Light-driven dynamic Archimedes spirals and periodic oscillatory patterns of topological solitons in anisotropic soft matter

Active transformations of topological structures in light-driven nematic disclination networks

SignificanceTopological defects are marvels of nature. Understanding their structures is important for their applications in, for example, directed self-assembly, sensing, and photonic devices. There is recent interest in active motion and transformation of topological defects in active nematics. In these nonequilibrium systems, however, the motion and transformation of disclinations are difficult to control, thereby hindering their applications. Here, we propose a surface-patterned system engendering periodic three-dimensional disclinations, which can be excited by light irradiation and undergo a programmable transformation between different topological states. Continuum simulations recapitulating these topological structures characterize the bending, breaking, and relinking events of the disclinations during the nonequilibrium process. Our work provides an alternative dynamic system in which active transformation of topological defects can be engineered.

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.

Multiple minimum-energy paths and scenarios of unwinding transitions in chiral nematic liquid crystals

We apply the minimum-energy paths (MEPs) approach to study the helix unwinding transition in chiral nematic liquid crystals. A mechanism of the transition is determined by a MEP passing through a first order saddle point on the free energy surface. The energy difference between the saddle point and the initial state gives the energy barrier of the transition. Two starting approximations for the paths are used to find the MEPs representing different transition scenarios: (a) the director slippage approximation with in-plane helical structures and (b) the anchoring breaking approximation that involves the structures with profound out-of-plane director deviations. It is shown that, at sufficiently low voltages, the unwinding transition is solely governed by the director slippage mechanism with the planar saddle-point structures. When the applied voltage exceeds its critical value below the threshold of the Fréedericksz transition, the additional scenario through the anchoring breaking transitions is found to come into play. For these transitions, the saddle-point structure is characterized by out-of-plane deformations localized near the bounding surface. The energy barriers for different paths of transitions are computed as a function of the voltage and the anchoring energy strengths.

Near-field imaging of surface-plasmon vortex-modes around a single elliptical nanohole in a gold film

We present scanning near-field images of surface plasmon modes around a single elliptical nanohole in 88 nm thick Au film. We find that rotating surface plasmon vortex modes carrying extrinsic orbital angular momentum can be induced under linearly polarized illumination. The vortex modes are obtained only when the incident polarization direction differs from one of the ellipse axes. Such a direct observation of the vortex modes is possible thanks to the ability of the SNOM technique to obtain information on both the amplitude and the phase of the near-field. The presence of the vortex mode is determined by the rotational symmetry breaking of the system. Finite element method calculations show that such a vorticity originates from the presence of nodal points where the phase of the field is undefined, leading to a circulation of the energy flow. The configuration producing vortex modes corresponds to a nonzero total topological charge (+1).

Effect of dynamically changing the substrate's easy axis on the response time of nematic samples

Recent discoveries of advanced photocontrolled materials have kindled a great deal of interest on their use as command surfaces that switch easy axis under light radiation. One noticeable point when using switchable surfaces on any application is how the dynamical process propagates to the bulk directors. In this paper, we theoretically study the effect of a relaxing easy axis over time on a nematic sample when finite anchoring energy and surface viscosity are included. We first consider the case where just one of the substrates decay over time in an initially distorted director organization. Next, we assume that both substrates can be switched simultaneously. From the calculated director we obtained the optical profile and finally the molecular response time of the material. The response time depends on both the materials and the surfaces properties including its decay time. Our results might be used for understanding and engineering liquid crystal displays and other electro-optical devices with photocontrolled alignment layers.

Self-assembled nematic colloidal motors powered by light

Biological motors are marvels of nature that inspire creation of their synthetic counterparts with comparable nanoscale dimensions, high efficiency and diverse functions. Molecular motors have been synthesized, but obtaining nanomotors through self-assembly remains challenging. Here we describe a self-assembled colloidal motor with a repetitive light-driven rotation of transparent micro-particles immersed in a liquid crystal and powered by a continuous exposure to unstructured ~1 nW light. A monolayer of azobenzene molecules defines how the liquid crystal's optical axis mechanically couples to the particle's surface, as well as how they jointly rotate as the light's polarization changes. The rotating particle twists the liquid crystal, which changes polarization of traversing light. The resulting feedback mechanism yields a continuous opto-mechanical cycle and drives the unidirectional particle spinning, with handedness and frequency robustly controlled by polarization and intensity of light. Our findings may lead to opto-mechanical devices and colloidal machines compatible with liquid crystal display technology.

Revolving supramolecular chiral structures powered by light in nanomotor-doped liquid crystals

Molecular machines operated by light have been recently shown to be able to produce oriented motion at the molecular scale^1,2 as well as do macroscopic work when embedded in supramolecular structures^3-5. However, any supramolecular movement irremediably ceases as soon as the concentration of the interconverting molecular motors or switches reaches a photo-stationary state^6,7. To circumvent this limitation, researchers have typically relied on establishing oscillating illumination conditions-either by modulating the source intensity^8,9 or by using bespoke illumination arrangements^10-13. In contrast, here we report a supramolecular system in which the emergence of oscillating patterns is encoded at the molecular level. Our system comprises chiral liquid crystal structures that revolve continuously when illuminated, under the action of embedded light-driven molecular motors. The rotation at the supramolecular level is sustained by the diffusion of the motors away from a localized illumination area. Above a critical irradiation power, we observe a spontaneous symmetry breaking that dictates the directionality of the supramolecular rotation. The interplay between the twist of the supramolecular structure and the diffusion ¹⁴ of the chiral molecular motors creates continuous, regular and unidirectional rotation of the liquid crystal structure under non-equilibrium conditions.

Surface induced twist in nematic and chiral nematic liquid crystals: stick-slip-like and constrained motion

Surface driven pattern formation is an intriguing phenomenon in the liquid crystal field. Owing to its ability to transmit torque, one can generate different patterns by propagating distortions on the optical wavelength scale in the sample from the surface. Here, we theoretically investigate (from the elasticity point of view) twist deformations induced by a rotating easy axis at one surface, by considering the anchoring energy and surface viscosity of nematic and chiral nematic samples. The model is solved analytically in the limit of strong anchoring and numerically for a low anchoring strength situation. Such rotation could be induced, in principle, by light-controlling the orientation of an azobenzene monolayer coated at one of the glass substrates or by an in-plane rotating field. We discuss the role of the surface parameters and the different distortions, and calculate light transmission using the Jones method. Three different regimes are identified: free twist, stick-slip twist, and constrained twist. The results obtained here may be relevant for liquid crystal active waveplates and for determining surface viscosity and the azimuthal anchoring energy.

Making waves in a photoactive polymer film

Oscillating materials1–4 that adapt their shape in response to an external stimulus are of interest for emerging applications in medicine and robotics. Liquid crystal networks have a prominent role in this area because they can be programmed to undergo stimulus-induced deformations in a variety of geometries, including in response to light5,6. In order to make these polymer networks photoresponsive, azobenzene molecules are often incorporated7–11. Most examples in the literature report on bending responses of these azobenzene modified films, where relaxation after photo-isomerization is rather slow. Modification of the core or addition of substituents to the azobenzene moiety can lead to drastic changes in photophysical and photochemical properties12–15 giving opportunity to circumvent the use of a complex set-up. Here we report on the incorporation of azo-derivatives with fast thermal relaxation into liquid crystal network films (LCN), to generate films that can exhibit continuous, directional macroscopic mechanical waves under constant light illumination, with a feedback loop driven by self-shadowing. A theoretical model and numerical simulation demonstrate this mechanism and show good qualitative agreement with experiments. We explore potential applications in light-driven locomotion and self-cleaning surfaces.

Squirming motion of baby skyrmions in nematic fluids

Skyrmions are topologically protected continuous field configurations that cannot be smoothly transformed to a uniform state. They behave like particles and give origins to the field of skyrmionics that promises racetrack memory and other technological applications. Unraveling the non-equilibrium behavior of such topological solitons is a challenge. We realize skyrmions in a chiral liquid crystal and, using numerical modeling and polarized video microscopy, demonstrate electrically driven squirming motion. We reveal the intricate details of non-equilibrium topology-preserving textural changes driving this behavior. Direction of the skyrmion’s motion is robustly controlled in a plane orthogonal to the applied field and can be reversed by varying frequency. Our findings may spur a paradigm of soliton dynamics in soft matter, with a rich interplay between topology, chirality, and orientational viscoelasticity.

A skyrmion is a topological object originally introduced to model elementary particles and a baby skyrmion is its two-dimensional counterpart which can be realized as a defect in liquid crystals. Here the authors show that an electric field can drive uniform motion of baby skyrmions in liquid crystals.

Polymorphic beams and Nature inspired circuits for optical current

Laser radiation pressure is a basis of numerous applications in science and technology such as atom cooling, particle manipulation, material processing, etc. This light force for the case of scalar beams is proportional to the intensity-weighted wavevector known as optical current. The ability to design the optical current according to the considered application brings new promising perspectives to exploit the radiation pressure. However, this is a challenging problem because it often requires confinement of the optical current within tight light curves (circuits) and adapting its local value for a particular task. Here, we present a formalism to handle this problem including its experimental demonstration. It consists of a Nature-inspired circuit shaping with independent control of the optical current provided by a new kind of beam referred to as polymorphic beam. This finding is highly relevant to diverse optical technologies and can be easily extended to electron and x-ray coherent beams.

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.