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.
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.
Interfaces between two phases may exhibit enthralling shapes. Optically driven phase transitions are a benchmark that enables spatial control in the order parameter. Dye-doped liquid crystals allow purely optically induced phase transitions. Here we show the temporal evolution of finger-like structures at the nematic-isotropic interface in a photoisomerization experiment in a liquid crystal mixture between E7 and methyl-red dye in twisted planar cells both in the turn-on and turn-o of light scenarios. From the nematic to isotropic liquid transition, triggered by turning on the light, the emergence, growth, and retraction of finger-like structures are observed and characterized. In contrast, the isotropic-to-nematic phase transition when the light turns off transient foam-like and labyrinthine textures are observed. A reduced model based on dopant concentration and the liquid crystal order parameter reproduces all the observed phenomena.
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.
Out of equilibrium systems under the influence of enough energy injection exhibit complex spa- tiotemporal 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 phe- nomenology. 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 spatiotem- poral dynamics. Experimental observations have a quite fair agreement with theoretical findings.
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