Turbulence is a complex spatiotemporal behavior and a fundamental concept in fluid dynamics,
which has been extended to other systems out of equilibrium, such as nonlinear optics, chemistry,
active matter, and economics. Fingerprint patterns with sustained spatiotemporal dynamics in a
liquid crystal light valve with an optical feedback experiment are studied. We show that the light intensity
field presents a dynamical regime simultaneously exhibiting phase and amplitude turbulence.
This bi-turbulent behavior of patterns is characterized by power-law spectra with exponents close
to -2 and -3 spatially and -2 temporally, for the phase and amplitude respectively. The pattern
orientation field also presents power-law spectra with exponents close to -2 and -3/4, spatially
and temporally. We characterize the observed chaotic dynamics by estimating the largest Lyapunov
exponent. We provide a theoretical model of pattern formation that explains the experimental
observations with good qualitative agreement.
Soft actuators are recognized as the intelligent robotics of the future. The main difference with other systems is the degree of freedom present and the shape of the stimuli. In this work, we focus on light stimuli and how light interacts with nanomaterials such as carbon nanotubes and hematite nanoparticles.
We prepared a monomer based on azo compounds derived from methyl red. Methyl red is known as a photoisomerization agent.
LLiquid crystal polymers with azo compounds exhibit photoisomerization with a lower degree of freedom of molecular reorientation than non-polymeric systems. However, photoisomerization not only exerts a transition order-disorder but also generates a stress relaxation process between the polymer chains. Depending on the percentage of components is possible to build different configurations with more or less crosslinked degrees. To incorporate monomers that only have one polymerizable side is possible to obtain an elastomer system and if only using monomers with two polymerizable sides the crosslinking is higher.
The incorporation of nanomaterials allows for modifying mechanical properties and can also incorporate some degree of polarization.
Systems with energy injection and dissipation self-organise by forming patterns of stripes, hexagons, squares, and superlattices at the onset of spatial instabilities. Increasing the disproportion between injection and dissipation of energy generates the emergence of disordered patterns with complex spatiotemporal behaviours. We investigate the turbulent dynamics of labyrinthine patterns far from the primary spatial instabilities in a liquid crystal light valve with optical feedback experiment. The structure functions associated with light intensity allow us to establish that the observed dynamical behaviours are also of intermittent nature.
Spatial branching processes are ubiquitous in nature, yet the mechanisms that drive their growth may vary significantly from one system to another. In soft matter physics, chiral nematic liquid crystals provide a playground to study the emergence of disordered branching patterns in a controlled setting. Via an appropriate forcing, a cholesteric phase may nucleate in a chiral nematic liquid crystal, which self-organizes into an extended branching pattern. It is known that branching events occur when the rounded tips of cholesteric fingers swell, become unstable, and split into two new cholesteric tips. The origin of this interfacial instability and the mechanisms that drive the large-scale spatial organization of these cholesteric patterns remain unclear. In this work, we investigate the spatial and temporal organization of thermally-driven branching patterns in chiral nematic liquid crystal cells experimentally. We describe the observations through a mean-field model and find that chirality is responsible for the creation of fingers, regulates their interactions, and controls the tip-splitting process. Furthermore, we show that the complex dynamics of the cholesteric pattern may be reduced to a small set of interaction rules that drive the large-scale morphological and topological organization. Our theoretical findings have a good agreement with the experimental observations.
By the application of electromagnetic fields onto an homeotropic nematic liquid crystal cell it is possible to induce vortices, which are particle-type defects with topological charge. The dynamics of the vortices is such that topological charge of the system is conserved, so these defects are always induced in pairs that annihilate after a short amount of time. Using a magnetic ring it is possible to induce a stable vortex triplet that allows the study of its dynamics, which is of an oscillatory kind when a low-frequency voltage is applied. Experimentally, we determine the region of parameters where the vortex triplet is stable, unstable, or becomes a lattice of vortices. We propose an amplitude equation which allow us to describe the vortex dynamics, and numerical simulations show agreement with experimental observations.
Metamaterials have subwavelength periodic structures that manipulate electromagnetic waves. Typically, difficulties are encountered in fabricating this type of materials due to the sophisticated techniques involved in their creation. Bubble domains in chiral nematic liquid crystals present a skyrmion lattice which has periodicity regions along a cell, which allow the observation of unconventional light-matter interaction. However, the interaction dynamics between vortices presents a challenge to ensure the order of the lattice throughout the space it covers. In this work we study the use of liquid crystal microdroplets as potential wells and the clustering of topological defects in them.
Optical coupling in pattern-forming systems brings out the emergence and transition of complex spatiotemporal behaviors. A liquid crystal light valve experiment with translational optical feedback shows the appearance of striped patterns. When the translational coupling length increases, the system exhibits transitions to traveling, spatiotemporal intermittency, and defect turbulence of striped waves. From the first principles, an order parameter equation valid close to the nascent of bistability together with a translationally coupling is derived. The dynamics of the liquid crystal light valve with translational optical feedback and the proposed minimal model system show qualitative agreement.
The interaction of light beams with helical objects allows the emergency of the optical vortices. Understanding and manipulating the dynamics of helical defects can generate versatile sources of optical vortex beams. Using a magnetic ring, matter vortices can be trapped on a nematic liquid crystal cell. By applying a low-frequency voltage, we observe oscillatory rotating and beating matter vortices. Experimntally, we determine the region of parameters where the dancing vortices are observed. The amplitude equation allows describing the dancing vortices, which presents similar behaviors to those observed experimentally.
Particle-type solutions are generic behaviors in out-of-equilibrium systems. These localized states are characterized by a discrete set of parameters such as position, width, and height. Even these solutions can have topological charges, localized vortices, which enriches the solutions and strengthens their respective stability. These solutions are characterized by exhibiting vorticity surrounded by a homogeneous state without vorticity. Frustrated chiral liquid crystals are a natural habitat for localized vortices, cholesteric bubbles. Here we study the emergence of chiral bubbles in the winding/unwinding transition of a chiral liquid crystal cell with homeotropic anchoring. Experimentally, we show that this winding/unwinding transition is subcritical in nature when one modifies the temperature, which also generates the emergence of spherulites through the contraction of cholesteric labyrinthine patterns. Theoretically, based on an amplitude equation inferred by symmetry arguments, we reveal the emergence of chiral bubbles from a cholesteric labyrinthine patterns.
Cholesteric liquid crystals have attracted the scientific community's attention in the last decades due to the impressive textures displayed in various experiments. In particular, when varying the temperature of a cholesteric liquid crystal sample with homeotropic anchoring, complex textures arise, which resemble labyrinthine patterns built on the connections of the so-called cholesteric fingers.
Near the winding/unwinding transition, we proposed a minimal phenomenological model that accounts for the first-order type transition and the symmetries in the system. At this transition, localized cholesteric fingers suffer a tip-splitting instability and the merging of pointed tips. We discuss the emergence of cholesteric labyrinths using experimental, analytical, and numerical techniques.
The fronts are waves that connect two equilibria. The liquid crystals are no stranger to these phenomena. Front dynamics also was observed in other physical contexts, such as walls separating magnetic domains, fluidized granular states, chemical reactions, solidification, and combustion processes, and population dynamics, to mention a few. We find these phenomena in differents interface dynamics, as part of a robust phenomenon this ranging from chemistry and biology to physics. The propagation and dynamics of fronts depend on the nature of the states that are being connected. The invasion of a state into another is characterized usually by front propagation into unstable states. In the present work, we investigate the anisotropic front propagation close to phase transition SmA-N*. The bifurcation diagram shows a subcritical behavior, and the front speed is according to the mathematical model. A spatiotemporal diagram shows an evolution of the front with preferential direction.”
We investigate topological states of matter in a system with injection and dissipation of energy. In an experiment involving a liquid crystal cell under the influence of a low frequency oscillatory electric field, we observe a transition from no vortex state to a state in which vortices persist. Depending on the period and the type of the forcing, the vortices self-organize forming square lattices, glassy states, and disordered vortex structures. Our results show that the matter maintained out of equilibrium by means of the temporal modulation of parameters can exhibit exotic states at room temperature.
We investigate a vortex triplet induced by the combination of an electric and magnetic field onto a homeotropic nematic liquid crystal cell. The electric and magnetic fields are generated by two parallel electrodes and a magnetic ring, respectively. The vortex triplet remains stable and trapped at the center of the magnetic ring. Based on forcing the Ginzburg-Landau equation, valid close to the re-orientational transition, allow us to establish the origin of the vortex triplet. Numerical simulations show a quite fair agreement with theoretical findings and experimental observations.
In ordinary consciousness, noise is associated with the term “hindrance”; it is considered as a nuisance that can lead to communication or signal transmission failure or prevent the detection of a weak signal to be measured. However, under certain conditions the impact of noise can be counter-intuitively a resource. In nonlinear systems, noise can induce novel regimes leading to the formation of synchronized structures, coherence between the output and the input of resonators or even to the amplification of weak signals. In other words, noise can play a constructive role, with potential benefits for signal processing or measurement for instance.
Single or coupled Nano-Opto-ElectroMechanical resonators whose design is based on suspended photonic crystal membrane could be used as a toy-system to pursue two main goals: stochastic amplification and chaos. As such noise-aided processes might have a strong impact in noise-assisted applications including signal processing or sensing.
Optical pattern formation is usually due either to the combination of diffraction and nonlinearity in a Kerr medium or the temporal modulation of light in a photosensitive chemical reaction. We present a different mechanism by which light spontaneously induces stripe domains between nematic states in a twisted nematic liquid crystal layer doped with azo-dyes. Due to the photoisomerization process of the dopants, light creates dissipative structures 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 Turing mechanism for this instability. Theoretically, the emergence of the stripe patterns is described by a model for the dopant concentration coupled with the nematic order parameter.
Extreme events are characterized by rare and high amplitude excursions of a given variable characterizing a physical system with respect to its long time average. Its study in optics has been primarily motivated by the analogy with rogue waves in hydrodynamics and includes ingredients such as spatial instabilities, nonlinearities and noise.
Here we consider a spatially extended microcavity laser with integrated saturable absorber in the self-pulsing regime. This system, thanks to its short typical timescales, allows large recordings and accurate statistics. Moreover, it does not display irregular or aperiodic dynamics without spatial coupling. Hence, the role of spatial coupling in the emergence of extreme events can be studied. With the help of a model and of numerical analysis together with the experimental observations, we unveil the dynamical origin of the extreme events in the occurrence of spatiotemporal chaos [1], rather than through collisions of coherent structures. Moreover, by investigating the fine structure of the maximum Lyapunov exponent, of the Lyapunov spectrum and of the Kaplan-Yorke dimension of the chaotic attractor, we are able to deduce that intermittency plays a key role in the proportion of extreme events measured. We assign the observed mechanism of generation of extreme events to quasi-periodic extended spatiotemporal intermittency [2]. The understanding of the formation mechanism of these extreme phenomena is an important step to devise strategies to control them.
[1] Selmi et al, Phy. Rev. Lett. 116, 013901 (2016).
[2] Coulibaly et al, Phys. Rev. A 95, 023816 (2017).
Stochastic resonance is a paradoxical phenomenon whereby a weak signal can be amplified by application of noise. Stochastic resonance occurs in a number of nonlinear systems, in neurobiology, mesoscopic physics, photonics, atomic physics, mechanics,... The classical picture of stochastic resonance involves the stochastic synchronisation of the motion of a fictious particle (representing the system's state) in a bistable potential subjected to a weak amplitude harmonic modulation (the input signal) and to amplitude noise. Stochastic amplification of the weak signal is revealed in the spectral amplification at the signal frequency for a non zero input noise strength.
We report on the observation of phase stochastic resonance in a nanomechanical, photonic crystal membrane with integrated electrical actuation. The nanomechanical oscillator is forced by a coherent driving signal which results in a bistable behavior. Bistability occurs in a bidimensional phase space since the system has a response in amplitude and in phase. We subject the oscillator to an additional slow phase modulation and to phase noise. We evidence a stochastic resonance phenomenon with amplification of the phase or amplitude response of the system for a non-zero input noise. Moreover, a theoretical analysis reveals that phase noise acts in a multiplicative fashion. This has important consequences on the optimal parameters for stochastic resonance to occur and explains the observed noise-induced detuning in the system. Phase stochastic resonance may have impact on several domains, including signal transmission telecommunication with coherent protocols such as Phase Shifting Keying, or metrology with improved detection.
Using self-induced vortex-like defects in the nematic liquid crystal layer of a light valve with photo-sensible wall, we demonstrate the realization of programable optical vortices lattices with arbitrary configuration in space. On each lattice site, every matter vortex acts as a photonic spin-to-orbital momentum coupler and an array of circularly polarized input beams is converted into an output array of vortex beams with topological charges consistent with the vortex matter lattice. The vortex arrangements are explained the basis of light-induced matter defects and topological rules.
Cavity solitons are localized light peaks in the transverse section of nonlinear resonators. These structures are usually formed under a coexistence condition between a homogeneous background of radiation and a self- organized patterns resulting from a Turing type of instabilities. In this issue, most of studies have been realized ignoring the nonlocal effects. Non-local effects can play an important role in the formation of cavity solitons in optics, population dynamics and plant ecology. Depending on the choice of the nonlocal interaction function, the nonlocal coupling can be strong or weak. When the nonlocal coupling is strong, the interaction between fronts is controlled by the whole non-local interaction function. Recently it has shown that this type of nonlocal coupling strongly affects the dynamics of fronts connecting two homogeneous steady states and leads to the stabilization of cavity solitons with a varying size plateau. Here, we consider a ring passive cavity filled with a Kerr medium like a liquid crystal or left-handed materials and driven by a coherent injected beam. We show that cavity solitons resulting for strong front interaction are stable in one and two-dimensional setting out of any type of Turing instability. Their spatial profile is characterized by a varying size plateau. Our results can apply to large class of spatially extended systems with strong nonlocal coupling.
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