Basics of Polarization

To begin, we will be making the assumption throughout this section that in free space, our beam is a harmonic, transverse electro-magnetic, or TEM, wave. The TEM assumption allows us to break down any beam of polarized light into its constituent $E_x$ and $E_y$ components (which are perpendicular to the direction of propagation of the beam along the z-direction), and the harmonic assumption allows us to work with only monochromatic light for the present moment. With this, the concept of polarization becomes much simpler: all we care about are the magnitudes of the $E_x$ and $E_y$ components and their phase relative to each other! Any polarized wave can be completely described if you know these two things. Of course, there are some more difficult scenarios when you have partially polarized or unpolarized light, or when you start introducing boundaries, but we will get to that all in good time! For now, let’s figure out how the magnitudes and relative phases of the components of our electric field give way to some interesting propagation.

Linear polarization refers to the case when the $E_x$ and $E_y$ components of the electric field vector are in phase such that their components add to a single polarization vector. This can be more clearly visualized in the following image: