Elliptical polarization: Difference between revisions

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In [[electrodynamics]], '''elliptical polarization''' is the [[polarization]] of [[electromagnetic radiation]] such that the tip of the [[electric field]] [[vector (geometry)|vector]] describes an [[ellipse]] in any fixed plane intersecting, and [[Surface normal|normal]] to, the direction of propagation. An elliptically polarized wave may be resolved into two [[linear polarization|linearly polarized wave]]s in [[Quadrature_phaseQuadrature phase|phase quadrature]], with their polarization planes at right angles to each other. Since the electric field can rotate clockwise or counterclockwise as it propagates, elliptically polarized waves exhibit [[chirality (physics)|chirality]].

Other forms of polarization, such as [[circular polarization|circular]] and [[linear polarization]], can be considered to be special cases of elliptical polarization.

[[Image:Elliptical Elliptical_polarization_schematicpolarization schematic.png|right|Elliptical polarization diagram]]

==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> |\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>.{{cnFact|date=November 2008}} 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> the wave is [[circular polarization | circularly polarized]].

==See also==

*[[Polarization of classical electromagnetic waves]]

[[Category:Polarization]]