Linear polarization

(Redirected from Plane polarization)

In electrodynamics, linear polarization or plane polarization of electromagnetic radiation is a confinement of the electric field vector or magnetic field vector to a given plane along the direction of propagation. The term linear polarization (French: polarisation rectiligne) was coined by Augustin-Jean Fresnel in 1822.[1] See polarization and plane of polarization for more information.

Diagram of the electric field of a light wave (blue), linear-polarized along a plane (purple line), and consisting of two orthogonal, in-phase components (red and green waves)

The orientation of a linearly polarized electromagnetic wave is defined by the direction of the electric field vector.[2] 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

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The classical sinusoidal plane wave solution of the electromagnetic wave equation for the electric and magnetic fields is (cgs units)

 
 

for the magnetic field, where k is the wavenumber,

 

is the angular frequency of the wave, and   is the speed of light.

Here   is the amplitude of the field and

 

is the Jones vector in the x-y plane.

The wave is linearly polarized when the phase angles   are equal,

 .

This represents a wave polarized at an angle   with respect to the x axis. In that case, the Jones vector can be written

 .

The state vectors for linear polarization in x or y are special cases of this state vector.

If unit vectors are defined such that

 

and

 

then the polarization state can be written in the "x-y basis" as

 .

See also

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References

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  • Jackson, John D. (1998). Classical Electrodynamics (3rd ed.). Wiley. ISBN 0-471-30932-X.
  1. ^ A. Fresnel, "Mémoire sur la double réfraction que les rayons lumineux éprouvent en traversant les aiguilles de cristal de roche suivant les directions parallèles à l'axe", read 9 December 1822; printed in H. de Senarmont, E. Verdet, and L. Fresnel (eds.), Oeuvres complètes d'Augustin Fresnel, vol. 1 (1866), pp. 731–51; translated as "Memoir on the double refraction that light rays undergo in traversing the needles of quartz in the directions parallel to the axis", Zenodo4745976, 2021 (open access); §9.
  2. ^ Shapira, Joseph; Shmuel Y. Miller (2007). CDMA radio with repeaters. Springer. p. 73. ISBN 978-0-387-26329-8.
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  This article incorporates public domain material from Federal Standard 1037C. General Services Administration. Archived from the original on January 22, 2022.