136 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
Positive Feedback Keeps Duration of Mitosis Temporally Insulated from Upstream Cell-Cycle Events
Cell division is characterized by a sequence of events by which a cell gives rise to two daughter cells. Quantitative measurements of cell-cycle dynamics in single cells showed that despite variability in G1-, S-, and G2 phases, duration of mitosis is short and remarkably constant. Surprisingly, there is no correlation between cell-cycle length and mitotic duration, suggesting that mitosis is temporally insulated from variability in earlier cell-cycle phases. By combining live cell imaging and computational modeling, we showed that positive feedback is the molecular mechanism underlying the temporal insulation of mitosis. Perturbing positive feedback gave rise to a sluggish, variable entry and progression through mitosis and uncoupled duration of mitosis from variability in cell cycle length. We show that positive feedback is important to keep mitosis short, constant, and temporally insulated and anticipate it might be a commonly used regulatory strategy to create modularity in other biological systems
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
A phase-space approach to directional switching in semiconductor ring lasers
We show that a topological investigation of the phase space of a
Semiconductor Ring Laser can be used to devise switching schemes which are
alternative to optical pulse injection of counter-propagating light. To provide
physical insight in these switching mechanisms, a full bifurcation analysis and
an investigation of the topology is performed on a two-dimensional asymptotic
model. Numerical simulations confirm the topological predictions.Comment: 9 pages, 7 figure
Quadratic cavity soliton optical frequency combs
We theoretically investigate the formation of frequency combs in a dispersive second-harmonic generation cavity system, and predict the existence of quadratic cavity solitons in the absence of a temporal walk-off
Excitability in semiconductor microring lasers: Experimental and theoretical pulse characterization
We characterize the operation of semiconductor microring lasers in an
excitable regime. Our experiments reveal a statistical distribution of the
characteristics of noise-triggered optical pulses that is not observed in other
excitable systems. In particular, an inverse correlation exists between the
pulse amplitude and duration. Numerical simulations and an interpretation in an
asymptotic phase space confirm and explain these experimentally observed pulse
characteristics.Comment: 9 pages, 10 figure
Exploring multi-stability in semiconductor ring lasers: theory and experiment
We report the first experimental observation of multi-stable states in a
single-longitudinal mode semiconductor ring laser. We show how the operation of
the device can be steered to either monostable, bistable or multi-stable
dynamical regimes in a controlled way. We observe that the dynamical regimes
are organized in well reproducible sequences that match the bifurcation
diagrams of a two-dimensional model. By analyzing the phase space in this
model, we predict how the stochastic transitions between multi-stable states
take place and confirm it experimentally.Comment: 4 pages, 5 figure
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
Topological insight into the non-Arrhenius mode hopping of semiconductor ring lasers
We investigate both theoretically and experimentally the stochastic switching
between two counter-propagating lasing modes of a semiconductor ring laser.
Experimentally, the residence time distribution cannot be described by a simple
one parameter Arrhenius exponential law and reveals the presence of two
different mode-hop scenarios with distinct time scales. In order to elucidate
the origin of these two time scales, we propose a topological approach based on
a two-dimensional dynamical system.Comment: 4 pages, 3 figure
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