Circular polarization - Knowledge (XXG)

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galactic background. The following resolution was adopted by Commissions 25 and 40: 'RESOLVED, that the frame of reference for the Stokes parameters is that of Right Ascension and Declination with the position angle of electric-vector maximum, q, starting from North and increasing through East. Elliptical polarization is defined in conformity with the definitions of the Institute of Electrical and Electronics Engineers (IEEE Standard 211, 1969). This means that the polarization of incoming radiation, for which the position angle, q, of the electric vector, measured at a fixed point in space, increases with time, is described as right-handed and positive.'"

2783:"... 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; 2823:"... circular and elliptical polarizations can be obtained using various feed arrangements or slight modifications made to the elements.... Circular polarization can be obtained if two orthogonal modes are excited with a 90° time-phase difference between them. This can be accomplished by adjusting the physical dimensions of the patch.... For a square patch element, the easiest way to excite ideally circular polarization is to feed the element at two adjacent edges.... The quadrature phase difference is obtained by feeding the element with a 90° power divider," p.859. 2653: 163: 259:

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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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.

2343: 1408: 2648:{\displaystyle {\begin{aligned}\psi _{\mathrm {R} }~&{\stackrel {\mathrm {def} }{=}}~{\frac {1}{\sqrt {2}}}\left(\cos \theta +i\sin \theta \exp \left(i\delta \right)\right)\exp \left(i\alpha _{x}\right)\\\psi _{\mathrm {L} }~&{\stackrel {\mathrm {def} }{=}}~{\frac {1}{\sqrt {2}}}\left(\cos \theta -i\sin \theta \exp \left(i\delta \right)\right)\exp \left(i\alpha _{x}\right)\end{aligned}}} 2859: 1817: 1180: 2724: 345:) will still emerge as right-handed, but elliptically, polarized. Light reflected by a metal at non-normal incidence will generally have its ellipticity changed as well. Such situations may be solved by decomposing the incident circular (or other) polarization into components of linear polarization parallel and perpendicular to the 735: 3178:

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.

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field's temporal rotation. It is considered clockwise circularly polarized because, from the point of view of the source, looking in the same direction of the wave's propagation, the field rotates in the clockwise direction. The second animation is that of left-handed or anti-clockwise light, using this same convention.

398:. 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 636: 1625: 711:

As stated earlier, there is significant confusion with regards to these two conventions. As a general rule, the engineering, quantum physics, and radio astronomy communities use the first convention, in which the wave is observed from the point of view of the source. In many physics textbooks dealing

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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

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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

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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.

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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

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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

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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

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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

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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

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IAU General Assembly Meeting, 1973, Commission 40 (Radio Astronomy/Radioastronomie), 8. POLARIZATION DEFINITIONS -- "A working Group chaired by Westerhout was convened to discuss the definition of polarization brightness temperatures used in the description of polarized extended objects and the

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As a specific example, refer to the circularly polarized wave in the first animation. Using this convention, that wave is defined as right-handed because when one points one's right thumb in the same direction of the wave's propagation, the fingers of that hand curl in the same direction of the

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Lectures on Physics Feynman (Vol. 1, ch.33-1) "If the end of the electric vector, when we look at it as the light comes straight toward us, goes around in an anti-clockwise direction, we call it right-hand circular polarization. ... Our convention for labeling left-hand and right-hand circular

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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

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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

1403:{\displaystyle {\begin{aligned}\mathbf {E} (\mathbf {r} ,t)&=\left|\,\mathbf {E} \,\right|\mathrm {Re} \left\{\mathbf {Q} \left|\psi \right\rangle \exp \left\right\}\\\mathbf {B} (\mathbf {r} ,t)&={\dfrac {1}{c}}{\hat {\mathbf {z} }}\times \mathbf {E} (\mathbf {r} ,t)\end{aligned}}} 3031:

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.),

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vectors of a traveling circularly polarized electromagnetic wave. This wave is right-handed/clockwise circularly polarized as defined from the point of view of the source, or left-handed/anti-clockwise circularly polarized if defined from the point of view of the

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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

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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.

2936:. 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 460: 287:

Left-handed/counterclockwise circularly polarized light displayed with and without the use of components. This would be considered right-handed/clockwise circularly polarized if defined from the point of view of the source rather than the

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Right-handed/counterclockwise circularly polarized light displayed with and without the use of components. This would be considered left-handed/clockwise circularly polarized if defined from the point of view of the source rather than the

2850:. 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. 428:

Circular polarization may be referred to as right-handed or left-handed, and clockwise or anti-clockwise, depending on the direction in which the electric field vector rotates. Unfortunately, two opposing historical conventions exist.

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The next pair of illustrations is that of left-handed, counterclockwise circularly polarized light when viewed by the receiver. Because it is left-handed, the rightward (relative to the direction of travel) horizontal component is now

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polarization is consistent with that which is used today for all the other particles in physics which exhibit polarization (e.g., electrons). However, in some books on optics the opposite conventions are used, so one must be careful."

1812:{\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}}} 3072:, 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.), 900: 3521:

Sparks, William B.; Hough, James; Germer, Thomas A.; Chen, Feng; DasSarma, Shiladitya; DasSarma, Priya; Robb, Frank T.; Manset, Nadine; Kolokolova, Ludmilla; Reid, Neill; Macchetto, F. Duccio; Martin, William (2009-05-12).

3112:, sec. 11.1, p. 61."the sense of polarization, or handedness ... is called right handed (left handed) if the direction of rotation is clockwise (anti-clockwise) for an observer looking in the direction of propagation" 3288:

In another location it is stated... "Note 4: Circular polarization may be referred to as "right-hand" or "left-hand", depending on whether the helix describes the thread of a right-hand or left-hand screw, respectively".

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IEEE Std 149-1979 (R2008), "IEEE Standard Test Procedures for Antennas". Reaffirmed December 10, 2008, Approved December 15, 1977, IEEE-SA Standards Board. Approved October 9, 2003, American National Standards Institute.

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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

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where the plus sign indicates left circular polarization, and the minus sign indicates right circular polarization. In the case of circular polarization, the electric field vector of constant magnitude rotates in the

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A left-handed/anti-clockwise circularly polarized wave as defined from the point of view of the source. It would be considered right-handed/clockwise circularly polarized if defined from the point of view of the

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A right-handed/clockwise circularly polarized wave as defined from the point of view of the source. It would be considered left-handed/anti-clockwise circularly polarized if defined from the point of view of the

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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

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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

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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.

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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

1917: 3036:, 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", 1610: 59:, 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 1131: 2253: 1090: 55:

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

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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.

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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

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in the plane wave article to better appreciate this dynamic. This light is considered to be right-hand, clockwise circularly polarized if viewed by the receiver. Since this is an

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Weaker sources of circular polarization in nature include multiple scattering by linear polarizers, as in the circular polarization of starlight, and selective absorption by

631:{\displaystyle \left(E_{x},\,E_{y},\,E_{z}\right)\propto \left(\cos {\frac {2\pi }{\lambda }}\left(ct-z\right),\,-\sin {\frac {2\pi }{\lambda }}\left(ct-z\right),\,0\right).} 187:, 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 127:

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.

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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

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Electromagnetic Waves & Antennas – S. J. Orfanidis: Footnote p.45, "most engineering texts use the IEEE convention and most physics texts, the opposite convention."

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of reflection, which are generally different for those two linear polarizations. Only in the special case of normal incidence, where there is no distinction between

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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

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regulations state that horizontal polarization is the standard for FM broadcasting, but that "circular or elliptical polarization may be employed if desired".

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When determining if the wave is clockwise or anti-clockwise circularly polarized, one again takes the point of view of the receiver and, while looking

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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.

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refers to as "mixed polarization", i.e. radio emissions that include both horizontally- and vertically-polarized components. In the United States,

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radio stations sometimes employ circular polarization to improve signal penetration into buildings and vehicles. It is one example of what the

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Circular polarization is often encountered in the field of optics and, in this section, the electromagnetic wave will be simply referred to as

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Electromagnetic Waves & Antennas – S. J. Orfanidis Pg 44 "Curl the fingers of your left and right hands into a fist and point both thumbs

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Quantum physicists also use this convention of handedness because it is consistent with their convention of handedness for a particle's spin.

191:, these vectors indicate that the electric field, from plane to plane, has a constant strength while its direction steadily rotates. Refer to 3839: 3817: 3608: 762: 3465: 179:

In a circularly polarized electromagnetic wave, the individual electric field vectors, as well as their combined vector, have a constant

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Tsyr-Huei Chiou; Sonja Kleinlogel; Tom Cronin; Roy Caldwell; Birte Loeffler; Afsheen Siddiqi; Alan Goldizen; Justin Marshall (2008).

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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

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A number of different types of antenna elements can be used to produce circularly polarized (or nearly so) radiation; following

2131:{\displaystyle |\mathrm {R} \rangle \ {\stackrel {\mathrm {def} }{=}}\ {1 \over {\sqrt {2}}}{\begin{pmatrix}1\\-i\end{pmatrix}}} 2237:{\displaystyle |\mathrm {L} \rangle \ {\stackrel {\mathrm {def} }{=}}\ {1 \over {\sqrt {2}}}{\begin{pmatrix}1\\i\end{pmatrix}}} 822: 814: 52:

of the wave has a constant magnitude and is rotating at a constant rate in a plane perpendicular to the direction of the wave.

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back down, its vertical component undergoes a phase shift. To an underwater observer looking up, the faint light outside

2010:{\displaystyle |\psi \rangle ={1 \over {\sqrt {2}}}{\begin{pmatrix}1\\\pm i\end{pmatrix}}\exp \left(i\alpha _{x}\right)} 113:

on 9 December 1822. Fresnel had first described the case of circular polarization, without yet naming it, in 1821.

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A. Fresnel, "Note sur le calcul des teintes que la polarisation développe dans les lames cristallisées" et seq.,

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the direction of propagation, and then matching the curling of one's fingers to the temporal rotation of the field.

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with optics, the second convention is used, in which the light is observed from the point of view of the receiver.

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oriented along the direction of propagation. A circularly polarized wave can rotate in one of two possible senses:

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Reversal of handedness of circularly polarized light by mirror. A demonstration – simple, cheap & instructive

3059:, vol. 7 (for 1820–23), Hendaye, Basses Pyrénées: Imprimerie de l'Observatoire d'Abbadia, 1916, p. 401. 2955: 846: 719: 196: 41: 3875: 3464:

Wynberg, Hans; Meijer, E.W.; Hummelen, J.C.; Dekkers, H.P.J.M.; Schippers, P.H.; Carlson, A.D. (7 August 1980).

3417:"Imaging polarimetry of the circularly polarizing cuticle of scarab beetles (Coleoptera: Rutelidae, Cetoniidae)" 1095: 1057: 91: 3230: 3057:

Procès-verbaux des séances de l'Académie tenues depuis la fondation de l'Institut jusqu'au mois d'août 1835

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Using this convention, the electric field vector of a left-handed circularly polarized wave is as follows:

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Circularly polarized light can be converted into linearly polarized light by passing it through a quarter-

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molecule. As a consequence, circular dichroism is exhibited by most biological molecules, because of the

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in magnitude to it. As a result, the magnetic field vectors would trace out a second helix if displayed.

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Balanis, Constantine A. "Antenna Theory: Analysis and Design", 2016, 4th Edition, John Wiley & Sons.

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of the reflected light is identical to that of the incident field. However, with propagation now in the

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is preferentially left-polarized. Since then, circular polarization has been measured in several other

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Circular polarization has been detected in light reflected from leaves and photosynthetic microbes.

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and the x amplitude equals the y amplitude, the wave is circularly polarized. The Jones vector is:

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direction of the wave's propagation, one observes the direction of the field's temporal rotation.

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Comparison of Circular Polarization with Linear and Elliptical Polarizations (YouTube Animation)

3504: 1423: 377:, are the Fresnel coefficients for the two components identical, leading to the above property. 1525: 3835: 3813: 3787: 3708: 3604: 3581: 3563: 3438: 3389: 3309:

Report 464-5, "Polarization of Emissions in Frequency-Modulation Broadcasting in Band 8 (VHF)"

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the direction of propagation, one observes the direction of the field's temporal rotation.

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Only a few mechanisms in nature are known to systematically produce circularly polarized

3763: 3694: 3651: 3549: 3484: 3377: 3279: 3782: 3735: 3576: 3523: 3328: 3290: 2863: 2774: 1823: 1569: 1551: 1171: 1167: 204: 200: 76: 24: 3361: 879:. The extent to which emissions are polarized is quantified in the same way it is for 3884: 3660: 3625: 3401: 2976: 2945: 2899: 2814: 648:(IEEE) standard and, as a result, it is generally used in the engineering community. 334: 247: 3524:"Detection of circular polarization in light scattered from photosynthetic microbes" 3450: 3257: 3231:"Glossary of terms used in photochemistry, 3rd edition (IUPAC Recommendations 2006)" 3720: 3500: 2885: 850: 795: 96: 2902:. In these cases, the underlying mechanism is the molecular-level helicity of the 312:

To convert circularly polarized light to the other handedness, one can use a half-

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Srinivasarao, Mohan; Park, Jung Ok; Crne, Matija; Sharma, Vivek (July 24, 2009).

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can achieve, corresponding to linearly polarized or unpolarized light, is zero.

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corresponds to the quantum yield of left-handed circularly polarized light, and

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the vertical component by one quarter of a wavelength, rather than leading it.

3870: 3865: 3832:: Electromagnetic Theory of Propagation, Interference and Diffraction of Light 3703: 3676: 2895: 1414: 889: 838: 826: 231: 192: 188: 184: 3567: 3558: 3385: 3249: 3173: 3171: 3013: 2998: 2988: 2941: 2858: 1616: 1159: 739: 395: 313: 255: 3791: 3712: 3585: 3442: 3393: 3278:

rotation in an anti-clockwise sense is designated left-hand polarization. "

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will also impart a distinct CD to its respective molecules. Therefore, the

3362:"Structural Origin of Circularly Polarized Iridescence in Jeweled Beetles" 3740: 3642: 2926: 856:

Also, under the right conditions, even non-chiral molecules will exhibit

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In general, this phenomenon will be exhibited in absorption bands of any

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The phenomenon of polarization arises as a consequence of the fact that

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Many optics textbooks use this second convention. It is also used by

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Sinusoidal plane-wave solutions of the electromagnetic wave equation

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have been reported to be able to detect circular polarized light.

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Radio emission from pulsars can be strongly circularly polarized.

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is also circularly polarized, as reported in 1980 for the species

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then the polarization state can be written in the "R-L basis" as:

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Polarized Light in Animal Vision: Polarization Patterns in Nature

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Radio astronomers also use this convention in accordance with an

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have CD spectral signatures representative of their structures.

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discovered that light reflected from the golden scarab beetle

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Hegedüs, Ramón; Győző Szélb; Gábor Horváth (September 2006).

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to that of right-handed light. The maximum absolute value of

860:— that is, circular dichroism induced by a magnetic field. 3677:"Circular polarization vision in a stomatopod crustacean" 3086:(Creative Commons), 2021; author's footnote to §16. 2797:"To achieve circular polarization ... the circumference 2749: 402:

than 45° will generally produce elliptical polarization.

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matrix whose columns span the transverse x-y plane; and

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sense with respect to the direction of propagation, and

3834:(7th ed.). Cambridge: Cambridge University Press. 3314:(Report). International Telecommunications Union. 1990. 2741: 829:) molecules they contain. Noteworthy as well is that a 254:

of the dot, relative to the center of the circle, vary

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Article on the mantis shrimp and circular polarization

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proposes two contradictory conventions of handedness.

183:, and with changing phase angle. Given that this is a 2667: 2346: 2256: 2150: 2041: 1920: 1890: 1862: 1835: 1628: 1584: 1554: 1528: 1462: 1426: 1346: 1183: 1098: 1060: 903: 463: 2805:/wavelength = 1 near optimum, and the spacing about 3466:"Circular polarization observed in bioluminescence" 2702: 2647: 2326: 2236: 2130: 2009: 1903: 1876: 1848: 1811: 1604: 1560: 1540: 1514: 1441: 1402: 1125: 1084: 1043: 630: 3630:Monthly Notices of the Royal Astronomical Society 701:International Union of Pure and Applied Chemistry 646:Institute of Electrical and Electronics Engineers 203:vector has a corresponding, but not illustrated, 3856:Circularly polarized light: beetles and displays 2703:{\displaystyle \delta =\alpha _{y}-\alpha _{x}.} 750:transmitter on Lake Mountain, Utah. It radiates 67:in which the electric field vector rotates in a 3866:Animation of Circular Polarization (on YouTube) 3528:Proceedings of the National Academy of Sciences 2962:therefore is (partially) circularly polarized. 794:. Circular dichroism is the basis of a form of 365:linear polarizations are found by applying the 357:respectively. The reflected components in the 2744:. Consider transferring direct quotations to 1605:{\displaystyle \left|\,\mathbf {E} \,\right|} 8: 2321: 2293: 2265: 2161: 2052: 1929: 1637: 3120: 3118: 3624:Gogoberidze, G.; Machabeli, G. Z. (2005). 1126:{\displaystyle \theta _{\mathrm {right} }} 644:This convention is in conformity with the 3781: 3771: 3753: 3702: 3659: 3641: 3575: 3557: 3539: 3432: 3081: 3041: 2846:. Polarization is a manifestation of the 2691: 2678: 2666: 2630: 2544: 2526: 2525: 2520: 2518: 2517: 2503: 2502: 2483: 2397: 2379: 2378: 2373: 2371: 2370: 2356: 2355: 2347: 2345: 2316: 2311: 2304: 2303: 2288: 2283: 2276: 2275: 2257: 2255: 2208: 2199: 2194: 2176: 2175: 2170: 2168: 2167: 2156: 2151: 2149: 2099: 2090: 2085: 2067: 2066: 2061: 2059: 2058: 2047: 2042: 2040: 1996: 1949: 1940: 1935: 1921: 1919: 1895: 1889: 1866: 1861: 1840: 1834: 1790: 1748: 1713: 1696: 1682: 1670: 1652: 1651: 1646: 1644: 1643: 1629: 1627: 1596: 1591: 1590: 1583: 1553: 1527: 1496: 1494: 1493: 1479: 1477: 1476: 1463: 1461: 1425: 1382: 1374: 1360: 1358: 1357: 1345: 1324: 1316: 1247: 1234: 1228: 1223: 1222: 1196: 1188: 1184: 1182: 1104: 1103: 1097: 1085:{\displaystyle \theta _{\mathrm {left} }} 1066: 1065: 1059: 1015: 1014: 991: 990: 965: 964: 941: 940: 933: 908: 902: 616: 576: 566: 526: 501: 496: 487: 482: 473: 462: 65:right-handed circular polarization (RHCP) 2032:If basis vectors are defined such that: 738:Crossed-dipole antenna array of station 418: 409: 73:left-handed circular polarization (LHCP) 18: 3734:Sonja Kleinlogel; Andrew White (2008). 3024: 230:vertical component by one quarter of a 2940:due to inhomogeneities inside aligned 662:From the point of view of the receiver 656:International Astronomical Union (IAU) 3194:the direction the wave is traveling." 3160: 3158: 2735:too many or overly lengthy quotations 763:International Telecommunication Union 234:, a 90° phase difference. It is this 7: 3599:Horváth, Gábor; Dezsö Varjú (2003). 3074:Oeuvres complètes d'Augustin Fresnel 3034:Oeuvres complètes d'Augustin Fresnel 887:, also sometimes referred to as the 433:From the point of view of the source 3404:– via science.sciencemag.org. 3229:S. E. Braslavsky (1 January 2009). 48:state in which, at each point, the 3046:, 2021 (open access); §§9–10. 2533: 2530: 2527: 2504: 2386: 2383: 2380: 2357: 2317: 2305: 2289: 2277: 2183: 2180: 2177: 2157: 2074: 2071: 2068: 2048: 1659: 1656: 1653: 1515:{\displaystyle \mathbf {Q} =\left} 1238: 1235: 1117: 1114: 1111: 1108: 1105: 1076: 1073: 1070: 1067: 1028: 1025: 1022: 1019: 1016: 1001: 998: 995: 992: 978: 975: 972: 969: 966: 951: 948: 945: 942: 875:or an ensemble of luminophores is 798:that can be used to determine the 246:To appreciate how this quadrature 14: 3812:(3rd ed.). New York: Wiley. 869:Circularly polarized luminescence 767:Federal Communications Commission 390:Conversion to linear polarization 211:to the electric field vector and 105:. All three terms were coined by 75:in which the vector rotates in a 3827:Born, M. & Wolf, E. (1999). 3661:10.1111/j.1365-2966.2005.09681.x 3267:from the original on 2022-10-09. 3070:Annales de Chimie et de Physique 2722: 1592: 1497: 1480: 1464: 1383: 1375: 1361: 1325: 1317: 1248: 1224: 1197: 1189: 277: 266: 161: 150: 139: 189:circularly polarized plane wave 3603:. Springer. pp. 100–103. 2848:spin angular momentum of light 2801:of the helix must be ... with 2312: 2284: 2258: 2152: 2043: 1922: 1630: 1501: 1484: 1393: 1379: 1365: 1335: 1321: 1207: 1193: 871:(CPL) can occur when either a 238:relationship that creates the 1: 3137:the direction of propagation" 1164:electromagnetic wave equation 120:behaves as a two-dimensional 3773:10.1371/journal.pone.0002190 3434:10.1016/j.visres.2006.02.007 2956:totally internally reflected 845:regions of proteins and the 99:is the easier-to-understand 3110:10.1109/IEEESTD.1979.120310 2842:view, light is composed of 1904:{\displaystyle \alpha _{x}} 1849:{\displaystyle \alpha _{y}} 1162:plane wave solution of the 858:magnetic circular dichroism 802:and secondary structure of 707:Uses of the two conventions 450:from the source and in the 3917: 3238:Pure and Applied Chemistry 3205:"The Polarization Ellipse" 2831: 1442:{\displaystyle \omega =ck} 894:. This value is given by: 776: 111:French Academy of Sciences 109:, in a memoir read to the 3810:Classical Electrodynamics 3808:Jackson, John D. (1999). 3704:10.1016/j.cub.2008.02.066 1541:{\displaystyle 2\times 2} 720:US Federal Standard 1037C 658:resolution made in 1973. 2876:Albert Abraham Michelson 2742:summarize the quotations 1884:radians with respect to 1151:Mathematical description 441:from the source, in the 3559:10.1073/pnas.0810215106 3386:10.1126/science.1172051 3250:10.1351/pac200779030293 3055:Académie des Sciences, 2809:= wavelength/4," p.571; 406:Handedness conventions 92:elliptical polarization 3009:Starlight polarization 2867: 2825: 2811: 2785: 2704: 2649: 2328: 2238: 2132: 2011: 1905: 1878: 1877:{\displaystyle \pi /2} 1850: 1813: 1606: 1562: 1542: 1516: 1443: 1404: 1127: 1086: 1045: 755: 632: 425: 416: 386: 303:Reversal of handedness 29: 3891:Astrophysics concepts 2927:Photuris lucicrescens 2861: 2832:Further information: 2821: 2795: 2781: 2705: 2650: 2329: 2239: 2133: 2012: 1906: 1879: 1851: 1814: 1607: 1563: 1543: 1517: 1444: 1405: 1128: 1087: 1046: 737: 633: 422: 413: 383: 326:plane of polarization 107:Augustin-Jean Fresnel 83:Circular polarization 50:electromagnetic field 38:circular polarization 22: 3896:Polarization (waves) 3830:Principles of Optics 2881:Chrysina resplendens 2828:In quantum mechanics 2665: 2344: 2254: 2148: 2039: 1918: 1888: 1860: 1833: 1626: 1582: 1552: 1526: 1460: 1424: 1181: 1096: 1058: 901: 752:circularly polarized 461: 367:Fresnel coefficients 207:vector that is at a 197:electromagnetic wave 42:electromagnetic wave 3764:2008PLoSO...3.2190K 3695:2008CBio...18..429C 3652:2005MNRAS.364.1363G 3550:2009PNAS..106.7816S 3485:1980Natur.286..641W 3378:2009Sci...325..449S 2967:circularly dichroic 2938:linear polarization 2933:Photuris versicolor 2834:Photon polarization 831:secondary structure 718:The archive of the 349:, commonly denoted 102:linear polarization 3295:2011-06-06 at the 3284:2011-05-14 at the 2894:, as well as some 2868: 2840:quantum mechanical 2700: 2645: 2643: 2324: 2234: 2228: 2128: 2122: 2007: 1972: 1901: 1874: 1846: 1826:in the x-y plane. 1822:is the normalized 1809: 1803: 1704: 1619:of the field, and 1602: 1558: 1538: 1512: 1439: 1400: 1398: 1355: 1123: 1082: 1041: 885:dissymmetry factor 883:, in terms of the 881:circular dichroism 784:Circular dichroism 779:Circular dichroism 756: 628: 426: 417: 387: 347:plane of incidence 30: 16:Polarization state 3901:Stellar astronomy 3841:978-0-521-64222-4 3819:978-0-471-30932-1 3610:978-3-540-40457-6 3534:(19): 7816–7821. 3479:(5773): 641–642. 3427:(17): 2786–2797. 3372:(5939): 449–451. 2891:Chrysina gloriosa 2767: 2766: 2554: 2553: 2543: 2538: 2512: 2407: 2406: 2396: 2391: 2365: 2206: 2204: 2193: 2188: 2166: 2097: 2095: 2084: 2079: 2057: 1947: 1945: 1669: 1664: 1642: 1561:{\displaystyle c} 1522:is an orthogonal 1504: 1487: 1454:angular frequency 1368: 1354: 1035: 925: 919: 800:optical isomerism 589: 539: 3908: 3845: 3823: 3796: 3795: 3785: 3775: 3757: 3731: 3725: 3724: 3706: 3672: 3666: 3665: 3663: 3645: 3643:astro-ph/0510116 3636:(4): 1363–1366. 3621: 3615: 3614: 3596: 3590: 3589: 3579: 3561: 3543: 3518: 3512: 3511: 3510:on 24 July 2011. 3509: 3503:. Archived from 3493:10.1038/286641a0 3470: 3461: 3455: 3454: 3436: 3412: 3406: 3405: 3357: 3351: 3347: 3341: 3338: 3332: 3331: 3322: 3316: 3315: 3313: 3305: 3299: 3275: 3269: 3268: 3266: 3235: 3226: 3220: 3219: 3217: 3215: 3201: 3195: 3187: 3181: 3175: 3166: 3162: 3153: 3149: 3138: 3131: 3125: 3122: 3113: 3093: 3087: 3085: 3066: 3060: 3053: 3047: 3045: 3029: 2790:helical elements 2762: 2759: 2753: 2726: 2725: 2718: 2709: 2707: 2706: 2701: 2696: 2695: 2683: 2682: 2654: 2652: 2651: 2646: 2644: 2640: 2636: 2635: 2634: 2611: 2607: 2606: 2602: 2555: 2549: 2545: 2541: 2540: 2539: 2537: 2536: 2524: 2519: 2510: 2509: 2508: 2507: 2493: 2489: 2488: 2487: 2464: 2460: 2459: 2455: 2408: 2402: 2398: 2394: 2393: 2392: 2390: 2389: 2377: 2372: 2363: 2362: 2361: 2360: 2333: 2331: 2330: 2325: 2320: 2315: 2310: 2309: 2308: 2292: 2287: 2282: 2281: 2280: 2261: 2243: 2241: 2240: 2235: 2233: 2232: 2207: 2205: 2200: 2195: 2191: 2190: 2189: 2187: 2186: 2174: 2169: 2164: 2160: 2155: 2137: 2135: 2134: 2129: 2127: 2126: 2098: 2096: 2091: 2086: 2082: 2081: 2080: 2078: 2077: 2065: 2060: 2055: 2051: 2046: 2016: 2014: 2013: 2008: 2006: 2002: 2001: 2000: 1977: 1976: 1948: 1946: 1941: 1936: 1925: 1910: 1908: 1907: 1902: 1900: 1899: 1883: 1881: 1880: 1875: 1870: 1855: 1853: 1852: 1847: 1845: 1844: 1818: 1816: 1815: 1810: 1808: 1807: 1800: 1796: 1795: 1794: 1758: 1754: 1753: 1752: 1709: 1708: 1701: 1700: 1687: 1686: 1667: 1666: 1665: 1663: 1662: 1650: 1645: 1640: 1633: 1611: 1609: 1608: 1603: 1601: 1597: 1595: 1567: 1565: 1564: 1559: 1547: 1545: 1544: 1539: 1521: 1519: 1518: 1513: 1511: 1507: 1506: 1505: 1500: 1495: 1489: 1488: 1483: 1478: 1467: 1448: 1446: 1445: 1440: 1409: 1407: 1406: 1401: 1399: 1386: 1378: 1370: 1369: 1364: 1359: 1356: 1347: 1328: 1320: 1311: 1307: 1306: 1302: 1301: 1297: 1262: 1251: 1241: 1233: 1229: 1227: 1200: 1192: 1132: 1130: 1129: 1124: 1122: 1121: 1120: 1091: 1089: 1088: 1083: 1081: 1080: 1079: 1050: 1048: 1047: 1042: 1040: 1036: 1034: 1033: 1032: 1031: 1006: 1005: 1004: 984: 983: 982: 981: 956: 955: 954: 934: 923: 917: 916: 915: 811:optically active 749: 745: 699:as well as the 637: 635: 634: 629: 624: 620: 612: 608: 590: 585: 577: 562: 558: 540: 535: 527: 511: 507: 506: 505: 492: 491: 478: 477: 281: 270: 236:quadrature phase 193:these two images 165: 154: 143: 3916: 3915: 3911: 3910: 3909: 3907: 3906: 3905: 3881: 3880: 3852: 3842: 3826: 3820: 3807: 3804: 3802:Further reading 3799: 3733: 3732: 3728: 3682:Current Biology 3674: 3673: 3669: 3623: 3622: 3618: 3611: 3598: 3597: 3593: 3520: 3519: 3515: 3507: 3468: 3463: 3462: 3458: 3421:Vision Research 3414: 3413: 3409: 3359: 3358: 3354: 3348: 3344: 3339: 3335: 3324: 3323: 3319: 3311: 3307: 3306: 3302: 3297:Wayback Machine 3286:Wayback Machine 3276: 3272: 3264: 3233: 3228: 3227: 3223: 3213: 3211: 3203: 3202: 3198: 3188: 3184: 3176: 3169: 3163: 3156: 3150: 3141: 3132: 3128: 3123: 3116: 3094: 3090: 3067: 3063: 3054: 3050: 3030: 3026: 3022: 2985: 2975:Two species of 2914:bioluminescence 2856: 2836: 2830: 2776:dipole elements 2763: 2757: 2754: 2748:or excerpts to 2739: 2727: 2723: 2716: 2687: 2674: 2663: 2662: 2642: 2641: 2626: 2622: 2618: 2595: 2591: 2560: 2556: 2513: 2498: 2495: 2494: 2479: 2475: 2471: 2448: 2444: 2413: 2409: 2366: 2351: 2342: 2341: 2299: 2271: 2252: 2251: 2227: 2226: 2220: 2219: 2209: 2146: 2145: 2121: 2120: 2111: 2110: 2100: 2037: 2036: 1992: 1988: 1984: 1971: 1970: 1961: 1960: 1950: 1916: 1915: 1891: 1886: 1885: 1858: 1857: 1836: 1831: 1830: 1802: 1801: 1786: 1782: 1778: 1760: 1759: 1744: 1740: 1736: 1714: 1703: 1702: 1692: 1689: 1688: 1678: 1671: 1624: 1623: 1589: 1585: 1580: 1579: 1550: 1549: 1524: 1523: 1475: 1471: 1458: 1457: 1422: 1421: 1413:where k is the 1397: 1396: 1338: 1313: 1312: 1281: 1277: 1273: 1269: 1252: 1246: 1242: 1221: 1217: 1210: 1179: 1178: 1153: 1146: 1139: 1099: 1094: 1093: 1061: 1056: 1055: 1010: 986: 985: 960: 936: 935: 929: 904: 899: 898: 866: 781: 775: 747: 743: 732: 709: 664: 595: 591: 578: 545: 541: 528: 519: 515: 497: 483: 469: 468: 464: 459: 458: 435: 408: 392: 322: 310: 305: 292: 291: 290: 289: 284: 283: 282: 273: 272: 271: 178: 176: 175: 174: 173: 168: 167: 166: 157: 156: 155: 146: 145: 144: 133: 131:Characteristics 122:transverse wave 34:electrodynamics 17: 12: 11: 5: 3914: 3912: 3904: 3903: 3898: 3893: 3883: 3882: 3879: 3878: 3873: 3868: 3863: 3858: 3851: 3850:External links 3848: 3847: 3846: 3840: 3824: 3818: 3803: 3800: 3798: 3797: 3726: 3667: 3616: 3609: 3591: 3513: 3456: 3407: 3352: 3342: 3333: 3317: 3300: 3270: 3244:(3): 293–465. 3221: 3196: 3182: 3167: 3154: 3139: 3126: 3114: 3088: 3061: 3048: 3023: 3021: 3018: 3017: 3016: 3011: 3006: 3001: 2996: 2991: 2984: 2981: 2960:Snell's window 2886:scarab beetles 2855: 2852: 2829: 2826: 2816:patch elements 2773:, one can use 2765: 2764: 2730: 2728: 2721: 2715: 2712: 2711: 2710: 2699: 2694: 2690: 2686: 2681: 2677: 2673: 2670: 2656: 2655: 2639: 2633: 2629: 2625: 2621: 2617: 2614: 2610: 2605: 2601: 2598: 2594: 2590: 2587: 2584: 2581: 2578: 2575: 2572: 2569: 2566: 2563: 2559: 2552: 2548: 2535: 2532: 2529: 2523: 2516: 2514: 2506: 2501: 2497: 2496: 2492: 2486: 2482: 2478: 2474: 2470: 2467: 2463: 2458: 2454: 2451: 2447: 2443: 2440: 2437: 2434: 2431: 2428: 2425: 2422: 2419: 2416: 2412: 2405: 2401: 2388: 2385: 2382: 2376: 2369: 2367: 2359: 2354: 2350: 2349: 2335: 2334: 2323: 2319: 2314: 2307: 2302: 2298: 2295: 2291: 2286: 2279: 2274: 2270: 2267: 2264: 2260: 2245: 2244: 2231: 2225: 2222: 2221: 2218: 2215: 2214: 2212: 2203: 2198: 2185: 2182: 2179: 2173: 2163: 2159: 2154: 2139: 2138: 2125: 2119: 2116: 2113: 2112: 2109: 2106: 2105: 2103: 2094: 2089: 2076: 2073: 2070: 2064: 2054: 2050: 2045: 2018: 2017: 2005: 1999: 1995: 1991: 1987: 1983: 1980: 1975: 1969: 1966: 1963: 1962: 1959: 1956: 1955: 1953: 1944: 1939: 1934: 1931: 1928: 1924: 1898: 1894: 1873: 1869: 1865: 1856:is rotated by 1843: 1839: 1820: 1819: 1806: 1799: 1793: 1789: 1785: 1781: 1777: 1774: 1771: 1768: 1765: 1762: 1761: 1757: 1751: 1747: 1743: 1739: 1735: 1732: 1729: 1726: 1723: 1720: 1719: 1717: 1712: 1707: 1699: 1695: 1691: 1690: 1685: 1681: 1677: 1676: 1674: 1661: 1658: 1655: 1649: 1639: 1636: 1632: 1613: 1612: 1600: 1594: 1588: 1570:speed of light 1557: 1537: 1534: 1531: 1510: 1503: 1499: 1492: 1486: 1482: 1474: 1470: 1466: 1450: 1449: 1438: 1435: 1432: 1429: 1411: 1410: 1395: 1392: 1389: 1385: 1381: 1377: 1373: 1367: 1363: 1353: 1350: 1344: 1341: 1339: 1337: 1334: 1331: 1327: 1323: 1319: 1315: 1314: 1310: 1305: 1300: 1296: 1293: 1290: 1287: 1284: 1280: 1276: 1272: 1268: 1265: 1261: 1258: 1255: 1250: 1245: 1240: 1237: 1232: 1226: 1220: 1216: 1213: 1211: 1209: 1206: 1203: 1199: 1195: 1191: 1187: 1186: 1152: 1149: 1144: 1137: 1119: 1116: 1113: 1110: 1107: 1102: 1078: 1075: 1072: 1069: 1064: 1052: 1051: 1039: 1030: 1027: 1024: 1021: 1018: 1013: 1009: 1003: 1000: 997: 994: 989: 980: 977: 974: 971: 968: 963: 959: 953: 950: 947: 944: 939: 932: 928: 922: 914: 911: 907: 865: 862: 777:Main article: 774: 771: 731: 728: 708: 705: 688: 684: 673: 669: 663: 660: 627: 623: 619: 615: 611: 607: 604: 601: 598: 594: 588: 584: 581: 575: 572: 569: 565: 561: 557: 554: 551: 548: 544: 538: 534: 531: 525: 522: 518: 514: 510: 504: 500: 495: 490: 486: 481: 476: 472: 467: 453: 449: 446:while looking 444: 440: 434: 431: 407: 404: 391: 388: 343:Brewster angle 321: 318: 309: 306: 304: 301: 286: 285: 276: 275: 274: 265: 264: 263: 262: 261: 205:magnetic field 201:electric field 170: 169: 160: 159: 158: 149: 148: 147: 138: 137: 136: 135: 134: 132: 129: 25:electric field 15: 13: 10: 9: 6: 4: 3: 2: 3913: 3902: 3899: 3897: 3894: 3892: 3889: 3888: 3886: 3877: 3874: 3872: 3869: 3867: 3864: 3862: 3859: 3857: 3854: 3853: 3849: 3843: 3837: 3833: 3831: 3825: 3821: 3815: 3811: 3806: 3805: 3801: 3793: 3789: 3784: 3779: 3774: 3769: 3765: 3761: 3756: 3751: 3747: 3743: 3742: 3737: 3730: 3727: 3722: 3718: 3714: 3710: 3705: 3700: 3696: 3692: 3689:(6): 429–34. 3688: 3684: 3683: 3678: 3671: 3668: 3662: 3657: 3653: 3649: 3644: 3639: 3635: 3631: 3627: 3620: 3617: 3612: 3606: 3602: 3595: 3592: 3587: 3583: 3578: 3573: 3569: 3565: 3560: 3555: 3551: 3547: 3542: 3537: 3533: 3529: 3525: 3517: 3514: 3506: 3502: 3498: 3494: 3490: 3486: 3482: 3478: 3474: 3467: 3460: 3457: 3452: 3448: 3444: 3440: 3435: 3430: 3426: 3422: 3418: 3411: 3408: 3403: 3399: 3395: 3391: 3387: 3383: 3379: 3375: 3371: 3367: 3363: 3356: 3353: 3346: 3343: 3337: 3334: 3330: 3327: 3321: 3318: 3310: 3304: 3301: 3298: 3294: 3291: 3287: 3283: 3280: 3274: 3271: 3263: 3259: 3255: 3251: 3247: 3243: 3239: 3232: 3225: 3222: 3210: 3206: 3200: 3197: 3193: 3186: 3183: 3180: 3174: 3172: 3168: 3161: 3159: 3155: 3148: 3146: 3144: 3140: 3136: 3130: 3127: 3121: 3119: 3115: 3111: 3107: 3103: 3102:0-471-08032-2 3099: 3092: 3089: 3084: 3079: 3075: 3071: 3065: 3062: 3058: 3052: 3049: 3044: 3039: 3035: 3028: 3025: 3019: 3015: 3012: 3010: 3007: 3005: 3002: 3000: 2997: 2995: 2992: 2990: 2987: 2986: 2982: 2980: 2978: 2977:mantis shrimp 2973: 2970: 2968: 2963: 2961: 2957: 2952: 2949: 2947: 2943: 2939: 2935: 2934: 2929: 2928: 2923: 2919: 2915: 2910: 2908: 2905: 2901: 2900:mantis shrimp 2897: 2893: 2892: 2887: 2883: 2882: 2877: 2873: 2865: 2860: 2853: 2851: 2849: 2845: 2841: 2835: 2827: 2824: 2820: 2818: 2817: 2810: 2808: 2804: 2800: 2794: 2792: 2791: 2784: 2780: 2778: 2777: 2772: 2761: 2751: 2747: 2743: 2737: 2736: 2731:This section 2729: 2720: 2719: 2713: 2697: 2692: 2688: 2684: 2679: 2675: 2671: 2668: 2661: 2660: 2659: 2637: 2631: 2627: 2623: 2619: 2615: 2612: 2608: 2603: 2599: 2596: 2592: 2588: 2585: 2582: 2579: 2576: 2573: 2570: 2567: 2564: 2561: 2557: 2550: 2546: 2521: 2515: 2499: 2490: 2484: 2480: 2476: 2472: 2468: 2465: 2461: 2456: 2452: 2449: 2445: 2441: 2438: 2435: 2432: 2429: 2426: 2423: 2420: 2417: 2414: 2410: 2403: 2399: 2374: 2368: 2352: 2340: 2339: 2338: 2300: 2296: 2272: 2268: 2262: 2250: 2249: 2248: 2229: 2223: 2216: 2210: 2201: 2196: 2171: 2144: 2143: 2142: 2123: 2117: 2114: 2107: 2101: 2092: 2087: 2062: 2035: 2034: 2033: 2030: 2028: 2024: 2003: 1997: 1993: 1989: 1985: 1981: 1978: 1973: 1967: 1964: 1957: 1951: 1942: 1937: 1932: 1926: 1914: 1913: 1912: 1896: 1892: 1871: 1867: 1863: 1841: 1837: 1827: 1825: 1804: 1797: 1791: 1787: 1783: 1779: 1775: 1772: 1769: 1766: 1763: 1755: 1749: 1745: 1741: 1737: 1733: 1730: 1727: 1724: 1721: 1715: 1710: 1705: 1697: 1693: 1683: 1679: 1672: 1647: 1634: 1622: 1621: 1620: 1618: 1598: 1586: 1578: 1577: 1576: 1573: 1571: 1555: 1535: 1532: 1529: 1508: 1490: 1472: 1468: 1456:of the wave; 1455: 1436: 1433: 1430: 1427: 1420: 1419: 1418: 1416: 1390: 1387: 1371: 1351: 1348: 1342: 1340: 1332: 1329: 1308: 1303: 1298: 1294: 1291: 1288: 1285: 1282: 1278: 1274: 1270: 1266: 1263: 1259: 1256: 1253: 1243: 1230: 1218: 1214: 1212: 1204: 1201: 1177: 1176: 1175: 1173: 1169: 1165: 1161: 1158: 1150: 1148: 1143: 1136: 1100: 1062: 1037: 1011: 1007: 987: 961: 957: 937: 930: 926: 920: 912: 909: 905: 897: 896: 895: 893: 891: 886: 882: 878: 874: 870: 863: 861: 859: 854: 852: 851:nucleic acids 848: 844: 840: 836: 832: 828: 824: 820: 816: 812: 807: 805: 801: 797: 793: 789: 785: 780: 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