196 research outputs found
Stable dark and bright soliton Kerr combs can coexist in normal dispersion resonators
Using the Lugiato-Lefever model, we analyze the effects of third order
chromatic dispersion on the existence and stability of dark and bright soliton
Kerr frequency combs in the normal dispersion regime. While in the absence of
third order dispersion only dark solitons exist over an extended parameter
range, we find that third order dispersion allows for stable dark and bright
solitons to coexist. Reversibility is broken and the shape of the switching
waves connecting the top and bottom homogeneous solutions is modified. Bright
solitons come into existence thanks to the generation of oscillations in the
switching wave profiles. Finally, oscillatory instabilities of dark solitons
are also suppressed in the presence of sufficiently strong third order
dispersion
Interaction of solitons and the formation of bound states in the generalized Lugiato-Lefever equation
Bound states, also called soliton molecules, can form as a result of the
interaction between individual solitons. This interaction is mediated through
the tails of each soliton that overlap with one another. When such soliton
tails have spatial oscillations, locking or pinning between two solitons can
occur at fixed distances related with the wavelength of these oscillations,
thus forming a bound state. In this work, we study the formation and stability
of various types of bound states in the Lugiato-Lefever equation by computing
their interaction potential and by analyzing the properties of the oscillatory
tails. Moreover, we study the effect of higher order dispersion and noise in
the pump intensity on the dynamics of bound states. In doing so, we reveal that
perturbations to the Lugiato-Lefever equation that maintain reversibility, such
as fourth order dispersion, lead to bound states that tend to separate from one
another in time when noise is added. This separation force is determined by the
shape of the envelope of the interaction potential, as well as an additional
Brownian ratchet effect. In systems with broken reversibility, such as third
order dispersion, this ratchet effect continues to push solitons within a bound
state apart. However, the force generated by the envelope of the potential is
now such that it pushes the solitons towards each other, leading to a null net
drift of the solitons.Comment: 13 pages, 13 figure
Drifting instabilities of cavity solitons in vertical cavity surface-emitting lasers with frequency selective feedback
In this paper we study the formation and dynamics of self-propelled cavity
solitons (CSs) in a model for vertical cavity surface-emitting lasers (VCSELs)
subjected to external frequency selective feedback (FSF), and build their
bifurcation diagram for the case where carrier dynamics is eliminated. For low
pump currents, we find that they emerge from the modulational instability point
of the trivial solution, where traveling waves with a critical wavenumber are
formed. For large currents, the branch of self-propelled solitons merges with
the branch of resting solitons via a pitchfork bifurcation. We also show that a
feedback phase variation of 2\pi can transform a CS (whether resting or moving)
into a different one associated to an adjacent longitudinal external cavity
mode. Finally, we investigate the influence of the carrier dynamics, relevant
for VCSELs. We find and analyze qualitative changes in the stability properties
of resting CSs when increasing the carrier relaxation time. In addition to a
drifting instability of resting CSs, a new kind of instability appears for
certain ranges of carrier lifetime, leading to a swinging motion of the CS
center position. Furthermore, for carrier relaxation times typical of VCSELs
the system can display multistability of CSs.Comment: 11 pages, 12 figure
Elementary Excitations of a Bose-Einstein Condensate in an Effective Magnetic Field
We calculate the low energy elementary excitations of a Bose-Einstein
Condensate in an effective magnetic field. The field is created by the
interplay between light beams carrying orbital angular momentum and the trapped
atoms. We examine the role of the homogeneous magnetic field, familiar from
studies of rotating condensates, and also investigate spectra for vector
potentials with a more general radial dependence. We discuss the instabilities
which arise and how these may be manifested.Comment: 8 pages, 4 figure
From one- to two-dimensional solitons in the Ginzburg-Landau model of lasers with frequency selective feedback
We use the cubic complex Ginzburg-Landau equation coupled to a dissipative
linear equation as a model of lasers with an external frequency-selective
feedback. It is known that the feedback can stabilize the one-dimensional (1D)
self-localized mode. We aim to extend the analysis to 2D stripe-shaped and
vortex solitons. The radius of the vortices increases linearly with their
topological charge, , therefore the flat-stripe soliton may be interpreted
as the vortex with , while vortex solitons can be realized as stripes
bent into rings. The results for the vortex solitons are applicable to a broad
class of physical systems. There is a qualitative agreement between our results
and those recently reported for models with saturable nonlinearity.Comment: Submitted to PR
Impact of nonlocal interactions in dissipative systems: towards minimal-sized localized structures
In order to investigate the size limit on spatial localized structures in a
nonlinear system, we explore the impact of linear nonlocality on their domains
of existence and stability. Our system of choice is an optical microresonator
containing an additional metamaterial layer in the cavity, allowing the
nonlocal response of the material to become the dominating spatial process. In
that case, our bifurcation analysis shows that this nonlocality imposes a new
limit on the width of localized structures going beyond the traditional
diffraction limit.Comment: 4 pages, 4 figure
Bifurcation structure of periodic patterns in the Lugiato-Lefever equation with anomalous dispersion
We study the stability and bifurcation structure of spatially extended
patterns arising in nonlin- ear optical resonators with a Kerr-type
nonlinearity and anomalous group velocity dispersion, as described by the
Lugiato-Lefever equation. While there exists a one-parameter family of patterns
with different wavelengths, we focus our attention on the pattern with critical
wave number k c arising from the modulational instability of the homogeneous
state. We find that the branch of solutions associated with this pattern
connects to a branch of patterns with wave number . This next branch
also connects to a branch of patterns with double wave number, this time
, and this process repeats through a series of 2:1 spatial resonances. For
values of the detuning parameter approaching from below the
critical wave number approaches zero and this bifurcation structure is
related to the foliated snaking bifurcation structure organizing spatially
localized bright solitons. Secondary bifurcations that these patterns undergo
and the resulting temporal dynamics are also studied.Comment: 13 pages, 13 figure
Coupled-mode theory for photonic band-gap inhibition of spatial instabilities
We study the inhibition of pattern formation in nonlinear optical systems using intracavity photonic crystals. We consider mean-field models for singly and doubly degenerate optical parametric oscillators. Analytical expressions for the new (higher) modulational thresholds and the size of the "band gap" as a function of the system and photonic crystal parameters are obtained via a coupled-mode theory. Then, by means of a nonlinear analysis, we derive amplitude equations for the unstable modes and find the stationary solutions above threshold. The form of the unstable mode is different in the lower and upper parts of the band gap. In each part there is bistability between two spatially shifted patterns. In large systems stable wall defects between the two solutions are formed and we provide analytical expressions for their shape. The analytical results are favorably compared with results obtained from the full system equations. Inhibition of pattern formation can be used to spatially control signal generation in the transverse plane
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