Propagation of Light in Cholesteric Liquid Crystals

We showed in last section that in a uniform anisotropic medium, for each propagation direction, there are two eigenmodes which are linearly polarized. The polarization state of the eigenmodes is invariant in space. In this section, we discuss the propagation of light in a special case of a non-uniform anisotropic medium a cholesteric liquid crystal which locally is optically uniaxial, but the optic axis twists uniformly in space [6,7]. Choose the z axis of the lab frame to be parallel to the helical axis of the cholesteric liquid crystal. The pitch P of the liquid crystal is the distance over which the liquid crystal director twists In. The components of the liquid crystal director of a right-handed cholesteric liquid crystal q 0) are given by 

Because the dielectric tensor in the local fi ame is a constant tensor, we presume that the polarization of the eigenmodes is invariant in space in this frame [4, 8], which will be proved true. 

In this case a = AIP 1. Using the approximation and the assumption A C 1, from Equation (2.129) we have 

After the light propagates the distance h along the + z direction, in the local frame the amphtude of the eigenmodes becomes 

Defining the total twist angle = lnhlP and total retardation angle Y = lnt nhlX, then 

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