Lasing and waveguiding in smectic A liquid crystal optical fibers

Topological liquid crystal superstructures as structured light lasers

Liquid crystals (LCs) form an extremely rich range of self-assembled topological structures with artificially or naturally created topological defects. Some of the main applications of LCs are various optical and photonic devices, where compared to their solid-state counterparts, soft photonic systems are fundamentally different in terms of unique properties such as self-assembly, self-healing, large tunability, sensitivity to external stimuli, and biocompatibility. Here we show that complex tunable microlasers emitting structured light can be generated from self-assembled topological LC superstructures containing topological defects inserted into a thin Fabry-Pérot microcavity. The topology and geometry of the LC superstructure determine the structuring of the emitted light by providing complex three-dimensionally varying optical axis and order parameter singularities, also affecting the topology of the light polarization. The microlaser can be switched between modes by an electric field, and its wavelength can be tuned with temperature. The proposed soft matter microlaser approach opens directions in soft matter photonics research, where structured light with specifically tailored intensity and polarization fields could be designed and implemented.

Light Propagation in Confined Nematic Liquid Crystals and Device Applications

Liquid crystals are interesting linear and nonlinear optical materials used to make a wide variety of devices beyond flat panel displays. Liquid crystalline materials can be used either as core or as cladding of switchable/reconfigurable waveguides with either an electrical or an optical control or both. In this paper, materials and main device structures of liquid crystals confined in different waveguide geometries are presented using different substrate materials, such as silicon, soda lime or borosilicate glass and polydimethylsiloxane. Modelling of the behaviour of liquid crystal nanometric molecular reorientation and related refractive index distribution under both low-frequency electric and intense optical fields is reported considering optical anisotropy of liquid crystals. A few examples of integrated optic devices based on waveguides using liquid crystalline materials as core for optical switching and filtering are reviewed. Reported results indicate that low-power control signals represent a significant feature of photonic devices based on light propagation in liquid crystals, with performance, which are competitive with analogous integrated optic devices based on other materials for optical communications and optical sensing systems.

Self-shaping liquid crystal droplets by balancing bulk elasticity and interfacial tension

Liquid crystal (LC) research is rapidly expanding to include studies of curved and topologically nontrivial structures. Here, we explore the role of the bulk LC elasticity and interfacial free energy under weak thermal stimuli to achieve structural transformations in LC emulsions using two different surfactants. Our method is universal and could be used for any LC material or phase. A theoretical model for transforming LC emulsions into uniform fibers and vice versa is presented. We also show the self-shaping of smectic vesicle structures and monodispersed droplet formation at the nematic–smectic transition, utilizing the LC bulk elasticity. This work shows the potential to obtain the controllable shape of complex curved structures for a constant volume of different LCs and other soft materials.

The shape diversity and controlled reconfigurability of closed surfaces and filamentous structures, universally found in cellular colonies and living tissues, are challenging to reproduce. Here, we demonstrate a method for the self-shaping of liquid crystal (LC) droplets into anisotropic and three-dimensional superstructures, such as LC fibers, LC helices, and differently shaped LC vesicles. The method is based on two surfactants: one dissolved in the LC dispersed phase and the other in the aqueous continuous phase. We use thermal stimuli to tune the bulk LC elasticity and interfacial energy, thereby transforming an emulsion of polydispersed, spherical nematic droplets into numerous, uniform-diameter fibers with multiple branches and vice versa. Furthermore, when the nematic LC is cooled to the smectic-A LC phase, we produce monodispersed microdroplets with a tunable diameter dictated by the cooling rate. Utilizing this temperature-controlled self-shaping of LCs, we demonstrate life-like smectic LC vesicle structures analogous to the biomembranes in living systems. Our experimental findings are supported by a theoretical model of equilibrium interface shapes. The shape transformation is induced by negative interfacial energy, which promotes a spontaneous increase of the interfacial area at a fixed LC volume. The method was successfully applied to many different LC materials and phases, demonstrating a universal mechanism for shape transformation in complex fluids.

Novel optofluidic concepts enabled by topological microfluidics-INVITED

The coupling between flow and director orientation of liquid crystals (LCs) has been long utilized to devise wide-ranging applications spanning modern displays, medical and environmental solutions, and bio-inspired designs and applications. LC-based optofluidic platforms offer a non-invasive handle to modulate light and material fields, both locally and dynamically. The flow-driven reorientation of the LC molecules can tailor distinct optical and mechanical responses in microfluidic confinements, and harness the coupling therein. Yet the synergy between traditional optofluidics with isotropic fluids and LC microfluidics remains at its infancy. Here, we discuss emerging optofluidic concepts based on Topological Microfluidics, leveraging microfluidic control of topological defects and defect landscapes. With a specific focus on the role of surface anchoring and microfluidic geometry, we present recent and ongoing works that harness flow-controlled director and defect configurations to modulate optical fields. The flow-induced optical attributes, and the corresponding feedback, is enhanced in the vicinity of the topological defects which geenerate distinct isotropic opto-material properties within an anisotropic matrix. By harnessing the rich interplay of confining geometry, anchoring and micro-scale nematodynamics, topological microfluidics offers a promising platform to ideate the next generation of optofluidic and optomechnical concepts.

Hierarchical assembly of smectic liquid crystal defects at undulated interfaces

The assembly of topological defects in liquid crystals has drawn significant interest in the last decade due to their ability to trap colloidal objects and direct their arrangements. They have also brought about a high impact in modern technologies, in particular in optics, e.g., microlens arrays, soft lithography templates, and optically selective masks. Here we study the formation of defects in smectic A liquid crystal with hybrid texture at undulated surfaces. We investigate the role of surface topography on the organization of focal conic domains (FCDs) in smectic films. We demonstrate new methods for assembling FCDs and disclinations into hierarchical structures. When the liquid crystal is heated to the nematic phase, we observe stable defect lines forming at specific locations. These defects are created to satisfy anchoring conditions and the geometry of confinement imposed by the boundaries. Once the liquid crystal is cooled to the smectic A phase, the disclinations maintain their positions, but periodic structures of reversible FCDs facing opposite directions arise between them. We report the correlation between the size of these FCDs and their eccentricities with the morphology of the interface. This work paves the way for creating new procedures to control the assembly of functional nanomaterials into tunable assemblies that may find relevance in the field of energy technology including in optoelectronic and photonic applications.

Nematic Liquid-Crystal Necklace Structure Made by Microfluidics System

We report a necklace structure made of liquid crystal dispersed in poly(vinyl alcohol) (PVA) aqueous solution, which is fabricated by a microfluidic device. In the necklace structure, liquid crystal droplets that are tens of micrometers in diameter are connected by microtethers, which are birefringent, are not penetrating the droplets, and can be elastically stretched by applying external force. The necklace structure was analyzed by fluorescent confocal microscopy, and the tethers were made of liquid crystal and PVA composite. The elastic constant of the tether was determined by using laser tweezers to stretch the tether. The Whispering Gallery Modes circulating inside individual droplets in the necklace structure were also observed.

Self-Regulated Smectic Emulsion with Switchable Lasing Application

A structurally reversible smectic liquid crystal (LC) emulsion made of semifluorinated rod-type molecules in silicon oil, which is controlled by simple heating and cooling, is presented. Without adding any kind of additives, such as surfactants, polymers or emulsifiers, and without using any special tools, such as microfluidics or gas bubbling, the LC molecules spontaneously form monodisperse spherical and myelin-like structures upon cooling from the isotropic temperature. The LC emulsion can easily trap guest materials, providing a platform for repeatable and reliable switchable emulsification. For example, this interesting system enables the realization of an on-off lasing system by confining fluorescent dyes in the LC droplets.

Whispering gallery mode lasing in mesomorphic liquid crystal microdroplets

In recent years, investigation on the non-display applications of liquid crystals has increased considerably. One of the emerging applications is whispering gallery mode (WGM) lasing. Here, we report experimental studies on the morphology and WGM lasing in nematic (N), smectic-A (SmA) and smectic-C (SmC) microdroplets dispersed in a highly transparent and low refractive index perfluopolymer. The mesomorphic microdroplets, obtained by varying the temperature, exhibit radial director configuration. The SmA microdroplets are found to be highly stable and robust against mechanical stress compared to the N and SmC microdroplets. We study lasing properties such as intensity, threshold pump energy and linewidth, and show that overall the SmA microdroplets are superior to the N and SmC microdroplets. The experimental results are discussed based on the orientation of the dye molecules, director fluctuations and tilting at the interface.

Liquid crystals in micron-scale droplets, shells and fibers

The extraordinary responsiveness and large diversity of self-assembled structures of liquid crystals are well documented and they have been extensively used in devices like displays. For long, this application route strongly influenced academic research, which frequently focused on the performance of liquid crystals in display-like geometries, typically between flat, rigid substrates of glass or similar solids. Today a new trend is clearly visible, where liquid crystals confined within curved, often soft and flexible, interfaces are in focus. Innovation in microfluidic technology has opened for high-throughput production of liquid crystal droplets or shells with exquisite monodispersity, and modern characterization methods allow detailed analysis of complex director arrangements. The introduction of electrospinning in liquid crystal research has enabled encapsulation in optically transparent polymeric cylinders with very small radius, allowing studies of confinement effects that were not easily accessible before. It also opened the prospect of functionalizing textile fibers with liquid crystals in the core, triggering activities that target wearable devices with true textile form factor for seamless integration in clothing. Together, these developments have brought issues center stage that might previously have been considered esoteric, like the interaction of topological defects on spherical surfaces, saddle-splay curvature-induced spontaneous chiral symmetry breaking, or the non-trivial shape changes of curved liquid crystal elastomers with non-uniform director fields that undergo a phase transition to an isotropic state. The new research thrusts are motivated equally by the intriguing soft matter physics showcased by liquid crystals in these unconventional geometries, and by the many novel application opportunities that arise when we can reproducibly manufacture these systems on a commercial scale. This review attempts to summarize the current understanding of liquid crystals in spherical and cylindrical geometry, the state of the art of producing such samples, as well as the perspectives for innovative applications that have been put forward.

Control of Periodic Zigzag Structures of DNA by a Simple Shearing Method

A periodic zigzag structure of DNA material is successfully fabricated by a simple shearing method. The periodicity of the pattern can be finely controlled by combining the mechanical shearing method with topographic patterns of microchannels. The resultant zigzag patterns can be used as a template to control the alignment of rod-like liquid crystals due to its highly regular periodicity.

A novel model for smectic liquid crystals: Elastic anisotropy and response to a steady-state flow

By means of a combination of equilibrium Monte Carlo and molecular dynamics simulations and nonequilibrium molecular dynamics we investigate the ordered, uniaxial phases (i.e., nematic and smectic A) of a model liquid crystal. We characterize equilibrium behavior through their diffusive behavior and elastic properties. As one approaches the equilibrium isotropic-nematic phase transition, diffusion becomes anisotropic in that self-diffusion D_⊥ in the direction orthogonal to a molecule's long axis is more hindered than self-diffusion D_∥ in the direction parallel to that axis. Close to nematic-smectic A phase transition the opposite is true, D_∥ < D_⊥. The Frank elastic constants K₁, K₂, and K₃ for the respective splay, twist, and bend deformations of the director field n̂ are no longer equal and exhibit a temperature dependence observed experimentally for cyanobiphenyls. Under nonequilibrium conditions, a pressure gradient applied to the smectic A phase generates Poiseuille-like or plug flow depending on whether the convective velocity is parallel or orthogonal to the plane of smectic layers. We find that in Poiseuille-like flow the viscosity of the smectic A phase is higher than in plug flow. This can be rationalized via the velocity-field component in the direction of the flow. In a sufficiently strong flow these smectic layers are not destroyed but significantly bent.

Liquid microlenses and waveguides from bulk nematic birefringent profiles

We demonstrate polarization-selective microlensing and waveguiding of laser beams by birefringent profiles in bulk nematic fluids using numerical modelling. Specifically, we show that radial escaped nematic director profiles with negative birefringence focus and guide light with radial polarization, whereas the opposite - azimuthal - polarization passes through unaffected. A converging lens is realized in a nematic with negative birefringence, and a diverging lens in a positive birefringence material. Tuning of such single-liquid lenses by an external low-frequency electric field and by adjusting the profile and intensity of the beam itself is demonstrated, combining external control with intrinsic self-adaptive focusing. Escaped radial profiles of birefringence are shown to act as single-liquid waveguides with a single distinct eigenmode and low attenuation. Finally, this work is an approach towards creating liquid photonic elements for all-soft matter photonics.

Relevance of saddle-splay elasticity in complex nematic geometries

We demonstrate the relevance of saddle-splay elasticity in nematic liquid crystalline fluids in the context of complex surface anchoring conditions and the complex geometrical confinement. Specifically, nematic cells with patterns of surface anchoring and colloidal knots are shown as examples where saddle-splay free energy contribution can have a notable role which originates from nonhomogeneous surface anchoring and the varying surface curvature. Patterned nematic cells are shown to exhibit various (meta)stable configurations of nematic field, with relative (meta)stability depending on the saddle-splay. We show that for high enough values of saddle-splay elastic constant K24 a previously unstable conformation can be stabilised, more generally indicating that the saddle-splay can reverse or change the (meta)stability of various nematic structures affecting their phase diagrams. Furthermore, we investigate saddle-splay elasticity in the geometry of highly curved boundaries - the colloidal particle knots in nematic - where the local curvature of the particles induces complex spatial variations of the saddle-splay contributions. Finally, a nematic order parameter tensor based saddle-splay invariant is shown, which allows for the direct calculation of saddle-splay free energy from the Q-tensor, a possibility very relevant for multiple mesoscopic modelling approaches, such as Landau-de Gennes free energy modelling.

Creation of liquid-crystal periodic zigzags by surface treatment and thermal annealing

The orientation control of soft matter to create a large area single domain is one of the most exciting research topics in materials science. Recently, this effort has been extended to fabricate two- or three-dimensional structures for electro-optical applications. Here, we create periodic zigzag structures in liquid crystals (LCs) using a combination of surface treatment and thermal annealing. The LC molecules in the nematic (N) phase were initially guided by the alignment layer of rubbed polymers, which were quenched and subsequently annealed in the smectic A (SmA) phase to create periodic zigzag structures that represent modulated layer structures. Direct investigation of the zigzags was performed using microscopy and diffraction techniques, showing the alternately arranged focal conic domains (FCDs) formed. The resulting macroscopic periodic structures will be of interest in further studies of the physical properties of soft matters.

Smectic Gardening on Curved Landscapes

Focal conic domains (FCDs) form in smectic-A liquid crystal films with hybrid anchoring conditions with eccentricity and size distribution that depend strongly on interface curvature. Assemblies of FCDs can be exploited in settings ranging from optics to material assembly. Here, using micropost arrays with different shapes and arrangement, we assemble arrays of smectic flower patterns, revealing their internal structure as well as defect size, location, and distribution as a function of interface curvature, by imposing positive, negative, or zero Gaussian curvature at the free surface. We characterize these structures, relating free surface topography, substrate anchoring strength, and FCD distribution. Whereas the largest FCDs are located in the thickest regions of the films, the distribution of sizes is not trivially related to height, due to Apollonian tiling. Finally, we mold FCDs around microposts of complex shape and find that FCD arrangements are perturbed near the posts, but are qualitatively similar far from the posts where the details of the confining walls and associated curvature fields decay. This ability to mold FCD defects into a variety of hierarchical assemblies by manipulating the interface curvature paves the way to create new optical devices, such as compound eyes, via a directed assembly scheme.

Nanosecond control and optical pulse shaping by stimulated emission depletion in a liquid crystal

We study anisotropic Stimulated Emission Depletion (STED) from dye molecules, which are collectively ordered in a host liquid crystal. Due to the ordering of fluorescent emitters, the STED efficiency depends on the polarization of the depletion beam and time-delay of the STED pulse. The depletion efficiency is highest at lower temperatures in the highly ordered smectic-A phase and deteriorates in the higher temperature nematic and isotropic phases. We demonstrate by temporal tuning of STED that it is possible to generate an arbitrary sequence of nanosecond fluorescent pulses with variable width and variable delay. Our results show that the STED mechanism in principle allows for very fast (GHz) and efficient control of light by light, which could in the future be used for all-optical control of the flow of light in photonic microdevices based on liquid crystals. Using STED anisotropy and time-control, new modalities of STED imaging in liquid crystals could be developed.

Ultrafast all-optical response of a nematic liquid crystal

Liquid crystals are superior optical materials for large area displays, but it is considered that their collective and slow-millisecond response makes them useless for ultrafast optical applications. In contrast to that, we here demonstrate an ultrafast optical response of a nematic liquid crystal, which is induced by an intense femtosecond optical impulse. We show that the refractive index of the nematic liquid crystal pentyl-cyanobiphenyl can be modulated at a time scale as fast as 500 fs via a coherently excited optical Kerr effect. The change in the refractive index is in the order of 10^-4 at a fluence of 4 mJ/cm² and is strongly polarization dependent. This unprecedented result opens new ways towards ultrafast all-optical modulation in liquid crystal-based devices.

Topological binding and elastic interactions of microspheres and fibres in a nematic liquid crystal

We present a detailed analysis of topological binding and elastic interactions between a long, and micrometer-diameter fiber, and a microsphere in a homogeneously aligned nematic liquid crystal. Both objects are surface treated to produce strong perpendicular anchoring of the nematic liquid crystal. We use the opto-thermal micro-quench of the laser tweezers to produce topological defects with prescribed topological charge, such as pairs of a Saturn ring and an anti-ring, hyperbolic and radial hedgehogs on a fiber, as well as zero-charge loops. We study the entanglement and topological charge interaction between the topological defects of the fiber and sphere and we observe a huge variety of different entanglement topologies and defect-mediated elastic bindings. We explain all observed phenomena with simple topological rule: like topological charges repel each other and opposite topological charges attract. These binding mechanisms not only demonstrate the fascinating topology of nematic colloids, but also open a novel route to the assembly of very complex topological networks of fibers, spheres and other objects for applications in liquid crystal photonics.

Stabilisation of 2D colloidal assemblies by polymerisation of liquid crystalline matrices for photonic applications

Colloidal crystals in anisotropic matrices are extremely stable and versatile, but disassemble as soon as the anisotropy of the matrix disappears. We present an approach to first custom-assemble colloidal structures and subsequently stabilize them through photo-polymerisation of the liquid crystalline matrix. The resulting 2D colloidal assemblies are stable at high temperatures and can even be obtained as free-standing films without a decrease in the degree of organization. This approach could be used to stabilize and extract recently proposed soft-matter photonic microcircuits based on liquid crystal optical microresonators, microlasers and microfibers, and opens up routes towards real soft matter photonic devices that are stable over extended time and temperatures.

Myelin structures formed by thermotropic smectic liquid crystals

We report on transient structures, formed by thermotropic smectic-A liquid crystals, resembling the myelin figures of lyotropic lamellar liquid crystals. The thermotropic myelin structures form during the solubilization of a smectic-A droplet in an aqueous phase containing a cationic surfactant at concentrations above the critical micelle concentration. Similar to the lyotropic myelin figures, the thermotropic myelins appear in an optical microscope as flexible tubelike structures growing at the smectic/aqueous interface. Polarizing microscopy and confocal fluorescence microscopy show that the smectic layers are parallel to the tube surface and form a cylindrically bent arrangement around a central line defect in the tube. We study the growth behavior of this new type of myelins and discuss similarities to and differences from the classical lyotropic myelin figures.