Slobodan Zumer

University of Ljubljana · Department of Physics

Geometric phase optical elements made of space-variant anisotropic media customarily find their optimal operating conditions when a half-wave retardance condition is fulfilled, which allows imparting polarization-dependent changes to an incident wavefront. In practice, intrinsic limitations of a man-made manufacturing process or a finite spectrum o...

Geometric phase optical elements made of space-variant anisotropic media customarily find their optimal operating conditions when the half-wave retardance condition is fulfilled, which allows imparting polarization-dependent changes to an incident wavefront. In practice, intrinsic limitations of man-made manufacturing process or the finite spectrum...

Cover image provided courtesy of Andriy Nych, Institute of Physics, National Academy of Sciences of Ukraine (Kyiv, Ukraine) and J. Stefan Institute (Ljubljana, Slovenia).

Solitons attract a great deal of interest in many fields, ranging from optics to fluid mechanics, cosmology, particle physics and condensed matter. However, solitons of these very different types rarely coexist and interact with each other. Here we develop a system that hosts optical solitons coexisting with topological solitonic structures localiz...

Liquid crystals have intrigued physicists as a platform that facilitates direct visualization of topological concepts. Here, the theoretical and experimental studies demonstrating that a thin film of a chiral liquid crystal forms topological entities known as half-Skyrmions, swirl-like orientational order that spans the hemisphere of the order para...

In this brief review, we give an introduction to selected colloidal and microfluidic nematic microstructures, as enabled by the inherent anisotropy and microscopic orientational ordering in complex liquid crystalline materials. We give a brief overview of the mesoscopic theory, for equilibrium and dynamics, of nematic fluids, that provides the fram...

We investigate numerically the lattice orientation of cholesteric blue phases in contact with surfaces enforcing unidirectional planar anchoring. Our study is based on the Landau-de Gennes continuum theory in which the orientational order of the liquid crystal is described by a second-rank tensor. We particularly focus on blue phase I (BP I) with i...

In practically all branches of physics, different types of solitons, with a number of them enjoying topological protection, are found. Here we explore how one- and two-dimensional topological solitons formed by spatially localized continuous orientational patterns of optical axis in uniaxial birefringent media interact with light. These solitons, i...

We experimentally and numerically show that chirality can play a major role in the nonlinear optical response of soft birefringent materials, by studying the nonlinear propagation of laser beams in frustrated cholesteric liquid crystal samples. Such beams exhibit a periodic nonlinear response associated with a bouncing pattern for the optical field...

We present a unified theoretical framework for paraxial and wide-angle beam propagation methods in inhomogeneous birefringent media based on a minimal set of physical assumptions. The advantage of our schemes is that they are based on differential operators with a clear physical interpretation and easy numerical implementation based on sparse matri...

Structural vivid colours can arise from the interference of light reflected from structures exhibiting periodicity on scales in the range of visible wavelengths. This effect is observed with light reflected from cell-walls of some plants and exoskeletons of certain insects. Sometimes the colour sequence observed for these structures consists of nea...

We report on the effect of reduced-graphene oxide nanosheets decorated by CoPt nanoparticles on the blue phase range of a chiral liquid crystal. By means of high-resolution ac calorimetry and polarizing optical microscopy, it is demonstrated that a small concentration of these nanosheets induces the stabilization of a single blue phase structure in...

Photonic crystals with optical bandgaps across the entire visible spectrum are generated by reconfiguring three-dimensional blue phase liquid crystalline lattices into long-lived metastable non-cubic structures using sequences of electric pulses.

Active nematics contain topological defects that (under sufficient activity) move, create, and annihilate in a chaotic quasi-steady state, called active turbulence. However, understanding active defects under confinement is an open challenge, especially in three dimensions. Here, we demonstrate the topology of three-dimensional active nematic turbu...

Active nematics contain topological defects which under sufficient activity move, create and annihilate in a chaotic quasi-steady state, called active turbulence. However, understanding active defects under confinement is an open challenge, especially in three-dimensions. Here, we demonstrate the topology of three-dimensional active nematic turbule...

Significance Microfibers existing in the tracheary systems of plants are crucial for the plants to survive. These microfilaments are curled up, forming left-handed helices that make the contour of tubes responsible for the transport of water and nutrients from the roots to the leaves. The microfilaments present mechanical properties that vary from...

We propose an efficient method to simulate light propagation in lossless and non-scattering uniaxial birefringent media, based on a standard ray-tracing technique supplemented by a newly-derived transport equation for the electric field amplitude along a ray and a tailored interpolation algorithm for the reconstruction of the electromagnetic fields...

Almost half a century ago, it was predicted that the confinement of quantum fluctuations could induce mechanical rotation — the Casimir torque. This prediction has now been confirmed using liquid crystals. Experimental evidence for the Casimir torque.

Skyrmions are swirl-like topological entities that have been shown to emerge in various condensed matter systems. Their identification has been carried out in different ways including scattering techniques and real-space observations. Here we show that Kossel diagrams can identify the formation of a hexagonal lattice of half-Skyrmions in a thin fil...

Liquid crystalline blue phase (BP) II sandwiched between a pair of confining surfaces with specifically designed patterns is studied using numerical simulation based on the Landau-de Gennes phenomenological approach. Directed by the surface patterns, quasi-two-dimensional half-Skyrmion lattices form. Specifically, we observe the formation of square...

Quasicrystalline ordering was first observed in synthetic multi-component metallic alloys. These solid state materials exhibit quasicrystalline atomic ordering at nanometer length scales. Softmatter systems are another class of versatile materials that can exhibit quasicrystalline ordering across supra-nanometer (>10 nm) to supra-micrometer (>10 μm...

We investigate numerically the optical properties of a hexagonal half-Skyrmion lattice exhibited by a highly chiral liquid crystal confined between two parallel plates. Our study focuses on the near and far-field reflection for normally incident light with di erent polarizations. We show that, when the wavelength of the incident light is longer tha...

Skyrmions are coreless vortex-like excitations emerging in diverse condensed-matter systems, and real-time observation of their dynamics is still challenging. Here we report the first direct optical observation of the spontaneous formation of half-skyrmions. In a thin film of a chiral liquid crystal, depending on experimental conditions including f...

We explore equilibrium structures and flow-driven deformations of nematic liquid crystals confined to 3D junctions of cylindrical micropores with homeotropic surface anchoring. The topological state of the nematic ordering field in such basic unit of porous networks is controlled by nematic orientation profiles in individual pores, anchoring frustr...

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 p...

We present a simple method for simulating optical polarised micrographs of director fields in optically birefringent structures. Jones matrix method is applied for simulating polarised micrographs with focusing optics that can sufficiently account for different focusing distances and numerical apertures (NAs) in the polarised microscopy, which are...

Three selected approaches for manipulation of light by complex nematic colloidal and non-colloidal structures are presented using different own custom developed theoretical and modelling approaches. Photonic crystals bands of distorted cholesteric liquid crystal helix and of nematic colloidal opals are presented, also revealing distinct photonic mo...

Microfibers with their elongated shape and translation symmetry can act as important components in various soft materials, notably for their mechanics on the microscopic level. Here we demonstrate the mechanical response of a micro-object to imposed chirality, in this case, the tilt of disclination rings in an achiral nematic medium caused by the c...

Significance Biological microfibers are remarkable materials with diverse structural and mechanical properties, such as high wear-resistance, elasticity, and biodegradability. However, with current techniques, there are few robust ways to sense the surface properties of the fibers, which crucially affect the organization of the fibers and their int...

Geometrical constrains and intrinsic chirality in nematic mesophases enable formation of stable and metastable complex defect structures. Recently selected knotted and linked disclinations have been formed using laser manipulation of nematic braids entangling colloidal particles in nematic colloids [Tkalec et al., Science 2011; Copar et al., PNAS 2...

Birefringent structures in liquid crystalline fluids, such as colloidal assemblies or topological defects, show high potential for use as photonic elements. Here, we present a brief overview of two photonic phenomena originating from coupling light fields with complex birefringent nematic profiles: (i) the generation of vector laser beams from simp...

We show that nematic colloids can serve as a highly variable and controllable platform for studying inclusions with changeable topology and their effects on the surrounding ordering fields. We explore morphing of toroidal and knotted colloidal particles into effective spheres, distinctively changing their Euler characteristic and affecting the surr...

This paper presents a 3D mesh adaptivity strategy on unstructured tetrahedral meshes by a posteriori error estimates based on metrics, studied on the case of a nonlinear finite element minimization scheme for the Landau-de Gennes free energy functional of nematic liquid crystals. Newton's iteration for tensor fields is employed with steepest descen...

Liquid crystals are starting to attract attention for applications beyond the display technology. Their high birefringence, softness, and possibility to form complex topological defect structures allow for easy light manipulation in systems ranging from cholesteric lasers to droplet resonators and wave guides. Recent interest in light-induced topol...

Significance Knot theory is a branch of topology that deals with study and classification of closed loops in 3D Euclidean space. Creation and control of knots in physical systems is the pinnacle of technical expertise, pushing forward state-of-the-art experimental approaches as well as theoretical understanding of topology in selected medium. We sh...

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 natu...

Creating, imaging, and transforming the topological charge(1,2) in a superconductor(3), a superfluid(4,5), a system of cold atoms', or a soft ferromagnet(7-9) is a difficult-if not impossible-task because of the shortness of the length scales and lack of control. The length scale and softness of defects in liquid crystals allow the easy observation...

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 n...

Lattice-based Monte Carlo simulations are performed to study a confined liquid crystal system with a topological disclination line entangling a colloidal nanoparticle. In our microscopic study the disclination line is stretched by moving the colloid, as in laser tweezing experiments, which results in a restoring force attempting to minimize the dis...

We report that guiding light beams, ranging from continuous beams to femtosecond pulses, along liquid crystal defect lines can transform them into vector beams with various polarization profiles. Using Finite Difference Time Domain numerical solving of Maxwell equations, we confirm that the defect in the orientational order of the liquid crystal in...

Modeling and experiments on nematic ordering in geometrically frustrated nematic and chiral nematic systems reveals diverse birefringent micro and sub-micro structures, including knotted and linked nematic braids, skyrmions, torons, and hopfions. Here, these complex defect structures are used to illustrate simulations of optical images and visualiz...

We demonstrate that high anisotropy of elastic constants of chromonic liquid crystals leads to a number of spontaneously twisted nematic director fields around colloidal particles in these non-chiral fluids. For spherical colloidal particles with surface inducing degenerate planar nematic ordering we observe that boojum defects at the particles' po...

Generalized Janus nematic colloids based on various morphologies of particle surface patches imposing homeotropic and planar surface anchoring are demonstrated. By using mesoscopic numerical modeling, multiple types of Janus particles are explored, demonstrating a variety of novel complex colloidal structures. We also show binding of Janus particle...

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...

Liquid crystal colloids are interesting for a variety of mechanisms—including self-assembly, optical-tweezers assisted assembly, topology, and material flow—that can be used to create various complex optical and photonic structures. Here, we present a brief overview of liquid crystal colloidal structures, as recently achieved by numerical modeling...

We numerically investigate structural and optical properties of a highly chiral liquid crystal when it is confined in a thin planar cell imposing strong homeotropic anchoring. Various stable exotic defect structures different from those of bulk cholesteric blue phases are found depending on temperature and cell thickness. We also study how a planar...

Significance Complex nematic fluids have the remarkable capability to organize microparticles and nanoparticles into regular structures of various symmetries and dimensionality, according to their micromolecular orientational order. Structures of particles such as chains, clusters, and crystals are found, but no quasicrystals. In this paper, we dem...

This article has no abstract.

Colloidal platelets are explored as elementary building blocks for the shape-controlled assembly of crystalline and quasicrystalline tilings. Using three-dimensional (3D) numerical modelling based on the minimization of Landau-de Gennes free energy for modelling of colloids combined with Finite Difference Time Domain calculations for optics, we dem...

Knotted fields are an emerging research topic relevant to different areas of physics where topology plays a crucial role. Recent realization of knotted nematic disclinations stabilized by colloidal particles raised a challenge of free-standing knots. Here we demonstrate the creation of free-standing knotted and linked disclination loops in the chol...

Colloidal dispersions in liquid crystals can serve as asoft-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 collo...

In analysis of numerically simulated or experimentally obtained nematic textures, data visualisation plays an important role in interpretation and comparison of results. We review both commonly used, and more recently developed visual presentation methods that expose different aspects of the textures, from director field patterns and topological co...

We present a simple Monte Carlo study of orientational ordering in a nematic liquid crystal with embedded chiral nanostructures. The nanostructures are shown to impose bulk chiral order in the nematic only for large enough values of the chiral pitch.

Liquid crystals in confined geometries exhibit numerous complex structures often including topological defects that are controlled by the nematic elasticity, chirality and surface anchoring. In this work, we study the structures of cholesteric droplets pierced by cellulose fibres with planar anchoring at droplet and fibre surfaces. By varying the t...

Disclination lines in nematic liquid crystals can exist in different geometric conformations, characterised by their director profile. In certain confined, colloidal and even more prominently in chiral nematics, the director profile may vary along the disclination line. We construct a robust geometric decomposition of director profile variations in...

Both uniaxial and biaxial nematic liquid crystals are defined by orientational ordering of their building blocks. While uniaxial nematics only orient the long molecular axis, biaxial order implies local order along three axes. As the natural degree of biaxiality and the associated frame, that can be extracted from the tensorial description of the n...

We show that forces between two colloidal particles in a thin layer of a chiral nematic liquid crystal strongly depend on the chirality of the liquid crystal. The observed pair potentials are attractive, but are oscillatory functions of colloidal separation. The number and the position of local energy minima increase with increasing chirality. The...

Nematic liquid crystals in frustrated environments are known to form a variety of topological defect conformations – possibly networks – with multiple meta-stable states of the nematic order. Here, we study the defect networks and their reconfigurability in a periodically spatially frustrated nematic, focusing specifically on the network formed in...

We investigate numerically the relaxational dynamics of the orientational order of a cholesteric blue phase (BP) in a planar cell enforcing normal alignment in response to the application and cessation of an external electric field. We focus on the cases where blue phase I (BP I) is stable in the bulk. We show how the reorganization processes of th...

A seminal paper [D. R. Nelson, Nano Lett., 2002, 2, 1125.] has proposed that a nematic coating could be used to create a valency for spherical colloidal particles through the functionalization of nematic topological defects. Experimental realizations however question the complex behaviour of solid particles and defects embedded in such a nematic sp...

Topology has long been considered as an abstract mathematical discipline with little connection to material science. Here we demonstrate that control over spatial and temporal positioning of topological defects allows for the design and assembly of three-dimensional nematic colloidal crystals, giving some unexpected material properties, such as gia...

Frustration of chiral ordering is explored in cholesteric liquid crystal droplets with planar degenerate anchoring using numerical modeling. Droplets of variable pitches are studied, demonstrating the role of a gradually increasing cholesteric pitch and the corresponding equilibrium structures. All previously known structures are identified but wit...

Disclination lines in nematic liquid crystals can exist in different geometric conformations, characterised by their director profile. In certain confined, colloidal and even more prominently in chiral nematics, the director profile may vary along the disclination line. We construct a robust geometric decomposition of director profile variations in...

We introduce the idea of transformation trajectories to describe the evolution of nematic shells in terms of defect locations and director field when the elastic anisotropy and the shell thickness heterogeneity vary. Experiments are compared to numerical results to clarify the exact role played by these two parameters. We demonstrate that heterogen...

We have recently demonstrated various quasi-2D disclination networks in blue phases confined to thin layers, ranging from rings, skyrmions, to double helices, which can provide arrays of trapping sites for an easy assembling of colloidal particles in complex 2D lattice structures. In this brief review, we summarize main findings of our phenomenolog...

Disclination lines in chiral nematic liquid crystals exhibit larger geometrical diversity than their counterparts in ordinary nematics and form rich entangled structures in systems with dispersed colloidal inclusions. Numerous metastable and stable states separated by low energy barriers allow for simple rewiring of the braids. Introducing a new vi...

Skyrmions are localized particle-like topological entities in a number of continuous fields that play important roles in various condensed matter systems, including two-dimensional electron gases exhibiting the quantum Hall effect, Bose--Einstein condensates, and chiral ferromagnets [1, 2]. Here we are using Landau - de Gennnes theoretical approach...

Directional media, such as nematic liquid crystals and ferromagnets, are characterized by their topologically stabilized defects in directional order. In nematics, boundary conditions and surface-treated inclusions often create complex structures, which are difficult to classify. Topological charge of point defects in nematics has ambiguously defin...

Nematic braids formed by disclinations entangling colloidal particles in chiral and achiral nematic liquid crystals are geometrically stabilized and restricted by topology. We report how self-linking number enables a classification of entangled defect lines [1, 2] and how a simple rewiring scheme for the orthogonal crossing of two half integer disc...

We present our numerical attempts to simulate the structures of a cholesteric blue phase (BP) confined in a thin cell. Our simulations are based on a Landau-de Gennes theory describing the orientational order of the liquid crystal by a second-rank symmetric tensor. When the cell thickness is small enough, of the order of the lattice constant of the...