Inhomogeneous Liquid Crystal Research Articles

Accurate Modeling for Wideband Characterization of Nematic Liquid Crystals for Microwave Applications

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Liquid crystals are attractive materials for use in millimeter-wave band communications devices due to their large birefringence and reconfigurability. However, characterizing these materials is challenging at these frequencies. This work describes the modeling tools that have been developed for the accurate analysis of the liquid crystal orientation and of the wave propagation through the inhomogeneous and anisotropic liquid crystal layer. It also shows how the modeling has been used in conjunction with experimental measurement to characterize liquid crystal materials over a wide frequency range. </para>

Generation of Helical Modes of Light by Spin-to-Orbital Angular Momentum Conversion in Inhomogeneous Liquid Crystals

The helical modes of an electromagnetic wave are characterized by a helical shape of the wavefront. They carry quantized angular momentum of an orbital kind, as opposed to the spin-like angular momentum that can be associated with circularly polarized waves. Here, I review recent results on a novel method for generating helical waves of light by letting a circularly-polarized non-helical wave pass through an azimuthally inhomogeneous birefringent plate made of a suitably patterned liquid crystal, a device dubbed “q-plate”. The q-plate converts the variation of spin angular momentum associated with the switching of light polarization handedness into orbital angular momentum, an optical process that had not been envisioned before. Generalizing this idea, patterned birefringent plates similar to q-plates may be used for shaping the optical wavefront of a circularly polarized beam in any prescribed way. Moreover, these plates allow fast switching between conjugate wavefronts by inverting the handedness of the input polarization. Devices based on this principle have been called Pancharatnam-Berry phase optical elements.

General polarized ray-tracing method for inhomogeneous uniaxially anisotropic media

Uniaxial optical anisotropy in the geometrical-optics approach is a classical problem, and most of the theory has been known for at least fifty years. Although the subject appears frequently in the literature, wave propagation through inhomogeneous anisotropic media is rarely addressed. The rapid advances in liquid-crystal lenses call for a good overview of the theory on wave propagation via anisotropic media. Therefore, we present a novel polarized ray-tracing method, which can be applied to anisotropic optical systems that contain inhomogeneous liquid crystals. We describe the propagation of rays in the bulk material of inhomogeneous anisotropic media in three dimensions. In addition, we discuss ray refraction, ray reflection, and energy transfer at, in general, curved anisotropic interfaces with arbitrary orientation and/or arbitrary anisotropic properties. The method presented is a clear outline of how to assess the optical properties of uniaxially anisotropic media.

CAPACITIVE INTERDIGITAL SENSOR WITH INHOMOGENEOUS NEMATIC LIQUID CRYSTAL FILM

The performance of capacitive interdigital sensors involved with anisotropic and inhomogeneous nematic liquid crystal (LC) film is investigated. These sensors have potential applications in chemical and biological systems. The theory for modeling the permittivity tensor of the LC film as a function of the molecular orientation is presented. The LC film is handled as inhomogeneous material where molecules are assumed to have different orientations with respect to the frame axes. Under these conditions, fringing field capacitances as functions of the molecular deformations are calculated. Examples of modeled capacitive interdigital sensors in the present of different inhomogeneous distributions of LC films will be studied and discussed.

Substrate patterning for liquid crystal alignment by optical interference

Inhomogeneous liquid crystal (LC) alignment surfaces comprising a succession of microdomains favoring different LC alignment directions have been demonstrated for a number of optoelectronic applications. However, the prevalent method used to fabricate these surfaces is time consuming and produce functional areas that are too small for practical use. Here, we demonstrate a simple method based on photopatterning of an azodye layer with an interference pattern produced by intercepting two coherent UV beams. This method can produce alignment patterns within seconds with a practical size of ∼(0.5cm)2.

Modeling of Defects Nucleation in the Inhomogeneous Liquid Crystal Director Field

With the fast Q-tensor method, which can model the defect dynamics in a liquid crystal director field, the nucleation and dynamical behavior of defects is modeled. In order to model the defect, hormeotropic aligned liquid crystal cell with step inhomogeneous electrode which has a height of $1\;{\mu}m$ is used. From the simulation, we can observe the nucleation and line of the defect from surface inhomogeneity and the experiment is performed for confirmation. The experimental result is compared with numerical modeling in order to verify the simulation of the defect nucleation.

Spatially resolved measurements of thermal parameters in colloidal suspensions in liquid crystals

We report on spatially resolved measurements with a spatial resolution of about 0.1 mm of the transition temperature and of the behavior of the heat capacity, thermal conductivity, and thermal diffusivity over the smectic A–nematic and nematic–isotropic phase transitions in an inhomogeneous aerosil dispersed 8CB liquid crystal. The results were obtained by means of a recently implemented photopyroelectric setup which combines the capability for high temperature resolution measurements with the possibility of visual access in the sample. It is shown that the results relative to different local concentration of particles are consistent with the ones obtained previously on homogeneous samples with different average particle concentration. Finally, the analysis of the local thermal conductivity values has led to an approximate estimate of the local particle concentration in the sample.

Particle Scattering, X-ray Diffraction, and Microstructure of Solids and Liquids

The investigation of the microstructure of solids using particle scattering techniques is a fairly mature field where both the experimental techniques and theoretical models have now reached a significant degree of sophistication. The set of lectures given at the 157th WE-Heraeus Seminar on 'Particle Scattering, X-ray Diffraction, and Microstructure of Solids and Liquids', edited by M L Ristig and K A Gernoth and published by Springer Verlag, gives a powerful introduction to the current state of theoretical methods and experimental techniques developed in the field. The lectures cover a broad range of advanced topics ranging from the 'zoological garden' of defects and excitations of condensed isotopes of helium to a fairly difficult treatment of diffraction and diffuse scattering associated with double-beam experiments. There are a number of specific points that I am sure will attract the attention of an interested reader. The last chapter of the book (by G Eckold) gives a nearly ideal introduction to the field of neutron scattering. Not only does it cover in just a few pages all the main points that a non-expert needs to know about inelastic neutron scattering, but it also directs the reader to a number of significant recent publications. The chapter on diffuse scattering by disorder and quasicrystals deserves special mention. It is very well written and the expertise of the author (F Frey) is illustrated by the quality of explanations of some fairly difficult concepts including, for example, the use of projection from higher-dimensional space in the treatment of scattering by quasicrystals (see e.g. figures 10 and 11). The reader will probably enjoy seeing a curious misprint in the definition of the Fourier transform in the very first equation of the chapter. The treatment of one- and two-body densities and their relation to Bragg and diffuse scattering given in the chapter written by K Gernoth is very powerful technically but could be made more readable if a discussion of relevant experimental observations as well as the treatment of effects of partial coherence had been included in the list of topics that he addresses in the chapter. A real jewel in the book is the chapter on simulation and theory of inhomogeneous liquid crystals written by M Allen. It is very rarely that one finds such an outstandingly brilliant and comprehensive description of some fairly difficult theoretical topics related to methods and concepts underlying our current level of understanding of the symmetry properties and dynamics of liquid crystals. It is unquestionably one of the best introductions to the subject available in the current literature. Unfortunately I found the chapter addressing the problem of diffuse scattering and molecular dynamics studies of silica somewhat disappointing and too technical. Some of the points described by the author (M Muser) are debatable and a potential reader would have benefited from the presentation of possible alternative points of view. For example, when discussing the fact that there is still room for improvements of classical potentials describing SiO2 the author does not mention the extreme difficulties associated with attempting to derive the potentials from density functional calculations. The presentation of material in the book would have benefited from the inclusion of a chapter on electron diffraction and scattering, particularly given that the most recent developments in that field (related to fluctuation microscopy) now offer the possibility of studying four-body correlations in condensed matter. Still, my overall impression is that it is an excellent and very useful book and I am delighted to have it as a reference on my desk.

Inhomogeneous nanoscale polymer-dispersed liquid crystals with gradient refractive index

Inhomogeneous polymer-dispersed liquid crystal devices having gradient droplet distribution were fabricated and their phase retardation characterized. The gradient refractive index profile can be used as switchable prism gratings, and positive and negative lenses with tunable focal lengths. Such a tunable electronic lens is a broadband device and can be used for unpolarized light.

Gyrotropy problem in nonhomogeneous media: The case of short-pitch chiral-smectic-C liquid crystals and incommensurate structures.

The question about the existence of macroscopic models for gyrotropy in inhomogeneous materials is examined. We have carried out a detailed polarimetric study on a short-pitch chiral-smectic-C liquid crystal, which has been taken as an example of an inhomogeneous optical medium. In accordance to the theoretical predictions, we have found that, as a first approximation, the inhomogeneous liquid crystal can be modeled as a homogeneous uniaxial medium with huge optical activity in a direction perpendicular to the optic axis. However, some deviations have been determined in the precise values of the optical activity predicted by the theory. These discrepancies have been attributed to higher-order gyration-like effects, which are usually negligible and have not been considered in previous theoretical approaches. The agreement improves when these higher-order effects are incorporated. In the light of the above results, the theory is applied to the case of incommensurate structures. The origin of gyrotropy in these materials is clarified, and it is shown that this quantity can be described by a usual macroscopic tensor. If the incommensurate structure has an inversion center we deduce that all gyration effects rigorously vanish, contrary to the opinion maintained by several authors.

Layer-thinning transitions in freely suspended smectic-A films

We outline the elements of a mean-field density functional theory of inhomogeneous liquid crystals which is able to account for surface-enhanced smectic ordering (SESO) at a free surface. The theory generates SESO without requiring an external anchoring potential, and depending only on the properties (i.e., strengths and ranges) of the anisotropic intermolecular forces. Application of the theory to explaining recent experimental findings of layer-thinning transitions in freely suspended smectic-A films is briefly summarized.

Director distortion in a nematic wetting layer

Nematic liquid-crystal wetting at a solid interface presents particularly interesting features when the nematic director orientation at the solid interface is antagonistic to that favoured by the emerging nematic - isotropic interface. We have used the Landau - de Gennes theory of an inhomogeneous liquid crystal to make a quantitative study of this phenomenon, for the case when the solid surface favours homeotropic anchoring but the nematic - isotropic surface favours planar anchoring. By generalizing the theory of Sheng to allow spatial variation of the director, we find a richer surface phase diagram exhibiting a prewetting line or boundary transition shifted from that discussed by Sheng, as well as a transition between two nematic wetting phases, at which the wetting layer director profile changes from a homeotropic to a distorted texture.

Smectic-A ordering in liquid crystal films

We modify an earlier density-functional theory of inhomogeneous liquid crystals so that it is now able to account for enhanced smectic-A ordering at a free surface. The main modification is the use of different spatial ranges for different angular components of the intermolecular pair potential. We show that the modified theory is able to generate both partial and complete wetting by the smectic-A phase, as well as discrete layering transitions at an interface between isotropic liquid and vapour phases. The major application of the theory is to investigate the properties and conditions required for the existence of ‘layer-thinning’ transitions in freely suspended smectic-A films. Despite the existence of surface-enhanced smectic ordering, we find that layer-thinning transitions do not occur in most parameter ranges of the theory, and instead that freely suspended films will generally tend to rupture on heating. Thinning transitions analogous to those observed experimentally are found to occur within very limited parameter ranges, and are associated with melting of the film interior to a nematic rather than isotropic liquid phase.

Optical bistability, multistability, and instabilities in liquid crystals

The physical aspects of the manifestation of optical bistability, instabilities, and stochasticity in strongly nonlinear media in the form of liquid crystals subjected to laser radiation fields are discussed. The stress is on experimental research. Optical bistability and multistability are considered for a number of light-induced effects in homogeneous and inhomogeneous liquid crystals. The special features of these effects in liquids crystals, associated with the field-induced structural phase transitions, are stressed and the concept of intrinsic (mirrorless) optical bistability is introduced. General nonlinear systems with optical bistability are considered. An analysis is made of instabilities and stochasticity manifested in experiments on light-induced reorientation of liquid crystals in the presence of fields of different origin, giving rise to oscillatory and chaotic processes in the case of self-modulation of the transmitted light.

Molecular statistical theory for inhomogeneous nematic liquid crystals with boundary conditions

We start with a multipole expansion of the London-van der Waals dispersion forces between elongated cylindrically symmetric molecules as a model for the two-particle interaction. This potential is rotationally invariant and anisotropic due to both the orientation and the position of two molecules. In the next step we define a self-consistent description of orientational ordering. If a nematogenic substance is bounded by two parallel plates, a preferred direction of equilibrium orientation is induced depending on the alignment of the molecules next to the surface of the plates. The alignment near the plates will effect the degree of order throughout the whole sample thickness via the two-particle interaction. For the two cases of parallel and perpendicular alignment to the walls, we describe the resulting inhomogeneous phase by locally-variable-order parameters and investigate the temperature dependence for several sample thicknesses. It is found that the ordering induced by alignment parallel to the walls is much weaker than in the case of alignment perpendicular to the walls. This behavior corresponds to the ratio of transverse to longitudinal correlation length in nematic liquid crystals. The ratio of the correlation lengths derived from the present interaction model is found to be in excellent agreement with the ratio of the elastic constants: k33/(1/2)(k11+k22) determined from experiments.