====== Polarization ======
An electromagnetic wave traveling in the $z$ direction can be projected onto the $x-y$ plane as

$\mathbf{E} = [\hat{x} E_x e^{i\phi_x} + \hat{y} E_y e^{i\phi_y}] e^{i(\mathbf{k}\cdot \hat{z}-\omega t)} $

where $\mathbf{k}$ is the **wave vector** with magnitude $2\pi/\lambda$ and direction along the $z$ axis, and $\omega\equiv 2\pi\nu$ is the **angular frequency** and $\delta=\phi_x-\phi_y$ is the **phase difference** between the orthogonal fields. The magnitude of the electric field

$$ E = \sqrt{E_x^2 + E_y^2}. $$

{{https://www.cv.nrao.edu/~sransom/web/x228.png?nolink&400}}