Bragg scattering, cholesterics

Another technique widely used to measure the cholesteric pitch is based on the Bragg scattering of monochromatic light (obtained by a helium-neon laser) from fingerprint or planar textures of the cholesteric32 Its angular dependence is strictly related to the cholesteric pitch. 

A direct method of studying the translational order (or the amplitude of the density wave) is by measuring the intensity of the Bragg scattering from the smectic planes. McMillan s experimental results on cholesteryl myr-istate are shown in fig. 5.2.6 and as can be seen there is excellent agreement with the refined model. The X-ray intensities reveal an appreciable pretransitional smectic-like behaviour in the cholesteric (nematic) phase. This aspect of the problem will be dealt with in a later section. 

Cholesteric liquid crystals have also been put to practical use. In this case, it is primarily the sensitivity of the pitch to changes in temperature, pressure, etc. that are of interest. Recall that when the pitch of a cholesteric is equal to an optical wavelength, Bragg scattering occurs. It is evident that by choosing a cholesteric of appropriate pitch, changes in temperature and pressure can be monitored by means... 

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. 

The reflection from cholesteric and blue phases is Bragg-type scattering, similar to the diffraction of X-rays by crystals. The wave vector of the incident light Ko, the wave vector of the scattered light Kg, and the wave vector of the dielectric constant component q must satisfy the Bragg condition ... 

In this expression, a is a factor proportional to the scattered light intensity, Sij q) is the amplitude of the Fourier component with wavevector q of the dielectric tensor fluctuation, while vectors f and i are polarizations of, respectively, reflected and incident light waves. In the context of Bragg reflection from the cholesteric helix, we know already from the expression (2.25) that there is just one Fourier component with wavevector 2q. Its amplitude is complex because the second term in the expression (2.25) can be written as... 

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