Optical properties of twisted nematic

In the calculation of the optical properties, the twisted nematic film is divided into N thin slabs with the thickness Ah = h N. Within each slab, the liquid crystal director can be approximately considered uniform. If the alignment direction of the liquid crystal director at the entrance plane is along the x axis, the rotation matrix of the ith layer is 

Because A is a 2 x 2 matrix, from Cayley-Hamilton theory [9], A can be expanded as 

A twisted nematic liquid crystal is the same as a cholesteric liquid crystal. The pitch P is related to the film thickness h and the total twist angle by P = hl( S l2n). It should be noted that in the derivation of Equation (3.34), reflection and interference effects have not been considered, which are important when the wavelength is comparable with the pitch. 

We consider the optical properties of a twisted nematic liquid crystal film in a few special cases. 

When the incident light is linearly polarized along the liquid crystal director at the entrance 

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C. H. Gooch and H. A. Tarry, The optical properties of twisted nematic liquid crystal stmctures with twisted angles 90°, J. Phys. D8, 1575 (1975). 

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