Bragg chiral nematics

Note 3 Chiral nematic mesophases exhibit Bragg scattering of circularly polarised light at a wavelength proportional to the pitch P (Xr = P, where is the mean refractive index). 

Fig. 1. Schematic representation of (a) nematic, (b) smectic and (c) cholesteric (or chiral nematic) liquid crystalline phases. In the nematic phase only orientational correlations are present with a mean alignment in the direction of the director n. In the smectic phase there are additional layer-like correlations between the molecules in planes perpendicular to the director. The planes, drawn as broken lines, are in reality due to density variations in the direction of the director. The interplane separation then corresponds to the period of these density waves. In the cholesteric phase the molecules lie in planes (defined by broken lines) twisted with respect to each other. Since the molecules in one plane exhibit nematic-like order with a mean alignment defined by the director n, the director traces out a right- or left-handed helix on translation through the cholesteric medium in a direction perpendicular to the planes. When the period of this helix is of the order of the wavelength of light, the cholesteric phase exhibits bright Bragg-like reflections. In these illustrations the space between the molecules (drawn as ellipsoids for simplicity) will be filled with the alkyl chains, etc., to give a fairly high packing...

The simplest case of Bragg diffraction is shown in Fig. 20 a for an ideal planar chiral nematic. If is the scattering vector, arising from the structure in, and local fluctuation of, e r), the dielectric tensor, then... 

Due to the giant periodic stmcture discussed above, the blue phase exhibits Bragg diffraction in the ultraviolet-to-visible range. Blue phase I mainly exhibits diffraction from the (110), (200), to (211) planes, and blue phase 2 shows diffraction from the (100) to (110) planes. Hence, there are several reflection peaks, which is not the case with the chiral nematic phase. Typically, the diffractions from the (110) and (200) planes in blue phase 1 and from the (100) plane in blue phase II are in the blue region, which is the origin of the name blue phase. ... 

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