A very simplified way to look at LCD screens is to break them down into their most critical components. These would be the backlight, polarizer layer, liquid crystal layer, color filter (if it’s a color LCD screen), and second polarizer layer (there can be more than two polarizer layers, but we will visualize how the LCD screen works using this simple model).
What happens within these screens is that a voltage is applied to the liquid crystal layer, causing the liquid crystal to twist. Between the polarizer layers and the twisting liquid crystal, the intensity of the backlight is decreased in each cell depending on the voltage applied and, thus, how the liquid crystal twists, causing polarization effects. Color emerges as a result of red, blue and green color filters. In each pixel of the screen, different intensities of red, blue, and green will create the colors we perceive.
Liquid crystal cells (LC cells) act as wave plates (also known as retardation plates). Wave plates change the polarization of the incident beam.
If we have N equal the number of wave plates, then an LC cell will have a Jone’s matrix that looks like…
MLC = MN ….M3 M2 M1
An example of a corresponding Jone’s vector model of a wave plate would be this:
(1) ![\begin{equation*} M_\delta = \dfrac{1}{\sqrt{2}}\left[ \begin {array}{ccc} e^{j\delta}&0\\ \noalign{\medskip} 0&e^{-j\delta} \end {array} \right] \end{equation*}](https://pages.vassar.edu/magnes/wp-content/ql-cache/quicklatex.com-e6eb01795d8c2f32c200ebdcdc2fb573_l3.png "Rendered by QuickLaTeX.com")
Where delta stands for the phase delay.
I am having trouble figuring out how to work Mathematica, but what I want to do is to create a graph that will show how each polarization has a different minimum, total twist angle, and retardation, and to particularly show this for viable commercial numbers.
The different twisting of the liquid crystal, as I said before, greatly affects what we see on the screen. When the twisting angle is much smaller than the double refraction (birefringence), the light is linearly polarized. While if the twist angle is large in comparison to the double refraction, the light in the cell will be circularly polarized.
The transmission of the LCD can be modeled using variations of the Gooch and Tarry formula:
(2) 
I am going to continue to play with this equation in order to look at how transmission is altered and when and why it peaks as well as what typically produces the best results for commercial usage.
Since PDP and CRT screens do not rely on polarization in order to adjust the intensity of light, I intend to investigate EMI shields and how they contribute to PDP screens to be of a better picture quality than CRT screens.
References:
Angelov, T., et. al. “High Temperature Formation of Polymer-Dispersed Hydrogen Bonded Liquid Crystals.” Journal of Optoelectronics and Advanced Materials Vol 7.1 (2005): 281-284.
Collett, Edward. Field Guide to Polarization. Washington: SPIE Press, 2005.
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.
Get used to identifying ALL of the variables presented in your work. Your diagrams are great and help a lot in understanding LCD’s.
Your diagram “Simplest LCD Diagram Ever” is a good introduction to this topic for someone (like myself) who has no previous knowledge of LCD technology! Before reading your blog posts, I had always wondered how scientists were able to switch from the big, bulky television sets to the modern, light-weight LCD screens. Also, I am guessing that the Jones matrix for the LC cell with N wave plates involves N matrix multiplications… is this true? And, if so, how can we possibly compute this many matrix multiplications for every single LC cell? Aside from that, in equation 1, you mention something called the phase delay.. could you explain what this parameter is? Also, explaining the difference between the light in an LC cell being linearly polarized vs. circularly polarized would help put your analyses into context. How does this transmission coefficient relate to the transmission coefficient we saw in Chapter 9 in Griffiths? (P.S.- Label the variables and parameters in equation 2, so that I know what is affecting the transmission!)