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The B7 phases of bent-core molecules are polarization splay modulated fluid smectics that exhibit an unusually complex variety of exotic macroscopic structures, textures, and defects visible in polarized light microscopy. Herein we describe optical studies of these structures using fluorescence confocal polarizing microscopy (FCPM) and depolarized transmission optical microscopy to probe their organization in three dimensions. These experiments utilize recently reported fluorescent bent-core molecules designed to give strong polarized fluorescence. This new bent-core molecular family provides the means for probing a variety of bent-core phases and structures by using FCPM and multiphoton fluorescence nonlinear imaging techniques. Comparative textural analysis of the B7 structures obtained using different types of imaging and the corresponding structural models are discussed., (© 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

We describe formation of defect-colloidal superstructures induced by microspheres with normal surface anchoring dispersed in chiral nematic liquid crystals in confinement-unwound homeotropic cells. Using three-dimensional nonlinear optical imaging of the director field, we demonstrate that some of the induced defects have nonsingular solitonic nature while others are singular point and line topological defects. The common director structures induced by individual microspheres have dipolar symmetry. These topological dipoles are formed by the particle and a hyperbolic point defect (or small disclination loop) of elementary hedgehog charge opposite to that of a sphere with perpendicular boundary conditions, which in cells with thickness over equilibrium cholesteric pitch ratio approaching unity are additionally interspaced by a looped double-twist cylinder of continuous director deformations. The long-range elastic interactions are probed by holographic optical tweezers and videomicroscopy, providing insights to the physical underpinnings behind self-assembled colloidal structures entangled by twisted solitons. Computer-simulated field and defect configurations induced by the colloidal particles and their assemblies, which are obtained by numerically minimizing the Landau-de Gennes free energy, are in agreement with the experimental findings.

Metastable configurations formed by defects, inclusions, elastic deformations and topological solitons in liquid crystals are a promising choice for building photonic crystals and metamaterials with a potential for new optical applications. Local optical modification of the director or introduction of colloidal inclusions into a moderately chiral nematic liquid crystal confined to a homeotropic cell creates localized multistable chiral solitons. Here we induce solitons that "dress" the dispersed spherical particles treated for tangential degenerate boundary conditions, and perform controlled switching of their state using focused optical beams. Two optically switchable distinct metastable states, toron and hopfion, bound to colloidal spheres into structures with different topological charges are investigated. Their structures are examined using Q-tensor based numerical simulations and compared to the profiles reconstructed from the experiments. A topological explanation of observed multistability is constructed.

Nematic and cholesteric liquid crystals are three-dimensional fluids that possess long-range orientational ordering and can support both topological defects and chiral superstructures. Implications of this ordering remain unexplored even for simple dynamic processes such as the ones found in so-called "fall experiments," or motion of a spherical inclusion under the effects of gravity. Here we show that elastic and surface anchoring interactions prompt periodic dynamics of colloidal microparticles in confined cholesterics when gravity acts along the helical axis. We explore elastic interactions between colloidal microparticles and confining surfaces as well as with an aligned ground-state helical structure of cholesterics for different sizes of spheres relative to the cholesteric pitch, demonstrating unexpected departures from Stokes-like behavior at very low Reynolds numbers. We characterize metastable localization of microspheres under the effects of elastic and surface anchoring periodic potential landscapes seen by moving spheres, demonstrating the important roles played by anchoring memory, confinement, and topological defect transformation. These experimental findings are consistent with the results of numerical modeling performed through minimizing the total free energy due to colloidal inclusions at different locations along the helical axis and with respect to the confining substrates. A potential application emerging from this work is colloidal sorting based on particle shapes and sizes.

Topologically nontrivial field excitations, including solitonic, linked, and knotted structures, play important roles in physical systems ranging from classical fluids and liquid crystals, to electromagnetism, classic, and quantum field theories. These excitations can appear spontaneously during symmetry-breaking phase transitions. For example, in cosmological theories, cosmic strings may have formed knotted configurations influencing the Early Universe development, whereas in liquid crystals transient tangled defect lines were observed during isotropic-nematic transitions, eventually relaxing to defect-free states. Knotted and solitonic fields and defects were also obtained using optical manipulation, complex-shaped colloids, and frustrated cholesterics. Here we use confinement of nematic liquid crystal by closed surfaces with varied genus and perpendicular boundary conditions for a robust control of appearance and stability of such field excitations. Theoretical modeling and experiments reveal structure of defect lines as a function of the surface topology and material and geometric parameters, establishing a robust means of controlling solitonic, knotted, linked, and other field excitations.

Nematic-like and helicoidally orientational self-assemblies of gold nanorods co-dispersed with cellulose nanocrystals to form liquid crystalline phases are developed. Polarization-sensitive extinction spectra and two-photon luminescence imaging are used to characterize orientations and spatial distributions of gold nanorods. Cholesteric-isotropic phase coexistence and continuous domains of single-phase regions are observed and qualitatively discussed on the basis of entropic and electrostatic interactions in co-dispersions of rigid rods of different aspect ratios. Potential applications include biologically compatible plasmonic composite nanomaterials for solar biofuel production and polarization-sensitive plasmonic papers and fabrics., (© 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

Unless stabilized by colloids or confinement with well-defined boundary conditions, defects in liquid crystals remain elusive short-lived objects that tend to disappear with time to minimize the medium's free energy. In this work we use multimodal three-dimensional imaging to visualize cholesteric director structures to show that self-assembled chiral molecular monolayer domains can stabilize topologically constrained defect configurations when in contact with a cholesteric liquid crystal. The cholesteric liquid crystal, having features of both coarse-grained lamellar and nematic liquid crystal with chiral symmetry breaking, allows us to explore the interplay of chirality and implications of layering on the formed defects and director configurations.

Particle shape and medium chirality are two key features recently used to control anisotropic colloidal self-assembly and dynamics in liquid crystals. Here, we study magnetically responsive gourd-shaped colloidal particles dispersed in cholesteric liquid crystals with periodicity comparable or smaller than the particle's dimensions. Using magnetic manipulation and optical tweezers, which allow one to position colloids near the confining walls, we measured the elastic repulsive interactions of these particles with confining surfaces and found that separation-dependent particle-wall interaction force is a non-monotonic function of separation and shows oscillatory behavior. We show that gourd-shaped particles in cholesterics reside not on a single sedimentation level, but on multiple long-lived metastable levels separated by a distance comparable to cholesteric periodicity. Finally, we demonstrate three-dimensional laser tweezers assisted assembly of gourd-shaped particles taking advantage of both orientational order and twist periodicity of cholesterics, potentially allowing new forms of orientationally and positionally ordered colloidal organization in these media.

Practical guest-host devices in which dichroic dye molecules follow electrical switching of a liquid crystal host remain elusive for decades despite promising efficient displays and emergent applications such as smart windows. This is mainly because of poor stability, surface precipitation, and limited means for property engineering of the dyes. To overcome these challenges, we develop plasmonic metal nanoparticle analogues of dichroic guest-host liquid crystals. Nematic dispersions of aligned anisotropic gold nanoparticles are obtained by polymer passivation of their surfaces to impose weak tangential boundary conditions for orientation of anisotropic host molecules. Control of the ensuing surface interactions leads to long-range ordered colloidal dispersions, allowing for collective optical and electrical switching of rod- and platelet-like nanoparticles. This facile control of mesostructured plasmonic medium's optical properties in visible and infrared spectral ranges is of interest for many applications.

We explore spatially localized solitonic configurations of a director field, generated using optical realignment and laser-induced heating, in frustrated chiral nematic liquid crystals confined between substrates with perpendicular surface anchoring. We demonstrate that, in addition to recently studied torons and Hopf-fibration solitonic structures (hopfions), one can generate a host of other axially symmetric stable and metastable director field configurations where local twist is matched to the surface boundary conditions through introduction of point defects and loops of singular and nonsingular disclinations. The experimentally demonstrated structures include the so-called "baby-skyrmions" in the form of double twist cylinders oriented perpendicular to the confining substrates where their double twist field configuration is matched to the perpendicular boundary conditions by loops of twist disclinations. We also generate complex textures with arbitrarily large skyrmion numbers. A simple back-of-the-envelope theoretical analysis based on free energy considerations and the nonpolar nature of chiral nematics provides insights into the long-term stability and diversity of these inter-related solitonic field configurations, including different types of torons, cholestric-finger loops, two-dimensional skyrmions, and more complex structures comprised of torons, hopfions, and various disclination loops that are experimentally observed in a confinement-frustrated chiral nematic system.

Colloidal crystals belong to a new class of materials with unusual properties in which the big challenge is to grow large-scale structures of a given symmetry in a well-controlled and inexpensive way. Recently, template-assisted crystallization was successfully exploited experimentally in the case of colloidal particles dispersed in isotropic fluids. In liquid crystal (LC) colloids, particles are subjected to long-range anisotropic elastic forces originating from the anisotropic deformation of the underlying order parameter. These effective interactions are easily tunable by external electric or magnetic fields, light, temperature, or confinement and, thus, provide additional handles for better control of colloidal assembly. Here we use the coupling between microsculptured bounding surfaces and LC elasticity in order to guide the self-assembly of large-scale colloidal structures. We present explicit numerical calculations of the free energy landscape of colloidal particles in the presence of convex protrusions modeled as squared pyramids comparable to the size of the particles. We show the existence of strong trapping potentials that are able to efficiently localize the colloidal particles and withstand thermal fluctuations. Three-dimensional optical imaging experiments support the theoretical predictions.

We describe dipolar nematic colloids comprising mutually bound solid microspheres, three-dimensional skyrmions, and point defects in a molecular alignment field of chiral nematic liquid crystals. Nonlinear optical imaging and numerical modeling based on minimization of Landau-de Gennes free energy reveal that the particle-induced skyrmions resemble torons and hopfions, while matching surface boundary conditions at the interfaces of liquid crystal and colloidal spheres. Laser tweezers and videomicroscopy reveal that the skyrmion-colloidal hybrids exhibit purely repulsive elastic pair interactions in the case of parallel dipoles and an unexpected reversal of interaction forces from repulsive to attractive as the center-to-center distance decreases for antiparallel dipoles. The ensuing elastic self-assembly gives rise to colloidal chains of antiparallel dipoles with particles entangled by skyrmions.

Surface plasmon polaritons (SPP) waves have been shown to significantly affect the near-field photophysical phenomenon. In particular, strong Coulombic interactions can enhance nearby non-linear optics and energy transfer process, while SPP waves also affect other photophysical processes like quenching observed in fluorescent and excitonic systems. Here, using different plasmonic substrates, we show the effect of plasmon-enhancement on quenching, phonon-assisted non-radiative decay, weak Purcell effect or electromagnetic field enhancement, and energy transfer rates of upconverting doped-lanthanide nanoparticles. While the resonant plasmons enhance the local electromagnetic field and the rate of energy transfer leading to enhanced upconversion photoluminescence of infrared radiation to visible light, it can also increase the quenching and non-radiative decay rates of photoexcited electron-hole pairs leading to losses and lower efficiency. These results can guide the design of optimized substrate geometry for using surface plasmons to modulate the photophysics in other applications too.

Polymer dispersed liquid crystals are a useful model system for studying the relationship between surface topology and defect structures. They are comprised of a polymer matrix with suspended spherical nematic drops and are topologically constrained to host defects of an elementary hedgehog charge per droplet, such as bulk or surface point defects or closed disclination loops. We control the genus of the closed surfaces confining such micrometer-sized nematic drops with tangential boundary conditions for molecular alignment imposed by the polymer matrix, allowing us to avoid defects or, on the contrary, to generate them in a controlled way. We show, both experimentally and through numerical modeling, that topological constraints in nematic microdrops can be satisfied by hosting topologically stable half-integer bulk defect lines anchored to opposite sides of handlebody surfaces. This enriches the interplay of topologies of closed surfaces and fields with nonpolar symmetry, yielding new unexpected configurations that cannot be realized in vector fields, having potential implications for topologically similar defects in cosmology and other fields.

We use both lyotropic liquid crystals composed of prolate micelles and thermotropic liquid crystals made of rod-like molecules to uniformly disperse and unidirectionally align relatively large gold nanorods and other complex-shaped nanoparticles at high concentrations. We show that some of these ensuing self-assembled orientationally ordered soft matter systems exhibit polarization-dependent plasmonic properties with strongly pronounced molar extinction exceeding that previously achieved in self-assembled composites. The long-range unidirectional alignment of gold nanorods is mediated mainly by anisotropic surface anchoring interactions at the surfaces of gold nanoparticles. Polarization-sensitive absorption, scattering, and extinction are used to characterize orientations of nanorods and other nanoparticles. The experimentally measured unique optical properties of these composites, which stem from the collective plasmonic effect of the gold nanorods with long-range order in a liquid crystal matrix, are reproduced in computer simulations. A simple phenomenological model based on anisotropic surface interaction explains the alignment of gold nanorods dispersed in liquid crystals and the physical underpinnings behind our observations.

Using liquid crystalline self-assembly of cellulose nanocrystals, we achieve long-range alignment of anisotropic metal nanoparticles in colloidal nanocrystal dispersions that are then used to deposit thin structured films with ordering features highly dependent on the deposition method. These hybrid films are comprised of gold nanorods unidirectionally aligned in a matrix that can be made of ordered cellulose nanocrystals or silica nanostructures obtained by using cellulose-based nanostructures as a replica. The ensuing long-range alignment of gold nanorods in both cellulose-based and nanoporous silica films results in a polarization-sensitive surface plasmon resonance. The demonstrated device-scale bulk nanoparticle alignment may enable engineering of new material properties arising from combining the orientational ordering of host nanostructures and properties of the anisotropic plasmonic metal nanoparticles. Our approach may also allow for scalable fabrication of plasmonic polarizers and nanoporous silica structures with orientationally ordered anisotropic plasmonic nanoinclusions.

Colloidal dispersions in liquid crystals can serve as a soft-matter toolkit for the self-assembly of composite materials with pre-engineered properties and structures that are highly dependent on particle-induced topological defects. Here, we demonstrate that bulk and surface defects in nematic fluids can be patterned by tuning the topology of colloidal particles dispersed in them. In particular, by taking advantage of two-photon photopolymerization techniques to make knot-shaped microparticles, we show that the interplay of the topologies of the knotted particles, the nematic field and the induced defects leads to knotted, linked and other topologically non-trivial field configurations. These structures match theoretical predictions made on the basis of the minimization of the elastic free energy and satisfy topological constraints. Our approach may find uses in self-assembled topological superstructures of knotted particles linked by nematic fields, in topological scaffolds supporting the decoration of defect networks with nanoparticles, and in modelling other physical systems exhibiting topologically analogous phenomena.

Despite the recent progress in physical control and manipulation of various condensed matter, atomic, and particle systems, including individual atoms and photons, our ability to control topological defects remains limited. Recently, controlled generation, spatial translation, and stretching of topological point and line defects have been achieved using laser tweezers and liquid crystals as model defect-hosting systems. However, many modes of manipulation remain hindered by limitations inherent to optical trapping. To overcome some of these limitations, we integrate holographic optical tweezers with a magnetic manipulation system, which enables fully holonomic manipulation of defects by means of optically and magnetically controllable colloids used as "handles" to transfer forces and torques to various liquid crystal defects. These colloidal handles are magnetically rotated around determined axes and are optically translated along three-dimensional pathways while mechanically attached to defects, which, combined with inducing spatially localized nematic-isotropic phase transitions, allow for geometrically unrestricted control of defects, including previously unrealized modes of noncontact manipulation, such as the twisting of disclination clusters. These manipulation capabilities may allow for probing topological constraints and the nature of defects in unprecedented ways, providing the foundation for a tabletop laboratory to expand our understanding of the role defects play in fields ranging from subatomic particle physics to early-universe cosmology.

Upconversion of infrared radiation into visible light has been investigated for applications in photovoltaics and biological imaging. However, low conversion efficiency due to small absorption cross-section for infrared light (Yb(3+)), and slow rate of energy transfer (to Er(3+) states) has prevented application of upconversion photoluminescence (UPL) for diffuse sunlight or imaging tissue samples. Here, we utilize resonant surface plasmon polaritons (SPP) waves to enhance UPL in doped-lanthanide nanocrystals. Our analysis indicates that SPP waves not only enhance the electromagnetic field, and hence weak Purcell effect, but also increase the rate of resonant energy transfer from Yb(3+) to Er(3+) ions by 6 fold. While we do observe strong metal mediated quenching (14-fold) of green fluorescence on flat metal surfaces, the nanostructured metal is resonant in the infrared and hence enhances the nanocrystal UPL. This strong Coulombic effect on energy transfer can have important implications for other fluorescent and excitonic systems too.

We study translational and rotational diffusion of anisotropic gold nanoparticles (NPs) dispersed in the bulk of a nematic liquid crystal fluid host. Experimental data reveal strong anisotropy of translational diffusion with respect to the uniform far-field director, which is dependent on shape and surface functionalization of colloids as well as on their ground-state alignment. For example, elongated NPs aligned parallel to the far-field director translationally diffuse more rapidly along the director whereas diffusion of NPs oriented normal to the director is faster in the direction perpendicular to it while they are also undergoing elasticity-constrained rotational diffusion. To understand physical origins of these rich diffusion properties of anisotropic nanocolloids in uniaxially anisotropic nematic fluid media, we compare them to diffusion of prolate and oblate ellipsoidal particles in isotropic fluids as well as to diffusion of shape-isotropic particles in nematic fluids. We also show that surface functionalization of NPs with photosensitive azobenzene groups allows for in situ control of their diffusivity through trans-cis isomerization that changes surface anchoring.

Layering is found and exploited in a variety of soft material systems, ranging from complex macromolecular self-assemblies to block copolymer and small-molecule liquid crystals. Because the control of layer structure is required for applications and characterization, and because defects reveal key features of the symmetries of layered phases, a variety of techniques have been developed for the study of soft-layer structure and defects, including X-ray diffraction and visualization using optical transmission and fluorescence confocal polarizing microscopy, atomic force microscopy, and SEM and transmission electron microscopy, including freeze-fracture transmission electron microscopy. Here, it is shown that thermal sublimation can be usefully combined with such techniques to enable visualization of the 3D structure of soft materials. Sequential sublimation removes material in a stepwise fashion, leaving a remnant layer structure largely unchanged and viewable using SEM, as demonstrated here using a lamellar smectic liquid crystal.

Films subsumed with topological defects are transformed into complex, topographical surface features with light irradiation of azobenzene-functionalized liquid crystal polymer networks (azo-LCNs). Using a specially designed optical setup and photoalignment materials, azo-LCN films containing either singular or multiple defects with strengths ranging from |½| to as much as |10| are examined. The local order of an azo-LCN material for a given defect strength dictates a complex, mechanical response observed as topographical surface features., (© 2013 WILEY-VCH Verlag GmbH 8 Co. KGaA, Weinheim.)

The Hopf fibration is an example of a texture: a topologically stable, smooth, global configuration of a field. Here we demonstrate the controlled sculpting of the Hopf fibration in nematic liquid crystals through the control of point defects. We demonstrate how these are related to torons by use of a topological visualization technique derived from the Pontryagin-Thom construction.

Topological defects that form on surfaces of ordered media, dubbed boojums, are ubiquitous in superfluids, liquid crystals (LCs), Langmuir monolayers, and Bose-Einstein condensates. They determine supercurrents in superfluids, impinge on electrooptical switching in polymer-dispersed LCs, and mediate chemical response at nematic-isotropic fluid interfaces, but the role of surface topology in the appearance, stability, and core structure of these defects remains poorly understood. Here, we demonstrate robust generation of boojums by controlling surface topology of colloidal particles that impose tangential boundary conditions for the alignment of LC molecules. To do this, we design handlebody-shaped polymer particles with different genus g. When introduced into a nematic LC, these particles distort the nematic molecular alignment field while obeying topological constraints and induce at least 2g - 2 boojums that allow for topological charge conservation. We characterize 3D textures of boojums using polarized nonlinear optical imaging of molecular alignment and explain our findings by invoking symmetry considerations and numerical modeling of experiment-matching director fields, order parameter variations, and nontrivial handle-shaped core structure of defects. Finally, we discuss how this interplay between the topologies of colloidal surfaces and boojums may lead to controlled self-assembly of colloidal particles in nematic and paranematic hosts, which, in turn, may enable reconfigurable topological composites.

We demonstrate an approach for background-free three-dimensional imaging of director fields in liquid crystals using stimulated Raman scattering microscopy. This imaging technique is implemented using a single femtosecond pulsed laser and a photonic crystal fiber, providing Stokes and pump frequencies needed to access Raman shifts of different chemical bonds of molecules and allowing for chemically selective and broadband imaging of both pristine liquid crystals and composite materials. Using examples of model three-dimensional structures of director fields, we show that the described technique is a powerful tool for mapping of long-range molecular orientation patterns in soft matter via polarized chemical-selective imaging.

Active elastomeric liquid crystal particles with initial cylindrical shapes are obtained by means of soft lithography and polymerization in a strong magnetic field. Gold nanocrystals infiltrated into these particles mediate energy transfer from laser light to heat, so that the inherent coupling between the temperature-dependent order and shape allows for dynamic morphing of these particles and well-controlled stable shapes. Continuous changes of particle shapes are followed by their spontaneous realignment and transformations of director structures in the surrounding cholesteric host, as well as locomotion in the case of a nonreciprocal shape morphing. These findings bridge the fields of liquid crystal solids and active colloids, may enable shape-controlled self-assembly of adaptive composites and light-driven micromachines, and can be understood by employing simple symmetry considerations along with electrostatic analogies.

Graphene recently emerged as a new two-dimensional material platform with unique optical, thermal and electronic properties. Single- or few-atom-thick graphene flakes can potentially be utilized to form structured bulk composites that further enrich these properties and enable a broad range of new applications. Here we describe optical manipulation of self-aligned colloidal graphene flakes in thermotropic liquid crystals of nematic and cholesteric types. Three-dimensional rotational and translational manipulation of graphene flakes by means of holographic optical tweezers allows for non-contact spatial patterning of graphene, control of liquid crystal defects, and low-power optical realignment of the liquid crystal director using these flakes. Potential applications include optically- and electrically-controlled reconfigurable liquid crystalline dispersions of spontaneously aligning colloidal graphene flakes and new electro-optic devices with graphene-based interconnected transparent electrodes at surfaces and in the bulk of liquid crystals.

Smoke, fog, jelly, paints, milk and shaving cream are common everyday examples of colloids, a type of soft matter consisting of tiny particles dispersed in chemically distinct host media. Being abundant in nature, colloids also find increasingly important applications in science and technology, ranging from direct probing of kinetics in crystals and glasses to fabrication of third-generation quantum-dot solar cells. Because naturally occurring colloids have a shape that is typically determined by minimization of interfacial tension (for example, during phase separation) or faceted crystal growth, their surfaces tend to have minimum-area spherical or topologically equivalent shapes such as prisms and irregular grains (all continuously deformable--homeomorphic--to spheres). Although toroidal DNA condensates and vesicles with different numbers of handles can exist and soft matter defects can be shaped as rings and knots, the role of particle topology in colloidal systems remains unexplored. Here we fabricate and study colloidal particles with different numbers of handles and genus g ranging from 1 to 5. When introduced into a nematic liquid crystal--a fluid made of rod-like molecules that spontaneously align along the so-called 'director'--these particles induce three-dimensional director fields and topological defects dictated by colloidal topology. Whereas electric fields, photothermal melting and laser tweezing cause transformations between configurations of particle-induced structures, three-dimensional nonlinear optical imaging reveals that topological charge is conserved and that the total charge of particle-induced defects always obeys predictions of the Gauss-Bonnet and Poincaré-Hopf index theorems. This allows us to establish and experimentally test the procedure for assignment and summation of topological charges in three-dimensional director fields. Our findings lay the groundwork for new applications of colloids and liquid crystals that range from topological memory devices, through new types of self-assembly, to the experimental study of low-dimensional topology.

We report a visible-range nonlinear photoluminescence (PL) from graphene oxide (GO) flakes excited by near-infrared femtosecond laser light. PL intensity has nonlinear dependence on the laser power, implying a multiphoton excitation process, and also strongly depends on a linear polarization orientation of excitation light, being at maximum when it is parallel to flakes. We show that PL can be used for a fully three-dimensional label-free imaging of isotropic, nematic, and lamellar liquid crystalline dispersions of GO flakes in water. This nonlinear PL is of interest for applications in direct label-free imaging of composite materials and study of orientational ordering in mesomorphic phases formed by these flakes, as well as in biomedical and sensing applications utilizing GO.

We describe a soft matter system of self-organized oblate micelles and plasmonic gold nanorods that exhibit a negative orientational order parameter. Because of anisotropic surface anchoring interactions, colloidal gold nanorods tend to align perpendicular to the director describing the average orientation of normals to the discoidal micelles. Helicoidal structures of highly concentrated nanorods with a negative order parameter are realized by adding a chiral additive and are further controlled by means of confinement and mechanical stress. Polarization-sensitive absorption, scattering, and two-photon luminescence are used to characterize orientations and spatial distributions of nanorods. Self-alignment and effective-medium optical properties of these hybrid inorganic-organic complex fluids match predictions of a simple model based on anisotropic surface anchoring interactions of nanorods with the structured host medium.

Condensed matter systems with topological defects in the ground states range from the Abrikosov phases in superconductors, to various blue phases and twist grain boundary phases in liquid crystals, and to phases of skyrmion lattices in chiral ferromagnets and Bose-Einstein condensates. In nematic and chiral nematic liquid crystals, which are true fluids with long-range orientational ordering of constituent molecules, point and line defects spontaneously occur as a result of symmetry-breaking phase transitions or due to flow, but they are unstable, hard to control, and typically annihilate with time. Here we describe the optical generation of two-dimensional crystalline, quasicrystalline, and arbitrary ensembles of particlelike structures manifesting both skyrmionlike and Hopf fibration features--dubbed "torons"--composed of looped double twist cylinders and point defects embedded in a uniform director field. In these two-dimensional lattices, we then introduce various dislocations, defects in positional ordering of the torons. We show that the periodic defect lattices with and without dislocation are light- and voltage-tunable reconfigurable two-dimensional diffraction gratings and can be used to generate various controlled phase singularities in the diffracted laser beams. The results of computer simulations of optical images, diffraction patterns, and phase distributions with optical vortices are in a good agreement with the corresponding experimental findings.

Colloidal systems find important applications ranging from fabrication of photonic crystals to direct probing of phenomena typically encountered in atomic crystals and glasses. New applications--such as nanoantennas, plasmonic sensors, and nanocircuits--pose a challenge of achieving sparse colloidal assemblies with tunable interparticle separations that can be controlled at will. We demonstrate reconfigurable multiscale interactions and assembly of colloids mediated by defects in cholesteric liquid crystals that are probed by means of laser manipulation and three-dimensional imaging. We find that colloids attract via distance-independent elastic interactions when pinned to the ends of cholesteric oily streaks, line defects at which one or more layers are interrupted. However, dislocations and oily streaks can also be optically manipulated to induce kinks, allowing one to lock them into the desired configurations that are stabilized by elastic energy barriers for structural transformation of the particle-connecting defects. Under the influence of elastic energy landscape due to these defects, sublamellar-sized colloids self-assemble into structures mimicking the cores of dislocations and oily streaks. Interactions between these defect-embedded colloids can be varied from attractive to repulsive by optically introducing dislocation kinks. The reconfigurable nature of defect-particle interactions allows for patterning of defects by manipulation of colloids and, in turn, patterning of particles by these defects, thus achieving desired colloidal configurations on scales ranging from the size of defect core to the sample size. This defect-colloidal sculpturing may be extended to other lamellar media, providing the means for optically guided self-assembly of mesoscopic composites with predesigned properties.

Stable optical trapping and manipulation of high-index particles in low-index host media is often impossible due to the dominance of scattering forces over gradient forces. Here we explore optical manipulation in liquid crystalline structured hosts and show that robust optical manipulation of high-index particles, such as GaN nanowires, is enabled by laser-induced distortions in long-range molecular alignment, via coupling of translational and rotational motions due to helicoidal molecular arrangement, or due to elastic repulsive interactions with confining substrates. Anisotropy of the viscoelastic liquid crystal medium and particle shape give rise to a number of robust unconventional trapping capabilities, which we use to characterize defect structures and study rheological properties of various thermotropic liquid crystals.

We describe laser-induced two-dimensional periodic photonic structures formed by localized particle-like excitations in an untwisted confined cholesteric liquid crystal. The individual particle-like excitations (dubbed "Torons") contain three-dimensional twist of the liquid crystal director matched to the uniform background director field by topological point defects. Using both single-beam-steering and holographic pattern generation approaches, the periodic crystal lattices are tailored by tuning their periodicity, reorienting their crystallographic axes, and introducing defects. Moreover, these lattices can be dynamically reconfigurable: generated, modified, erased and then recreated, depending on the needs of a particular photonic application. This robust control is performed by tightly focused laser beams of power 10-100 mW and by low-frequency electric fields at voltages ~10 V applied to the transparent electrodes.

We demonstrate scaffolding of plasmonic nanoparticles by topological defects induced by colloidal microspheres to match their surface boundary conditions with a uniform far-field alignment in a liquid crystal host. Displacing energetically costly liquid crystal regions of reduced order, anisotropic nanoparticles with concave or convex shapes not only stably localize in defects but also self-orient with respect to the microsphere surface. Using laser tweezers, we manipulate the ensuing nanoparticle-microsphere colloidal dimers, probing the strength of elastic binding and demonstrating self-assembly of hierarchical colloidal superstructures such as chains and arrays., (© 2012 American Chemical Society)

Topological defect lines are ubiquitous and important in a wide variety of fascinating phenomena and theories in many fields ranging from materials science to early-universe cosmology, and to engineering of laser beams. However, they are typically hard to control in a reliable manner. Here we describe facile erasable "optical drawing" of self-assembled defect clusters in liquid crystals. These quadrupolar defect clusters, stabilized by the medium's chirality and the tendency to form twisted configurations, are shaped into arbitrary two-dimensional patterns, including reconfigurable phase gratings capable of generating and controlling optical phase singularities in laser beams. Our findings bridge the studies of defects in condensed matter physics and optics and may enable applications in data storage, singular optics, displays, electro-optic devices, diffraction gratings, as well as in both optically- and electrically-addressed pixel-free spatial light modulators.

Noncontact optical trapping and manipulation of micrometer- and nanometer-sized particles are typically achieved by use of forces and torques exerted by tightly focused high-intensity laser beams. Although they were instrumental for many scientific breakthroughs, these approaches find few technological applications mainly because of the small-area manipulation capabilities, the need for using high laser powers, limited application to anisotropic fluids and low-refractive-index particles, as well as complexity of implementation. To overcome these limitations, recent research efforts have been directed toward extending the scope of noncontact optical control through the use of optically-guided electrokinetic forces, vortex laser beams, plasmonics, and optofluidics. Here we demonstrate manipulation of colloidal particles and self-assembled structures in nematic liquid crystals by means of single-molecule-thick, light-controlled surface monolayers. Using polarized light of intensity from 1,000 to 100,000 times smaller than that in conventional optical tweezers, we rotate, translate, localize, and assemble spherical and complex-shaped particles of various sizes and compositions. By controlling boundary conditions through the monolayer, we manipulate the liquid crystal director field and the landscape of ensuing elastic forces exerted on colloids by the host medium. This permits the centimeter-scale, massively parallel manipulation of particles and complex colloidal structures that can be dynamically controlled by changing illumination or assembled into stationary stable configurations dictated by the "memorized" optoelastic potential landscape due to the last illumination pattern. We characterize the strength of optically guided elastic forces and discuss the potential uses of this noncontact manipulation in fabrication of novel optically- and electrically-tunable composites from liquid crystals and colloids.

We describe a simple microrheology method to measure the viscosity coefficients of lyotropic liquid crystals. This approach is based on the use of a rotating laser-trapped optically anisotropic microsphere. In aligned liquid crystals that have negligible effect on trapping beam's polarization, the optical torque is transferred from circularly polarized laser trapping beam to the optically anisotropic microparticle and creates the shear flow in the liquid crystalline fluid. The balance of optical and viscous torques yields the local effective viscosity coefficients of the studied lyotropic systems in cholesteric and lamellar phases. This simple yet powerful method is capable of probing viscosity of complex anisotropic fluids for small amounts of sample and even in the presence of defects that obstruct the use of conventional rheology techniques.

We use Langmuir-Blodgett molecular monolayers and nematic liquid crystals as model two- and three-dimensional orientationally ordered systems to study the stability and healing of topological defects at their contact interfaces. Integer-strength defects at the monolayer induce disclinations of similar strength in the nematic that, however, do not propagate deep into the bulk, but rather form single- or double-split arch-shaped loops pinned to the interface. This behavior is qualitatively independent of the far-field director orientation and involves either half-integer singular or twist-escaped unity-strength nonsingular nematic disclinations. These two defect configurations can be selected by varying sample preparation given their comparable free energy, consistently with direct probing by use of laser tweezers., (© 2011 American Physical Society)

We demonstrate optical trapping and orientational control over colloidal particles having complex shapes in an anisotropic host fluid using a dynamic holographic optical tweezers system. Interactions between a colloidal particle and the toroidal intensity distributions of focused Laguerre-Gaussian beams allow for stable optical tweezing and provide a tunable tilt of the particle out of the focal plane. Use of an aligned nematic liquid crystal as the host fluid suppresses rotations about the optical axis arising from angular momentum transfer from the beam and effectively defines a rotational axis for the colloid within the trap.

We report a simple and versatile technique for oriented assembly of gold nanorods on aligned single-walled carbon nanotube (SWNT) macrostructures, such as thin nanotube films and nanotube fibers. The deposition and assembly is accomplished via drop drying of dilute gold nanorod suspensions on SWNT macrostructures under ambient conditions. Guided by anisotropic interactions, gold nanorods, and polygonal platelets spontaneously align with SWNTs, resulting in macroscopic arrays of locally ordered nanorods supported on aligned SWNT substrates. SEM reveals that the scalar order parameter of rods relative to the local average SWNT alignment is 0.7 for rods on SWNT films and 0.9 for rods on SWNT fibers. This self-alignment is enabled by anisotropic gold nanoparticle-SWNT interactions and is observed for a wide range of nanoparticles, including nanorods with aspect ratios ranging from 2-35, thin gold triangular and other polygonal platelets. The plasmonic properties of aligned gold nanorods together with superior electronic, chemical and mechanical properties of SWNTs make these hybrid nanocomposites valuable for the design of self-assembled multifunctional optoelectronic materials and optical metamaterials.

We report alignment of anisotropic amphiphilic dye molecules within oblate and prolate anisotropic micelles and lamellae, the basic building blocks of surfactant-based lyotropic liquid crystals. Absorption and fluorescence transition dipole moments of these dye molecules orient either parallel or orthogonal to the liquid crystal director. This alignment enables three-dimensional visualization of director structures and defects in different lyotropic mesophases by means of fluorescence confocal polarizing microscopy and two-photon excitation fluorescence polarizing microscopy. The studied structures include nematic tactoids, Schlieren texture with disclinations in the calamitic nematic phase, oily streaks in the lamellar phase, developable domains in the columnar hexagonal phase, and various types of line defects in the discotic cholesteric phase. Orientational three-dimensional imaging of structures in the lyotropic cholesterics reveals large Burgers vector dislocations in cholesteric layering with singular disclinations in the dislocation cores that are not common for their thermotropic counterparts., (© 2011 American Chemical Society)

We demonstrate an integrated holographic optical tweezers system with double-helix point spread function (DH-PSF) imaging for high precision three-dimensional multi-particle tracking. The tweezers system allows for the creation and control of multiple optical traps in three-dimensions, while the DH-PSF allows for high precision, 3D, multiple-particle tracking in a wide field. The integrated system is suitable for particles emitting/scattering either coherent or incoherent light and is easily adaptable to existing holographic tweezers systems. We demonstrate simultaneous tracking of multiple micro-manipulated particles and perform quantitative estimation of the lateral and axial forces in an optical trap by measuring the fluid drag force exerted on the particles. The system is thus capable of unveiling complex 3D force landscapes that make it suitable for quantitative studies of interactions in colloidal systems, biological materials, and a variety of soft matter systems.

We explore the effects of nanoscale morphology of supporting solid substrates on alignment, defects, and director structures exhibited by thin films of triphenylamine-based discotic liquid crystals. Fluorescence confocal polarizing microscopy and intrinsic polarized fluorescence properties of studied molecules are used to visualize three-dimensional director fields in the liquid crystal films. We demonstrate that, by controlling surface anchoring on supporting or confining solid substrates such as those of carbon nanotube electrodes on glass plates, both uniform homeotropic and in-plane (edge-on) alignment and nonuniform structures with developable domains can be achieved for the same discotic liquid crystal material.

We develop an integrated system of holographic optical trapping and multimodal nonlinear microscopy and perform simultaneous three-dimensional optical manipulation and non-invasive structural imaging of composite soft-matter systems. We combine different nonlinear microscopy techniques such as coherent anti-Stokes Raman scattering, multi-photon excitation fluorescence and multi-harmonic generation, and use them for visualization of long-range molecular order in soft materials by means of their polarized excitation and detection. The combined system enables us to accomplish manipulation in composite soft materials such as colloidal inclusions in liquid crystals as well as imaging of each separate constituents of the composite material in different nonlinear optical modalities. We also demonstrate optical generation and control of topological defects and simultaneous reconstruction of their three-dimensional long-range molecular orientational patterns from the nonlinear optical images.

Recently, the topographic patterning of surfaces by lithography and nanoimprinting has emerged as a new and powerful tool for producing single structural domains of liquid crystals and other soft materials. Here the use of surface topography is extended to the organization of liquid crystals of bent-core molecules, soft materials that, on the one hand, exhibit a rich, exciting, and intensely studied array of novel phases, but that, on the other hand, have proved very difficult to align. Among the most notorious in this regard are the polarization splay modulated (B7) phases, in which the symmetry-required preference for ferroelectric polarization to be locally bouquet-like or "splayed" is expressed. Filling space with splay of a single sign requires defects and in the B7 splay is accommodated in the form of periodic splay stripes spaced by defects and coupled to smectic layer undulations. Upon cooling from the isotropic phase this structure grows via a first order transition in the form of an exotic array of twisted filaments and focal conic defects that are influenced very little by classic alignment methods. By contrast, growth under conditions of confinement in rectangular topographic channels is found to produce completely new growth morphology, generating highly ordered periodic layering patterns. The resulting macroscopic order will be of great use in further exploration of the physical properties of bent-core phases and offers a route for application of difficult-to-align soft materials as are encountered in organic electronic and optical applications.

We describe field-induced multiaxis rotations of colloids in a nematic liquid crystal. Anchoring of the nematic director to the colloidal platelet's surface and interplay of dielectric and elastic energies enable robust control over colloid orientation that cannot be achieved in isotropic liquids. Because of the anisotropy of the fluid and the platelike shape of particles, the colloids can be forced to rotate about four different rotational axes even for a fixed direction of the applied field. The time scale of these unexpected voltage-dependent dynamics varies over four orders of magnitude (10⁻²-10²  s) and promises a number of novel electro-optic, photonic, and display applications.

We demonstrate orientation-sensitive multimodal nonlinear optical polarizing microscopy capable of probing orientational, polar, and biaxial features of mesomorphic ordering in soft matter. This technique achieves simultaneous imaging in broadband coherent anti-Stokes Raman scattering, multiphoton excitation fluorescence, and multiharmonic generation polarizing microscopy modes and is based on the use of a single femtosecond laser and a photonic crystal fiber as sources of the probing light. We show the viability of this technique for mapping of three-dimensional patterns of molecular orientations and show that images obtained in different microscopy modes are consistent with each other.