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F r o m W i k i p e d i a , t h e f r e e e n c y c l o p e d i a
T h i s i s t h e c u r r e n t r e v i s i o n o f t h i s p a g e , a s e d i t e d b y T a p e w o r m s 2 7 ( t a l k | c o n t r i b s ) at 0 1 : 3 6 , 2 3 J u n e 2 0 2 3 . T h e p r e s e n t a d d r e s s ( U R L ) i s a p e r m a n e n t l i n k t o t h i s v e r s i o n .
( d i f f ) ← P r e v i o u s r e v i s i o n | L a t e s t r e v i s i o n ( d i f f ) | N e w e r r e v i s i o n → ( d i f f )
Electromagnetic radiation special case
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. 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.
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 [ edit ]
The classical sinusoidal plane wave solution of the electromagnetic wave equation for the electric and magnetic fields is (cgs units)
E
(
r
,
t
)
=
|
E
|
R
e
{
|
ψ
⟩
exp
[
i
(
k
z
−
ω
t
)
]
}
{\displaystyle \mathbf {E} (\mathbf {r} ,t)=|\mathbf {E} |\mathrm {Re} \left\{|\psi \rangle \exp \left[i\left(kz-\omega t\right)\right]\right\}}
B
(
r
,
t
)
=
z
^
×
E
(
r
,
t
)
/
c
{\displaystyle \mathbf {B} (\mathbf {r} ,t)={\hat {\mathbf {z} }}\times \mathbf {E} (\mathbf {r} ,t)/c}
for the magnetic field, where k is the wavenumber ,
ω
=
c
k
{\displaystyle \omega _{}^{}=ck}
is the angular frequency of the wave, and
c
{\displaystyle c}
is the speed of light .
Here
∣
E
∣
{\displaystyle \mid \mathbf {E} \mid }
is the amplitude of the field and
|
ψ
⟩
=
d
e
f
(
ψ
x
ψ
y
)
=
(
cos
θ
exp
(
i
α
x
)
sin
θ
exp
(
i
α
y
)
)
{\displaystyle |\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
α
x
,
α
y
{\displaystyle \alpha _{x}^{},\alpha _{y}}
are equal,
α
x
=
α
y
=
d
e
f
α
{\displaystyle \alpha _{x}=\alpha _{y}\ {\stackrel {\mathrm {def} }{=}}\ \alpha }
.
This represents a wave polarized at an angle
θ
{\displaystyle \theta }
with respect to the x axis. In that case, the Jones vector can be written
|
ψ
⟩
=
(
cos
θ
sin
θ
)
exp
(
i
α
)
{\displaystyle |\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
⟩
=
d
e
f
(
1
0
)
{\displaystyle |x\rangle \ {\stackrel {\mathrm {def} }{=}}\ {\begin{pmatrix}1\\0\end{pmatrix}}}
and
|
y
⟩
=
d
e
f
(
0
1
)
{\displaystyle |y\rangle \ {\stackrel {\mathrm {def} }{=}}\ {\begin{pmatrix}0\\1\end{pmatrix}}}
then the polarization state can be written in the "x-y basis" as
|
ψ
⟩
=
cos
θ
exp
(
i
α
)
|
x
⟩
+
sin
θ
exp
(
i
α
)
|
y
⟩
=
ψ
x
|
x
⟩
+
ψ
y
|
y
⟩
{\displaystyle |\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 [ edit ]
References [ edit ]
Jackson, John D. (1998). Classical Electrodynamics (3rd ed.) . Wiley. ISBN 0-471-30932-X .
^ 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", Zenodo : 4745976 , 2021 (open access); §9.
^ Shapira, Joseph; Shmuel Y. Miller (2007). CDMA radio with repeaters . Springer. p. 73. ISBN 978-0-387-26329-8 .
External links [ edit ]
This article incorporates public domain material from Federal Standard 1037C . General Services Administration . Archived from the original on January 22, 2022.
R e t r i e v e d f r o m " https://en.wikipedia.org/w/index.php?title=Linear_polarization&oldid=1161488246 "
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