Textures cholesteric planar

Fig. 4.29 Measurements of the pitch of the helix in a cholesteric, (a) Geometry for mraiochro-matic light diffraction on the focal-conic texture. The pitch is found from the angle 2i between the incident and diffracted beams with wavevectors ko and kr, (b) Spectral measniemtaits of the light transmissicm by a planar cholesteric texture (Jo and 7t are intensities of the incidoit and transmitted beam)...

Fig. 12.1 Spectra of optical rotatory power (OR) and selective reflection (R) of a planar cholesteric texture for light propagation parallel to the helical axis.

Fig. 12.8 Influence of a magnetic field H on the planar cholesteric texture having Xa > 0. The helical axis is parallel to z. Horizontal lines show the projections of the director parallel to H. Helix unwinding according to de Gennes (a) and Meyer experiment (b)...

The calculated field induced transmission of the same planar cholesteric texture in the non-polarized light is shown in Fig. 12.12. It is clearly seen that, with increasing field, the Bragg minimum is only slightly shifted to shorter wavelengths due to a distortion of the helix seen in the previous figure and then disappeared at a field of about 25 V/pm. Therefore, in the absence of defects the field cannot increase the period of the helix. An essential increase of the cell thickness does not influence the result. The measurements of the field dependence of the transmission spectra of a cholesteric with the same parameters have confirmed the absence of the red shift of the Bragg minimum [15]. 

Fig. 12.12 Calculated optical transmission spectra of the planar cholesteric texture as functions of the electric voltage applied (unpolarized light). Principal refraction indices used are ri = 1.550, = 1.474, for other parameters see Pig. 12.11...

Fig. 12.14 Calculated transmission spectra of a planar cholesteric texture in zero field and in field = 5.7 V/)im applied perpendicular to the helical axis. Note appearance of the strong second order photonic stop-band even for nonpolarized light...

Let us now briefly summarize the basic conclusions of the theory for the case of light incident normally on the planar cholesteric texture [1, 6, 7, 8] ... 

For the case of the oblique incidence of light onto the planar cholesteric texture the following features are typical [1, 9] ... 

FIGURE 6.5. Operating principle of the polarized light source based on the planar cholesteric texture. 

FIGURE 6.8. Illustration of a dielectric instability of a planar cholesteric texture when Ae > 0. 

So, when d = Pq/2, the bands of the domains are parallel to the direction of the rubbing of the glass surfaces, and when d = Pq they are perpendicular to it, i.e., the domains are always perpendicular to the director in the middle of the layer. With thicknesses significantly less than the helical pitch, the planar cholesteric texture is in fact not different from the planar oriented nematic liquid crystal, and the Prederiks transition takes place with a critical field determined by the elastic constant Ku [24]. 

Stepwise untwisting of the helix, by an electrical field perpendicular to its axis, has been observed for the case of a planar cholesteric texture with As > 0, and with strong anchoring of the molecules to the limiting surfaces... 

When an electric or magnetic field is applied to a liquid crystal cell, a texture transition occurs to minimize the free energy of the system. These texture changes in cholesteric liquid crystals are physically similar to the Frederiks transition in a nematic liquid crystal and result in a significant change in the optical properties of the layer. Texture transitions have been reviewed previously [8, 9] with allowance made for the sign of the dielectric or diamagnetic anisotropy, the initial texture, and the direction of the applied field. Here, we consider only the instability of the planar cholesteric texture, which has been widely discussed in recent literature. 

Qualitatively similar results were obtained by Cohen and Hornreich [ 125]. In addition, it was claimed that the presence of a pretilt in the planar cholesteric texture decreases the tendency of the system to undergo transition to a periodically modulated (ripple) phase. 

Field untwisting of a helix for thin cells with planar boundary conditions occurs differently from the case of an infinite cholesteric medium. For a field perpendicular to the axis of a cholesteric helix in the planar texture, a stepwise change in the pitch with increase in the field is predicted [128]. The size of the step increases with a decrease in the ratio 2electric field perpendicular to the helix axis has been observed for the case of planar cholesteric texture with a>0 and with strong anchoring of the molecules to the limiting surfaces [129]. Under these conditions the relaxation of the field-induced (i.e. untwisted) state is accompanied by the formation of spatially modulated structures in the form of strips or grids. 

These results show that rapid polymerization of monomers in the cholesteric mesophase pwmits freezing this mesophase, although the planar cholesteric texture formed in the polymer-monomer composite is not an equilibrium texture. Nevertheless, this method makes it possible to obtain polymer films with defined optical properties. 

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