arXiv subjects

M. San Miguel

Publications and source records attributed to M. San Miguel.

At least 37 records · Page 2Linked to original sources

arXiv2002

Quantum properties of transverse pattern formation in second-harmonic generation

We investigate the spatial quantum noise properties of the one dimensional transverse pattern formation instability in intra-cavity second-harmonic generation. The Q representation of a quasi-probability distribution is implemented in terms of nonlinear stochastic Langevin equations. We study these equations through extensive numerical simulations and analytically in the linearized limit. Our study, made below and above the threshold of pattern formation, is guided by a microscopic scheme of photon interaction underlying pattern formation in second-harmonic generation. Close to the threshold for pattern formation, beams with opposite direction of the off-axis critical wave numbers are shown to be highly correlated. This is observed for the fundamental field, for the second harmonic field and also for the cross-correlation between the two fields. Nonlinear correlations involving the homogeneous transverse wave number, which are not identified in a linearized analysis, are also described. The intensity differences between opposite points of the far fields are shown to exhibit sub-Poissonian statistics, revealing the quantum nature of the correlations. We observe twin beam correlations in both the fundamental and second-harmonic fields, and also nonclassical correlations between them.

quant-ph↗

arXiv2001

Polarisation Patterns and Vectorial Defects in Type II Optical Parametric Oscillators

Previous studies of lasers and nonlinear resonators have revealed that the polarisation degree of freedom allows for the formation of polarisation patterns and novel localized structures, such as vectorial defects. Type II optical parametric oscillators are characterised by the fact that the down-converted beams are emitted in orthogonal polarisations. In this paper we show the results of the study of pattern and defect formation and dynamics in a Type II degenerate optical parametric oscillator for which the pump field is not resonated in the cavity. We find that traveling waves are the predominant solutions and that the defects are vectorial dislocations which appear at the boundaries of the regions where traveling waves of different phase or wave-vector orientation are formed. A dislocation is defined by two topological charges, one associated with the phase and another with the wave-vector orientation. We also show how to stabilize a single defect in a realistic experimental situation. The effects of phase mismatch of nonlinear interaction are finally considered.

physics.optics↗

arXiv2001

Dynamics of Defects in the Vector Complex Ginzburg-Landau Equation

Coupled Ginzburg-Landau equations appear in a variety of contexts involving instabilities in oscillatory media. When the relevant unstable mode is of vectorial character (a common situation in nonlinear optics), the pair of coupled equations has special symmetries and can be written as a vector complex Ginzburg-Landau equation. Dynamical properties of localized structures of topological character in this vector-field case are considered. Creation and annihilation processes of different kinds of vector defects are described, and some of them interpreted in theoretical terms. A transition between different regimes of spatiotemporal dynamics is described.

nlin.PS↗

arXiv2001

Phase-Locked Spatial Domains and Bloch Domain Walls in Type-II Optical Parametric Oscillators

We study the role of transverse spatial degrees of freedom in the dynamics of signal-idler phase locked states in type-II Optical Parametric Oscillators. Phase locking stems from signal-idler polarization coupling which arises if the cavity birefringence and/or dichroism is not matched to the nonlinear crystal birefringence. Spontaneous Bloch domain wall formation is theoretically predicted and numerically studied. Bloch walls connect, by means of a polarization transformation, homogeneous regions of self-phase locked solutions. The parameter range for their existence is analytically found. The polarization properties and the dynamics of walls in one- and two transverse spatial dimensions is explained. Transition from Bloch to Ising walls is characterized, the control parameter being the linear coupling strength. Wall dynamics governs spatiotemporal dynamical states of the system, which include transient curvature driven domain growth, persistent dynamics dominated by spiraling defects for Bloch walls, and labyrinthine pattern formation for Ising walls.

nlin.PS↗

arXiv2000

Period Stabilization in the Busse-Heikes Model of the Kuppers-Lortz Instability

The Busse-Heikes dynamical model is described in terms of relaxational and nonrelaxational dynamics. Within this dynamical picture a diverging alternating period is calculated in a reduced dynamics given by a time-dependent Hamiltonian with decreasing energy. A mean period is calculated which results from noise stabilization of a mean energy. The consideration of spatial-dependent amplitudes leads to vertex formation. The competition of front motion around the vertices and the Kuppers-Lortz instability in determining an alternating period is discussed.

nlin.PS↗

arXiv1999

Selfsimilar Domain Growth, Localized Structures and Labyrinthine Patterns in Vectorial Kerr Resonators

We study domain growth in a nonlinear optical system useful to explore different scenarios that might occur in systems which do not relax to thermodynamic equilibrium. Domains correspond to equivalent states of different circular polarization of light. We describe three dynamical regimes: a coarsening regime in which dynamical scaling holds with a growth law dictated by curvature effects, a regime in which localized structures form, and a regime in which polarization domain walls are modulationally unstable and the system freezes in a labyrinthine pattern.

patt-sol↗

arXiv1999

Self-Pulsating Semiconductor Lasers: Theory and Experiment

We report detailed measurements of the pump-current dependency of the self-pulsating frequency of semiconductor CD lasers. A distinct kink in this dependence is found and explained using rate-equation model. The kink denotes a transition between a region where the self-pulsations are weakly sustained relaxation oscillations and a region where Q-switching takes place. Simulations show that spontaneous emission noise plays a crucial role for the cross-over.

physics.optics↗

arXiv1999

Noise induced transition from an absorbing phase to a regime of stochastic spatiotemporal intermittency

We introduce a stochastic partial differential equation capable of reproducing the main features of spatiotemporal intermittency (STI). Additionally the model displays a noise induced transition from laminarity to the STI regime. We show by numerical simulations and a mean-field analysis that for high noise intensities the system globally evolves to a uniform absorbing phase, while for noise intensities below a critical value spatiotemporal intermittence dominates. A quantitative computation of the loci of this transition in the relevant parameter space is presented.

cond-mat↗

arXiv1997

Fronts, Domain Growth and Dynamical Scaling in a d=1 non-Potential System

We present a study of dynamical scaling and front motion in a one dimensional system that describes Rayleigh-Benard convection in a rotating cell. We use a model of three competing modes proposed by Busse and Heikes to which spatial dependent terms have been added. As long as the angular velocity is different from zero, there is no known Lyapunov potential for the dynamics of the system. As a consequence the system follows a non-relaxational dynamics and the asymptotic state can not be associated with a final equilibrium state. When the rotation angular velocity is greater than some critical value, the system undergoes the Kuppers-Lortz instability leading to a time dependent chaotic dynamics and there is no coarsening beyond this instability. We have focused on the transient dynamics below this instability, where the dynamics is still non-relaxational. In this regime the dynamics is governed by a non-relaxational motion of fronts separating dynamically equivalent homogeneous states. We classify the families of fronts that occur in the dynamics, and calculate their shape and velocity. We have found that a scaling description of the coarsening process is still valid as in the potential case. The growth law is nearly logarithmic with time for short times and becomes linear after a crossover, whose width is determined by the strength of the non-potential terms.

cond-mat↗

arXiv1997

Domain Growth in a Multivariable non Potential System

We present a study of dynamical scaling and domain growth in a non potential system that models Rayleigh-Benard convection in a rotating cell. In d=1, dynamical scaling holds, but the non potential terms modify the characteristic growth law with a crossover from logarithmic to linear in time. In d=2 the non potential terms prevent coarsening for any value of the angular rotation speed.

cond-mat.stat-mech↗

arXiv1997

Wound-up phase turbulence in the Complex Ginzburg-Landau equation

We consider phase turbulent regimes with nonzero winding number in the one-dimensional Complex Ginzburg-Landau equation. We find that phase turbulent states with winding number larger than a critical one are only transients and decay to states within a range of allowed winding numbers. The analogy with the Eckhaus instability for non-turbulent waves is stressed. The transition from phase to defect turbulence is interpreted as an ergodicity breaking transition which occurs when the range of allowed winding numbers vanishes. We explain the states reached at long times in terms of three basic states, namely quasiperiodic states, frozen turbulence states, and riding turbulence states. Justification and some insight into them is obtained from an analysis of a phase equation for nonzero winding number: rigidly moving solutions of this equation, which correspond to quasiperiodic and frozen turbulence states, are understood in terms of periodic and chaotic solutions of an associated system of ordinary differential equations. A short report of some of our results has been published in [Montagne et al., Phys. Rev. Lett. 77, 267 (1996)].

chao-dyn↗

arXiv1996

Synchronization of Spatiotemporal Chaos: The regime of coupled Spatiotemporal Intermittency

Synchronization of spatiotemporally chaotic extended systems is considered in the context of coupled one-dimensional Complex Ginzburg-Landau equations (CGLE). A regime of coupled spatiotemporal intermittency (STI) is identified and described in terms of the space-time synchronized chaotic motion of localized structures. A quantitative measure of synchronization as a function of coupling parameter is given through distribution functions and information measures. The coupled STI regime is shown to dissapear into regular dynamics for situations of strong coupling, hence a description in terms of a single CGLE is not appropiate.

chao-dyn↗

arXiv1996

Winding number instability in the phase-turbulence regime of the Complex Ginzburg-Landau Equation

We give a statistical characterization of states with nonzero winding number in the Phase Turbulence (PT) regime of the one-dimensional Complex Ginzburg-Landau equation. We find that states with winding number larger than a critical one are unstable, in the sense that they decay to states with smaller winding number. The transition from Phase to Defect Turbulence is interpreted as an ergodicity breaking transition which occurs when the range of stable winding numbers vanishes. Asymptotically stable states which are not spatio-temporally chaotic are described within the PT regime of nonzero winding number.

chao-dyn↗

arXiv1996

Wave-unlocking transition in resonantly coupled complex Ginzburg-Landau equations

We study the effect of spatial frequency-forcing on standing-wave solutions of coupled complex Ginzburg-Landau equations. The model considered describes several situations of nonlinear counterpropagating waves and also of the dynamics of polarized light waves. We show that forcing introduces spatial modulations on standing waves which remain frequency locked with a forcing-independent frequency. For forcing above a threshold the modulated standing waves unlock, bifurcating into a temporally periodic state. Below the threshold the system presents a kind of excitability.

patt-sol↗

arXiv1995

Numerical Study of a Lyapunov Functional for the Complex Ginzburg-Landau Equation

We numerically study in the one-dimensional case the validity of the functional calculated by Graham and coworkers as a Lyapunov potential for the Complex Ginzburg-Landau equation. In non-chaotic regions of parameter space the functional decreases monotonically in time towards the plane wave attractors, as expected for a Lyapunov functional, provided that no phase singularities are encountered. In the phase turbulence region the potential relaxes towards a value characteristic of the phase turbulent attractor, and the dynamics there approximately preserves a constant value. There are however very small but systematic deviations from the theoretical predictions, that increase when going deeper in the phase turbulence region. In more disordered chaotic regimes characterized by the presence of phase singularities the functional is ill-defined and then not a correct Lyapunov potential.

cond-mat↗

arXiv1995

MULTIPLE FRONT PROPAGATION IN A POTENTIAL NON-GRADIENT SYSTEM

A classification of dynamical systems in terms of their variational properties is reviewed. Within this classification, front propagation is discussed in a non-gradient relaxational potential flow. The model is motivated by transient pattern phenomena in nematics. A front propagating into an unstable homogenous state leaves behind an unstable periodic pattern, which decays via a second front and a second periodic state. An interface between unstable periodic states is shown to be a source of propagating fronts in opposite directions.

patt-sol↗

arXiv1993

Multiple Front Propagation Into Unstable States

The dynamics of transient patterns formed by front propagation in extended nonequilibrium systems is considered. Under certain circumstances, the state left behind a front propagating into an unstable homogeneous state can be an unstable periodic pattern. It is found by a numerical solution of a model of the Fréedericksz transition in nematic liquid crystals that the mechanism of decay of such periodic unstable states is the propagation of a second front which replaces the unstable pattern by a another unstable periodic state with larger wavelength. The speed of this second front and the periodicity of the new state are analytically calculated with a generalization of the marginal stability formalism suited to the study of front propagation into periodic unstable states. PACS: 47.20.Ky, 03.40.Kf, 47.54.+r

cond-mat↗

arXiv1993

Fluctuations and Pattern Selection Near an Eckhaus Instability

We study the effect of fluctuations in the vicinity of an Eckhaus instability. The classical stability limit, which is defined in the absence of fluctuations, is smeared out into a region in which fluctuations and nonlinearities dominate the decay of unstable states. The width of this region is shown to grow as $ D^{1/2} $, where $D$ is the intensity of the fluctuations. We find an effective stability boundary that depends on $D$. A numerical solution of the stochastic Swift-Hohenberg equation in one dimension is used to test this prediction and to study pattern selection when the initial unstable state lies within the fluctuation dominated region. The asymptotically selected state differs from the predictions of previous analyses. Finally, the nonlinear relaxation for $D > 0$ is shown to exhibit a scaling form.

cond-mat↗