Linear polarization: Difference between revisions

Revision as of 04:59, 22 August 2014

Revision as of 22:37, 7 January 2015

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| doi =

| id =

| isbn = 0-387-26329-2}}</ref> For example, if the electric field vector is vertical (alternately up and down as the wave travels) the radiation is said to be vertically polarized.

==Mathematical description of linear polarization==

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:<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>

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

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

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

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

Here

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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 wave is linearly polarized when the phase angles <math> \alpha_x^{ } , \alpha_y </math> are equal,

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:<math> |\psi\rangle = \cos\theta \exp \left ( i \alpha \right ) |x\rangle + \sin\theta \exp \left ( i \alpha \right ) |y\rangle = \psi_x |x\rangle + \psi_y |y\rangle </math>.

== See also ==

*[[Sinusoidal plane-wave solutions of the electromagnetic wave equation]]

*[[Polarization (waves)|Polarization]]

**[[Circular polarization]]

**[[Elliptical polarization]]

*[[Photon polarization]]

==References==

*{{cite book |author=Jackson, John D.|title=Classical Electrodynamics (3rd ed.)|publisher=Wiley|yeardate=1998|isbn=0-471-30932-X}}

{{Reflist}}

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*[http://www.youtube.com/watch?v=Q0qrU4nprB0 Comparison of Linear Polarization with Circular and Elliptical Polarizations (YouTube Animation)]

== See also ==

*[[Sinusoidal plane-wave solutions of the electromagnetic wave equation]]

*[[Polarization (waves)|Polarization]]

**[[Circular polarization]]

**[[Elliptical polarization]]

*[[Photon polarization]]

{{FS1037C}}