M. F. Ledney

Influence of anchoring at a nematic cell surface on threshold spatially periodic reorientation of a director

We have analysed the influence of surface director anchoring in a planar flexoelectric nematic cell on the threshold spatially periodic reorientation of the director in an external dc electric field. By minimizing the free energy of the nematic cell we obtained the equations for a director and numerically solved them in the one elastic constant approximation. The dependences of the threshold electric field and the spatial period of director structure on the azimuthal and polar anchoring energy, as well as the flexoelectric parameters, are determined. It is shown that the domain of the flexoelectric parameter values, at which the spatially periodic reorientation of a director takes place, increases with decreasing azimuthal anchoring energy and increasing polar anchoring energy.

Freedericksz transition in a nematic cell with periodic anchoring energy in electric field

The threshold value and shape of the spatially inhomogeneous threshold distribution of the director in an electric field in a planar nematic cell with periodic polar nematic anchoring energy with the cell surface have been determined. It is shown that the threshold value depends nonmonotonically on the number of anchoring energy periods per cell length. An analytical expression for the Freedericksz transition threshold at small anchoring energy modulation amplitudes is obtained, and a numerical calculation of threshold values at large amplitudes is performed. The spatial period of the director structure arising at Freedericksz transition depends strongly on the ratio of Frank elastic constants (K2/K1) and the number of anchoring-energy modulation periods per cell length, but is hardly affected by the anchoring energy modulation amplitude.

Influence of the anchoring energy on hysteresis at the Freedericksz transition in confined light beams in a nematic cell

The influence of the finite value of a nematic director anchoring energy on the hysteresis of the light-induced Freedericksz transition induced by a normal incident linearly polarized one-dimensional bounded light beam is considered. The intensity distribution throughout the cross section of the beam is described by a Heaviside function. Values of the Freedericksz transition threshold and the director deviation angle jumps with increasing and decreasing incident light intensity are numerically obtained and are dependent on the director anchoring energy magnitude and the light beam cross section. Allowable regions of the light beam widths, anchoring energy values and values of the parameters , at which the Freedericksz transition is accompanied by hysteresis are determined.

Electro-optical effect in a planar nematic cell with electric field sensitive boundary conditions

ABSTRACT Dynamics of planar-planar director reorientation under an electrostatic field is studied in nematic cell with the director easy axis gliding. Two cases of the electric field interaction with easy axis at the cell substrate is assumed, linear and quadratic in the electric field. In the case of quadratic interaction the director instability has a threshold. Dependence of the director dynamics on the anchoring energy and the electric field interaction with the easy axis are studied. We calculated the light transmittance of the cell and show that it reflects the director dynamics.

Modelling of director equilibrium states in a nematic cell with relief surface

ABSTRACT We study two-dimensional equilibrium configurations of nematic liquid crystal (NLC) director in a cell bounded by two parallel surfaces. One surface is planar and the other one is spatially modulated. The relief of the modulated surface is described by a smooth periodic sine-like function. The orientation of NLC director easy axis is assumed to be homeotropic at one cell surface and planar at the other one. The NLC director anchoring with cell surfaces is assumed to be strong. We consider the case where disclination lines occur in the bulk of NLC above the extrema of the modulated surface. These disclination lines run along the crests and troughs of the surface relief. If the orientation of director at both bounding surfaces is of the same type, then NLC director field is continuous. For both configurations mentioned above (with defects and without defects), we obtain analytical expressions for director distribution in the bulk of NLC in the approximation of planar director deformations. Equilibrium distances from disclination lines to the spatially modulated surface are calculated when the defects occur. The dependences of these equilibrium distances on the period and depth of surface relief and the cell thickness are investigated in detail. GRAPHICAL ABSTRACT

Orientational instability of nematic liquid crystal in a homeotropic cell with boundary conditions controlled by an electric field

ABSTRACT We study the orientational instability of the director in a homeotropic nematic liquid crystal (NLC) cell in a DC electric field. The electric field is applied along or perpendicular to a cell surface depending on whether anisotropy of dielectric permittivity of NLC is positive or negative. The easy axis on one of the cell polymer substrates is allowed to deviate in perpendicular to the substrate plane due to the influence of the NLC and the electric field. It was established that the orientational instability of the director can have a threshold as well as be thresholdless which depends on the character of the coupling of the easy axis with the electric field. The temporal behaviour of a director and the easy axis during transition to the stationary state after turning on electric field and returning to the initial homogeneous state after turning off the field was investigated. In the case of the negative anisotropy of the static permittivity, the comparison of experimental and calculated time dependences of the easy axis reorientation angle let us to estimate values of the mobile easy axis viscosity coefficient and coupling parameter describing the coupling between the easy axis and the electric field. Graphical Abstract

Generalised technique for calculation of plane director profiles in bounded nematic liquid crystals

ABSTRACT We propose an improved conformal mapping technique for analytical calculation of two-dimensional profiles of the nematic liquid crystal (NLC) director in a cell with a simply connected cross-sectional region. We consider the case of the strong anchoring and the piecewise constant director pretilt on the piecewise smooth curve which bounds the region. Obtained expressions for the director profile explicitly depend on the conformal mapping which maps the region onto the upper half plane of a complex plane. An advantage of our method in comparison with the standard conformal mapping technique is that it does not require the knowledge of the inverse mapping and the calculation of the integral in the Poisson formula. Proposed technique allows to take into account topological defects in the bulk of the NLC on the symmetry axis of the region. As an example of how the method can be used, we find an analytical expression for the director profile in a horizontal cylindrical groove partly filled with the NLC. We consider the case where a disclination line parallel to the axis of the groove occurs in the bulk of the NLC. The equilibrium position of the disclination line is found. Graphical Abstract

Interaction of electromagnetic waves in nematic waveguide

ABSTRACT Controlled by an electric field, the interaction of two coupled TE-modes at the dynamic grating in a planar waveguide with a thin layer of nematic liquid crystal has been studied theoretically. The dynamic grating is induced by an external electric field due to the periodicity of the anchoring energy of nematic with waveguide surface. Metal and dielectric waveguides have been studied. The transmission of TE-modes and its reflection from the periodic structure of the nematic layer have been investigated. The intensity of a signal- mode at the output of the waveguide has been calculated. The dependence of intensity on the anchoring energy amplitude and modulation period, dimensions of the nematic layer and an external electric field has been analyzed. It was shown that the frequency interval of a TE-mode reflection expands with increasing of the electric field. The primary maximum of the reflected mode intensity, as function of the nematic layer length, increases monotonously with growing s number of anchoring energy periods placed on the layer length. The primary peak reaches the largest value of 1 for s ∼ 10÷100 (metal waveguide) and for s ∼ 1000 (dielectric waveguide). The same dependence for the signal-mode, which propagates through the NLC layer, has nonmonotonous form and a complete energy exchange is reached only for certain values of s and the length of the nematic layer.

Interaction of electromagnetic waves in planar waveguide with a nematic layer

This work is a theoretical study of energy exchange between two coupled TE-wave modes on director diffraction grating in a planar waveguide containing a layer of nematic liquid crystal. The diffraction grating is produced by an external electric field in the nematic layer with spatial periodic anchoring energy between director and waveguide surface. The intensity of a signal mode at the output of the nematic layer has been calculated in dependence of anchoring energy amplitude and modulation period, the size of nematic layer and electrical field value. The cases of co-propagating and oppositely propagating modes have been analysed. The analytical expressions that describe the maximum values of signal mode intensity have been derived. The maximum intensity value output from the nematic has been shown to depend monotonously on the anchoring energy parameters in the case of oppositely propagating wave modes and non-monotonously in the case of co-propagating wave modes. In both cases, the maximum value of signal mode intensity grows with the increase in electric field.

Energy exchange between electromagnetic waves on the director diffraction grating in planar waveguide with nematic layer

The energy exchange between two coupled TE modes on the diffraction grating of the director in a planar waveguide containing a nematic liquid crystal layer is calculated. The diffraction grating is induced by an external electric field in the nematic layer with periodic anchoring energy at the waveguide surface. The intensity of the signal mode at the output of the nematic layer is calculated as a function of the amplitude and period of the anchoring-energy modulation, the nematic layer sizes, and the electric-field strength. The cases of modes with the same and opposite directions are considered. Analytical expressions for the maximum intensities of the signal mode are derived. In both cases the maximum intensity of the signal mode increases with an increase in the electric-field strength.