Hyperbolic metamaterials are uniaxial birefringent materials with the eigenvalues of the tensorial permittivity opposite in sign. In this work, we were interested in homogeneous hyperbolic metamaterials with optical axis spatially varying in a defect manner, and observing how such structure in uences the extraordinarily polarized light wave. More broadly, this work is an attempt towards realising liquid crystal-like performing metamaterials.
Sub-wavelength periodic metallic nanostructures give rise to very interesting optical phenomena like effective refractive index, perfect absorption, cloaking, etc. However, such metallic structures result in high dissipative losses and hence dielectric nanostructures are being considered increasingly to be an efficient alternative to plasmonic materials. High refractive index (RI) dielectric nanostructures exhibit magnetic and electric resonances simultaneously giving rise to interesting properties like perfect magnetic mirrors, etc. In the present work, we study light-matter interaction of cubic dielectric structures made of very high refractive index material Te in air. We observe a distinct band-like structure in both transmission and reflection spectra resulting from the interaction between magnetic and electric dipolar modes. FDTD simulations using CST software are performed to analyse the different modes excited at the band frequencies. The medium when replaced with liquid crystal gives rise to asymmetry in the band structure emphasizing one of the dominant magnetic modes at resonance frequencies. This will help in achieving a greater control on the excitation of the predominant magnetic dipolar modes at resonance frequencies with applications as perfect magnetic mirrors.
There is a great increase of interest in the nematic defect structures, where interplay of confinement, elasticity, anchoring, and chirality leads to complex ordering fields with singular topological defects and nonsingular solitonic deformations. Beside numerous advanced microscopy techniques, the standard polarized optical microscopy is still an elementary first-to-take tool in use. To fully capture its potential and understand the limitations in unveiling the details of complex structures, we apply a recently extended Jones matrix approach based on ray-tracing that allows to include also effects of focusing and numerical aperture. The approach is illustrated with results of recent studies of cholesteric droplets.
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
modes and density of states. Light propagation along half-integer nematic disclinations is shown with changes in the
light polarization of various winding numbers. As third, simulated light transmission polarization micrographs of
nematic torons are shown, offering a new insight into the complex structure characterization. Finally, this work is a
contribution towards using complex soft matter in optics and photonics for advanced light manipulation.
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 2015]. In unwinded chiral nematic phases stable and metastable toron and hopfion defects have been implemented by laser tweezers [Smalyukh et al., Nature Materials 2010; Chen et al., PRL2013] and in chiral nematic colloids particles dressed by solitonic deformations [Porenta et al., Sci. Rep. 2014]. Modelling studies based on the numerical minimisation of the phenomenological free energy, supported with the adapted topological theory [Copar and Zumer, PRL 2011; Copar, Phys. Rep. 2014] allow describing the observed nematic defect structures and also predicting numerous structures in confined blue phases [Fukuda and Zumer, Nature Comms 2011 and PRL 2011] and stable knotted disclinations in cholesteric droplets with homeotropic boundary [Sec et al., Nature Comms 2014]. Coupling the modeling with finite difference time domain light field computation enables understanding of light propagation and light induced restructuring in these mesophases. The method was recently demonstrated for the description of low intensity light beam changes during the propagation along disclination lines [Brasselet et al., PRL 2009; Cancula et al., PRE 2014]. Allowing also high intensity light an order restructuring is induced [Porenta et al., Soft Matter 2012; Cancula et al., 2015]. These approaches help to uncover the potential of topological structures for beyond-display optical and photonic applications.
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 topological defects and light propagation along the defects stimulated us to develop a customized version of the Finite-Difference Time-Domain (FDTD) method for solving Maxwell's equations on a discrete time and space lattice. Here, we present an overview of our recent simulations, modeling the time-evolution of electromagnetic fields along birefringent structures in nematic liquid crystals, specifically light propagation along nematic defect lines. In the regime of high light intensity beams the modelling approach includes also a light induced modification of local nematic ordering obtained via a qtensor free energy minimization procedure. We show how topological invariants of the nematic and polarization fields combine and also affect the beam intensity profile. Finally, off-axis propagation of beams with respect to the defect lines is considered.
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 visualization of complex nematic fields. Particular attention is given to simulations of images obtained by three-photon excitation fluorescence polarizing microscopy that can unveil complex three dimensional nematic fields at the micrometer scale.
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 demonstrate the self-assembly and optical (transmission) properties of triangular, square and pentagonal sub-micrometer sized platelets in a thin layer of nematic liquid crystal. Interactions between platelets are explored, providing an insight into the assembly process. Two-dimensional tilings of various-shaped colloidal platelets are demonstrated, and their use as diffraction layers is explored by using FDTD simulations. Designing symmetry-breaking surface anchoring profiles on pentagonal platelets opens also a possibility to achieve interactions that could lead to tilings with non-crystalline symmetry.
Complex optical field-induced defect structures are presented in nematic and chiral nematic liquid crystals, as imprinted
by Laguerre–Gaussian (LG) laser beams. Our modeling study is based on the phenomenological free energy approach,
which dielectrically couples the nematic optical axis with the polarization of the LG beams. The symmetry of the
presented structures proves to be conditioned by the beam helical indices. The beam intensity, strength of the nematic
elastic constant, and local intensity-induced control of the nematic order via absorption of the light are demonstrated as
possible mechanisms for producing, imprinting, and tuning of the field-induced complex defect structures in achiral and
In confined blue phases numerous quasi 2D disclination networks ranging from rings to double helices can be stable. We
have recently demonstrated how such networks act as arrays of trapping sites that can lead to easy assembling of
colloidal particles in complex 2D lattice structures. In this short overview we summarize main results of our Landau - de
Gennes modeling combined with topology that was proven to be useful in bulk blue phase colloids. Effects of
confinement, particle anchoring, and particle sizes that can range from micron to nanometre scale are presented. Quasi
2D colloidal crystals that can be easily manipulated by external stimuli via affecting liquid crystal and/or colloidal
particles are expected to have possible photonic applications.
We examine the possibilities to use the intrinsic 3D defect networks in blue phases I and II as arrays of trapping sites for
colloidal particles. Our approach based on the phenomenological Landau-de Gennes description and topological theory
has proven to be extremely useful in dealing with nematic colloids. A perturbed orientational order leads to effective
anisotropic long range inter-particle coupling and consequently to numerous organizations of colloidal particles not
present in simple liquids. Recent developments that led to the blue phases with extended stability range make them more
attractive for use. In these phases the competition between nematic ordering and intrinsic tendency to form double
twisted deformations yields complex director patterns and disclination networks. The spatially deformed order that
mediates the attraction of particles to the network sets the ground for a possible self-assembling of 3D superstructures
with extended stability ranges. Here we first describe the trapping mechanism on the case of a single discilination line
and then use the results to demonstrate the trapping in the blue phase II. Effects of particle sizes ranging from submicron
to 50 nanometers are examined. The assembling in blue phases is expected to form photonic crystals that can be easily
manipulated via affecting the liquid crystal matrix and/or colloidal particles.
The interactions between different types of colloidal particles are measured and analyzed. We use these interactions to
build different self-assembled microstructures, such as dimers, chains, wires, crystals and superstructures. In the
experiments we have used different size, different symmetry of colloids (elastic dipoles and quadrupoles) and different
way of colloidal binding (via localized defects and via entangled defects). We use optical tweezers for directed selfassembly
of colloidal particles. Special attention is devoted to the hierarchical superstructures of large and small
particles. We show that smaller, submicron colloidal particles are trapped into the topological defect rings or loops,
twisting around larger colloidal particles, which are sources of strong nematic deformations. Various possible
applications are discussed, especially in photonics and metamaterials.
We describe and analyze experiments, where optical manipulation of small colloidal particles in the nematic liquid
crystal (NLC) was used to create artificial colloidal structures, such as 1D chains and 2D colloidal crystals, and
superstructures of different types of colloids. In all cases, the colloidal particles are strongly bound to each other, with a
typical pair interaction energy of several 1000 k<sub>B</sub>T per 1μm size particle. There are two distinct mechanisms of colloidal
binding in a spatially homogeneous NLC: (i) binding via spatially localized topological (point) defects, and (ii) binding
via entangled topological defects, where the defect line winds around and wraps several colloidal particles.
Colloidal structures assembled in confined nematic liquid crystals are examined. Theoretical predictions based on
Landau-type approaches are complemented with the latest studies of laser assisted colloidal assembling. Effective
colloidal interactions are particularly sensitive to the confinement and external fields. Their complexity leads to
numerous stable or metastable colloidal superstructures not present in isotropic solvents. Particularly important are
colloidal structures coupled by entangled disclinations. Such a string-like coupling is very robust and opens new routes
to assemble new photonic materials.
The ability to generate regular spatial arrangements of particles on different length scales is one of the central issues of
the "bottom-up" approach in nanotechnology. Current techniques rely on single atom or molecule manipulation by the
STM, colloidal particle manipulation by laser or optoelectronic tweezers, microfluidics, optofluidics, micromanipulation
and classical lithography. Of particular interest is self-assembly, where the pre-determined spatial arrangements of
particles, such as 3D photonic crystals, could be realized spontaneously. Dispersions of particles in liquid crystals show
several novel classes of anisotropic forces between inclusions, which result in an amazing diversity of self-assembled
patterns, such as linear chains and 2D photonic crystals of microspheres. The forces between the particles in nematic
colloids are extremely strong and long-range, resulting in several thousand times stronger binding compared to the
binding in water based colloids. The mechanisms of self-assembly in nematic colloids are discussed, showing this is a
novel paradigm in colloidal science, which can lead to new approaches in colloidal self-assembly for photonic devices.
We describe and analyze laser trapping of small colloidal particles in a nematic liquid crystal, where the index of refraction of colloidal particles is smaller compared to the indices of the liquid crystal. Two mechanisms are identified that are responsible for this anomalous trapping: (i) below the optical Freedericksz transition, the trapping is due to the anisotropic dielectric interaction of the polarized light with the inhomogeneous director field around the colloidal particle, (ii) above the optical Freedericksz transition, the optical trapping is accompanied by the elasticity-mediated interaction between the optically distorted region of a liquid crystal and the particle. In majority of the experiments, the trapping above the Freedericksz transition is highly anisotropic. Qualitative agreement is found with a numerical analysis, considering nematic director elastic distortion, dielectric director-light field coupling and optical repulsion due to low refraction index colloid in a high index surroundings.