Optical textures: characterizing spatiotemporal chaos

Optical feedback-induced spatiotemporal patterns with power law spectra in a liquid crystal light valve

Pattern formation can be induced by coupling electromagnetic fields to a polarizable and lossy medium. Increasing energy injection patterns can exhibit aperiodic behaviors. We investigate the self-organization of unidimensional aperiodic patterns. Based on a liquid crystal light valve (LCLV) with optical feedback, we observed aperiodic one-dimensional patterns with power laws in the temporal and spatial spectrum density of the light intensity, and their pseudo envelope and phase characteristic of spatiotemporal complexity. Theoretically, a local model describes the system close to nascent bistability and spatial instability. Numerical simulations of this model show chaotic spatiotemporal patterns whose temporal and spatial spectra have exponents similar to those observed experimentally.

Transition from nonradiative to radiative oscillons in parametrically driven systems

Nonequilibrium systems exhibit particle-type solutions. Oscillons are one of the best-known localized states of systems with time-dependent forcing or parametrically driven systems. We investigate the transition from nonradiative to radiative oscillons in the parametrically driven sine-Gordon model in two spatial dimensions. The bifurcation takes place when the strength of the forcing (frequency) increases (decreases) above a certain threshold. As a result of this transition, the oscillon emits radially symmetric evanescent waves. Numerically, we provide the phase diagram and show the supercritical nature of this transition. For small oscillations, based on the amplitude equation approach, the sine-Gordon equation with time-dependent forcing is transformed into the parametrically driven damped nonlinear Schrödinger model in two spatial dimensions. This amplitude equation exhibits a transition between nonradiative to radiative localized structures, consistently. Both models show quite good agreement.

Transition to Spatiotemporal Intermittency and Defect Turbulence in Systems under Translational Coupling

Out of equilibrium systems under the influence of enough energy injection exhibit complex spatiotemporal behaviors. Based on a liquid crystal light valve experiment with translational optical feedback, we observe propagation, spatiotemporal intermittency, and defect turbulence of striped waves. A prototype model of pattern formation with translational coupling shows the same phenomenology. Close to the spatial instability, a local amplitude equation is derived. This amplitude equation allows us to reveal the origin and bifurcation diagram of the observed complex spatiotemporal dynamics. Experimental observations have a qualitative agreement with theoretical findings.

Correlations between the leading Lyapunov vector and pattern defects for chaotic Rayleigh-Bénard convection

We probe the effectiveness of using topological defects to characterize the leading Lyapunov vector for a high-dimensional chaotic convective flow field. This is accomplished using large-scale parallel numerical simulations of Rayleigh-Bénard convection for experimentally accessible conditions. We quantify the statistical correlations between the spatiotemporal dynamics of the leading Lyapunov vector and different measures of the flow field pattern's topology and dynamics. We use a range of pattern diagnostics to describe the flow field structures which includes many of the traditional diagnostics used to describe convection as well as some diagnostics tailored to capture the dynamics of the patterns. We use the ideas of precision and recall to build a statistical description of each pattern diagnostic's ability to describe the spatial variation of the leading Lyapunov vector. The precision of a diagnostic indicates the probability that it will locate a region where the Lyapunov vector is larger than a threshold value. The recall of a diagnostic indicates its ability to locate all of the possible spatial regions where the Lyapunov vector is above threshold. By varying the threshold used for the Lyapunov vector magnitude, we generate precision-recall curves which we use to quantify the complex relationship between the pattern diagnostics and the spatiotemporally varying magnitude of the leading Lyapunov vector. We find that pattern diagnostics which include information regarding the flow history outperform pattern diagnostics that do not. In particular, an emerging target defect has the highest precision of all of the pattern diagnostics we have explored.

Front propagation transition induced by diffraction in a liquid crystal light valve

Driven optical systems can exhibit coexistence of equilibrium states. Traveling waves or fronts between different states present complex spatiotemporal dynamics. We investigate the mechanisms that govern the front spread. Based on a liquid crystal light valve experiment with optical feedback, we show that the front propagation does not pursue a minimization of free energy. Depending on the free propagation length in the optical feedback loop, the front speed exhibits a supercritical transition. Theoretically, from first principles, we use a model that takes it into account, characterizing the speed transition from a plateau to a growing regime. The theoretical and experimental results show quite fair agreement.

Stochastic resonance based on modulation instability in spatiotemporal chaos

A novel dynamic of stochastic resonance in spatiotemporal chaos is presented, which is based on modulation instability of perturbed partially coherent wave. The noise immunity of chaos can be reinforced through this effect and used to restore the coherent signal information buried in chaotic perturbation. A theoretical model with fluctuations term is derived from the complex Ginzburg-Landau equation via Wigner transform. It shows that through weakening the nonlinear threshold and triggering energy redistribution, the coherent component dominates the instability damped by incoherent component. The spatiotemporal output showing the properties of stochastic resonance may provide a potential application of signal encryption and restoration.