Elliptical polarization: Difference between revisions

Revision as of 02:21, 10 September 2010

Revision as of 00:26, 4 November 2010

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==Mathematical description of elliptical polarization==

The [[Classical physics|classical]] [[sinusoidal]] plane wave solution of the [[electromagnetic wave equation]] for the [[Electric field|electric]] and [[Magnetic field|magnetic]] fields is ([[Centimeter gram second system of units|cgs units]])

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

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

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

:<math> \omega_{ }^{ } = c k</math>

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

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:<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>.{{Citation needed|date=November 2008}} If <math>\alpha_x</math> and <math>\alpha_y</math> are equal the wave is [[linear polarization|linearly polarized]]. If they differdiffa by <math>\pi/2\,</math> the wave is [[circular polarization|circularly polarized]].

==See also==