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{{short description|Polarization state}}
[[Image:Circular.Polarization.Circularly.Polarized.Light Left.Hand.Animation.305x190.255Colors.gif|thumb|305px|The [[electric field]] vectors of a traveling circularly polarized electromagnetic wave. This wave is right-handed/clockwise circularly
In [[Classical electromagnetism|electrodynamics]], '''circular polarization''' of an [[Electromagnetic radiation|electromagnetic wave]] is a [[Polarization (waves)|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 the direction of the wave.
In electrodynamics, the strength and direction of an electric field is defined by its electric field vector. In the case of a circularly polarized wave, the tip of the electric field [[Euclidean vector|vector]], at a given point in space, relates to the phase of the light as it travels through time and space. At any instant of time, the electric field vector of the wave indicates a point on a [[helix]] oriented along the direction of propagation. A circularly polarized wave can rotate in one of two possible senses:
''Circular polarization'' is a [[limiting case (mathematics)|limiting case]] of ''[[elliptical polarization]]''. The other [[special case]] is the easier-to-understand ''[[linear polarization]]''. All three terms were coined by [[Augustin-Jean Fresnel]], in a memoir read to the [[French Academy of Sciences]] on 9 December 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 December 1822; printed in H. de Senarmont, E. Verdet, and L. Fresnel (eds.), ''Oeuvres complètes d'Augustin Fresnel'', vol. 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 access); §§9–10.</ref><ref>Académie des Sciences, ''Procès-verbaux des séances de l'Académie tenues depuis la fondation de l'Institut jusqu'au mois d'août 1835'', vol. 7 (for 1820–23), Hendaye, Basses Pyrénées: Imprimerie de l'Observatoire d'Abbadia, 1916, p. 401.</ref> Fresnel had first described the case of circular polarization, without yet naming it, in 1821.<ref name=fresnel-1821a>A. Fresnel, "Note sur le calcul des teintes que la polarisation développe dans les lames cristallisées" et seq., ''Annales de Chimie et de Physique'', Ser. 2, vol. 17, pp. 102–11 (May 1821), 167–96 (June 1821), 312–15 ("Postscript", July 1821); reprinted (with added section nos.) in H. de Senarmont, E. Verdet, and L. Fresnel (eds.), ''Oeuvres complètes d'Augustin Fresnel'', vol. 1 (1866), pp. 609–48; translated as "On the calculation of the tints that polarization develops in crystalline plates, & postscript", {{Zenodo|4058004}} (Creative Commons), 2021; author's footnote to §16.</ref>
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The phenomenon of polarization arises as a consequence of the fact that [[light]] behaves as a two-dimensional [[Transverse wave#Explanation|transverse wave]].
Circular polarization occurs when the two orthogonal electric field component vectors are of equal magnitude and are out of phase by exactly 90°, or one-quarter wavelength.
== Characteristics ==
{{multiple image
| direction = vertical
| footer = Right-handed/
| footer_align = left
| width = 440
| image1 = Circular.Polarization.Circularly.Polarized.Light_Without.Components_Right.Handed.svg
| image2 = Circular.Polarization.Circularly.Polarized.Light_With.Components_Right.Handed.svg
| image3 = Circular polarization cross section.gif
}}
In a circularly polarized electromagnetic wave, the individual electric field vectors, as well as their combined vector, have a constant [[Magnitude (vector)|magnitude]], and with changing phase angle. Given that this is a [[plane wave]], each vector represents the magnitude and direction of the electric field for an entire plane that is perpendicular to the optical axis. Specifically, given that this is a [[Plane wave#Polarized electromagnetic plane waves|circularly polarized plane wave]], these vectors indicate that the electric field, from plane to plane, has a constant strength while its direction steadily rotates. Refer to [[
Circular polarization is often encountered in the field of optics and, in this section, the electromagnetic wave will be simply referred to as [[light]].
The nature of circular polarization and its relationship to other polarizations is often understood by thinking of the electric field as being divided into two [[Euclidean vector|components]] that are perpendicular to each other. The vertical component and its corresponding plane are illustrated in blue, while the horizontal component and its corresponding plane are illustrated in green. Notice that the rightward (relative to the direction of travel) horizontal component leads the vertical component by one quarter of a [[wavelength]], a 90° phase difference. It is this [[In-phase and quadrature components|quadrature phase]] relationship that creates the [[helix]] and causes the points of maximum magnitude of the vertical component to correspond with the points of zero magnitude of the horizontal component, and vice versa. The result of this alignment are select vectors, corresponding to the helix, which exactly match the maxima of the vertical and horizontal components.
To appreciate how this quadrature [[phase (waves)|phase]] shift corresponds to an electric field that rotates while maintaining a constant magnitude, imagine a dot traveling clockwise in a circle. Consider how the vertical and horizontal [[Displacement (vector)|displacements]] of the dot, relative to the center of the circle, vary [[Sine wave|sinusoidally]] in time and are out of phase by one quarter of a cycle. The displacements are said to be out of phase by one quarter of a cycle because the horizontal maximum displacement (toward the left) is reached one quarter of a cycle before the vertical maximum displacement is reached. Now referring again to the illustration, imagine the center of the circle just described, traveling along the axis from the front to the back. The circling dot will trace out a helix with the displacement toward our viewing left, leading the vertical displacement. Just as the horizontal and vertical displacements of the rotating dot are out of phase by one quarter of a cycle in time, the magnitude of the horizontal and vertical components of the electric field are out of phase by one quarter of a wavelength.
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The handedness of polarized light is reversed reflected off a surface at normal incidence. Upon such reflection, the rotation of the [[plane of polarization]] of the reflected light is identical to that of the incident field. However, with propagation now in the ''opposite'' direction, the same rotation direction that would be described as "right-handed" for the incident beam, is "left-handed" for propagation in the reverse direction, and vice versa. Aside from the reversal of handedness, the ellipticity of polarization is also preserved (except in cases of reflection by a [[Birefringence|birefringent]] surface).
Note that this principle only holds strictly for light reflected at normal incidence. For instance, right circularly polarized light reflected from a dielectric surface at grazing incidence (an angle beyond the [[Brewster's angle|Brewster angle]]) will still emerge as right-handed, but elliptically
[[File:Reversal of handedness of circularly polarized light reflected by mirror 2s.gif|thumbnail|A 3-slide series of pictures taken with and without a pair of MasterImage 3D circularly polarized movie glasses of some dead European rose chafers (Cetonia aurata) whose shiny green color comes from left-polarized light. Note that, without glasses, both the beetles and their images have shiny color. The right-polarizer removes the color of the beetles but leaves the color of the images. The left-polarizer does the opposite, showing reversal of handedness of the reflected light.]]
===Conversion to
Circularly polarized light can be converted into linearly polarized light by passing it through a quarter-[[waveplate]]. Passing linearly polarized light through a quarter-waveplate with its axes at 45° to its polarization axis will convert it to circular polarization. In fact, this is the most common way of producing circular polarization in practice. Note that passing linearly polarized light through a quarter-waveplate at an angle ''other'' than 45° will generally produce elliptical polarization.
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=== From the point of view of the source ===
Using this convention, polarization is defined from the point of view of the source. When using this convention, left- or right-handedness is determined by pointing one's left or right thumb {{em|away}} from the source, in the {{em|same}} direction that the wave is propagating, and matching the curling of one's fingers to the direction of the temporal rotation of the field at a given point in space. When determining if the wave is clockwise or anti-clockwise circularly polarized, one again takes the point of view of the source, and while looking {{em|away}} from the source and in the {{em|same}} direction of the wave's propagation, one observes the direction of the field's
Using this convention, the electric field vector of a left-handed circularly polarized wave is as follows:
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=== From the point of view of the receiver ===
In this alternative convention, polarization is defined from the point of view of the receiver. Using this convention, left- or right-handedness is determined by pointing one's left or right thumb {{em|toward}} the source, {{em|against}} the direction of propagation, and then matching the curling of one's fingers to the
When using this convention, in contrast to the other convention, the defined handedness of the wave matches the handedness of the screw type nature of the field in space. Specifically, if one freezes a right-handed wave in time, when one curls the fingers of one's right hand around the helix, the thumb will point in the direction of progression for the helix, given the sense of rotation. Note that, in the context of the nature of all screws and helices, it does not matter in which direction you point your thumb when determining its handedness.
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Just as in the other convention, right-handedness corresponds to a clockwise rotation, and left-handedness corresponds to an anti-clockwise rotation.
Many optics textbooks use this second convention.<ref name="Polarization_in_Spectral_Lines_Section_1.2">Polarization in Spectral Lines. 2004 E. Landi Degl'innocenti, M Landolfi Section 1.2 "When ... the tip of the electric field vector rotates clockwise for an observer facing the radiation source, ... (it will be considered)... positive (or righthanded) circular polarization, Our convention ... agrees with those proposed in the classical textbooks on polarized light by Shurcliff (1952) and by Clarke and Grainger (1971). The same convention is also used, although with some few exceptions, by optical astronomers working in the field of polarimetry. Many radio astronomers, on the other hand, use the opposite convention. [https://books.google.com/books?id=8sl2CkmZNWIC&dq=circular+polarization+conventions&pg=PA5]</ref><ref>HANDBOOK OPTICS Volume I, Devices, Measurements and Properties, Michael Bass Page 272 Footnote: "Right-circularly polarized light is defined as a clockwise rotation of the electric vector when the observer is looking ''against'' the direction the wave is traveling."</ref> It is also used by [[SPIE]]<ref>{{cite web|title=The Polarization Ellipse|url=https://spie.org/publications/fg05_p07-09_polarization_ellipse|website=spie.org|access-date=13 April 2018}}</ref> as well as the [[International Union of Pure and Applied Chemistry]] (IUPAC).<ref>{{cite journal |title=Glossary of terms used in photochemistry, 3rd edition (IUPAC Recommendations 2006) |author=S. E. Braslavsky |url=https://www.degruyter.com/downloadpdf/journals/pac/79/3/article-p293.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://www.degruyter.com/downloadpdf/journals/pac/79/3/article-p293.pdf |archive-date=2022-10-09 |url-status=live |journal=Pure and Applied Chemistry |volume=79 |issue=3 |pages=293–465 |date=1 January 2009 |doi=10.1351/pac200779030293|s2cid=96601716 }}</ref>
=== Uses of the two conventions ===
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To avoid confusion, it is good practice to specify "as defined from the point of view of the source" or "as defined from the point of view of the receiver" when discussing polarization matters.
The archive of the [https://web.archive.org/web/20090822015912/http://www.its.bldrdoc.gov/fs-1037/ US Federal Standard 1037C] proposes two contradictory conventions of handedness.<ref>In one ___location it is stated..."Note 1. ... In general, the figure, i.e., polarization, is elliptical and is traced in a clockwise or anti-clockwise sense, as viewed in the direction of propagation. ... Rotation of the electric vector in a clockwise sense is designated right-hand polarization, and rotation in an anti-clockwise sense is designated left-hand polarization. "[http://www.its.bldrdoc.gov/fs-1037//dir-028/_4059.htm] {{Webarchive|url=https://web.archive.org/web/20110514080812/http://www.its.bldrdoc.gov/fs-1037/dir-028/_4059.htm
Note that the IEEE defines RHCP and LHCP the opposite as those used by physicists. The IEEE 1979 Antenna Standard will show RHCP on the South Pole of the Poincare Sphere. The IEEE defines RHCP using the right hand with thumb pointing in the direction of transmit, and the fingers showing the direction of rotation of the E field with time. The rationale for the opposite conventions used by Physicists and Engineers is that Astronomical Observations are always done with the incoming wave traveling toward the observer, where as for most engineers, they are assumed to be standing behind the transmitter watching the wave traveling away from them. This article is not using the IEEE 1979 Antenna Standard and is not using the +t convention typically used in IEEE work.
== FM radio ==
[[File:KHTB-FM broadcasting antennas LakeMountain.jpg|thumb|upright=0.6|Crossed-dipole antenna array of station [[KENZ (FM)|KENZ]]'s {{nowrap|94.9 MHz}}, {{nowrap|48 kW}} transmitter on Lake Mountain, Utah. It radiates circularly polarized radio waves.]]
[[FM broadcasting|FM broadcast]] radio stations sometimes employ circular polarization to improve signal penetration into buildings and vehicles. It is one example of what the [[International Telecommunication Union]] refers to as "mixed polarization", i.e. radio emissions that include both horizontally- and vertically-polarized components.<ref>{{cite report |title=Report 464-5, "Polarization of Emissions in Frequency-Modulation Broadcasting in Band 8 (VHF)" |year=1990 |url=https://www.itu.int/dms_pub/itu-r/opb/rep/r-rep-bs.464-5-1990-pdf-e.pdf |publisher=International Telecommunications Union}}</ref> In the United States, [[Federal Communications Commission]] regulations state that horizontal polarization is the standard for FM broadcasting, but that "circular or elliptical polarization may be employed if desired".<ref>{{CodeFedReg |47|73|316}}</ref>
==Dichroism==
{{Main article|Circular dichroism}}
'''Circular dichroism''' ('''CD
In general, this phenomenon will be exhibited in absorption bands of any [[optical activity|optically active]] molecule. As a consequence, circular dichroism is exhibited by most biological molecules, because of the [[Dextrorotation and levorotation|dextrorotary]] (e.g., some [[sugar]]s) and [[Dextrorotation and levorotation|levorotary]] (e.g., some [[amino acid]]s) molecules they contain. Noteworthy as well is that a [[secondary structure]] will also impart a distinct CD to its respective molecules. Therefore, the [[alpha helix]], [[beta sheet]] and [[random coil]] regions of proteins and the [[Nucleic acid double helix|double helix]] of [[nucleic acid]]s have CD spectral signatures representative of their structures.
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:<math>\begin{align}
\mathbf{E} ( \mathbf{r}, t ) &= \left| \,\mathbf{E}\, \right| \mathrm{Re} \left\{ \mathbf{Q} \left|\psi\right\rangle \exp \left[ i \left( kz - \omega t \right) \right] \right\} \\
\mathbf{B} ( \mathbf{r}, t ) &= \dfrac{1}{c} \hat{ \mathbf{z} } \times \mathbf{E} ( \mathbf{r} , t )
\end{align}</math>
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==Antennas==
{{Over-quotation|section|date=April 2018}}
A number of different types of antenna elements can be used to produce circularly polarized (or nearly so) radiation; following [[Constantine A. Balanis|Balanis]],<ref name=Balanis>Balanis, Constantine A. "Antenna Theory
<blockquote>"... two crossed dipoles provide the two orthogonal field components.... If the two dipoles are identical, the field intensity of each along zenith ... would be of the same intensity. Also, if the two dipoles were fed with a 90° degree time-phase difference (phase quadrature), the polarization along zenith would be circular.... One way to obtain the 90° time-phase difference between the two orthogonal field components, radiated respectively by the two dipoles, is by feeding one of the two dipoles with a transmission line which is 1/4 wavelength longer or shorter than that of the other," p.80;</blockquote>
or [[Helical antenna|''helical elements'']]:
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==In quantum mechanics==
{{further|Photon polarization}}
In the [[quantum mechanical]] view, light is composed of [[photons]]. Polarization is a manifestation of the [[spin angular momentum of light]]. More specifically, in quantum mechanics, the direction of spin of a photon is tied to the handedness of the circularly polarized light, and the spin of a beam of photons is similar to the spin of a beam of particles, such as electrons.<ref>Introduction to Quantum Theory 2ED David Park Sec 2.2 Pg32 "... the polarization of a beam of light is exactly the same kind of thing as the spin of a beam of electrons, the differences of terminology reflecting only the accidents of the historical order of discovery."</ref> In the [[physics]] convention (from the point of view of the source), a right-handed circular polarization corresponds to a positive spin (denoted <math>\sigma^+</math>), whereas a left-handed circular polarization corresponds to a negative spin (denoted <math>\sigma^-</math>).<ref>W. Demtröder, [https://emineter.wordpress.com/wp-content/uploads/2015/03/atoms-molecules-and-photons-demtrc3b6der-springer-2005.pdf "Atoms, molecules and photons"], 2006, Springer, sec. 3.1, p. 91. The author uses the optics convention. "If left circularly-
polarized light (σ+-polarization) propagating in the z
direction is absorbed by atoms, the z component of
their angular momentum Jz is changed by ∆Jz = +ℏ". </ref>
==In nature==
[[File:Cetonia-aurata.jpg|thumb|right|The [[Cetonia aurata|rose chafer]]'s external surface reflects almost exclusively left-circularly polarized light.]]
Only a few mechanisms in nature are known to systematically produce circularly polarized [[light]]. In 1911, [[Albert A. Michelson|Albert Abraham Michelson]] discovered that light reflected from the golden scarab beetle ''[[Chrysina resplendens]]'' is preferentially left-polarized. Since then, circular polarization has been measured in several other [[Scarabaeidae|scarab beetles]] such as ''[[Chrysina gloriosa]]'',<ref>{{Cite journal|url=https://www.science.org/doi/10.1126/science.1172051|title=Structural Origin of Circularly Polarized Iridescence in Jeweled Beetles|first1=Mohan|last1=Srinivasarao|first2=Jung Ok|last2=Park|first3=Matija|last3=Crne|first4=Vivek|last4=Sharma|date=July 24, 2009|journal=Science|volume=325|issue=5939|pages=449–451|via=science.sciencemag.org|doi=10.1126/science.1172051|pmid=19628862|bibcode=2009Sci...325..449S|s2cid=206519071|url-access=subscription}}</ref> as well as some [[crustacean]]s such as the [[mantis shrimp]]. In these cases, the underlying mechanism is the molecular-level helicity of the [[chitin]]ous [[cuticle]].<ref name="Hegedüs">{{cite journal |title=Imaging polarimetry of the circularly polarizing cuticle of scarab beetles (Coleoptera: Rutelidae, Cetoniidae) |author1=Hegedüs, Ramón |author2=Győző Szélb |author3=Gábor Horváth |doi=10.1016/j.visres.2006.02.007 |journal=Vision Research |volume=46 |issue=17 |date=September 2006 |pages=2786–2797 |pmid=16564066 |s2cid=14974820 |doi-access=free }}</ref>
The [[bioluminescence]] of the [[larva]]e of [[firefly|fireflie]]s is also circularly polarized, as reported in 1980 for the species ''[[Photuris|Photuris lucicrescens]]'' and ''[[Photuris versicolor]]''. For fireflies, it is more difficult to find a microscopic explanation for the polarization, because the left and right lanterns of the larvae were found to emit polarized light of opposite senses. The authors suggest that the light begins with a [[linear polarization]] due to inhomogeneities inside aligned [[photocyte]]s, and it picks up circular polarization while passing through linearly [[Birefringence|birefringent]] tissue.<ref>{{cite journal |title=Circular polarization observed in bioluminescence |author1=Wynberg, Hans |author2=Meijer, E.W. |author3=Hummelen, J.C. |author4=Dekkers, H.P.J.M. |author5=Schippers, P.H. |author6=Carlson, A.D. |url=http://keur.eldoc.ub.rug.nl/FILES/wetenschappers/10/29/29.pdf |journal=Nature |volume=286 |issue=5773 |pages=641–642 |date=7 August 1980 |doi=10.1038/286641a0 |bibcode=1980Natur.286..641W |s2cid=4324467 |url-status=dead |archive-url=https://web.archive.org/web/20110724164914/http://keur.eldoc.ub.rug.nl/FILES/wetenschappers/10/29/29.pdf |archive-date=24 July 2011 }}</ref>
Circular polarization has been detected in light reflected from leaves and photosynthetic microbes.<ref name="b966">{{cite journal | last1=Sparks | first1=William B. | last2=Hough | first2=James | last3=Germer | first3=Thomas A. | last4=Chen | first4=Feng | last5=DasSarma | first5=Shiladitya | last6=DasSarma | first6=Priya | last7=Robb | first7=Frank T. | last8=Manset | first8=Nadine | last9=Kolokolova | first9=Ludmilla | last10=Reid | first10=Neill | last11=Macchetto | first11=F. Duccio | last12=Martin | first12=William | title=Detection of circular polarization in light scattered from photosynthetic microbes | journal=Proceedings of the National Academy of Sciences | volume=106 | issue=19 | date=2009-05-12 | issn=0027-8424 | pmid=19416893 | pmc=2674403 | doi=10.1073/pnas.0810215106 | pages=7816–7821| doi-access=free | arxiv=0904.4646 | bibcode=2009PNAS..106.7816S }}</ref>
Water-air interfaces provide another source of circular polarization. Sunlight that gets scattered back up towards the surface is linearly polarized. If this light is then [[total internal reflection|totally internally reflected]] back down, its vertical component undergoes a phase shift. To an underwater observer looking up, the faint light outside [[Snell's window]] therefore is (partially) circularly polarized.<ref>{{cite book |title=Polarized Light in Animal Vision: Polarization Patterns in Nature |author1=Horváth, Gábor |author2=Dezsö Varjú |year=2003 |publisher=Springer |isbn=978-3-540-40457-6 |pages=100–103}}</ref>
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Weaker sources of circular polarization in nature include multiple scattering by linear polarizers{{dubious|date=June 2021}}, as in the circular polarization of starlight, and selective absorption by [[circular dichroism|circularly dichroic]] media.
Radio emission from pulsars can be strongly circularly polarized.<ref>{{cite journal|doi=10.1111/j.1365-2966.2005.09681.x |title=On the origin of the circular polarization in radio pulsars |date=2005 |last1=Gogoberidze |first1=G. |last2=Machabeli |first2=G. Z. |journal=Monthly Notices of the Royal Astronomical Society |volume=364 |issue=4 |pages=1363–1366 |doi-access=free |arxiv=astro-ph/0510116 |bibcode=2005MNRAS.364.1363G }}</ref>
Two species of [[mantis shrimp]] have been reported to be able to detect circular polarized light.<ref>{{cite journal|author1=Tsyr-Huei Chiou |author2=Sonja Kleinlogel |author3=Tom Cronin |author4=Roy Caldwell |author5=Birte Loeffler |author6=Afsheen Siddiqi |author7=Alan Goldizen |author8=Justin Marshall |title=Circular polarization vision in a stomatopod crustacean |journal=[[Current Biology]] |year=2008 |volume=18 |issue=6 |pages=429–34 |doi=10.1016/j.cub.2008.02.066 |pmid=18356053|s2cid=6925705 |doi-access=free |bibcode=2008CBio...18..429C }}</ref><ref name="Kleinlogel et al.">{{cite journal |author1=Sonja Kleinlogel |author2=Andrew White |title=The secret world of shrimps: polarisation vision at its best |journal=[[PLoS ONE]] |year=2008 |doi=10.1371/journal.pone.0002190 |volume=3 |issue=5 |pages=e2190 |pmid=18478095 |pmc=2377063 |bibcode=2008PLoSO...3.2190K|arxiv = 0804.2162 |doi-access=free }}</ref>
==See also==
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*[https://www.youtube.com/watch?v=Q0qrU4nprB0 Comparison of Circular Polarization with Linear and Elliptical Polarizations (YouTube Animation)]
*[http://nagyelte.blogspot.hu/2015/01/reversal-of-handedness-of-circularly.html Reversal of handedness of circularly polarized light by mirror. A demonstration – simple, cheap & instructive]
{{DEFAULTSORT:Circular Polarization}}
[[Category:Concepts in astrophysics]]
[[Category:Polarization (waves)]]
[[Category:Stellar astronomy]]
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