arXiv subjects

Pere Colet

Publications and source records attributed to Pere Colet.

34 records · Page 2Linked to original sources

arXiv2010

Non-universal results induced by diversity distribution in coupled excitable systems

We consider a system of globally coupled active rotators near the excitable regime. The system displays a transition to a state of collective firing induced by disorder. We show that this transition is found generically for any diversity distribution with well defined moments. Singularly, for the Lorentzian distribution (widely used in Kuramoto-like systems) the transition is not present. This warns about the use of Lorentzian distributions to understand the generic properties of coupled oscillators.

cond-mat.stat-mech↗

arXiv2008

Dynamical instabilities of dissipative solitons in nonlinear optical cavities with nonlocal materials

In this work we characterize the dynamical instabilities of localized structures exhibited by a recently introduced Gelens et al., Phys. Rev. A 75, 063812 2007 generalization of the Lugiato-Lefever model that includes a weakly nonlocal response of an intracavity metamaterial. A rich scenario, in which the localized structures exhibit different types of oscillatory instabilities, tristability, and excitability, including a regime of conditional excitability in which the system is bistable, is presented and discussed. Finally, it is shown that the scenario is organized by a pair of Takens-Bogdanov codimension-2 points.

nlin.PS↗

arXiv2008

Effects of a localized beam on the dynamics of excitable cavity solitons

We study the dynamical behavior of dissipative solitons in an optical cavity filled with a Kerr medium when a localized beam is applied on top of the homogeneous pumping. In particular, we report on the excitability regime that cavity solitons exhibits which is emergent property since the system is not locally excitable. The resulting scenario differs in an important way from the case of a purely homogeneous pump and now two different excitable regimes, both Class I, are shown. The whole scenario is presented and discussed, showing that it is organized by three codimension-2 points. Moreover, the localized beam can be used to control important features, such as the excitable threshold, improving the possibilities for the experimental observation of this phenomenon.

physics.optics↗

arXiv2008

Determination of phase noise spectra in optoelectronic microwave oscillators: a Langevin approach

We introduce a stochastic model for the determination of phase noise in optoelectronic oscillators. After a short overview of the main results for the phase diffusion approach in autonomous oscillators, an extension is proposed for the case of optoelectronic oscillators where the microwave is a limit-cycle originated from a bifurcation induced by nonlinearity and time-delay. This Langevin approach based on stochastic calculus is also successfully confronted with experimental measurements.

physics.optics↗

arXiv2007

Phase-space structure of two-dimensional excitable localized structures

In this work we characterize in detail the bifurcation leading to an excitable regime mediated by localized structures in a dissipative nonlinear Kerr cavity with a homogeneous pump. Here we show how the route can be understood through a planar dynamical system in which a limit cycle becomes the homoclinic orbit of a saddle point (saddle-loop bifurcation). The whole picture is unveiled, and the mechanism by which this reduction occurs from the full infinite-dimensional dynamical system is studied. Finally, it is shown that the bifurcation leads to an excitability regime, under the application of suitable perturbations. Excitability is an emergent property for this system, as it emerges from the spatial dependence since the system does not exhibit any excitable behavior locally.

nlin.PS↗

arXiv2005

Excitability mediated by localized structures

We find and characterize an excitability regime mediated by localized structures in a dissipative nonlinear optical cavity. The scenario is that stable localized structures exhibit a Hopf bifurcation to self-pulsating behavior, that is followed by the destruction of the oscillation in a saddle-loop bifurcation. Beyond this point there is a regime of excitable localized structures under the application of suitable perturbations. Excitability emerges from the spatial dependence since the system does not exhibit any excitable behavior locally. We show that the whole scenario is organized by a Takens-Bogdanov codimension-2 bifurcation point.

nlin.PS↗

arXiv2004

Phase Synchronization and Polarization Ordering of Globally-Coupled Oscillators

We introduce a prototype model for globally-coupled oscillators in which each element is given an oscillation frequency and a preferential oscillation direction (polarization), both randomly distributed. We found two collective transitions: to phase synchronization and to polarization ordering. Introducing a global-phase and a polarization order parameters, we show that the transition to global-phase synchrony is found when the coupling overcomes a critical value and that polarization order enhancement can not take place before global-phase synchrony. We develop a self-consistent theory to determine both order parameters in good agreement with numerical results.

physics.optics↗

arXiv2002

Non-classical behavior in multimode and disordered transverse structures in OPO. Use of the Q representation

We employ the Q representation to study the non-classical correlations that are present from below to above-threshold in the degenerate optical parametric oscillator. Our study shows that such correlations are present just above threshold, in the regime in which stripe patterns are formed, but that they also persist further above threshold in the presence of spatially disordered structures.

quant-ph↗

arXiv2002

Fluctuations and correlations in hexagonal optical patterns

We analyze the influence of noise in transverse hexagonal patterns in nonlinear Kerr cavities. The near field fluctuations are determined by the neutrally stable Goldstone modes associated to translational invariance and by the weakly damped soft modes. However these modes do not contribute to the far field intensity fluctuations which are dominated by damped perturbations with the same wave vectors than the pattern. We find strong correlations between the intensity fluctuations of any arbitrary pair of wave vectors of the pattern. Correlation between pairs forming 120 degrees is larger than between pairs forming 180 degrees, contrary to what a naive interpretation of emission in terms of twin photons would suggest.

cond-mat.stat-mech↗

arXiv2002

Macroscopic quantum fluctuations in noise-sustained optical patterns

We investigate quantum effects in pattern-formation for a degenerate optical parametric oscillator with walk-off. This device has a convective regime in which macroscopic patterns are both initiated and sustained by quantum noise. Familiar methods based linearization about a pseudo-classical field fail in this regime and new approaches are required. We employ a method in which the pump field is treated as a $c$-number variable but is driven by the $c$-number representation of the quantum sub-harmonic signal field. This allows us to include the effects of the fluctuations in the signal on the pump, which in turn act back on the signal. We find that the non-classical effects, in the form of squeezing, survive just above the threshold of the convective regime. Further above threshold the macroscopic quantum noise suppresses these effects.

quant-ph↗

arXiv2001

Stable droplets and growth laws close to the modulational instability of a domain wall

We consider the curvature driven dynamics of a domain wall separating two equivalent states in systems displaying a modulational instability of a flat front. We derive an amplitude equation for the dynamics of the curvature close to the bifurcation point from growing to schrinking circular droplets. We predict the existence of stable droplets with a radius $R$ that diverges at the bifurcation point, where a curvature driven growth law $R(t) \approx t^{1/4}$ is obtained. Our general analytical predictions, which are valid for a wide variety of systems including models of nonlinear optical cavities and reaction-diffusion systems, are illustrated in the parametrically driven complex Ginzburg-Landau equation.

nlin.PS↗

arXiv2000

Dynamics of localized structures in vector waves

Dynamical properties of topological defects in a twodimensional complex vector field are considered. These objects naturally arise in the study of polarized transverse light waves. Dynamics is modeled by a Vector Complex Ginzburg-Landau Equation with parameter values appropriate for linearly polarized laser emission. Creation and annihilation processes, and selforganization of defects in lattice structures, are described. We find "glassy" configurations dominated by vectorial defects and a melting process associated to topological-charge unbinding.

patt-sol↗

arXiv1999

Defect-freezing and Defect-unbinding in the Vector Complex Ginzburg-Landau Equation

We describe the dynamical behavior found in numerical solutions of the Vector Complex Ginzburg-Landau equation in parameter values where plane waves are stable. Topological defects in the system are responsible for a rich behavior. At low coupling between the vector components, a {\sl frozen} phase is found, whereas a {\sl gas-like} phase appears at higher coupling. The transition is a consequence of a defect unbinding phenomena. Entropy functions display a characteristic behavior around the transition.

chao-dyn↗

arXiv1999

Spatiotemporal Chaos, Localized Structures and Synchronization in the Vector Complex Ginzburg-Landau Equation

We study the spatiotemporal dynamics, in one and two spatial dimensions, of two complex fields which are the two components of a vector field satisfying a vector form of the complex Ginzburg-Landau equation. We find synchronization and generalized synchronization of the spatiotemporally chaotic dynamics. The two kinds of synchronization can coexist simultaneously in different regions of the space, and they are mediated by localized structures. A quantitative characterization of the degree of synchronization is given in terms of mutual information measures.

chao-dyn↗

arXiv1999

Patterns arising from the interaction between scalar and vectorial instabilities in two-photon resonant Kerr cavities

We study pattern formation associated with the polarization degree of freedom of the electric field amplitude in a mean field model describing a nonlinear Kerr medium close to a two-photon resonance, placed inside a ring cavity with flat mirrors and driven by a coherent $\hat x$-polarized plane-wave field. In the self-focusing case, for negative detunings the pattern arises naturally from a codimension two bifurcation. For a critical value of the field intensity there are two wave numbers that become unstable simultaneously, corresponding to two Turing-like instabilities. Considered alone, one of the instabilities would originate a linearly polarized hexagonal pattern whereas the other instability is of pure vectorial origin and would give rise to an elliptically polarized stripe pattern. We show that the competition between the two wavenumbers can originate different structures, being the detuning a natural selection parameter.

cond-mat↗

arXiv1999

Convective and Absolute Instabilities in the Subcritical Ginzburg-Landau Equation

We study the nature of the instability of the homogeneous steady states of the subcritical Ginzburg-Landau equation in the presence of group velocity. The shift of the absolute instability threshold of the trivial steady state, induced by the destabilizing cubic nonlinearities, is confirmed by the numerical analysis of the evolution of its perturbations. It is also shown that the dynamics of these perturbations is such that finite size effects may suppress the transition from convective to absolute instability. Finally, we analyze the instability of the subcritical middle branch of steady states, and show, analytically and numerically, that this branch may be convectively unstable for sufficiently high values of the group velocity.

cond-mat↗