Structural units optical polarisability

Having defined the different forms of chiral nematogen structure with regard to the positioning of the chiral moiety relative to the liquid-crystalline core unit, it is now necessary to describe further and more precisely the exact nature of this structural relationship. It has been understood for many years that optical properties, such as helical twist sense and the direction of rotation of plane polarised light, depend intimately on the absolute spatial configuration of the chiral centre, the distance the chiral centre is sep-... 

Here Cp and Ca are the unit vectors defined by the polariser and analyser direction, Ri(p) are rotation matrices, and Pj(p) induces the appropriate phase shifts to ordinary and extraordinary components of light in the ith segment. More precisely, Ri(p) represents a simple rotation of the optical axis Oi around k going fi om the i-1 interval to the i interval. Introducing Hd as a direction of the symmetry axis of the structure we define the angle ct, between the reference Uo-k plane and the k-local optic axis (Oj or 6p or 6a) plane and express the rotation matrix as ... 

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