Topology-commanded optical properties of bistable electric-field-induced torons in cholesteric bubble domains

Propagation of periodic director and flow patterns in a cholesteric liquid crystal under electroconvection

The electroconvection of liquid crystals is a typical example of a dissipative structure generated by complicated interactions between three factors: convective flow, structural deformation, and the migration of charge carriers. In this study, we found that the periodic structural deformation of a cholesteric liquid crystal propagates in space, like a wave, under an alternating-current electric field. The existence of convection and charge carriers was confirmed by flow-field measurements and dielectric relaxation spectroscopy. Given that the wave phenomenon results from electroconvection, we suggest a possible model for describing the mechanism of wave generation. The validity of the model was examined using the Onsager variational principle. Consequently, it was suggested that wave generation can be described by four effects: the electrostatic potential, mixing entropy, anisotropic friction due to charge migration, and viscous dissipation of the liquid crystal.

Morphogenesis of a chiral liquid crystalline droplet with topological reconnection and Lehmann rotation

Morphogenesis is a hierarchical phenomenon that produces various macroscopic structures in living organisms, with high reproducibility. This study demonstrates that such structural formation can also be observed in a chiral liquid crystalline droplet under a temperature gradient. Through specific control of the temperature change process, we were able to switch the final structure obtained as a result of the formation via the appearance and reconnection of loop defects in the transient state during structure formation. Simultaneously, the existence of the gradient resulted in a characteristic rotational phenomenon called Lehmann rotation, which was prominently induced in the transient state. By demonstrating three-dimensional measurements of the flow field, we revealed the existence of Marangoni convection in the state. Consequently, it is indicated that the convection results in high-speed Lehmann rotation and large structural deformation with topological changes, thereby playing a significant role in the structure formation.

Mechanical Actuation via Homeomorphic Transformations of Topological Solitons within Polymer Coatings

Topological solitons are currently under investigation for their exotic properties, especially in nonlinear physics, optics, and material sciences. However, challenges of robust generation and limited stability over time have hindered their practical uses. To address this issue, an approach is developed to form structured arrays of solitons in films of polymerizable liquid crystals. Their complex molecular architecture is preserved by in situ photopolymerization forming a stable liquid crystal network. Most excitingly, their properties are advanced to include responsiveness functions. When thermally actuated, these topological solitons mediate the reconfiguration of surface topographies. Complex shape changes occur depending on the intrinsic complex spatial distribution of the director, which may even lead to full shape inversion and topographical changes as high as ≈40% of the initial thickness. Conversely, the shape changes provide information on the initial director profile, which is consistent with the mathematical model. The soliton-containing polymer coatings are applicable in multiple domains, ranging from tunable optics to haptics, and from shape-coupled sensing systems to temperature-coupled heat management.

Fabrication of Arrays of Topological Solitons in Patterned Chiral Liquid Crystals for Real-Time Observation of Morphogenesis

Topological solitons have knotted continuous field configurations embedded in a uniform background, and occur in cosmology, biology, and electromagnetism. However, real-time observation of their morphogenesis and dynamics is still challenging because their size and timescale are enormously large or tiny. Liquid crystal (LC) structures are promising candidates for a model-system to study the morphogenesis of topological solitons, enabling direct visualization due to the proper size and timescale. Here, a new way is found to rationalize the real-time observation of the generation and transformation of topological solitons using cholesteric LCs confined in patterned substrates. The experimental demonstration shows the topologically protected structures arise via the transformation of topological defects. Numerical modeling based on minimization of free energy closely reconstructs the experimental findings. The fundamental insights obtained from the direct observations pose new theoretical challenges in understanding the morphogenesis of different types of topological solitons within a broad range of scales.

Numerical modeling of optical modes in topological soft matter

Vector and vortex laser beams are desired in many applications and are usually created by manipulating the laser output or by inserting optical components in the laser cavity. Distinctly, inserting liquid crystals into the laser cavity allows for extensive control over the emitted light due to their high susceptibility to external fields and birefringent nature. In this work we demonstrate diverse optical modes for lasing as enabled and stablised by topological birefringent soft matter structures using numerical modelling. We show diverse structuring of light-with different 3D intensity and polarization profiles-as realised by topological soft matter structures in radial nematic droplet, in 2D nematic cavities of different geometry and including topological defects with different charges and winding numbers, in arbitrary varying birefringence fields with topological defects and in pixelated birefringent profiles. We use custom written FDFD code to calculate emergent electromagnetic eigenmodes. Control over lasing is of a particular interest aiming towards the creation of general intensity, polarization and topologically shaped laser beams.

Photoaligned Liquid Crystal Devices with Switchable Hexagonal Diffraction Patterns

Highly efficient optical diffraction can be realized with the help of micrometer-thin liquid crystal (LC) layers with a periodic modulation of the director orientation. Electrical tunability is easily accessible due to the strong stimuli-responsiveness in the LC phase. By using well-designed photoalignment patterns at the surfaces, we experimentally stabilize two dimensional periodic LC configurations with switchable hexagonal diffraction patterns. The alignment direction follows a one-dimensional periodic rotation at both substrates, but with a 60° or 120° rotation between both grating vectors. The resulting LC configuration is studied with the help of polarizing optical microscopy images and the diffraction properties are measured as a function of the voltage. The intricate bulk director configuration is revealed with the help of finite element Q-tensor simulations. Twist conflicts induced by the surface anchoring are resolved by introducing regions with an out-of-plane tilt in the bulk. This avoids the need for singular disclinations in the structures and gives rise to voltage induced tuning without hysteretic behavior.

Photo-reconfigurable twisting structure in chiral liquid crystals triggered by photoresponsive surface

Shape-transformable molecular additives with photoresponsivity, such as azobenzene or spiropyran, in matter are known to decrease the local order parameter and lead to drastic state variations under light irradiation. For example, a liquid crystalline state can be transformed to an isotropic liquid state by photo-exciting a tiny amount of azobenzene additives from trans- to cis-conformers. On the other hand, structural or shape transformation without changing the phase state is also intriguing since it offers an opportunity for manipulating specific structures. Here, we demonstrate an active control of the topology of chiral particle-like twisting structures, dubbed toron, by light. Interestingly, the individual twisting structure is fully reconfigurable between spherical and unique branched topological states. We reveal that the shape transformation is driven by the free-energy competition between the variation of surface anchoring strength and the elastic energy stored in the twisting structure. The mean-field simulation based on the Landau-de Gennes framework shows that the elastic anisotropy plays the dominant role in modifying the toron topology upon weak anchoring. The results offer a new path for understanding the process of topology-involved shape transformation and fabrication of novel functional materials.

Review: knots and other new topological effects in liquid crystals and colloids

Humankind has been obsessed with knots in religion, culture and daily life for millennia, while physicists like Gauss, Kelvin and Maxwell already involved them in models centuries ago. Nowadays, colloidal particles can be fabricated to have shapes of knots and links with arbitrary complexity. In liquid crystals, closed loops of singular vortex lines can be knotted by using colloidal particles and laser tweezers, as well as by confining nematic fluids into micrometer-sized droplets with complex topology. Knotted and linked colloidal particles induce knots and links of singular defects, which can be interlinked (or not) with colloidal particle knots, revealing the diversity of interactions between topologies of knotted fields and topologically nontrivial surfaces of colloidal objects. Even more diverse knotted structures emerge in nonsingular molecular alignment and magnetization fields in liquid crystals and colloidal ferromagnets. The topological solitons include hopfions, skyrmions, heliknotons, torons and other spatially localized continuous structures, which are classified based on homotopy theory, characterized by integer-valued topological invariants and often contain knotted or linked preimages, nonsingular regions of space corresponding to single points of the order parameter space. A zoo of topological solitons in liquid crystals, colloids and ferromagnets promises new breeds of information displays and a plethora of data storage, electro-optic and photonic applications. Their particle-like collective dynamics echoes coherent motions in active matter, ranging from crowds of people to schools of fish. This review discusses the state of the art in the field, as well as highlights recent developments and open questions in physics of knotted soft matter. We systematically overview knotted field configurations, the allowed transformations between them, their physical stability and how one can use one form of knotted fields to model, create and imprint other forms. The large variety of symmetries accessible to liquid crystals and colloids offer insights into stability, transformation and emergent dynamics of fully nonsingular and singular knotted fields of fundamental and applied importance. The common thread of this review is the ability to experimentally visualize these knots in real space. The review concludes with a discussion of how the studies of knots in liquid crystals and colloids can offer insights into topologically related structures in other branches of physics, with answers to many open questions, as well as how these experimentally observable knots hold a strong potential for providing new inspirations to the mathematical knot theory.

Topological solitons, cholesteric fingers and singular defect lines in Janus liquid crystal shells

Topological solitons are non-singular but topologically nontrivial structures in fields, which have fundamental significance across various areas of physics, similar to singular defects. Production and observation of singular and solitonic topological structures remain a complex undertaking in most branches of science - but in soft matter physics, they can be realized within the director field of a liquid crystal. Additionally, it has been shown that confining liquid crystals to spherical shells using microfluidics resulted in a versatile experimental platform for the dynamical study of topological transformations between director configurations. In this work, we demonstrate the triggered formation of topological solitons, cholesteric fingers, singular defect lines and related structures in liquid crystal shells. We show that to accommodate these objects, shells must possess a Janus nature, featuring both twisted and untwisted domains. We report the formation of linear and axisymmetric objects, which we identify as cholesteric fingers and skyrmions or elementary torons, respectively. We then take advantage of the sensitivity of shells to numerous external stimuli to induce dynamical transitions between various types of structures, allowing for a richer phenomenology than traditional liquid crystal cells with solid flat walls. Using gradually more refined experimental techniques, we induce the targeted transformation of cholesteric twist walls and fingers into skyrmions and elementary torons. We capture the different stages of these director transformations using numerical simulations. Finally, we uncover an experimental mechanism to nucleate arrays of axisymmetric structures on shells, thereby creating a system of potential interest for tackling crystallography studies on curved spaces.

Thermo-Optical Generation of Particle-Like Structures in Frustrated Chiral Nematic Film

The creation of metastable particle-like structures in frustrated (unwound) chiral nematic film containing light-absorbing additive is studied. It is shown that such localized structures can be generated by the thermo-optical action of a focused laser beam or arise spontaneously at a phase transition from an isotropic to a liquid crystal state. Observed axisymmetric patterns resemble cholesteric spherulites with toroidal double-twisted director-field configuration.

Orientational structures in cholesteric droplets with homeotropic surface anchoring

The dependency of orientational structures in cholesteric droplets with homeotropic surface anchoring on the helicity parameter has been studied by experiment and simulations. We have observed a sequence of structures, in which the director configurations and topological defects were identified by comparison of polarized microscopy pictures with simulated textures. A toron-like and low-symmetry intermediate layer-like structures have been revealed and studied in detail. The ranges of stability of the observed structures have been summarized in a general diagram and explained by the helicity parameter dependence of the free energy terms.

Dynamic Control of Light Direction Enabled by Stimuli-Responsive Liquid Crystal Gratings

The ability to control light direction with tailored precision via facile means is long-desired in science and industry. With the advances in optics, a periodic structure called diffraction grating gains prominence and renders a more flexible control over light propagation when compared to prisms. Today, diffraction gratings are common components in wavelength division multiplexing devices, monochromators, lasers, spectrometers, media storage, beam steering, and many other applications. Next-generation optical devices, however, demand nonmechanical, full and remote control, besides generating higher than 1D diffraction patterns with as few optical elements as possible. Liquid crystals (LCs) are great candidates for light control since they can form various patterns under different stimuli, including periodic structures capable of behaving as diffraction gratings. The characteristics of such gratings depend on several physical properties of the LCs such as film thickness, periodicity, and molecular orientation, all resulting from the internal constraints of the sample, and all of these are easily controllable. In this review, the authors summarize the research and development on stimuli-controllable diffraction gratings and beam steering using LCs as the active optical materials. Dynamic gratings fabricated by applying external field forces or surface treatments and made of chiral and nonchiral LCs with and without polymer networks are described. LC gratings capable of switching under external stimuli such as light, electric and magnetic fields, heat, and chemical composition are discussed. The focus is on the materials, designs, applications, and future prospects of diffraction gratings using LC materials as active layers.

Low-voltage-driven smart glass based on micro-patterned liquid crystal Fresnel lenses

We disclose a method of fabricating a low-voltage-driven smart glass based on micro-patterned liquid crystal (LC) Fresnel lenses and implement three proof-of-concept prototypes. Distinct from the conventional LC-based smart windows with the scattering state, the prominence of our proposed LC smart glass in blurry state under both normal and oblique observations stems from the image distortion caused by LC Fresnel lenses. In addition, the high transmittance (>90%) in clear state is obtained by applying a low voltage of 2 V to each prototype. Moreover, by elaborating the design of the LC smart glass, the reversed switching states [i.e., a clear (voltage OFF) state and a blurry (voltage ON) state] and fast switching time can be simultaneously achieved.