its derivation in 1987, when this meanfield
model was introduced to describe nonlinear optical cavities. The LLE was originally derived to describe a
ring cavity or a Fabry-Perot resonator with a transverse spatial extension and partially filled with a nonlinear
medium but it has also been shown to be applicable to other types of cavities, such as fiber resonators and
microresonators.
Depending on the parameters used, the LLE can present a monostable or bistable input-output response
curve. A large number of theoretical studies have been done in the monostable regime, but the bistable regime
has remained widely unexplored. One of the reasons for this was that previous experimental setups were not able
to works in such regimes of the parameter space. Nowadays the possibility of reaching such parameter regimes
experimentally has renewed the interest in the LLE.
In this contribution, we present an in-depth theoretical study of the different dynamical regimes that can
appear in parameter space, focusing on the dynamics of localized solutions, also known as cavity solitons (CSs).
We show that time-periodic oscillations of a 1D CS appear naturally in a broad region of parameter space. More
than this oscillatory regime, which has been recently demonstrated experimentally,1 we theoretically report on
several kinds of chaotic dynamics. We show that the existence of CSs and their dynamics is related with the
spatial dynamics of the system and with the presence of a codimension-2 point known as a Fold-Hopf bifurcation
point. These dynamical regimes can become accessible by using devices such as microresonators, for instance
widely used for creating optical frequency combs.
Optical frequency combs can be used to measure light frequencies and time intervals more easily and precisely
than ever before, opening a large avenue for applications. Traditional frequency combs are usually associated
with trains of evenly spaced, very short pulses. More recently, a new generation of comb sources has been
demonstrated in compact high-Q optical microresonators with a Kerr nonlinearity pumped by continuous-wave
laser light. These combs are now referred to as Kerr frequency combs and have attracted a lot of interest in the
last few years.
Kerr frequency combs can be modeled in a way that is strongly reminiscent of temporal cavity solitons (CSs)
in nonlinear cavities. Temporal CSs have been experimentally studied in fiber resonators and their description
is based on a now classical equation, the Lugiato-Lefever equation, that describes pattern formation in optical
systems.
In this work, we first perform a theoretical study of the correspondence between the CSs and patterns with
frequency combs. It is known that the CSs appear in reversible systems that present bistability between a
pattern and a homogeneous steady state through what it is called a homoclinic snaking structure. In this
snaking region, single and multi-peak CSs coexist with patterns and homogeneous solutions, creating a largely
multistable landscape. We study the changes of the homoclinic snaking for different parameter regimes in the
Lugiato-Lefever equation and determine the stability and shape of the frequency combs through comparison with
the underlying CSs and patterns. Secondly, we include third order dispersion in the system and study its effect
on the multistable snaking structure. For high dispersion strengths the CS structures and the corresponding
Kerr frequency combs disappear.
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