Mueller matrix of twisted nematic liquid crystals

6 Mueller matrix of twisted nematic liquid crystals 

We now consider the Mueller matrix of a uniformly twisted nematic (or cholesteric) liquid crystal. The problem can be simplified if we consider the Stokes vector and the Mueller matrix in the local frame x y, in which the liquid crystal director lies along the x axis. Divide the liquid crystal film into N thin slabs. The thickness of each slab is dz = h/N, where h is the thickness of the liquid crystal film. The angle between the liquid crystal director of two neighboring slabs is dxff = qdz, where q is the twisting rate. The retardation angle of a slab is liT = k Andz. If the 

Stokes vector (in the local frame) of the light incident on a slab is S, then the Stokes vector of the light incident on the next slab is (from Equations (3.73) and (3.76)) 

In deriving the above equation, only first-order terms are kept when dz- 6. a component form we have 

If the Stokes vector of the light incident on the liquid crystal film is 5 f = (), then we have the boundary condition equations (z = 0)  

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