# Experiments with Polarized Light

## Investigation of Liquid Crystal Displays

### Liquid Crystals

Liquid crystal (LC) is a state of matter that is intermediate between the crystalline solid and the amorphous liquid. The nematic LCs are organic compounds consisting of long-shaped needle-like molecules. The orientation of the molecules can be easily aligned and controlled by applying an electrical field. Uniform or well prescribed orientation of the LC molecules is required in most LC devices. The structure of the LC cell used in this experiment is shown in Fig 1. Rubbing the polyimide film can produce a well-aligned preferred orientation for LC molecules on substrate surfaces, thus due to the molecular interaction the whole slab of LC can achieve uniform molecular orientation. The local molecular orientation is called the director of LC at that point. The LC cell exhibits the so-called double refraction phenomenon with two principal refractive indices. When light propagates along the direction of the director, all polarization components travel with the same speed $\setbox0\hbox{v_o = c / n_o}% \message{//depth:\the\dp0//}% \box0%$ , where $\setbox0\hbox{n_o}% \message{//depth:\the\dp0//}% \box0%$ is called the ordinary index of refraction. This propagation direction (direction of the director) is called the optical axis of the LC cell. When a light beam propagates in the direction perpendicular to the optical axis, in general, there are two speeds of propagation. The electric field of the light polarized perpendicular (or parallel) to the optical axis travels with the speed of $\setbox0\hbox{v_o = c / n_o}% \message{//depth:\the\dp0//}% \box0%$ (or $\setbox0\hbox{v_e = c / n_e}% \message{//depth:\the\dp0//}% \box0%$, where $\setbox0\hbox{n_e}% \message{//depth:\the\dp0//}% \box0%$ is called the extraordinary index of refraction). The birefringence (optical anisotropy) is defined as the difference between the extraordinary and the ordinary indices of refraction $\setbox0\hbox{\Delta n=n_e - n_o}% \message{//depth:\the\dp0//}% \box0%$.

 Fig. 1. LC cell structure

### 90o Twisted Nematic LC Cell

In the 90o twisted nematic (TN) cell shown in Fig. 2, the LC director of the back surface is twisted 90o with respect to the front surface. The front local director is set parallel to the transmission axis of the polarizer. An incident unpolarized light is converted into a linearly polarized light by the front polarizer.

 Fig. 2. 90o TN LC cell

When a linearly polarized light traverses through a 90o TN cell, its polarization follows the twist of the LC directors (polarized light sees $\setbox0\hbox{n_e}% \message{//depth:\the\dp0//}% \box0%$ only) so that the output beam remains linearly polarized except for that its polarization axis is rotated by 90o (it’s called the polarizing rotary effect by $\setbox0\hbox{n_e}% \message{//depth:\the\dp0//}% \box0%$; similarly we can also find polarizing rotary effect by $\setbox0\hbox{n_o}% \message{//depth:\the\dp0//}% \box0%$). Thus, for a normally black (NB) mode using a 90o TN cell, the analyzer’s (a second polarizer) transmission axis is set to be parallel to the polarizer’s transmission axis, as shown in Fig. 3. However, when the applied voltage V across the LC cell exceeds a critical value $\setbox0\hbox{V_c}% \message{//depth:\the\dp0//}% \box0%$, the director of LC molecules tends to align along the direction of applied external electrical field which is in the direction of the propagation of light. Hence, the polarization guiding effect of the LC cell is gradually diminishing and the light leaks through the analyzer. Its electro-optical switching slope $\setbox0\hbox{\gamma}% \message{//depth:\the\dp0//}% \box0%$ is defined as $\setbox0\hbox{(V_{90}–V_{10})/V_{10}}% \message{//depth:\the\dp0//}% \box0%$, where $\setbox0\hbox{V_{10}}% \message{//depth:\the\dp0//}% \box0%$ and $\setbox0\hbox{V_{90}}% \message{//depth:\the\dp0//}% \box0%$ are the applied voltages enabling output light signal reaches up to 10% and 90% of its maximum light intensity, respectively.

 Fig. 3. NB mode operation of a 90o TN cell