Polarization applies to the orientation of the spin of electrons, protons, and …

Polarization is a complicated way of saying "orientation." We don't use orientation, because polarization is more nuanced and allows us to shortcut through a whole lot of detailed explanation. We will take light as our example, but polarization is used more generally and also applies to the orientation of the spin of electrons, protons, and neutrons.

Light is made up of changing electric and magnetic fields; the changing electric field generates a magnetic field and vice versa. As an electric field collapses to zero, it generates an increasingly strong magnetic field. When the electric field vanishes, the magnetic field stops growing and begins to fail. As it fails, it regenerates the electric field, but in a different spatial location. This process repeats continuously, leading to a moving set of electric and magnetic fields that we know and love as light.

Polarization describes the spatial relationship between the electromagnetic fields and some fixed orientation, defined by the experiment (e.g., the laboratory table). A single photon is the smallest amount of light, and it has two "natural" polarizations, called left and right circular polarized. In these polarizations, the total strength of the electric field never changes, but it corkscrews around as the photon propagates—the direction of the corkscrew being clockwise for right circular polarized light and anti-clockwise for left circular polarized light.

If we look from side on, though, we will see the electric field grow and collapse (along with a magnetic field that collapses and grows). From the top, we will also see an electric field that collapses and grows. We can combine these two views so that if we add up the electric field seen from the side and the top, they will always sum to a constant value.

Light can also be linearly polarized. In this case, if we look from side on, we will see a growing and collapsing electric field, but, from the top, there is no electric field at all, ever. Interestingly, any orientation of linear polarized light can be described by adding up left and right circular polarized light photons in the appropriate way—known as superposition. Here is the brain-bending bit: although it takes two photons of left and right circular polarized light to get linearly polarized light, there are still single photons that are linearly polarized.

This is because polarization is always relative to some arbitrary plane or line. Circular polarizations are natural because the direction that the light is moving defines an internal orientation that is independent of an experiment. But the fact remains that we could just as easily re-write the mathematics in terms of linearly polarized light, and then it would take two photons—one vertically polarized and one horizontally polarized—to make up a circular polarized light field.

These polarization states can then be added up to create elliptically polarized light. As with circular polarized light, the total electric field never entirely vanishes and, when looking from the side or the top, we see an oscillating field that does vanish. Now, however, the sum of these two views does not add up to a constant value.

Finally, I should note that there is also unpolarized light. In this case, the electric field still oscillates rhythmically in time, but, as it passes through zero strength (from any particular view), it may grow in a completely different orientation. In other words, one cannot use measurements to predict the orientation of the electric field into the future.

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