Mario Wilson

Extreme events induced by spatiotemporal chaos in experimental optical patterns

Extreme events such as rogue waves are often associated with the merging of coherent structures. We report on experimental results in the physics of extreme events emerging in a liquid-crystal light valve subjected to optical feedback, and we establish the relation of this phenomenon with the appearance of spatiotemporal chaos. This system, under particular conditions, exhibits stationary roll patterns that can be destabilized into quasi-periodic and chaotic textures when control parameters are properly modified. We have identified the parameter regions where extreme fluctuations of the amplitude can emerge and established their origin through its direct relation with the experimental largest Lyapunov exponents, the proportion of extreme events, and the normed kurtosis.

Stable Cnoidal Wave Formation in an Erbium-Doped Fiber Laser

We demonstrate the formation of stable cnoidal waves in an erbium-doped fiber laser using an electrooptic modulator in the laser cavity. Properties of the cnoidal wave such as pulse shape, width, intensity, and frequency can be controlled through the electrooptic modulator or the length of the doped fiber. This system can be described using a three-level laser model, which shows that for any cavity loss there is a modulation frequency that makes stable cnoidal waves possible. Numerical and experimental results are presented.

Nonvariational mechanism of front propagation: Theory and experiments

Multistable systems exhibit a rich front dynamics between equilibria. In one-dimensional scalar gradient systems, the spread of the fronts is proportional to the energy difference between equilibria. Fronts spreading proportionally to the energetic difference between equilibria is a characteristic of one-dimensional scalar gradient systems. Based on a simple nonvariational bistable model, we show analytically and numerically that the direction and speed of front propagation is led by nonvariational dynamics. We provide experimental evidence of nonvariational front propagation between different molecular orientations in a quasi-one-dimensional liquid-crystal light valve subjected to optical feedback. Free diffraction length allows us to control the variational or nonvariational nature of this system. Numerical simulations of the phenomenological model have quite good agreement with experimental observations.

Optical textures: characterizing spatiotemporal chaos.

Macroscopic systems subjected to injection and dissipation of energy can exhibit complex spatiotemporal behaviors as result of dissipative self-organization. Here, we report a one- and two-dimensional pattern forming setup, which exhibits a transition from stationary patterns to spatiotemporal chaotic textures, based on a nematic liquid crystal layer with spatially modulated input beam and optical feedback. Using an adequate projection of spatiotemporal diagrams, we determine the largest Lyapunov exponent. Jointly, this exponent and Fourier transform allow us to distinguish between spatiotemporal chaos and amplitude turbulence concepts, which are usually merged.

Optical resonators and dynamic maps

In this article the dynamical behavior of a beam within a ring phase-conjugated resonator is modeled using two dimensional iterative maps. In particular it is explicitly shown how the difference equations of the Duffing and Tinkerbell maps can be used to describe the dynamic behavior of what we call Duffing and Tinkerbell beams i.e. beams that behave according to the Duffing and Tinkerbell maps. The matrix of a map generating device is found in terms of the maps parameters, the state variables and the resonator parameters. The mathematical characteristics of an optical device in an optical cavity are stated so that a chaotic map is obtained as the dynamics for the ray beams.

Spontaneous light-induced Turing patterns in a dye-doped twisted nematic layer

Optical pattern formation is usually due either to the combination of diffraction and nonlinearity in a Kerr medium or to the temporal modulation of light in a photosensitive chemical reaction. Here, we show a different mechanism by which light spontaneously induces stripe domains between nematic states in a twisted nematic liquid crystal layer doped with azo-dyes. Thanks to the photoisomerization process of the dopants, light in the absorption band of the dopants creates spontaneous patterns without the need of temporal modulation, diffraction, Kerr or other optical nonlinearity, but based on the different scales for dopant transport processes and nematic order parameter, which identifies a genuine Turing mechanism for this instability. Theoretically, the emergence of the stripe patterns is described on the basis of a model for the dopant concentration coupled with the nematic order parameter.

Experimental Spatiotemporal Chaotic Textures in a Liquid Crystal Light Valve with Optical Feedback

Macroscopic systems subjected to external forcing exhibit complex spatiotemporal behaviors as result of dissipative self-organization. Based on a nematic liquid crystal layer with spatially modulated input beam and optical feedback, we set up a two-dimensional pattern forming system which exhibits a transition from stationary to spatiotemporal chaotic patterns. Using an adequate projection of spatiotemporal diagrams, we determine the largest Lyapunov exponent. This exponent allows us to characterize the transition presented by this system. This exponent and Fourier transforms lead to a reconciliation of experimental observations of spatiotemporal complexity and theoretical developments.

Generation of stable cnoidal waves in an erbium doped fiber laser system

In this work an all-fiber laser system able to produce stable cnoidal waves in both limits, i.e. in sinusoidal and soliton limits, is presented. The system is constructed using an erbium highly-doped fiber as an active media and an electrooptic modulator as the core of the control tool. This control tool is able to modulate the cavity losses. The direct modulation allows to control the pulses properties, shape, width and intensity. The proposed system is well described by a three level laser model based on the Statz-de Mars rate equations. Numerical and Experimental results are presented.

Recurrent noise-induced phase singularities in drifting patterns

We show that the key ingredients for creating recurrent traveling spatial phase defects in drifting patterns are a noise-sustained structure regime together with the vicinity of a phase transition, that is, a spatial region where the control parameter lies close to the threshold for pattern formation. They both generate specific favorable initial conditions for local spatial gradients, phase, and/or amplitude. Predictions from the stochastic convective Ginzburg-Landau equation with real coefficients agree quite well with experiments carried out on a Kerr medium submitted to shifted optical feedback that evidence noise-induced traveling phase slips and vortex phase-singularities.