Editing Elliptical polarization (section)

==Mathematical description==
The [[Classical physics|classical]] [[sinusoidal]] plane wave solution of the [[electromagnetic wave equation]] for the [[Electric field|electric]] and [[Magnetic field|magnetic]] fields is ([[Gaussian units]])

:<math> \mathbf{E} ( \mathbf{r} , t ) = \left| \mathbf{E} \right|  \mathrm{Re} \left \{  |\psi\rangle  \exp \left [ i \left  ( kz-\omega t  \right ) \right ] \right \}  </math>

:<math> \mathbf{B} ( \mathbf{r} , t ) = \hat { \mathbf{z} } \times \mathbf{E} ( \mathbf{r} , t )   </math>

for the magnetic field, where k is the [[wavenumber]],

:<math> \omega = c k</math>

is the [[angular frequency]] of the wave propagating in the +z direction, and <math> c </math> is the [[speed of light]].

Here <math>| \mathbf{E} |</math> is the [[amplitude]] of the field and

:<math>   |\psi\rangle  \ \stackrel{\mathrm{def}}{=}\  \begin{pmatrix} \psi_x  \\ \psi_y   \end{pmatrix} =   \begin{pmatrix} \cos\theta \exp \left ( i \alpha_x \right )   \\ \sin\theta \exp \left ( i \alpha_y \right )   \end{pmatrix}   </math>

is the normalized [[Jones vector]]. This is the most complete representation of polarized electromagnetic radiation and corresponds in general to elliptical polarization.