Circular polarization
Encyclopedia
In electrodynamics, circular polarization of an electromagnetic wave is a polarization in which the electric field of the passing wave does not change strength but only changes direction in a rotary type manner.
In electrodynamics the strength and direction of an electric field
is defined by what is called an 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. If the wave is frozen in time the electric field vectors of the wave describe a helix along the direction of propagation.
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 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. It 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 maximums 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.
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.
One should appreciate that our choice to focus on the horizontal and vertical components was arbitrary. Given the symmetry of circularly polarized light, we could have in fact selected any other two orthogonal components and found the same phase relationship between them.
To convert a given handedness of polarized light to the other handedness one can use a half-wave plate. A half-wave plate shifts a given component of light one half of a wavelength relative to the component to which it is orthogonal.
The handedness of polarized light is also reversed when it is reflected off of a mirror. Initially, as a result of the interaction of the electromagnetic field with the conducting surface of the mirror, both orthogonal components are effectively shifted by one half of a wavelength. However as a result of the change in direction, a mirror image of the wave is created and the two components' phase relationship is reversed.
For a better appreciation of the nature of circularly polarized light one may find it useful to read how circularly polarized light is converted to and from linearly polarized light in the circular polarizer article.
Circular polarization may be referred to as right-handed or left-handed, and clockwise or counter-clockwise, depending on the direction in which the electric field vector rotates. Unfortunately, two opposing historical conventions exist.
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 counter-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.
Quantum physicists also use this convention of handedness because it is consistent with their convention of handedness for a particle’s spin. 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.
Many radio astronomers also use this convention.
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 counter-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.
Many optics textbooks use this second convention.
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.
.
. Circular dichroism is the basis of a form of spectroscopy
that can be used to determine the optical isomerism and secondary structure of molecule
s.
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 sugar
s) and levorotary (e.g. some amino acid
s) molecules they contain. Noteworthy as well is that a secondary structure
will also impart a distinct CD to its respective molecules. Therefore, the alpha helix
, beta sheet
and random coil
regions of proteins and the double helix of nucleic acids have CD spectral signatures representative of their structures.
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 factorhttp://www.answers.com/topic/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.
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 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
:
or helical elements
:
or patch elements:
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-handed. Since then, circular polarization has been measured in several other scarab beetles
like Chrysina gloriosa, as well as some crustacean
s such as the mantis shrimp
. In these cases, the underlying mechanism is the molecular-level helicity of the chitin
ous cuticle
.
The bioluminescence
of the larva
e of fireflie
s 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.
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.
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.
.
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 out the galactic magnetic field. The degree of polarization is on the order of 1.5% for stars at 1000 parsec
s distance.
Normally, a much smaller fraction of circular polarization is found in starlight. Serkowski, Mathewson and Ford 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, 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. 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 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 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.
An optically thick circumstellar environment can potentially produce much larger CP than the interstellar medium. Martin 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, to explain the CP measured in 6 T-Tauri stars at a wavelength of 768 nm. They found a maximum CP of
. Serkowski measured CP of 
for the red supergiant NML Cygni and 
in the long period variable M star VY Canis Major
is in the H band, ascribing the CP to multiple scattering in circumstellar envelope
s. Chrysostomou et al. 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. They found values of
, which is higher than for ordinary stars, presumably because of multiple scattering from dust grains.
In electrodynamics the strength and direction of an electric field
Electric field
In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...
is defined by what is called an 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. If the wave is frozen in time the electric field vectors of the wave describe a helix along the direction of propagation.
Circular polarization is a limiting case of the more general condition of elliptical polarization
Elliptical polarization
In electrodynamics, elliptical polarization is the polarization of electromagnetic radiation such that the tip of the electric field vector describes an ellipse in any fixed plane intersecting, and normal to, the direction of propagation...
. The other special case is the easier-to-understand linear polarization
Linear polarization
In electrodynamics, linear polarization or plane polarization of electromagnetic radiation is a confinement of the electric field vector or magnetic field vector to a given plane along the direction of propagation...
.
General description
On the right is an illustration of the electric field vectors of a circularly polarized electromagnetic wave.The electric field vectors have a constant magnitude but their direction changes in a rotary manner. Given that this is a plane wave
Plane wave
In the physics of wave propagation, a plane wave is a constant-frequency wave whose wavefronts are infinite parallel planes of constant peak-to-peak amplitude normal to the phase velocity vector....
, 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. It is considered to be right-hand, clockwise circularly polarized if viewed by the receiver. Since this is an electromagnetic wave each electric field
Electric field
In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...
vector has a corresponding, but not illustrated, magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
vector that is at a right angle
Right angle
In geometry and trigonometry, a right angle is an angle that bisects the angle formed by two halves of a straight line. More precisely, if a ray is placed so that its endpoint is on a line and the adjacent angles are equal, then they are right angles...
to the electric field vector and proportional
Proportionality (mathematics)
In mathematics, two variable quantities are proportional if one of them is always the product of the other and a constant quantity, called the coefficient of proportionality or proportionality constant. In other words, are proportional if the ratio \tfrac yx is constant. We also say that one...
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
Light
Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...
.
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
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
. It is this quadrature phase relationship which creates the helix
Helix
A helix is a type of smooth space curve, i.e. a curve in three-dimensional space. It has the property that the tangent line at any point makes a constant angle with a fixed line called the axis. Examples of helixes are coil springs and the handrails of spiral staircases. A "filled-in" helix – for...
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 maximums of the vertical and horizontal components. (To minimize visual clutter these are the only helix vectors displayed.)
To appreciate how this quadrature phase shift
Phase (waves)
Phase in waves is the fraction of a wave cycle which has elapsed relative to an arbitrary point.-Formula:The phase of an oscillation or wave refers to a sinusoidal function such as the following:...
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
Displacement (vector)
A displacement is the shortest distance from the initial to the final position of a point P. Thus, it is the length of an imaginary straight path, typically distinct from the path actually travelled by P...
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.
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.
One should appreciate that our choice to focus on the horizontal and vertical components was arbitrary. Given the symmetry of circularly polarized light, we could have in fact selected any other two orthogonal components and found the same phase relationship between them.
To convert a given handedness of polarized light to the other handedness one can use a half-wave plate. A half-wave plate shifts a given component of light one half of a wavelength relative to the component to which it is orthogonal.
The handedness of polarized light is also reversed when it is reflected off of a mirror. Initially, as a result of the interaction of the electromagnetic field with the conducting surface of the mirror, both orthogonal components are effectively shifted by one half of a wavelength. However as a result of the change in direction, a mirror image of the wave is created and the two components' phase relationship is reversed.
For a better appreciation of the nature of circularly polarized light one may find it useful to read how circularly polarized light is converted to and from linearly polarized light in the circular polarizer article.
Left/right handedness conventions
Circular polarization may be referred to as right-handed or left-handed, and clockwise or counter-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 temporal rotation of the field at a given point in space. When determining if the wave is clockwise or counter-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 temporal rotation.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 counter-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.
Quantum physicists also use this convention of handedness because it is consistent with their convention of handedness for a particle’s spin. 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.
Many radio astronomers also use this convention.
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 counter-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.
Many optics textbooks use this second convention.
Uses of the two conventions
As stated earlier, there is significant confusion with regards to these two conventions. As a general rule the engineering and quantum physics community use the first convention where the wave is observed from the point of view of the source. In many physics textbooks dealing with optics the second convention is used where the light is observed from the point of view of receiver.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.
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), 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 (or simply unpolarized). See Stokes parametersStokes parameters
The Stokes parameters are a set of values that describe the polarization state of electromagnetic radiation. They were defined by George Gabriel Stokes in 1852, as a mathematically convenient alternative to the more common description of incoherent or partially polarized radiation in terms of its...
.
Circular dichroism
Circular dichroism (CD) is the differential absorption of left- and right-handed circularly polarized lightLight
Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...
. Circular dichroism is the basis of a form of spectroscopy
Spectroscopy
Spectroscopy is the study of the interaction between matter and radiated energy. Historically, spectroscopy originated through the study of visible light dispersed according to its wavelength, e.g., by a prism. Later the concept was expanded greatly to comprise any interaction with radiative...
that can be used to determine the optical isomerism and secondary structure of molecule
Molecule
A molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...
s.
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 sugar
Sugar
Sugar is a class of edible crystalline carbohydrates, mainly sucrose, lactose, and fructose, characterized by a sweet flavor.Sucrose in its refined form primarily comes from sugar cane and sugar beet...
s) and levorotary (e.g. some amino acid
Amino acid
Amino acids are molecules containing an amine group, a carboxylic acid group and a side-chain that varies between different amino acids. The key elements of an amino acid are carbon, hydrogen, oxygen, and nitrogen...
s) molecules they contain. Noteworthy as well is that a secondary structure
Secondary structure
In biochemistry and structural biology, secondary structure is the general three-dimensional form of local segments of biopolymers such as proteins and nucleic acids...
will also impart a distinct CD to its respective molecules. Therefore, the alpha helix
Alpha helix
A common motif in the secondary structure of proteins, the alpha helix is a right-handed coiled or spiral conformation, in which every backbone N-H group donates a hydrogen bond to the backbone C=O group of the amino acid four residues earlier...
, beta sheet
Beta sheet
The β sheet is the second form of regular secondary structure in proteins, only somewhat less common than the alpha helix. Beta sheets consist of beta strands connected laterally by at least two or three backbone hydrogen bonds, forming a generally twisted, pleated sheet...
and random coil
Random coil
A random coil is a polymer conformation where the monomer subunits are oriented randomly while still being bonded to adjacent units. It is not one specific shape, but a statistical distribution of shapes for all the chains in a population of macromolecules...
regions of proteins and the double helix of nucleic acids have CD spectral signatures representative of their structures.
Circularly polarized luminescence
Circularly polarized luminescence (CPL) can occur when either a luminophoreLuminophore
A luminophore is an atom or atomic grouping in a chemical compound that manifests luminescence. There exist organic and inorganic luminophores. It should be stressed that the correct, textbook terminology is luminophore, not lumophore, although the latter term has been frequently but erroneously...
or an ensemble of luminophores is chiral
Chirality (chemistry)
A chiral molecule is a type of molecule that lacks an internal plane of symmetry and thus has a non-superimposable mirror image. The feature that is most often the cause of chirality in molecules is the presence of an asymmetric carbon atom....
. The extent to which emissions are polarized is quantified in the same way it is for circular dichroism
Circular dichroism
Circular dichroism refers to the differential absorption of left and right circularly polarized light. This phenomenon was discovered by Jean-Baptiste Biot, Augustin Fresnel, and Aimé Cotton in the first half of the 19th century. It is exhibited in the absorption bands of optically active chiral...
, in terms of the dissymmetry factorhttp://www.answers.com/topic/dissymmetry-factor, also sometimes referred to as the anisotropy
Anisotropy
Anisotropy is the property of being directionally dependent, as opposed to isotropy, which implies identical properties in all directions. It can be defined as a difference, when measured along different axes, in a material's physical or mechanical properties An example of anisotropy is the light...
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 classicalClassical physics
What "classical physics" refers to depends on the context. When discussing special relativity, it refers to the Newtonian physics which preceded relativity, i.e. the branches of physics based on principles developed before the rise of relativity and quantum mechanics...
sinusoidal plane wave solution of the electromagnetic wave equation
Electromagnetic wave equation
The electromagnetic wave equation is a second-order partial differential equation that describes the propagation of electromagnetic waves through a medium or in a vacuum...
for the electric
Electric field
In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...
and magnetic
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
fields is
where k is the wavenumber
Wavenumber
In the physical sciences, the wavenumber is a property of a wave, its spatial frequency, that is proportional to the reciprocal of the wavelength. It is also the magnitude of the wave vector...
,
is the angular frequency
Angular frequency
In physics, angular frequency ω is a scalar measure of rotation rate. Angular frequency is the magnitude of the vector quantity angular velocity...
of the wave,
is an orthogonal matrix whose columns span the transverse x-y plane and is the speed of lightSpeed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...
.
Here
is the amplitude
Amplitude
Amplitude is the magnitude of change in the oscillating variable with each oscillation within an oscillating system. For example, sound waves in air are oscillations in atmospheric pressure and their amplitudes are proportional to the change in pressure during one oscillation...
of the field and
is the 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 iswhere 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 utilized to produce circularly polarized (or nearly so) radiation; following Balanis, one can use dipole elementsDipole antenna
A dipole antenna is a radio antenna that can be made of a simple wire, with a center-fed driven element. It consists of two metal conductors of rod or wire, oriented parallel and collinear with each other , with a small space between them. The radio frequency voltage is applied to the antenna at...
:
"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 90º degree time-phase difference (phase quadrature), the polarization along zenith would be circular... One way to obtain the 90º 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
Helical antenna
A helical antenna is an antenna consisting of a conducting wire wound in the form of a helix. In most cases, helical antennas are mounted over a ground plane. The feed line is connected between the bottom of the helix and the ground plane...
:
"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 90º 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 90º power divider", p.859.
In nature
Albert Abraham Michelson
Albert Abraham Michelson was an American physicist known for his work on the measurement of the speed of light and especially for the Michelson-Morley experiment. In 1907 he received the Nobel Prize in Physics...
discovered that light
Light
Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...
reflected from the golden scarab beetle Chrysina resplendens
Chrysina resplendens
Chrysina resplendens is a golden scarab beetle found in Costa Rica, Panama, El Salvador and other countries in Central America.-External links:*...
is preferentially left-handed. Since then, circular polarization has been measured in several other scarab beetles
Scarabaeidae
The family Scarabaeidae as currently defined consists of over 30,000 species of beetles worldwide. The species in this large family are often called scarabs or scarab beetles. The classification of this family is fairly unstable, with numerous competing theories, and new proposals appearing quite...
like Chrysina gloriosa, as well as some crustacean
Crustacean
Crustaceans form a very large group of arthropods, usually treated as a subphylum, which includes such familiar animals as crabs, lobsters, crayfish, shrimp, krill and barnacles. The 50,000 described species range in size from Stygotantulus stocki at , to the Japanese spider crab with a leg span...
s such as the mantis shrimp
Mantis shrimp
Mantis shrimp or stomatopods are marine crustaceans, the members of the order Stomatopoda. They are neither shrimp nor mantids, but receive their name purely from the physical resemblance to both the terrestrial praying mantis and the shrimp. They may reach in length, although exceptional cases of...
. In these cases, the underlying mechanism is the molecular-level helicity of the chitin
Chitin
Chitin n is a long-chain polymer of a N-acetylglucosamine, a derivative of glucose, and is found in many places throughout the natural world...
ous cuticle
Cuticle
A cuticle , or cuticula, is a term used for any of a variety of tough but flexible, non-mineral outer coverings of an organism, or parts of an organism, that provide protection. Various types of "cuticles" are non-homologous; differing in their origin, structure, function, and chemical composition...
.
The bioluminescence
Bioluminescence
Bioluminescence is the production and emission of light by a living organism. Its name is a hybrid word, originating from the Greek bios for "living" and the Latin lumen "light". Bioluminescence is a naturally occurring form of chemiluminescence where energy is released by a chemical reaction in...
of the larva
Larva
A larva is a distinct juvenile form many animals undergo before metamorphosis into adults. Animals with indirect development such as insects, amphibians, or cnidarians typically have a larval phase of their life cycle...
e of fireflie
Firefly
Lampyridae is a family of insects in the beetle order Coleoptera. They are winged beetles, and commonly called fireflies or lightning bugs for their conspicuous crepuscular use of bioluminescence to attract mates or prey. Fireflies produce a "cold light", with no infrared or ultraviolet frequencies...
s 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
Linear polarization
In electrodynamics, linear polarization or plane polarization of electromagnetic radiation is a confinement of the electric field vector or magnetic field vector to a given plane along the direction of propagation...
due to inhomogeneties inside aligned photocytes, and it picks up circular polarization while passing through linearly birefringent tissue.
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
Total internal reflection
Total internal reflection is an optical phenomenon that happens when a ray of light strikes a medium boundary at an angle larger than a particular critical angle with respect to the normal to the surface. If the refractive index is lower on the other side of the boundary and the incident angle is...
back down, its vertical component undergoes a phase shift. To an underwater observer looking up, the faint light outside Snell's window
Snell's window
Snell's window is a phenomenon by which an underwater viewer sees everything above the surface through a cone of light of width of about 96 degrees. This phenomenon is caused by refraction of light entering water, and is governed by Snell's Law...
therefore is (partially) circularly polarized.
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
Circular dichroism
Circular dichroism refers to the differential absorption of left and right circularly polarized light. This phenomenon was discovered by Jean-Baptiste Biot, Augustin Fresnel, and Aimé Cotton in the first half of the 19th century. It is exhibited in the absorption bands of optically active chiral...
media.
Starlight
The circular polarization of starlight has been observed to be a function of the linear polarization of starlightStarlight
Starlight refers to the visible radiation emitted by stars other than the Sun.Starlight may also refer to:-Comics:* Starlight , Dr...
.
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
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
. 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
Perpendicular
In geometry, two lines or planes are considered perpendicular to each other if they form congruent adjacent angles . The term may be used as a noun or adjective...
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 out the galactic magnetic field. The degree of polarization is on the order of 1.5% for stars at 1000 parsec
Parsec
The parsec is a unit of length used in astronomy. It is about 3.26 light-years, or just under 31 trillion kilometres ....
s distance.
Normally, a much smaller fraction of circular polarization is found in starlight. Serkowski, Mathewson and Ford 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, 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. 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 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 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
Crab Nebula
The Crab Nebula is a supernova remnant and pulsar wind nebula in the constellation of Taurus...
by Martin, Illing and Angel.
An optically thick circumstellar environment can potentially produce much larger CP than the interstellar medium. Martin 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, to explain the CP measured in 6 T-Tauri stars at a wavelength of 768 nm. They found a maximum CP of
. Serkowski measured CP of for the red supergiant NML Cygni and in the long period variable M star VY Canis MajorCanis Major
Canis Major is one of the 88 modern constellations, and was included in the 2nd-century astronomer Ptolemy's 48 constellations. Its name is Latin for 'greater dog', and is commonly represented as one of the dogs following Orion the hunter...
is in the H band, ascribing the CP to multiple scattering in circumstellar envelope
Circumstellar envelope
Circumstellar envelope is the part of the star,having roughly spherical shape and not gravitationally bound to the star core.Usually circumstellar envelopes are formed from the dense stellar wind or presentbefore formation of the star...
s. Chrysostomou et al. found CP with q of up to 0.17 in the Orion
Orion Nebula
The Orion Nebula is a diffuse nebula situated south of Orion's Belt. It is one of the brightest nebulae, and is visible to the naked eye in the night sky. M42 is located at a distance of and is the closest region of massive star formation to Earth. The M42 nebula is estimated to be 24 light...
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
Milky Way
The Milky Way is the galaxy that contains the Solar System. This name derives from its appearance as a dim un-resolved "milky" glowing band arching across the night sky...
diffuse galactic light was measured at wavelength of 550 nm by Wolstencroft and Kemp. They found values of
, which is higher than for ordinary stars, presumably because of multiple scattering from dust grains.See also
- Circular polarizer
- 3-D films
- HandednessHandednessHandedness is a human attribute defined by unequal distribution of fine motor skills between the left and right hands. An individual who is more dexterous with the right hand is called right-handed and one who is more skilled with the left is said to be left-handed...
- Photon polarizationPhoton polarizationPhoton polarization is the quantum mechanical description of the classical polarized sinusoidal plane electromagnetic wave. Individual photons are completely polarized...
- Sinusoidal plane-wave solutions of the electromagnetic wave equationSinusoidal plane-wave solutions of the electromagnetic wave equationSinusoidal 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...
- Wave plateWave plateA wave plate or retarder is an optical device that alters the polarization state of a light wave travelling through it.- Operation :A wave plate works by shifting the phase between two perpendicular polarization components of the light wave. A typical wave plate is simply a birefringent crystal...