Wikipedia

Linear polarization

Also found in: Dictionary, Encyclopedia.

(redirected from Plane polarization)

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)

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. See polarization and plane of polarization for more information.

The orientation of a linearly polarized electromagnetic wave is defined by the direction of the electric field vector.^[1] 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

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

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

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

for the magnetic field, where k is the wavenumber,

\omega_{ }^{ } = c k

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

Here $\mid {\mathbf {E}}\mid$ is the amplitude of the field and

|\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}

is the Jones vector in the x-y plane.

The wave is linearly polarized when the phase angles $\alpha_x^{ } , \alpha_y$ are equal,

\alpha _{x}=\alpha _{y}\ {\stackrel {{\mathrm {def}}}{=}}\ \alpha

.

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

|\psi \rangle ={\begin{pmatrix}\cos \theta \\\sin \theta \end{pmatrix}}\exp \left(i\alpha \right)

.

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

If unit vectors are defined such that

|x\rangle \ {\stackrel {{\mathrm {def}}}{=}}\ {\begin{pmatrix}1\\0\end{pmatrix}}

and

|y\rangle \ {\stackrel {{\mathrm {def}}}{=}}\ {\begin{pmatrix}0\\1\end{pmatrix}}

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

|\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

.

See also

Sinusoidal plane-wave solutions of the electromagnetic wave equation
Polarization
- Circular polarization
- Elliptical polarization
- Plane of polarization
Photon polarization

References

Jackson, John D. (1998). Classical Electrodynamics (3rd ed.). Wiley. ISBN 0-471-30932-X.

^ Shapira, Joseph; Shmuel Y. Miller (2007). CDMA radio with repeaters. Springer. p. 73. ISBN 978-0-387-26329-8.

External links

This article incorporates public domain material from the General Services Administration document: "Federal Standard 1037C".

This article is copied from an article on Wikipedia® - the free encyclopedia created and edited by its online user community. The text was not checked or edited by anyone on our staff. Although the vast majority of Wikipedia® encyclopedia articles provide accurate and timely information, please do not assume the accuracy of any particular article. This article is distributed under the terms of GNU Free Documentation License.

Copyright © 2003-2025 Farlex, Inc Disclaimer

All content on this website, including dictionary, thesaurus, literature, geography, and other reference data is for informational purposes only. This information should not be considered complete, up to date, and is not intended to be used in place of a visit, consultation, or advice of a legal, medical, or any other professional.