On-off intermittency in chaotic rotation induced in liquid crystals by competition between spin and orbital angular momentum of light

Lévy on-off intermittency

We present an alternative form of intermittency, Lévy on-off intermittency, which arises from multiplicative α-stable white noise close to an instability threshold. We study this problem in the linear and nonlinear regimes, both theoretically and numerically, for the case of a pitchfork bifurcation with fluctuating growth rate. We compute the stationary distribution analytically and numerically from the associated fractional Fokker-Planck equation in the Stratonovich interpretation. We characterize the system in the parameter space (α,β) of the noise, with stability parameter α∈(0,2) and skewness parameter β∈[-1,1]. Five regimes are identified in this parameter space, in addition to the well-studied Gaussian case α=2. Three regimes are located at 1<α<2, where the noise has finite mean but infinite variance. They are differentiated by β and all display a critical transition at the deterministic instability threshold, with on-off intermittency close to onset. Critical exponents are computed from the stationary distribution. Each regime is characterized by a specific form of the density and specific critical exponents, which differ starkly from the Gaussian case. A finite or infinite number of integer-order moments may converge, depending on parameters. Two more regimes are found at 0<α≤1. There, the mean of the noise diverges, and no critical transition occurs. In one case, the origin is always unstable, independently of the distance μ from the deterministic threshold. In the other case, the origin is conversely always stable, independently of μ. We thus demonstrate that an instability subject to nonequilibrium, power-law-distributed fluctuations can display substantially different properties than for Gaussian thermal fluctuations, in terms of statistics and critical behavior.

Multistate intermittency on the route to chaos of a semiconductor laser subjected to optical feedback from a long external cavity

We observe experimentally two regimes of intermittency on the route to chaos of a semiconductor laser subjected to optical feedback from a long external cavity as the feedback level is increased. The first regime encountered corresponds to multistate intermittency involving two or three states composed of several combinations of periodic, quasiperiodic, and subharmonic dynamics. The second regime is observed for larger feedback levels and involves intermittency between period-doubled and chaotic regimes. This latter type of intermittency displays statistical properties similar to those of on-off intermittency.

On-and-off dynamics of a creeping frictional system

We report on the dynamics of a model frictional system submitted to minute external perturbations. The system consists of a chain of sliders connected through elastic springs that rest on an incline. By introducing cyclic expansions and contractions of the rest length of the springs, we induce the reptation of the chain. Decreasing the amplitude of the perturbation below a critical value, we observe an intermittent creep regime characterized by alternated periods of reptation (flowing state) and rest (quiescent state). A further decrease of the perturbation leads to the disappearance of the reptation. The width of the transition region between the continuous creep and the full stop (i.e., the range of excitation amplitudes where the intermittent creep is observed) is shown to depend on the difference between the static (μ(s)) and the dynamic (μ(d)) friction coefficients. For μ(s) = μ(d) the intermittent creep is not observed. Studying the statistical features of the intermittent creep regime for any given perturbation amplitude, we find that the time the system resides in each state (flowing or quiescent) suggests that: i) reptation events are uncorrelated, and ii) rest events are history dependent. We show that this latter history dependence is consistent with the aging of the stress state inside the chain of sliders during the quiescent periods.

On-off intermittency in an optically injected semiconductor laser

We report on the observation of on-off intermittency in an optically injected dual-mode semiconductor laser. It is shown that quasi-single-mode chaotic dynamics of the injected mode are accompanied by intermittent and irregular bursts of the intensity of the uninjected mode. We define a threshold intensity of the uninjected mode to distinguish laminar and bursting states of the system. For small values of the threshold parameter we observe excellent agreement with the predictions of theory for the distribution of the laminar phase durations. For larger values of the threshold parameter, a gap appears in the distribution of laminar phase durations. Numerical simulations demonstrate that this gap is a consequence of the fact that in this case the on states of the system define large intensity spikes, which can belong either to the same or to distinct bursts away from the single-mode manifold.

On-off intermittency over an extended range of control parameter

We propose a simple phenomenological model exhibiting on-off intermittency over an extended range of control parameter. We find that the distribution of the "off" periods has a power-law tail with an exponent varying continuously between -1 and -2, at odds with standard on-off intermittency which occurs at a specific value of the control parameter and leads to the exponent -3/2. This nontrivial behavior results from the competition between a strong slowing down of the dynamics at small values of the observable and a systematic drift toward large values.

Intermittent outgassing through a non-Newtonian fluid

We report an experimental study of the intermittent dynamics of a gas flowing through a column of a non-Newtonian fluid. In a given range of the imposed constant flow rate, the system spontaneously alternates between two regimes: bubbles emitted at the bottom either rise independently one from the other or merge to create a winding flue which then connects the bottom air entrance to the free surface. The observations are reminiscent of the spontaneous changes in the degassing regime observed on volcanoes and suggest that, in the nature, such a phenomenon is likely to be governed by the non-Newtonian properties of the magma. We focus on the statistical distribution of the lifespans of the bubbling and flue regimes in the intermittent steady state. The bubbling regime exhibits a characteristic time whereas, interestingly, the flue lifespan displays a decaying power-law distribution. The associated exponent, which is significantly smaller than the value 1.5 often reported experimentally and predicted in some standard intermittency scenarios, depends on the fluid properties and can be interpreted as the ratio of two characteristic times of the system.

Three-dimensional model for light-induced chaotic rotations in liquid crystals under spin and orbital angular momentum transfer processes

Liquid crystals interacting with light represent a unique class of soft-matter systems that exhibit various generic nonlinear behaviors, including chaotic rotational dynamics. Despite several experimental observations, complex nematic liquid crystal director rotations in presence of spin and orbital angular momentum transfer processes were left unexplained. We present a self-consistent three-dimensional model able to describe the previous experimental observations, accounting for the dependence on the incident beam intensity, polarization, finite size and shape. More generally, our model is able to describe quantitatively the dynamics of, and beyond, the optical Fréedericksz transition under realistic experimental conditions almost three decades after its experimental discovery.

Light-driven liquid-crystalline nonlinear oscillator under optical periodic forcing

An all-optically driven strategy to govern a liquid-crystalline collective molecular nonlinear oscillator is discussed. It does not require external feedback of any kind while the oscillator and a time-dependent perturbation both are sustained by incident light. Various dynamical regimes such as frequency-locked, quasiperiodic, forced, and chaotic are observed, in agreement with a theoretical approach developed in the limit of the plane-wave approximation.

Nonlinear dynamics induced in liquid crystals in the presence of the orbital and spin angular momentum of light

We studied the dynamical effects induced in a homeotropic nematic film when a normally incident circularly polarized light beam with an elliptical intensity profile is used. A three-dimensional dynamical model shows that, besides the spin, the orbital angular momentum of photons also plays a role in the reorientation process. Our measurements fairly reproduce the main dynamical features predicted by the model in the near threshold region. The model, however, does not work, as it is, at higher incident laser power where chaotic director rotation was reported [A. Vella, A. Setaro, B. Piccirillo, E. Santamato, Phys. Rev. E 67, 051704 (2003)].

Light-induced chaotic rotations in nematic liquid crystals

Various nonlinear rotation regimes are observed in an optically excited nematic liquid-crystal film under boundary conditions (for the light and material) that are invariant by rotation. The excitation light is circularly polarized, the intensity profile is circularly symmetric, and the beam diameter at the sample location is a few times smaller than the cell thickness. A transition to chaos via quasiperiodicity is identified when the light intensity is taken as the control parameter. Transverse nonlocal effects are suggested to be the cause of the observed dynamics, and a simple model consisting of a collection of coupled rotators is developed to provide a qualitative explanation.

Light angular momentum flux and forces in birefringent inhomogeneous media

The angular momentum carried by a monochromatic optical field is separated into an orbital and a spin part beyond the paraxial approximation. These quantities have been distinguished on the grounds of the different mechanical effects they produce in transparent and birefringent media endowed with internal degrees of freedom. The orbital and the spin angular momentum flux densities exhibited are shown to be divergence free in homogeneous and isotropic media and to give back the correct expressions in the paraxial limit.

Optically induced dynamics in nematic liquid crystals: The role of finite beam size

We report on the influence of a finite beam size on the molecular reorientation dynamics when a nematic liquid crystal film is excited by a laser beam. We present experimental evidence of a new class of nonlinear dynamics when the excitation is a Gaussian shaped, circularly polarized laser beam at normal incidence. Various nonlinear regimes, periodic, quasiperiodic, intermittent, and possibly chaotic, are observed. A physical interpretation based on walk-off effects is proposed and its implications on current research in the field are discussed.