Linear polarization: Difference between revisions

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{{Short description|Electromagnetic radiation special case}}

{{short description|Confinement of the electric field vector or magnetic field vector to a given plane along the direction of propagation}}

{{Use American English|date=March 2021}}

{{Use mdy dates|date=March 2021}}

{{More footnotes|date=May 2020}}

[[File:Linear polarization schematic.png|162px|thumb|right|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 (waves)|polarization]]'' and ''[[plane of polarization]]'' for more information.

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.<ref name=fresnel-1822z>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&nbsp;December 1822; printed in H.&nbsp;de Senarmont, E.&nbsp;Verdet, and L.&nbsp;Fresnel (eds.), ''Oeuvres complètes d'Augustin Fresnel'', vol.&nbsp;1 (1866), pp.{{nnbsp}}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&nbsp;access); §9.</ref> See ''[[Polarization (waves)|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.<ref name="Shapira,">{{cite book

| last = Shapira

| first = Joseph

| authorlink =

|author2=Shmuel Y. Miller

| title = CDMA radio with repeaters

| publisher = Springer

| date = 2007

| ___location =

| pages = 73

| url = https://books.google.com/books?id=Yd56YZY1RpAC&pg=PA73&dqq=%5Bpolarization+of+radio+waves%5D&hlpg=en&sa=X&ei=ZQx-T7_HNYT9iQKm59SeDg&ved=0CFgQ6AEwBQ#v=onepage&q=%5Bpolarization%20of%20radio%20waves%5D&f=falsePA73

| isbn = 978-0-387-26329-28}}</ref> 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.

| doi =

| id =

| isbn = 0-387-26329-2}}</ref> 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 of linear 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 (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>

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