Circular polarization

In electrodynamics, circular polarization of an electromagnetic wave is a polarization state in which, at each point, the electric field of the wave has a constant magnitude but its direction rotates with time at a steady 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, as seen in the accompanying animation, the tip of the electric field vector, at a given point in space, describes a circle as time progresses. At any instant of time, the electric field vector of the wave describes a helix along the direction of propagation. A circularly polarized wave can be in one of two possible states, right circular polarization in which the electric field vector rotates in a right-hand sense with respect to the direction of propagation, and left circular polarization in which the vector rotates in a left-hand sense.

Circular polarization is a limiting case of the more general condition of elliptical polarization. The other special case is the easier-to-understand linear polarization.

The phenomenon of polarization arises as a consequence of the fact that light behaves as a two-dimensional transverse wave.

Circular.Polarization.Circularly.Polarized.Light Left.Hand.Animation.305x190.255Colors
The electric field vectors of a traveling circularly polarized electromagnetic wave. This wave is right-circularly-polarized, since the direction of rotation of the vector is related by the right-hand rule to the direction the wave is moving; or left-circularly-polarized according to alternative convention.

General description

Right-handed/clockwise circularly polarized light displayed with and without the use of components. This would be considered left-handed/counter-clockwise circularly polarized if defined from the point of view of the source rather than the receiver. Refer to the below convention section.[1]

Circular.Polarization.Circularly.Polarized.Light Without.Components Right.Handed
Circular.Polarization.Circularly.Polarized.Light With.Components Right.Handed

On the right is an illustration of the electric field vectors of a circularly polarized electromagnetic wave.[1] The electric field vectors have a constant magnitude but their direction changes in a rotary manner. 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 axis. Specifically, given that this is a 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 these two images in the plane wave article to better appreciate this. This light is considered to be right-hand, clockwise circularly polarized if viewed by the receiver. Since this is an electromagnetic wave each electric field vector has a corresponding, but not illustrated, magnetic field vector that is at a right angle to the electric field vector and proportional in magnitude to it. As a result, the magnetic field vectors would trace out a second helix if displayed.

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 components which are at right angles to each other. Refer to the second illustration on the right. 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. It is this quadrature phase relationship which 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 is that there are select vectors, corresponding to the helix, which exactly match the maxima of the vertical and horizontal components. (To minimize visual clutter these are the only helix vectors displayed.)

To appreciate how this quadrature 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 displacements of the dot, relative to the center of the circle, vary 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.

Left-handed/anti-clockwise 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 receiver.

Circular.Polarization.Circularly.Polarized.Light Without.Components Left.Handed
Circular.Polarization.Circularly.Polarized.Light With.Components Left.Handed

The next pair of illustrations is that of left-handed, counter-clockwise 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 lagging the vertical component by one quarter of a wavelength rather than leading it.

Reversal of handedness by phase shift

To convert a given handedness of polarized light to the other handedness one can use a half-waveplate. A half-waveplate shifts a given component of light one half of a wavelength relative to the component to which it is orthogonal.

Reversal of handedness by reflection

The handedness of polarized light is also reversed when it is 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 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 angle) 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 plane of incidence, commonly denoted p and s respectively. The reflected components in the p and s linear polarizations are found by applying the Fresnel coefficients 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 p and s, are the Fresnel coefficients for the two components identical, leading to the above property.

Reversal of handedness of circularly polarized light reflected by mirror 2s
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 and from linear polarization

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.

Left-/right-handedness conventions

Circular.Polarization.Circularly.Polarized.Light Left.Hand.Animation.305x190.255Colors
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 receiver.
Circular.Polarization.Circularly.Polarized.Light Right.Handed.Animation.305x190.255Colors
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 receiver.

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.

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 away from the source, in the same direction that the wave is propagating, and matching the curling of one's fingers to the direction of the spatial 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 away from the source and in the same direction of the wave's propagation, one observes the direction of the field's spatial rotation.

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

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 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.

This convention is in conformity with the Institute of Electrical and Electronics Engineers (IEEE) standard and as a result it is generally used in the engineering community.[2][3][4]

Quantum physicists also use this convention of handedness because it is consistent with their convention of handedness for a particle's spin.[5]

Radio astronomers also use this convention in accordance with an International Astronomical Union (IAU) resolution made in 1973.[6]

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

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 which the helix progresses given that sense of rotation. Note that it is the nature of all screws and helices that it does not matter in which direction you point your thumb when determining its handedness.

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

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.[7][8] It is also used by SPIE.[9]

Uses of the two conventions

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 where the wave is observed from the point of view of the source.[3][5][6] In many physics textbooks dealing with optics the second convention is used where the light is observed from the point of view of the receiver.[5][7]

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 US Federal Standard 1037C proposes two contradictory conventions of handedness.[10]

FM radio

The term "circular polarization" is often used erroneously to describe mixed polarity signals used mostly in FM radio (87.5 to 108.0 MHz in the USA), where a vertical and a horizontal component are propagated simultaneously by a single or a combined array. This has the effect of producing greater penetration into buildings and difficult reception areas than a signal with just one plane of polarization. This would be an instance where the polarization would more appropriately be called random polarization because the polarization at a receiver, although constant, will vary depending on the direction from the transmitter and other factors in the transmitting antenna design. See Stokes parameters.
The term "FM radio" above refers to FM broadcasting, not 2-way radio (more properly called land mobile radio), which uses vertical polarization almost exclusively.

Circular dichroism

Circular dichroism (CD) is the differential absorption of left- and right-handed circularly polarized light. Circular dichroism is the basis of a form of spectroscopy that can be used to determine the optical isomerism and secondary structure of molecules.

In general, this phenomenon will be exhibited in absorption bands of any optically active molecule. As a consequence, circular dichroism is exhibited by most biological molecules, because of the dextrorotary (e.g. some sugars) and levorotary (e.g. some amino acids) 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 double helix of nucleic acids have CD spectral signatures representative of their structures.

Also, under the right conditions, even non-chiral molecules will exhibit magnetic circular dichroism, that is, circular dichroism induced by a magnetic field.

Circularly polarized luminescence

Circularly polarized luminescence (CPL) can occur when either a luminophore or an ensemble of luminophores is chiral. The extent to which emissions are polarized is quantified in the same way it is for circular dichroism, in terms of the dissymmetry factor, also sometimes referred to as the anisotropy factor. This value is given by

where corresponds to the quantum yield of left-handed circularly polarized light, and to that of right-handed light. The maximum absolute value of gem, corresponding to purely left- or right-handed circular polarization, is therefore 2. Meanwhile, the smallest absolute value that gem can achieve, corresponding to linearly polarized or unpolarized light, is zero.

Mathematical description

The classical sinusoidal plane wave solution of the electromagnetic wave equation for the electric and magnetic fields is

where k is the wavenumber,

is the angular frequency of the wave, is an orthogonal matrix whose columns span the transverse x-y plane and is the speed of light.

Here

is the amplitude of the field and

is the normalized Jones vector in the x-y plane.

If is rotated by radians with respect to and the x amplitude equals the y amplitude the wave is circularly polarized. The Jones vector is

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 x-y plane.

If basis vectors are defined such that

and

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

where

and

Antennas

A number of different types of antenna elements can be used to produce circularly polarized (or nearly so) radiation; following Balanis,[11] one can use dipole elements:

"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;

or helical elements:

"To achieve circular polarization [in axial or end-fire mode] ... the circumference C of the helix must be ... with C/wavelength = 1 near optimum, and the spacing about S = wavelength/4." p.571;

or patch elements:

"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.

Quantum mechanics

In the quantum mechanical view, light is composed of photons. Polarization is a manifestation of the intrinsic angular momentum (the spin) of the photon. 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.[12]

In nature

Cetonia-aurata
The 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 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 scarab beetles like Chrysina gloriosa,[13] as well as some crustaceans such as the mantis shrimp. In these cases, the underlying mechanism is the molecular-level helicity of the chitinous cuticle.[14]

The bioluminescence of the larvae of fireflies is also circularly polarized, as reported in 1980 for the species 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 inhomogeneties inside aligned photocytes, and it picks up circular polarization while passing through linearly birefringent tissue.[15]

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 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.[16]

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

Two species of mantis shrimp have been reported to be able to detect circular polarized light.[17][18]

Starlight

The circular polarization of starlight has been observed to be a function of the linear polarization of starlight.

Starlight becomes partially linearly polarized by scattering from elongated interstellar dust grains whose long axes tend to be oriented perpendicular to the galactic magnetic field. According to the Davis–Greenstein mechanism, the grains spin rapidly with their rotation axis along the magnetic field. Light polarized along the direction of the magnetic field perpendicular to the line of sight is transmitted, while light polarized in the plane defined by the rotating grain is blocked. Thus the polarization direction can be used to map the galactic magnetic field. The degree of polarization is on the order of 1.5% for stars at 1,000 parsecs' distance.[19]

Normally, a much smaller fraction of circular polarization is found in starlight. Serkowski, Mathewson and Ford[20] measured the polarization of 180 stars in UBVR filters. They found a maximum fractional circular polarization of , in the R filter.

The explanation is that the interstellar medium is optically thin. Starlight traveling through a kiloparsec column undergoes about a magnitude of extinction, so that the optical depth ~ 1. An optical depth of 1 corresponds to a mean free path, which is the distance, on average that a photon travels before scattering from a dust grain. So on average, a starlight photon is scattered from a single interstellar grain; multiple scattering (which produces circular polarization) is much less likely. Observationally,[19] the linear polarization fraction p ~ 0.015 from a single scattering; circular polarization from multiple scattering goes as , so we expect a circularly polarized fraction of .

Light from early-type stars has very little intrinsic polarization. Kemp et al.[21] measured the optical polarization of the Sun at sensitivity of ; they found upper limits of for both (fraction of linear polarization) and (fraction of circular polarization).

The interstellar medium can produce circularly polarized (CP) light from unpolarized light by sequential scattering from elongated interstellar grains aligned in different directions. One possibility is twisted grain alignment along the line of sight due to variation in the galactic magnetic field; another is the line of sight passes through multiple clouds. For these mechanisms the maximum expected CP fraction is , where is the fraction of linearly polarized (LP) light. Kemp & Wolstencroft[22] found CP in six early-type stars (no intrinsic polarization), which they were able to attribute to the first mechanism mentioned above. In all cases, in blue light.

Martin[23] showed that the interstellar medium can convert LP light to CP by scattering from partially aligned interstellar grains having a complex index of refraction. This effect was observed for light from the Crab Nebula by Martin, Illing and Angel.[24]

An optically thick circumstellar environment can potentially produce much larger CP than the interstellar medium. Martin[23] suggested that LP light can become CP near a star by multiple scattering in an optically thick asymmetric circumstellar dust cloud. This mechanism was invoked by Bastien, Robert and Nadeau,[25] to explain the CP measured in 6 T-Tauri stars at a wavelength of 768 nm. They found a maximum CP of . Serkowski[26] measured CP of for the red supergiant NML Cygni and in the long-period variable M star VY Canis Majoris in the H band, ascribing the CP to multiple scattering in circumstellar envelopes. Chrysostomou et al.[27] found CP with q of up to 0.17 in the Orion OMC-1 star-forming region, and explained it by reflection of starlight from aligned oblate grains in the dusty nebula.

Circular polarization of zodiacal light and Milky Way diffuse galactic light was measured at wavelength of 550 nm by Wolstencroft and Kemp.[28] They found values of , which is higher than for ordinary stars, presumably because of multiple scattering from dust grains.

See also

References

  1. ^ a b For handedness conventions refer to the well referenced section Left/Right Handedness Conventions
  2. ^ 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. ISBN 0-471-08032-2. doi:10.1109/IEEESTD.1979.120310, 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"
  3. ^ a b Electromagnetic Waves & Antennas – S. J. Orfanidis: Footnote p.45, "most engineering texts use the IEEE convention and most physics texts, the opposite convention."
  4. ^ Electromagnetic Waves & Antennas – S. J. Orfanidis Pg 44 "Curl the fingers of your left and right hands into a fist and point both thumbs towards the direction of propagation"
  5. ^ a b c 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 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."
  6. ^ a b 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 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.'"
  7. ^ a b 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. [1]
  8. ^ 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."
  9. ^ "The Polarization Ellipse". spie.org. Retrieved 13 April 2018.
  10. ^ 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 a anti-clockwise sense is designated left-hand polarization . "[2] Archived 2011-03-11 at WebCite 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." [3]
  11. ^ Balanis, Constantine A. "Antenna Theory – Analysis and Design", 2005, 3rd Edition, John Wiley & Sons.
  12. ^ 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."
  13. ^ Structural Origin of Circularly Polarized Iridescence in Jeweled Beetles.
  14. ^ Hegedüs, Ramón; Győző Szélb; Gábor Horváth (September 2006). "Imaging polarimetry of the circularly polarizing cuticle of scarab beetles (Coleoptera: Rutelidae, Cetoniidae)" (PDF). Vision Research. 46 (17): 2786–2797. doi:10.1016/j.visres.2006.02.007. PMID 16564066. Archived from the original (PDF) on 2011-07-21.
  15. ^ Wynberg, Hans; Meijer, E.W.; Hummelen, J.C.; Dekkers, H.P.J.M.; Schippers, P.H.; Carlson, A.D. (7 August 1980). "Circular polarization observed in bioluminescence" (PDF). Nature. 286 (5773): 641–642. Bibcode:1980Natur.286..641W. doi:10.1038/286641a0. Archived from the original (PDF) on 24 July 2011.
  16. ^ Horváth, Gábor; Dezsö Varjú (2003). Polarized Light in Animal Vision: Polarization Patterns in Nature. Springer. pp. 100–103. ISBN 978-3-540-40457-6.
  17. ^ Tsyr-Huei Chiou; Sonja Kleinlogel; Tom Cronin; Roy Caldwell; Birte Loeffler; Afsheen Siddiqi; Alan Goldizen; Justin Marshall (2008). "Circular polarization vision in a stomatopod crustacean". Current Biology. 18 (6): 429–34. doi:10.1016/j.cub.2008.02.066. PMID 18356053.
  18. ^ Sonja Kleinlogel; Andrew White (2008). "The secret world of shrimps: polarisation vision at its best". PLoS ONE. 3 (5): e2190. arXiv:0804.2162. Bibcode:2008PLoSO...3.2190K. doi:10.1371/journal.pone.0002190. PMC 2377063. PMID 18478095.
  19. ^ a b Fosalba, Pablo; Lazarian, Alex; Prunet, Simon; Tauber, Jan A. (2002). "Statistical Properties of Galactic Starlight Polarization". Astrophysical Journal. 564 (2): 762–772. arXiv:astro-ph/0105023. Bibcode:2002ApJ...564..762F. doi:10.1086/324297.
  20. ^ Serkowski, K.; Mathewson and Ford (1975). "Wavelength dependence of interstellar polarization and ratio of total to selective extinction". Astrophysical Journal. 196: 261. Bibcode:1975ApJ...196..261S. doi:10.1086/153410.
  21. ^ Kemp, J. C.; et al. (1987). "The optical polarization of the Sun measured at a sensitivity of parts in ten million". Nature. 326 (6110): 270–273. Bibcode:1987Natur.326..270K. doi:10.1038/326270a0.
  22. ^ Kemp, James C.; Wolstencroft (1972). "Interstellar Circular Polarization: Data for Six Stars and the Wavelength Dependence". Astrophysical Journal. 176: L115. Bibcode:1972ApJ...176L.115K. doi:10.1086/181036.
  23. ^ a b Martin (1972). "Interstellar circular polarization". MNRAS. 159 (2): 179–190. Bibcode:1972MNRAS.159..179M. doi:10.1093/mnras/159.2.179.
  24. ^ Martin, P.G.; Illing, R.; Angel, J. R. P. (1972). "Discovery of interstellar circular polarization in the direction of the Crab nebula". MNRAS. 159 (2): 191–201. Bibcode:1972MNRAS.159..191M. doi:10.1093/mnras/159.2.191.
  25. ^ Bastein, Pierre; Robert and Nadeau (1989). "Circular polarization in T Tauri stars. II - New observations and evidence for multiple scattering". Astrophysical Journal. 339: 1089. Bibcode:1989ApJ...339.1089B. doi:10.1086/167363.
  26. ^ Serkowski, K. (1973). "Infrared Circular Polarization of NML Cygni and VY Canis Majoris". Astrophysical Journal. 179: L101. Bibcode:1973ApJ...179L.101S. doi:10.1086/181126.
  27. ^ Chrysostomou, Antonio; et al. (2000). "Polarimetry of young stellar objects - III. Circular polarimetry of OMC-1". MNRAS. 312 (1): 103–115. Bibcode:2000MNRAS.312..103C. CiteSeerX 10.1.1.46.3044. doi:10.1046/j.1365-8711.2000.03126.x.
  28. ^ Wolstencroft, Ramon D.; Kemp (1972). "Circular Polarization of the Nightsky Radiation". Astrophysical Journal. 177: L137. Bibcode:1972ApJ...177L.137W. doi:10.1086/181068.

External links

Further reading

  • Jackson, John D. (1999). Classical Electrodynamics (3rd ed.). New York: Wiley. ISBN 978-0-471-30932-1.
  • Born, M. & Wolf, E. (1999). Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (7th ed.). Cambridge: Cambridge University Press. ISBN 978-0-521-64222-4.
AN/APQ-174

The AN/APQ-174 is an American Ku band radar used on military helicopters for navigation, particularly at low level.

It was developed during the late 1980s, as a derivative of the AN/APQ-168 and LANTIRN radars. It was initially procured in the early 1990s for a variety of platforms, including U.S. Army MH-47 Chinooks and MH-60s. The radar can be used for a variety of missions, including: combat search and rescue and special forces insertion and extraction.

This podded radar has a variety of modes, including terrain-following and terrain-avoidance, ground mapping, air-to-ground ranging, weather detection/tracking, navigation, beacon interrogation, cross scan modes and power management.

Angular scan times are 5.5º/sec and the weather mode is improved during heavy rain by the use of circular polarization.

AO-51

AO-51 is the in-orbit name designation of a now defunct (following battery failure) LEO amateur radio satellite of the OSCAR series; formerly known as ECHO, built by AMSAT. It was launched on June 29, 2004 from Baikonur Cosmodrome, Kazakhstan on a Dnepr launch vehicle. It is in sun synchronous low Earth orbit.

AO-51 contained an FM repeater with both 144 MHz (V band) and 1.2 GHz (L band) uplinks and 435 MHz (U band) and 2.4 GHz (S band) downlinks. It also contained a digital subsystem that transmitted telemetry on 70 cm and provided a complete PACSAT BBS that could be configured on both V band and S band uplinks. As well, there was a 10-meter PSK uplink.

AO-51 had four VHF receivers, two UHF transmitters, six modems, and 56 channels of telemetry. The two UHF transmitters were connected to four phased antennas, yielding right-hand circular polarization for the 435.300 downlink and left-hand circular polarization for the 435.150 downlink.

The AO-51 FM satellite was easily workable with an amateur radio VHF dual band hand-held radio, as long as you knew when the satellite's footprint was within reach. Transatlantic contacts had been made without much effort, as long as the satellite was approximately mid-Atlantic so that the edge of the satellites footprint was within reach on either continent.

As of May 2011 the satellite faced problems with the battery. By September, a work around for the battery issue was found, bringing the repeater back in use. On November 29, 2011, the AO-51 Command Team announced that AO-51 has ceased transmission and is not responding to commands.

Axial ratio

Axial ratio, for any structure or shape with two or more axes, is the ratio of the length (or magnitude) of those axes to each other - the longer axis divided by the shorter.

In chemistry or materials science, the axial ratio (symbol P) is used to describe rigid rod-like molecules. It is defined as the length of the rod divided by the rod diameter.

In physics, the axial ratio describes electromagnetic radiation with elliptical, or circular, polarization. The axial ratio is the ratio of the magnitudes of the major and minor axis defined by the electric field vector.

Chirality (electromagnetism)

The term chiral describes an object, especially a molecule, which has or produces a non-superposable mirror image of itself. In chemistry, such a molecule is called an enantiomer or is said to exhibit chirality or enantiomerism. The term "chiral" comes from the Greek word for the human hand, which itself exhibits such non-superimposeability of the left hand precisely over the right. Due to the opposition of the fingers and thumbs, no matter how the two hands are oriented, it is impossible for both hands to exactly coincide. Helices, chiral characteristics (properties), chiral media, order, and symmetry all relate to the concept of left- and right-handedness.

Cosmology Large Angular Scale Surveyor

The Cosmology Large Angular Scale Surveyor (CLASS) is an array of microwave telescopes at a high-altitude site in the Atacama Desert of Chile as part of the Parque Astronómico de Atacama. The CLASS experiment aims to test the theory of cosmic inflation and distinguish between inflationary models of the very early universe by making precise measurements of the polarization of the Cosmic Microwave Background (CMB) over 65% of the sky at multiple frequencies in the microwave region of the electromagnetic spectrum.

Ekran

For the Soviet animation studio see page Studio EkranEkran (Russian: "Экран", "Screen") was a Soviet-Russian type of geostationary satellite, developed for a national system of Direct-To-Home television.

The first satellite of Ekran series was launched in 1976. Each satellite in the Ekran series was designed to provide one TV and 2 radio program channels to cable TV systems throughout the USSR and to individual home receivers in northern Siberia. Ekran's downlink is in the UHF range.

Early Ekran satellites used orbital positions in the range from 48 degrees E to 95 degrees E, but recent Ekrans, including the current Ekran 20, have been stationed at 99 degrees E. These 3-axis stabilized satellites carry a single 24 MHz, 200 W transponder, feeding a 28 dB gain antenna transmitting on right-hand circular polarization to produce equivalent isotropically radiated powers in Siberia in the range 50 to 55 dBW at 714 MHz. The corresponding feeder link uses left-hand circular polarization at 6200 MHz. Therefore, almost every householder could receive the TV signal at home from Ekran's transponder using a simple Yagi-Uda antenna. There were also various kinds of collective or individual satellite receivers, such as Ekran KR-10, Ekran-KR-01 and Ekran. Latest version of receiver represents a simple individual TV set-top box itself. A modified version of Ekran was called Ekran-M. Ekran satellites have been replaced by improved geostationary craft for DBS, such as Gorizont, Gals, and Express.

On June 23, 1978 the Ekran-2 spacecraft exploded due to a catastrophic discharge of its battery, contributing to the increase in Space Debris on the GEO orbit.

Electron magnetic circular dichroism

Electron magnetic circular dichroism (EMCD) (also known as electron energy-loss magnetic chiral dichroism) is the EELS equivalent of XMCD.

The effect was first proposed in 2003 and experimentally confirmed in 2006 by the group of Prof. Peter Schattschneider at the Vienna University of Technology.

Similarly to XMCD, EMCD is a difference spectrum of two EELS spectra taken in a magnetic field with opposite helicities. Under appropriate scattering conditions virtual photons with specific circular polarizations can be absorbed, giving rise to spectral differences. The largest difference is expected between the case where one virtual photon with left circular polarization and one with right circular polarization are absorbed. By closely analyzing the difference in the EMCD spectrum, information can be obtained on the magnetic properties of the atom, such as its spin and orbital magnetic moment.In the case of transition metals such as iron, cobalt, and nickel, the absorption spectra for EMCD are usually measured at the L-edge. This corresponds to the excitation of a 2p electron to a 3d state by the absorption of a virtual photon providing the ionisation energy. The absorption is visible as a spectral feature in the electron energy loss spectrum (EELS). Because the 3d electron states are the origin of the magnetic properties of the elements, the spectra contain information on the magnetic properties. Moreover, since the energy of each transition depends on the atomic number, the information obtained is element specific, that is, it is possible to distinguish the magnetic properties of a given element by examining the EMCD spectrum at its characteristic energy (708 eV for iron).

Since in both EMCD and XMCD the same electronic transitions are probed, the information obtained is the same. However EMCD has a higher spatial resolution and depth sensitivity than its X-ray counterpart. Moreover, EMCD can be measured on any TEM equipped with an EELS detector, whereas XMCD is normally measured only on dedicated synchrotron beamlines.

It has been recently demonstrated that electron vortex beams can be also used to measure EMCD.

Gonodactylus smithii

Gonodactylus smithii, the purple spot mantis shrimp, is a species of mantis shrimp of the smasher type. It is found from New Caledonia to the western part of the Indian Ocean, including Australia's north coast and the Great Barrier Reef.It is the only organism known to simultaneously detect the four linear and two circular polarization components required for Stokes parameters, which yield a full description of polarization. It is thus believed to have optimal polarization vision.The specific epithet smithii is in commemoration of Sir Percy William Bassett-Smith.

Imbert–Fedorov effect

The Imbert–Fiodaraŭ effect (named after Fiodar Ivanavič Fiodaraŭ (1911 – 1994) and Christian Imbert (1937 – 1998) is an optical phenomenon in which a beam of circularly or elliptically polarized light undergoes a small sideways shift, when refracted or totally internally reflected. The sideways shift is perpendicular to the plane containing the incident and reflected beams. This effect is the circular polarization analog of the Goos–Hänchen effect.

Orbital angular momentum multiplexing

Orbital angular momentum (OAM) multiplexing is a physical layer method for multiplexing signals carried on electromagnetic waves using the orbital angular momentum of the electromagnetic waves to distinguish between the different orthogonal signals.Orbital angular momentum is one of two forms of angular momentum of light. OAM is distinct from, and should not be confused with, light spin angular momentum. The spin angular momentum of light offers only two orthogonal quantum states corresponding to the two states of circular polarization, and can be demonstrated to be equivalent to a combination of polarization multiplexing and phase shifting. OAM on the other hand relies on an extended beam of light, and the higher quantum degrees of freedom which come with the extension. OAM multiplexing can thus access a potentially unbounded set of states, and as such offer a much larger number of channels, subject only to the constraints of real-world optics.

As of 2013, although OAM multiplexing promises very significant improvements in bandwidth when used in concert with other existing modulation and multiplexing schemes, it is still an experimental technique, and has so far only been demonstrated in the laboratory. Following the early claim that OAM exploits a new quantum mode of information propagation, the technique has become controversial; however nowadays it can be understood to be a particular form of tightly modulated MIMO multiplexing strategy, obeying classical information theoretic bounds.

POlarization Emission of Millimeter Activity at the Sun

The POlarization Emission of Millimeter Activity at the Sun (POEMAS) is a solar patrol system composed of two radio telescopes with superheterodyne circular polarization receivers at 45 and 90 GHz. Since their half power beam width is around 1.4°, they observe the full sun. The acquisition system allows to gather 100 values per second at both frequencies and polarizations, with a sensitivity of around 20 solar flux units (SFU) (1 SFU ≡ 104 Jy). The telescope saw first light in November 2011, and showed excellent performance during two years, when it observed many flares. Since November 2013 is stopped for repairing. The main interest of POEMAS is the observation of solar flares in a frequency range where there are very few detectors and fill the gap between microwaves observed with the Radio Solar Telescope Network (1 to 15.4 GHz) and submillimeter observations of the Solar Submillimeter Telescope (212 and 405 GHz). Moreover, POEMAS is the only current telescope capable of carrying on circular polarization solar flare observations at 90 GHz. (Although, in principle, ALMA band 3 may also observe at 90 GHz with circular polarization).

Photon polarization

Photon polarization is the quantum mechanical description of the classical polarized sinusoidal plane electromagnetic wave. An individual photon

can be described as having right or left circular polarization, or a superposition of the two. Equivalently, a photon can be described as having horizontal or vertical linear polarization, or a superposition of the two.

The description of photon polarization contains many of the physical concepts and much of the mathematical machinery of more involved quantum descriptions, such as the quantum mechanics of an electron in a potential well. Polarization is an example of a qubit degree of freedom, which forms a fundamental basis for an understanding of more complicated quantum phenomena. Much of the mathematical machinery of quantum mechanics, such as state vectors, probability amplitudes, unitary operators, and Hermitian operators, emerge naturally from the classical Maxwell's equations in the description. The quantum polarization state vector for the photon, for instance, is identical with the Jones vector, usually used to describe the polarization of a classical wave. Unitary operators emerge from the classical requirement of the conservation of energy of a classical wave propagating through lossless media that alter the polarization state of the wave. Hermitian operators then follow for infinitesimal transformations of a classical polarization state.

Many of the implications of the mathematical machinery are easily verified experimentally. In fact, many of the experiments can be performed with two pairs (or one broken pair) of polaroid sunglasses.

The connection with quantum mechanics is made through the identification of a minimum packet size, called a photon, for energy in the electromagnetic field. The identification is based on the theories of Planck and the interpretation of those theories by Einstein. The correspondence principle then allows the identification of momentum and angular momentum (called spin), as well as energy, with the photon.

Polarization (waves)

Polarization (also polarisation) is a property applying to transverse waves that specifies the geometrical orientation of the oscillations. In a transverse wave, the direction of the oscillation is perpendicular to the direction of motion of the wave. A simple example of a polarized transverse wave is vibrations traveling along a taut string (see image); for example, in a musical instrument like a guitar string. Depending on how the string is plucked, the vibrations can be in a vertical direction, horizontal direction, or at any angle perpendicular to the string. In contrast, in longitudinal waves, such as sound waves in a liquid or gas, the displacement of the particles in the oscillation is always in the direction of propagation, so these waves do not exhibit polarization. Transverse waves that exhibit polarization include electromagnetic waves such as light and radio waves, gravitational waves, and transverse sound waves (shear waves) in solids. In some types of transverse waves, the wave displacement is limited to a single direction, so these also do not exhibit polarization; for example, in surface waves in liquids (gravity waves), the wave displacement of the particles is always in a vertical plane.

An electromagnetic wave such as light consists of a coupled oscillating electric field and magnetic field which are always perpendicular; by convention, the "polarization" of electromagnetic waves refers to the direction of the electric field. In linear polarization, the fields oscillate in a single direction. In circular or elliptical polarization, the fields rotate at a constant rate in a plane as the wave travels. The rotation can have two possible directions; if the fields rotate in a right hand sense with respect to the direction of wave travel, it is called right circular polarization, or, if the fields rotate in a left hand sense, it is called left circular polarization.

Light or other electromagnetic radiation from many sources, such as the sun, flames, and incandescent lamps, consists of short wave trains with an equal mixture of polarizations; this is called unpolarized light. Polarized light can be produced by passing unpolarized light through a polarizer, which allows waves of only one polarization to pass through. The most common optical materials (such as glass) are isotropic and do not affect the polarization of light passing through them; however, some materials—those that exhibit birefringence, dichroism, or optical activity—can change the polarization of light. Some of these are used to make polarizing filters. Light is also partially polarized when it reflects from a surface.

According to quantum mechanics, electromagnetic waves can also be viewed as streams of particles called photons. When viewed in this way, the polarization of an electromagnetic wave is determined by a quantum mechanical property of photons called their spin. A photon has one of two possible spins: it can either spin in a right hand sense or a left hand sense about its direction of travel. Circularly polarized electromagnetic waves are composed of photons with only one type of spin, either right- or left-hand. Linearly polarized waves consist of photons that are in a superposition of right and left circularly polarized states, with equal amplitude and phases synchronized to give oscillation in a plane.Polarization is an important parameter in areas of science dealing with transverse waves, such as optics, seismology, radio, and microwaves. Especially impacted are technologies such as lasers, wireless and optical fiber telecommunications, and radar.

Quantum eraser experiment

In quantum mechanics, the quantum eraser experiment is an interferometer experiment that demonstrates several fundamental aspects of quantum mechanics, including quantum entanglement and complementarity.

The double-slit quantum eraser experiment described in this article has three stages:

First, the experimenter reproduces the interference pattern of Young's double-slit experiment by shining photons at the double-slit interferometer and checking for an interference pattern at the detection screen.

Next, the experimenter marks through which slit each photon went and demonstrates that thereafter the interference pattern is destroyed. This stage indicates that it is the existence of the "which-path" information that causes the destruction of the interference pattern.

Third, the "which-path" information is "erased," whereupon the interference pattern is recovered. (Rather than removing or reversing any changes introduced into the photon or its path, these experiments typically produce another change that obscures the markings earlier produced.)A key result is that it does not matter whether the eraser procedure is done before or after the photons arrive at the detection screen.Quantum erasure technology can be used to increase the resolution of advanced microscopes.

Raman optical activity

Raman optical activity (ROA) is a vibrational spectroscopic technique that is reliant on the difference in intensity of Raman scattered right and left circularly polarised light due to molecular chirality.

Sinusoidal plane-wave solutions of the electromagnetic wave equation

Sinusoidal plane-wave solutions are particular solutions to the electromagnetic wave equation.

The general solution of the electromagnetic wave equation in homogeneous, linear, time-independent media can be written as a linear superposition of plane-waves of different frequencies and polarizations.

The treatment in this article is classical but, because of the generality of Maxwell's equations for electrodynamics, the treatment can be converted into the quantum mechanical treatment with only a reinterpretation of classical quantities (aside from the quantum mechanical treatment needed for charge and current densities).

The reinterpretation is based on the theories of Max Planck and the interpretations by Albert Einstein of those theories and of other experiments. The quantum generalization of the classical treatment can be found in the articles on Photon polarization and Photon dynamics in the double-slit experiment.

Spin polarization

Spin polarization is the degree to which the spin, i.e., the intrinsic angular momentum of elementary particles, is aligned with a given direction. This property may pertain to the spin, hence to the magnetic moment, of conduction electrons in ferromagnetic metals, such as iron, giving rise to spin-polarized currents. It may refer to (static) spin waves, preferential correlation

of spin orientation with ordered lattices (semiconductors or insulators).

It may also pertain to beams of particles, produced for particular aims, such as polarized neutron scattering or muon spin spectroscopy. Spin polarization of electrons or of nuclei, often called simply magnetization, is also produced by the application of a magnetic field. Curie law is used to produce an induction signal in Electron spin resonance (ESR or EPR) and in Nuclear magnetic resonance (NMR).

Spin polarization is also important for spintronics, a branch of electronics. Magnetic semiconductors are being researched as possible spintronic materials.

The spin of free electrons is measured either by a LEED image from a clean wolfram-crystal (SPLEED) or by an electron microscope composed purely of electrostatic lenses and a gold foil as a sample. Back scattered electrons are decelerated by annular optics and focused onto a ring shaped electron multiplier at about 15°. The position on the ring is recorded. This whole device is called a Mott-detector. Depending on their spin the electrons have the chance to hit the ring at different positions. 1% of the electrons are scattered in the foil. Of these 1% are collected by the detector and then about 30% of the electrons hit the detector at the wrong position. Both devices work due to spin orbit coupling.

The circular polarization of electromagnetic fields is due to spin polarization of their constituent photons.

In the most generic context, spin polarization is any alignment of the components of a non-scalar

(vectorial, tensorial, spinor) field with its arguments, i.e., with the nonrelativistic three spatial or

relativistic four spatiotemporal regions over which it is defined. In this sense, it also includes

gravitational waves and any field theory that couples its constituents with the differential

operators of vector analysis.

Turnstile antenna

A turnstile antenna, or crossed-dipole antenna, is a radio antenna consisting of a set of two identical dipole antennas mounted at right angles to each other and fed in phase quadrature; the two currents applied to the dipoles are 90° out of phase. The name reflects the notion the antenna looks like a turnstile when mounted horizontally. The antenna can be used in two possible modes. In normal mode the antenna radiates horizontally polarized radio waves perpendicular to its axis. In axial mode the antenna radiates circularly polarized radiation along its axis.

Specialized normal mode turnstile antennas called superturnstile or batwing antennas are used as television broadcasting antennas. Axial mode turnstiles are widely used for satellite ground station antennas in the VHF and UHF bands, as circular polarization is often used for satellite communication since it is not sensitive to the orientation of the satellite antenna in space.

WESU

WESU is a college/community non-commercial FM radio station owned by Wesleyan University and licensed to Middletown, Connecticut. It was founded in 1939 as an unofficial AM carrier current campus radio station in the basement of Clark Hall. Upon gaining recognition, the station operated under the unofficial call sign WES. In the 1950s, the call sign became WESU. Then on February 25, 1961, it began operating an FM station at 88.1 MHz, eventually abandoning the AM station. Between 1967 and 1990, WESU was owned and operated by an independent student group, the now-defunct Wesleyan Broadcast Association, Inc.

Today, it is owned by the Trustees of Wesleyan University, and operated by students and community volunteers. In 1999, the station moved offices and studios from the basement of Clark Hall to its current location next the Wesleyan Argus on 45 Broad Street.

WESU operates 24 hours a day. Until 2004, WESU's format had been entirely freeform, with DJs and student staff having complete freedom to program what they wanted. The university then announced its intention to seek an affiliation with National Public Radio (NPR), and to change the station's daytime format. Douglas Bennet, then president of Wesleyan University, was a former president of NPR. The station now broadcasts news and information shows during the day. Nights and weekends, WESU continues to operate as a free-form station.WESU broadcasts with 6,000 watts effective radiated power (ERP), circular polarization, from the top of Wesleyan University's Exley Science Center in Middletown. The programming is a mix of freeform music, National Public Radio, Public Radio International (PRI) and Pacifica Radio Network programs. From NPR and PRI, WESU airs Morning Edition, Diane Rehm, The Takeaway, Weekend Edition, The Best of Car Talk and Science Friday. From Pacifica, it broadcasts Democracy Now!, Free Speech Radio News, The Ralph Nader Hour and Exploration in Science with Dr. Michio Kaku. The station airs Connecticut-made programs like Voice of the City with J.Cherry. Acoustic Blender with Bill Revill and Nutmeg Junction. Most hours during the day, it airs NPR News at the beginning of the hour.

The radio station was featured in a plot on the TV comedy series "How I Met Your Mother." At the end of the episode "The Possimpible", Ted Mosby (played by Josh Radnor) is deleting his work experience at the radio station from his resume.

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