An object viewed through certain crystals will appear as a double image. Such crystals demonstrate double refraction; i.e., the two directionally dependent refractive indices through the material result in one image being displaced from the other. The explanation of this effect led to our current understanding of polarization effects.
A wide range of devices incorporate polarization; one of the most common of these in use today is the liquid crystal display. Liquid crystals were discovered in the late 1800s and have only recently become the primary display technology. More traditional devices based on polarization include Pockels cells, Nicol prism, Glan–Thompson prism, and more.
Polarization, which can be induced by reflection, is found in nature, an example of which is sunlight glancing off of a body of water. A similar effect can be created by light interacting with a collection of thin glass plates. It is important to appreciate that there is a difference between simple reflection and a polarization effect on reflected light.
Polarization of light is an important topic and often does not receive the consideration that it should be accorded in many optic courses. Here, we are interested in the mathematics involved in calculating polarization using matrix methods. The two formalisms, the Jones calculus and the Mueller calculus provide an effective means of determining the influence of a polarizer on a beam of light.
In this chapter we will see how two different yet related matrix approaches are applied in polarization calculations and how to set up the calculations in MATLAB. Interestingly, under certain conditions these two matrix approaches can be transformed from one to the other.
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