For a wave propagating in the $\hat{z}$ direction, the direction of the $\vec{E}$ field determines its polarization. A wave with $E_{y}=0$ is said to be $\hat{x}$-polarized and waves with $E_{x}=0$ are considered $\hat{y}$-polarized. More generally, the wave can follow a polarization ellipse defined by $ \vec{E}(z)=E_{x}e^{-jkz}(\hat{x}+Ae^{j\phi}\hat{y}) $ resulting in $x=\cos\omega t$ and $y=A\cos(\omega t+\phi)$ TE / TM / TEM notes