Bragg reflection cholesteric liquid crystal

The natural pitch P of cholesteric liquid crystals is in general in the order of 102 nm, comparable with the visible band of light. The Bragg reflection from cholesteric liquid crystal occurs at the wavelength... 

Cholesteric liquid crystals, e.g., those of cholesteroylnonaoate (see Sec. 3.2), produce a Bragg-type scattering, which depends on temperature and angles of incidence and observation. Either total reflection or total transmission of circular polarized light is observed, which effect provides the basis of the dark-bright liquid crystal display in the Schadt-Helfrich cell (Fig. 3.5.3) as well as color reflection. 

Fig. 12.5 Comparison of the non-polarized light transmission by a stack of dielectric layers and a cholesteric liquid crystal (CLC). The two materials have the same Bragg reflection frequency (numerical calculations, for parameters see the text), (a) Transmission spectra on the frequency scale showing the absence of high harmonics in the case of CLC (b) blown transmission spectra at the wavelength scale showing the flat form of the CLC Bragg band and oscillations of transmission at the edges of the band...

D. W. Berreman and T. J. Scheffer, Bragg reflection of light from single-domain cholesteric liquid crystal films, Phys. Rev. Lett., 25, 577 (1970). 

The above solutions describe the characteristics of linear wave propagation in a cholesteric liquid crystal along the helical axis. In particular, if X - 11 < la I, then m. is purely imaginary, and the corresponding wave should be totally reflected. We realize that x 1 or X = 2 nc/(j)t =p (la 1 1 usually) is just the condition for Bragg reflection from the helical structure. If we transform Eq. (5) back into the lab frame, we have... 

Thus, we are now interested in the case of Bragg reflection, or more accurately, we want to establish why only one diffraction maximum of selective reflection (Fig. 6.4(b)) is observed, in experiments with the normal incidence of light, on the planar texture of the cholesteric liquid crystal,... 

Selective Bragg Reflection from a Cholesteric Liquid Crystal... 

Figure 2.16. Samples for demonstration of the Bragg reflection from cholesteric liquid crystal.

Cholesteric liquid crystals (CLCs) show very distinctly that molecular structure and external fields have a profound effect on cooperative behavior and phase structure (see also Chapters 2 and 3). CLCs possess a supermolecular periodic helical structure due to the chirality of molecules. The spatial periodicity (helical pitch) of cholesterics can be of the same order of magnitude as the wavelength of visible light. If so, a visible Bragg reflection occurs. On the other hand, the helix pitch is very sensitive to the influence of external conditions. A combination of these properties leads to the unique optical properties of cholesterics which are of both scientific and practical interest. 

In the helical structure, the optical ellipsoid of the smectic C phase rotates together with the tilt plane. Like in cholesterics, we can imagine that helical turns form a stuck of equidistant quasi-layers that results in optical Bragg reflections in the visible range. Therefore, like cholesterics, smectic C liquid crystals are onedimensional photonic crystals. However, in the case of SmC, the distance between the reflecting layers is equal to the full pitch Pq and not to the half-pitch as in cholesterics, because at each half-pitch the molecules in the SmC are tilted in opposite directions. Hence, we have a situation physically different from that in cholesterics. 

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