Nonlocal model for nematic liquid-crystal elastomers.

We have developed a fully nonlocal model to describe the dynamic behavior of nematic liquid-crystal elastomers. The free energy, incorporating both elastic and nematic contributions, is a function of the material displacement vector and the orientational order parameter tensor. The free energy cost of spatial variations of these order parameters is taken into account through nonlocal interactions rather than through the use of gradient expansions. We also give an expression for the Rayleigh dissipation function. The equations of motion for displacement and orientational order are obtained from the free energy and the dissipation function by the use of a Lagrangian approach. We examine the free energy and the equations of motion in the limit of long-wavelength and small-amplitude variations of the displacement and the orientational order parameter. We compare our results with those in the literature. If the scalar order parameter is held fixed, we recover the usual viscoelastic theory for nematic liquid crystals.

Electric-field-induced nematic-cholesteric transition and three-dimensional director structures in homeotropic cells.

We study the phase diagram of director structures in cholesteric liquid crystals of negative dielectric anisotropy in homeotropic cells of thickness d which is smaller than the cholesteric pitch p. The basic control parameters are the frustration ratio d/p and the applied voltage U. Upon increasing U, the direct transition from completely unwound homeotropic structure to the translationally invariant configuration (TIC) with uniform in-plane twist is observed at small d/p < or = 0.5. Cholesteric fingers that can be either isolated or arranged periodically occur at 0.5 < or = d/p<1 and at the intermediate U between the homeotropic unwound and TIC structures. The phase boundaries are also shifted by (1) rubbing of homeotropic substrates that produces small deviations from the vertical alignment; (2) particles that become nucleation centers for cholesteric fingers; (3) voltage driving schemes. A novel reentrant behavior of TIC is observed in the rubbed cells with frustration ratios 0.6 < or = d/p < or = 0.75, which disappears with adding nucleation sites or using modulated voltages. In addition, fluorescence confocal polarizing microscopy (FCPM) allows us to directly and unambiguously determine the three-dimensional director structures. For the cells with strictly vertical alignment, FCPM confirms the director models of the vertical cross sections of four types of fingers previously either obtained by computer simulations or proposed using symmetry considerations. For rubbed homeotropic substrates, only two types of fingers are observed, which tend to align along the rubbing direction. Finally, the new means of control are of importance for potential applications of the cholesteric structures, such as switchable gratings based on periodically arranged fingers and eyewear with tunable transparency based on TIC.

Optically induced periodic structures in smectic-C liquid crystals.

We explore periodic structures of smectic-C (SmC) liquid crystals, induced optically by a polarization grating. The studied cells contain a passive surface of rubbed polyimide and an active photosensitive substrate of azo-dye doped polyimide. In a nematic phase the director field can be periodic independent of the angle between the grating vector and the rubbing direction. In the SmA phase periodic structure can be induced only by layer undulations. The SmC behaves similarly to the nematic phase, but the director can rotate only on a cone, which results in a more complex geometry. The periodic pattern is superimposed with four different director and layer structures. In spite of the coexistence of the nonuniform structures the diffraction efficiency is better in the SmC, than in the nematic phase.

Ultraviolet lasing in cholesteric liquid crystals.

We report the observation of stimulated emission and mirrorless lasing in pure cholesteric liquid crystals. The lasing action is attributed to the combination of the fluorescence and the distributed feedback that are due to the inherent periodic structure of the liquid crystal. If the reflection band matches the intrinsic emission of the cholesteric liquid crystal, the crystal becomes a natural laser material, which will self-lase, without any optical elements or the addition of dyes, under picosecond excitation at 355 nm. Samples have been made to lase at different wavelengths in the near UV by shifting of the edge of the reflection band in the range of 385-405 nm. Typical linewidths observed are of the order of 0.5 nm.

Propagation of TM modes in a nonlinear liquid-crystal waveguide.

A cpylindrical nematic liquid-crystal waveguide with an infinite homogeneous isotropic cladding is considered. The dielectric tensor of the liquid-crystal core that governs wave propagation is determined by the configuration of the nematic director. Propagating optical fields can alter the director configuration and thus change the dielectric tensor. We use an iterative numerical scheme to determine the propagation constant as a function of optical power.

TE and TM modes in a cylindrical liquid-crystal waveguide.

We consider a cylindrical waveguide consisting of an inhomogeneous anisotropic liquid-crystal core embedded in an infinite homogeneous isotropic cladding. The wave equations for the pure modes are uncoupled but may have complex coefficients owing to the inhomogeneity and anisotropy of the liquid crystal. A simple numerical method is proposed for solving these equations. For the configuration considered, numerical results for the TE modes agree exactly with the analytical solution. For the TM modes, no analytical solution is available, and the unusual result obtained is that the phase of the fields inside the core depends on the distance from the cylinder axis.