![Linear polarization schematic](https://upload.wikimedia.org/wikipedia/commons/2/2e/Linear_polarization_schematic.png)
In
electrodynamics
In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions o ...
, linear polarization or plane polarization of
electromagnetic radiation
In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visible) li ...
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
Augustin-Jean Fresnel (10 May 1788 – 14 July 1827) was a French civil engineer and physicist whose research in optics led to the almost unanimous acceptance of the wave theory of light, excluding any remnant of Newton's corpuscular th ...
in 1822.
[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", , 2021 (open access); §9.] See ''
polarization'' and ''
plane of polarization
The term ''plane of polarization'' refers to the direction of polarization of '' linearly-polarized'' light or other electromagnetic radiation. Unfortunately the term is used with two contradictory meanings. As originally defined by Étienne-Lou ...
'' for more information.
The orientation of a linearly polarized electromagnetic wave is defined by the direction of the
electric field vector.
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
Electricity is the set of physical phenomena associated with the presence and motion of matter that has a property of electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnetism, as described by ...
and
magnetic fields is (cgs units)
:
:
for the magnetic field, where k is the
wavenumber
In the physical sciences, the wavenumber (also wave number or repetency) is the '' spatial frequency'' of a wave, measured in cycles per unit distance (ordinary wavenumber) or radians per unit distance (angular wavenumber). It is analogous to te ...
,
:
is the
angular frequency
In physics, angular frequency "''ω''" (also referred to by the terms angular speed, circular frequency, orbital frequency, radian frequency, and pulsatance) is a scalar measure of rotation rate. It refers to the angular displacement per unit tim ...
of the wave, and
is the
speed of light
The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
.
Here
is the
amplitude
The amplitude of a periodic variable is a measure of its change in a single period (such as time or spatial period). The amplitude of a non-periodic signal is its magnitude compared with a reference value. There are various definitions of am ...
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
*
Sinusoidal plane-wave solutions of the electromagnetic wave equation
*
Polarization
**
Circular polarization
In electrodynamics, circular polarization of an electromagnetic wave is a polarization state in which, at each point, the electromagnetic field of the wave has a constant magnitude and is rotating at a constant rate in a plane perpendicular to ...
**
Elliptical polarization
In electrodynamics, elliptical polarization is the polarization of electromagnetic radiation such that the tip of the electric field vector describes an ellipse in any fixed plane intersecting, and normal to, the direction of propagation. An el ...
**
Plane of polarization
The term ''plane of polarization'' refers to the direction of polarization of '' linearly-polarized'' light or other electromagnetic radiation. Unfortunately the term is used with two contradictory meanings. As originally defined by Étienne-Lou ...
*
Photon polarization
Photon polarization is the quantum mechanical description of the classical polarized sinusoidal plane electromagnetic wave. An individual photon
can be described as having right or left circular polarization, or a superposition of the two. Equ ...
References
*
External links
Animation of Linear Polarization (on YouTube) Comparison of Linear Polarization with Circular and Elliptical Polarizations (YouTube Animation)
{{FS1037C
Polarization (waves)
ja:直線偏光
pl:Polaryzacja_fali#Polaryzacja_liniowa