Carlos G. Avendaño

Anchoring effects on the electrically controlled optical band gap in twisted photonic liquid crystals

We study a one-dimensional twisted photonic liquid crystal (TPLC), consisting of various nematic liquid crystal cells adopting a twisted configuration intercalated by isotropic dielectric layers, submitted to a dc electric field (Edc ) aligned along the periodicity axis. We write the corresponding Euler–Lagrange equations describing the nematic layer configuration. By assuming arbitrary anchoring quasi-planar boundary conditions, we calculate the equilibrium textures for the nematic, parametrized by the two types of strength of its interaction (polar and azimuthal) with the plane walls. We write the electromagnetic equations in a 4 × 4 matrix representation and using the transfer matrix formalism, we obtain the transmittance and reflectance coefficients for normal incidence as functions of the external electric field and anchoring strengths. We have observed a remarkable dependence of the electric field on the transmission and reflection spectra in opening and closing band gaps.

Tunable omni-directional mirror based on one-dimensional photonic structure using twisted nematic liquid crystal: the anchoring effects.

We present the tunability of the omnidirectional band gap (OBG) in a one-dimensional photonic structure consisting of N nematic liquid-crystal slabs in a twisted configuration. It is alternated by N isotropic dielectric layers by a dc electric field aligned along the periodicity axis. We consider the general case for which arbitrary anchoring of the nematic at the boundaries is taken into account. The threshold electric field for which the OBG is created decreases as the anchoring strength diminishes. The width of this band gets larger as the electric field increases and its center frequency is modified slightly.

Electrically tuned optical reflection band for an artificial helicoidal structure

ABSTRACT We analysed the control of optical band gaps for axially propagating electromagnetic waves throughout a nanocomposite structurally chiral medium under the influence of a low-frequency (dc) electric field aligned along the same axis as the periodic structure. This medium is made of metallic nanoballs (silver) randomly dispersed in a structurally chiral material whose dielectric properties can be represented by a resonant effective uniaxial tensor. Structurally chiral material is taken to possess locally a point group symmetry and the Pockels effect is assumed. By establishing the Maxwell equations in a matrix representation, we have computed the eigenvalues and eigenvectors of the corresponding matrix in the system rotating along with the helical structure as function of the filling factor and the electric field. We found that the band gap properties of the periodic system depend strongly on the applied low-frequency electric field which is able to increase the bandwidths of the two sub-band gaps generated by the presence of the metallic inclusions obtained above a given filling factor. The applied electric field is even able to open the mentioned band gaps when they are initially closed. We note that by increasing the filling factor, also by keeping the inclination angle and the electric field fixed, the bands are opened and closed. Then when changing the angle of inclination and the electric field the bands shift, they break and new sub-band gaps appear.

Temperature-dependent optical band structure and defect mode in a one-dimensional photonic liquid crystal

ABSTRACT We analysed the propagation of an electromagnetic wave in a one-dimensional periodic system composed of a finite set of E7 liquid crystal mixture slabs in a twisted configuration alternated by homogeneous and isotropic dielectric layers. For different incident angles of the circularly polarised wave, we studied the optical band structure for reflectance and transmittance considering that the dielectric matrix of the device depends on temperature and wavelength. We demonstrated that the position of the band can be moved from visible to short-infrared spectrum region by increasing the thickness of the layers. We found that for a fixed incident angle, the band spectrum shifts towards the short-wavelength region as the temperature gets increasing, whereas, for a constant temperature, such a spectrum moves towards larger frequencies as the incident angle increases. We show that when one of the homogeneous and isotropic slabs has a different size compared with the remaining ones, a defect mode is induced in the band structure whose frequency can be thermally tuned. Graphical Abstract

Multiple solution for a nematic liquid crystal flowing in converging and divergent channels

We consider a nematic liquid crystal flowing in converging and divergent channels delimited by two intersecting solid planes forming angular sector region. There is a source or sink of nematic, at the planes intersection, whether the nematic flow is outwards or inwards. We find the planar multiple configurations of the director of the nematic satisfying in-plane planar hard-anchoring boundary conditions for 4′-n-pentyl-4-cyanobiphenyl (5CB). Also, we obtain the corresponding velocity profiles parametrised by the Reynolds number for non-slip boundary conditions. We have obtained both symmetric and asymmetric velocity profiles for outwards and inwards flows, nevertheless, none of these profiles has counterflows regions as it occurs for isotropic liquids. Finally, we calculate the mass rate and Frank’s elastic energy for the same multiple velocity profiles and nematic textures we found. We hope this model can be useful as an extreme confining case which helps to understand the industrially important processes of blade coating and cavity filling of liquid crystalline materials.

Cholesteric Elastomers with Mechanical Control of Optical Spectra

Elastomers are elastic media which mixes as no one, also, they have three important properties: orientational order of large range in amorphous soft materials, macroscopic susceptibility to the molecular shape, and quenching to the topological constraints. Classical liquid crystals are fluids typically composed by rigid molecules, which with a continuous model, are represented by bars and exhibit an orientational order of large range. The simplest order displayed by these systems is the nematic, for which, all the molecules are aligned in average. Complementary, the polymeric long chains embodying anisotropic rigid units can be nematically aligned and may form polymeric liquid crystals. However, the long chains are elongated when their rigid monomeric components are oriented, giving rise to an anisotropic material. If additionally, the polymeric chains are joint to a backbone in such way that their topology is restrained, hence the melt condenses in a very elastic solid or rubber. It is convenient to mention that in general, within the rubbers, the nematic monomeric molecules retain the same mobility as in a liquid phase. These soft constrictions make the resulting material, which is then a solid very extensible. Rubbers resist mechanic deformations since the polymeric chains reach their maximum entropy when they stay in their natural state without deformation. The polymerization of these compounds creates links between the chains which joint to the backbone formed collectively among themselves. It is to be expected that in this process, the anisotropic rigid units of nematic character, for instance (nematogens) which lie in the inner of the medium, form spontaneously domains distributed in all the rubber, whose preferred orientation is to be in different directions. This variety of domains causes light scattering giving rise to a macroscopic turbid appearance to the material. One very important advance in the design of these materials was managed by Finkelman, by developing a procedure for obtaining samples which form a single domain. The basic idea consists in applied electric field to the melt substance in order to align the anisotropic monomeric units while the polimerization is taking place and/or the temperature