# Explanation of the linear polarization from the photon spin

The following is from Wikipedia: "Circularly polarized electromagnetic waves are composed of photons with only one type of spin, either right- or left-hand. Linearly polarized waves consist of equal numbers of right and left hand spinning photons, with their phase synchronized so they superpose to give oscillation in a plane." Now my question: Can someone elaborate this explanation and explain the linear polarization considering photon spin. I mean by explains the photon spin only, as the explanation based on direction of electric field in the light wave is well known.

Basically, what it comes down to is that one can represent and state of polarization with a little complex-valued unit vector form as a linear combination of the complex-valued unit vectors for the two circular states of polarization $$\hat{v} = \hat{L} \alpha + \hat{R} \beta ,$$ where $|\alpha|^2+|\beta|^2=1$ and $\hat{L}$ and $\hat{R}$ represent the unit vectors for left- and right circular polarization, respectively. If the light propagates in the $z$-direction. Then $$\hat{L},\hat{R} = \hat{x}\pm i\hat{y} .$$ (The assignment of the signs depends on convention.)