Elliptical polarization: Difference between revisions

Revision as of 01:52, 22 November 2008

Revision as of 05:14, 22 November 2008

Line 18:

is the [[angular frequency]] of the wave, and <math> c </math> is the [[speed of light]].

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

Here

:<math> \mid \mathbf{E} \mid </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 [[Jones vector]] in the x-y plane. The axes of the ellipse have lengths <math> \sqrt{\tfrac{1 - \sin(2\theta)\cos(\alpha_x - \alpha_y + \pi/2)}{2}},</math> and <math>\sqrt{\tfrac{1 + \sin(2\theta)\cos(\alpha_x - \alpha_y + \pi/2)}{2}} </math>.{{cn}} If <math> \alpha_x </math> and <math> \alpha_y </math> are equal the wave is [[linear polarization | linearly polarized]]. If they differ by <math>\pi/2\,</math> theythe arewave is [[circular polarization | circularly polarized]].

==See also==