I am going to start out my calculations by writing out the general form of a Jones matrix for TN-LCD as expressed in “Jones-matrix models for twisted-nematic liquid crystal devices” by Makoto Yamauchi:
and represents the constant absolute phase.
representing the total birefrigence.
The R in equation (1) is the rotation matrix and is represented by
And M is the MLC Jones matrix.
We can use this equation in conjunction with the Gooch and Tarry formula in order to help us model the transmission of TN-LCD.
As stated in my Preliminary Data, the Gooch and Tarry formula is written as
Since we will be focusing on TN-LCDs, the twist angle will be 900 and the transmission can then be modeled as
I then used this variation on the Gooch and Tarry formula in order to graph transmission vs. d∆n/λ
This graph shows us the first few transmission peaks (Mathematica Code). Transmission operates at 100% when
For N= 1, 2, 3…
Where N stands for the number of wave plates (an LC-cell being thought of as N wave plates).
With respect to our graph, then, the transmission peaks are occurring when
This helps us to visualize how the twisted nematic effect operates.
Gooch, C.H. and H.A. Tarry. “The optical properties of twisted nematic liquid crystal structures with twist angles less than or equal to 90 degrees.” Applied Physics Vol. 8(1975): 1575-1584.
Yamauchi, Makoto. “Jones-matrix models for twisted-nematic liquid crystal devices.” Applied Optics Vol. 44.21(2005): 4484-4493.