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{{Short description|Concept in optics}}
[[File:Field-vectors-and-propagation-directions.svg|thumb|300px|'''Fig.{{nnbsp}}1''':{{big| }}Field vectors ('''E''',{{hsp}}'''D''',{{hsp}}'''B''',{{hsp}}'''H''') and propagation directions (ray and wave-normal) for linearly-polarized plane electromagnetic waves in a non-magnetic birefringent crystal.{{r|lunney-weaire-2006}} The plane of vibration, containing both electric vectors ('''E''' & '''D''') and both propagation vectors, is sometimes called the "plane of polarization" by modern authors. Fresnel's "plane of polarization", traditionally used in optics, is the plane containing the magnetic vectors ('''B''' & '''H''') and the ''wave-normal''. Malus's original "plane of polarization" was the plane containing the magnetic vectors and the ''ray''. (In an isotropic medium, {{math|''θ'' {{=}} 0}} and Malus's plane merges with Fresnel's.)]]
For [[light]] and other [[electromagnetic radiation]], the '''plane of polarization''' is the [[plane (geometry)|plane]] spanned by the direction of propagation and either the [[electric vector]] or the [[magnetic vector]], depending on the convention. It can be defined for [[polarization (physics)|polarized]] light, remains fixed in space for ''[[linear polarization|linearly-polarized]]'' light, and undergoes [[axial rotation]] for ''[[circular polarization|circularly-polarized]]'' light.
The term '''''plane of polarization''''' refers to the direction of [[polarization (waves)|polarization]] of ''[[linear polarization|linearly-polarized]]'' light or other [[electromagnetic radiation]]. Unfortunately the term is used with two contradictory meanings. As originally defined by [[Étienne-Louis Malus]] in 1811,<ref name=buch54>Buchwald, 1989, p.{{hsp}}54.</ref> the plane of polarization coincided (although this was not known at the time) with the plane containing the direction of propagation and the ''magnetic'' vector.<ref>Stratton, 1941, p.{{hsp}}280; Born & Wolf, 1970, pp.{{nnbsp}}43,{{tsp}}681.</ref> In modern literature, the term ''plane of polarization'', if it is used at all, is likely to mean the plane containing the direction of propagation and the ''electric'' vector,<ref name=luntz/> because the electric field has the greater propensity to interact with matter.<ref name="bw28">Born & Wolf, 1970, p.{{hsp}}28.</ref>▼
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For waves in a [[birefringence|birefringent]] (doubly-refractive) crystal, under the old definition, one must also specify whether the direction of propagation means the ray direction or the wave-[[normal (geometry)|normal]] direction, because these directions generally differ and are both perpendicular to the magnetic vector (Fig.{{nnbsp}}1). Malus, as an adherent of the [[corpuscular theory of light]], could only choose the ray direction. But [[Augustin-Jean Fresnel]], in his successful effort to explain double refraction under the [[wave theory of light|wave theory]] (1822 onward), found it more useful to choose the wave-normal direction, with the result that the supposed vibrations of the medium were then consistently perpendicular to the plane of polarization.<ref name=fh318>Fresnel, 1827, tr. Hobson, p.{{nnbsp}}318.</ref> In an [[isotropy|isotropic]] medium such as air, the ray and wave-normal directions are the same, and Fresnel's modification makes no difference.▼
▲For waves in a [[birefringence|birefringent]] (doubly-refractive) crystal, under the old definition, one must also specify whether the direction of propagation means the ray direction ([[Poynting vector]]) or the wave-[[normal (geometry)|normal]] direction, because these directions generally differ and are both perpendicular to the magnetic vector (Fig.{{nnbsp}}1). Malus, as an adherent of the [[corpuscular theory of light]], could only choose the ray direction. But [[Augustin-Jean Fresnel]], in his successful effort to explain double refraction under the [[wave theory of light|wave theory]] (1822 onward), found it more useful to choose the wave-normal direction, with the result that the supposed vibrations of the medium were then consistently perpendicular to the plane of polarization.<ref name=fh318>Fresnel, 1827, tr. Hobson, p.{{nnbsp}}318.</ref> In an [[isotropy|isotropic]] medium such as air, the ray and wave-normal directions are the same, and Fresnel's modification makes no difference.
Fresnel also admitted that, had he not felt constrained by the received terminology, it would have been more natural to define the plane of polarization as the plane containing the vibrations and the direction of propagation.<ref name=fy406>Fresnel, 1822, tr. Young, part 7, [https://books.google.com/books?id=N69MAAAAYAAJ&pg=PA406 p.{{nnbsp}}406].</ref> That plane, which became known as the plane of ''vibration'', is perpendicular to Fresnel's "plane of polarization" but identical with the plane that modern writers tend to call by that name!▼
▲Fresnel also admitted that, had he not felt constrained by the received terminology, it would have been more natural to define the plane of polarization as the plane containing the vibrations and the direction of propagation.<ref name=fy406>Fresnel, 1822, tr. Young, part 7, [https://books.google.com/books?id=N69MAAAAYAAJ&pg=PA406 p.{{nnbsp}}406].</ref> That plane, which became known as the '''plane of
It has been argued that the term ''plane of polarization'', because of its historical ambiguity, should be avoided in original writing. One can easily specify the orientation of a particular field vector; and even the term ''plane of vibration'' carries less risk of confusion than ''plane of polarization''.<ref>Born & Wolf, 1970, pp.{{nnbsp}}28,{{hsp}}43.</ref>
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Because innumerable materials are [[dielectric]]s or [[electrical conductor|conductors]] while comparatively few are [[ferromagnetism|ferromagnets]], the [[reflection (physics)|reflection]] or [[refraction]] of EM waves (including [[light]]) is more often due to differences in the ''electric'' properties of media than to differences in their magnetic properties. That circumstance tends to draw attention to the ''electric'' vectors, so that we tend to think of the direction of polarization as the direction of the electric vectors, and the "plane of polarization" as the plane containing the electric vectors and the direction of propagation.
[[File:Screen dish antenna.jpg|thumb|left|'''Fig.{{nnbsp}}3''':{{big| }}Vertically
Indeed, that is the convention used in the online ''Encyclopædia Britannica'',{{r|luntz}} and in [[Richard Feynman|Feynman]]'s lecture on polarization.{{r|feynman-1963}} In the latter case one must infer the convention from the context: Feynman keeps emphasizing the direction of the ''electric'' ('''E''') vector and leaves the reader to presume that the "plane of polarization" contains that vector — and this interpretation indeed fits the examples he gives. The same vector is used to describe the polarization of radio signals and [[antenna (radio)#Polarization|antennas]] (Fig.{{nnbsp}}3).<ref name="auto">Stratton, 1941, p.{{hsp}}280.</ref>
If the medium is magnetically isotropic but electrically ''non''-
This "natural" definition, however, depends on the theory of EM waves developed by [[James Clerk Maxwell]] in the 1860s — whereas the word ''polarization'' was coined about 50 years earlier, and the associated mystery dates back even further.
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[[File:Calcite and polarizing filter.gif|frame|'''Fig.{{nnbsp}}4''':{{big| }}Printed label seen through a doubly-refracting calcite crystal{{hsp}} and a modern polarizing filter (rotated to show the different polarizations of the two images).]]
Polarization was discovered — but not named or understood — by [[Christiaan Huygens]], as he investigated the
Huygens defined a ''principal section'' of a calcite crystal as a plane normal to a natural surface and parallel to the axis of the obtuse solid angle.<ref>Huygens, 1690, tr. Thompson, pp.{{nnbsp}}55–6.</ref> This axis was parallel to the axes of the [[spheroid]]al [[Huygens–Fresnel principle|secondary waves]] by which he (correctly) explained the directions of the extraordinary refraction.
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[[File:Augustin Fresnel.jpg|thumb|<div style="text-align: center;">Augustin-Jean Fresnel (1788–1827).</div>]]
In 1821, [[Augustin-Jean Fresnel]] announced his hypothesis that light waves are exclusively ''[[transverse wave|transverse]]'' and therefore ''always'' polarized in the sense of having a particular transverse orientation, and that what we call ''[[unpolarized
Fresnel himself found this implication inconvenient; later that year he wrote:
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In most contexts, however, the concept of a "plane of polarization" distinct from a plane containing the electric "vibrations" has arguably become redundant, and has certainly become a source of confusion. In the words of Born & Wolf, "it is… better not to use this term."<ref>Born & Wolf, 1970, p.{{hsp}}43.</ref>
==See also==
*[[E-plane and H-plane]]
*[[Plane of incidence]]
==Notes==
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<ref name=carcione-cavallini-1995>J.M. Carcione and F. Cavallini, [http://www.lucabaradello.it/carcione/CC95b.pdf "On the acoustic-electromagnetic analogy"], ''Wave Motion'', vol.{{nnbsp}}21 (1995), pp.{{nnbsp}}149–62. (Note that the authors' analogy is only two-dimensional.)</ref>
<ref name=feynman-1963>R.P. Feynman, R.B. Leighton, and M. Sands, ''The Feynman Lectures on Physics'', California Institute of Technology, 1963–2013, Volume {{serif|I}}, [
<ref name=jenkins-white-1976>Cf. F.A. Jenkins and H.E. White, ''Fundamentals of Optics'', 4th Ed., New York: McGraw-Hill, 1976, {{ISBN|0-07-032330-5}}, pp.{{nnbsp}}553–4, including Fig.{{nnbsp}}26{{serif|I}}.</ref>
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* W.S. Aldis, 1879, [https://archive.org/details/chapteronfresnel00aldirich ''A Chapter on Fresnel's Theory of Double Refraction''], 2nd Ed., Cambridge: Deighton, Bell, & Co. / London: George Bell & Sons.
* M. Born and E. Wolf, 1970, ''[[Principles of Optics]]'', 4th Ed., Oxford: Pergamon Press.
* J.Z. Buchwald, 1989, ''The Rise of the Wave Theory of Light: Optical Theory and Experiment in the Early Nineteenth Century'', University of Chicago Press, {{ISBN|0-226-07886-8}}.
* O. Darrigol, 2012, ''A History of Optics: From Greek Antiquity to the Nineteenth Century'', Oxford, {{ISBN|978-0-19-964437-7}}.
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* B. Powell (July 1856), [https://archive.org/stream/s4philosophicalmag12londuoft#page/n13/mode/2up "On the demonstration of Fresnel's formulas for reflected and refracted light; and their applications"], ''Philosophical Magazine and Journal of Science'', Series 4, vol.{{nnbsp}}12, no.{{hsp}}76, pp.{{nnbsp}}1–20.
* J.A. Stratton, 1941, ''Electromagnetic Theory'', New York: McGraw-Hill.
* [[E. T. Whittaker]], 1910, [
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[[Category:Antennas (radio)]]
[[Category:History of physics]]
[[Category:Planes (geometry)]]
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