Inelectrodynamics,circular polarization of anelectromagnetic wave is apolarization state in which, at each point, theelectromagnetic field of the wave has a constant magnitude and is rotating at a constant rate in a plane perpendicular to the direction of the wave.

In electrodynamics, the strength and direction of an electric field is defined by its electric field vector. In the case of a circularly polarized wave, the tip of the electric fieldvector, at a given point in space, relates to the phase of the light as it travels through time and space. At any instant of time, the electric field vector of the wave indicates a point on ahelix oriented along the direction of propagation. A circularly polarized wave can rotate in one of two possible senses:right-handed circular polarization (RHCP) in which the electric field vector rotates in aright-hand sense with respect to the direction of propagation, andleft-handed circular polarization (LHCP) in which the vector rotates in aleft-hand sense.

Circular polarization is alimiting case ofelliptical polarization. The otherspecial case is the easier-to-understandlinear polarization. All three terms were coined byAugustin-Jean Fresnel, in a memoir read to theFrench Academy of Sciences on 9 December 1822.^[1][2] Fresnel had first described the case of circular polarization, without yet naming it, in 1821.^[3]

The phenomenon of polarization arises as a consequence of the fact thatlight behaves as a two-dimensionaltransverse wave.

Circular polarization occurs when the two orthogonal electric field component vectors are of equal magnitude and are out of phase by exactly 90°, or one-quarter wavelength.

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

In a circularly polarized electromagnetic wave, the individual electric field vectors, as well as their combined vector, have a constantmagnitude, and with changing phase angle. Given that this is aplane wave, each vector represents the magnitude and direction of the electric field for an entire plane that is perpendicular to the optical axis. Specifically, given that this is acircularly polarized plane wave, these vectors indicate that the electric field, from plane to plane, has a constant strength while its direction steadily rotates. Refer tothese two images in the plane wave article to better appreciate this dynamic. This light is considered to be right-hand, clockwise circularly polarized if viewed by the receiver. Since this is anelectromagnetic wave, eachelectric field vector has a corresponding, but not illustrated,magnetic field vector that is at aright angle to the electric field vector andproportional 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 aslight.

The nature of circular polarization and its relationship to other polarizations is often understood by thinking of the electric field as being divided into twocomponents that are perpendicular to each other. The vertical component and its corresponding plane are illustrated in blue, while the horizontal component and its corresponding plane are illustrated in green. Notice that the rightward (relative to the direction of travel) horizontal component leads the vertical component by one quarter of awavelength, a 90° phase difference. It is thisquadrature phase relationship that creates thehelix and causes the points of maximum magnitude of the vertical component to correspond with the points of zero magnitude of the horizontal component, and vice versa. The result of this alignment are select vectors, corresponding to the helix, which exactly match the maxima of the vertical and horizontal components.

To appreciate how this quadraturephase 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 horizontaldisplacements of the dot, relative to the center of the circle, varysinusoidally 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/counterclockwise circularly polarized light displayed with and without the use of components. This would be considered right-handed/clockwise circularly polarized if defined from the point of view of the source rather than the receiver.

The next pair of illustrations is that of left-handed, counterclockwise circularly polarized light when viewed by the receiver. Because it is left-handed, the rightward (relative to the direction of travel) horizontal component is nowlagging the vertical component by one quarter of a wavelength, rather than leading it.

To convert circularly polarized light to the other handedness, one can use a half-waveplate. A half-waveplate shifts a given linear component of light one half of a wavelength relative to its orthogonal linear component.

The handedness of polarized light is reversed reflected off a surface at normal incidence. Upon such reflection, the rotation of theplane of polarization of the reflected light is identical to that of the incident field. However, with propagation now in theopposite 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 abirefringent 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 theBrewster 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 theplane of incidence, commonly denotedp ands respectively. The reflected components in thep ands linear polarizations are found by applying theFresnel 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 betweenp ands, are the Fresnel coefficients for the two components identical, leading to the above property.

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 angleother than 45° will generally produce elliptical polarization.

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.

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 thumbaway from the source, in thesame direction that the wave is propagating, and matching the curling of one's fingers to the direction of the temporal rotation of the field at a given point in space. When determining if the wave is clockwise or anti-clockwise circularly polarized, one again takes the point of view of the source, and while lookingaway from the source and in thesame direction of the wave's propagation, one observes the direction of the field's temporal rotation.

Using this convention, the electric field vector of a left-handed circularly polarized wave is as follows:${\displaystyle \left(E_x,E_y,E_z\right)\propto \left(\cos \frac{2\pi }{\lambda }\left(ct-z\right),-\sin \frac{2\pi }{\lambda }\left(ct-z\right),0\right).}$

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 theInstitute of Electrical and Electronics Engineers (IEEE) standard and, as a result, it is generally used in the engineering community.^[4][5][6]

Quantum physicists also use this convention of handedness because it is consistent with their convention of handedness for a particle's spin.^[7]

Radio astronomers also use this convention in accordance with anInternational Astronomical Union (IAU) resolution made in 1973.^[8]

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

When determining if the wave is clockwise or anti-clockwise circularly polarized, one again takes the point of view of the receiver and, while lookingtoward 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.^[9][10] It is also used bySPIE^[11] as well as theInternational Union of Pure and Applied Chemistry (IUPAC).^[12]

As stated earlier, there is significant confusion with regards to these two conventions. As a general rule, the engineering, quantum physics, and radio astronomy communities use the first convention, in which the wave is observed from the point of view of the source.^[5][7][8] In many physics textbooks dealing with optics, the second convention is used, in which the light is observed from the point of view of the receiver.^[7][9]

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 theUS Federal Standard 1037C proposes two contradictory conventions of handedness.^[13]

Note that the IEEE defines RHCP and LHCP the opposite as those used by physicists. The IEEE 1979 Antenna Standard will show RHCP on the South Pole of the Poincare Sphere. The IEEE defines RHCP using the right hand with thumb pointing in the direction of transmit, and the fingers showing the direction of rotation of the E field with time. The rationale for the opposite conventions used by Physicists and Engineers is that Astronomical Observations are always done with the incoming wave traveling toward the observer, where as for most engineers, they are assumed to be standing behind the transmitter watching the wave traveling away from them. This article is not using the IEEE 1979 Antenna Standard and is not using the +t convention typically used in IEEE work.

FM broadcast radio stations sometimes employ circular polarization to improve signal penetration into buildings and vehicles. It is one example of what theInternational Telecommunication Union refers to as "mixed polarization", i.e. radio emissions that include both horizontally- and vertically-polarized components.^[14] In the United States,Federal Communications Commission regulations state that horizontal polarization is the standard for FM broadcasting, but that "circular or elliptical polarization may be employed if desired".^[15]

Circular dichroism (CD) is the differential absorption of left- and right-handed circularly polarizedlight. Circular dichroism is the basis of a form ofspectroscopy that can be used to determine theoptical isomerism and secondary structure ofmolecules.

In general, this phenomenon will be exhibited in absorption bands of anyoptically active molecule. As a consequence, circular dichroism is exhibited by most biological molecules, because of thedextrorotary (e.g., somesugars) andlevorotary (e.g., someamino acids) molecules they contain. Noteworthy as well is that asecondary structure will also impart a distinct CD to its respective molecules. Therefore, thealpha helix,beta sheet andrandom coil regions of proteins and thedouble helix ofnucleic acids have CD spectral signatures representative of their structures.

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

Circularly polarized luminescence (CPL) can occur when either aluminophore or an ensemble of luminophores ischiral. The extent to which emissions are polarized is quantified in the same way it is forcircular dichroism, in terms of thedissymmetry factor, also sometimes referred to as theanisotropy factor. This value is given by:

${\displaystyle g_{em}=2\left(\frac{{\theta }_{\mathrm{l}\mathrm{e}\mathrm{f}\mathrm{t}}-{\theta }_{\mathrm{r}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{t}}}{{\theta }_{\mathrm{l}\mathrm{e}\mathrm{f}\mathrm{t}}+{\theta }_{\mathrm{r}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{t}}}\right)}$

where${\displaystyle {\theta }_{\mathrm{l}\mathrm{e}\mathrm{f}\mathrm{t}}}$ corresponds to the quantum yield of left-handed circularly polarized light, and${\displaystyle {\theta }_{\mathrm{r}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{t}}}$ to that of right-handed light. The maximum absolute value ofg_em, corresponding to purely left- or right-handed circular polarization, is therefore 2. Meanwhile, the smallest absolute value thatg_em can achieve, corresponding to linearly polarized or unpolarized light, is zero.

Theclassicalsinusoidal plane wave solution of theelectromagnetic wave equation for theelectric andmagnetic fields is:

where k is thewavenumber;

${\displaystyle \omega =ck}$

is theangular frequency of the wave;${\displaystyle \mathbf{Q}=\left[\hat{\mathbf{x}},\hat{\mathbf{y}}\right]}$ is an orthogonal${\displaystyle 2\times 2}$ matrix whose columns span the transverse x-y plane; and${\displaystyle c}$ is thespeed of light.

Here,

${\displaystyle \left|\mathbf{E}\right|}$

is theamplitude of the field, and

${\displaystyle |\psi ⟩\stackrel{\mathrm{d}\mathrm{e}\mathrm{f}}{=}\left(\begin{array}{c}{\psi }_x\\ {\psi }_y\end{array}\right)=\left(\begin{array}{c}\cos \theta \exp \left(i{\alpha }_x\right)\\ \sin \theta \exp \left(i{\alpha }_y\right)\end{array}\right)}$

is the normalizedJones vector in the x-y plane.

If${\displaystyle {\alpha }_y}$ is rotated by${\displaystyle \pi /2}$ radians with respect to${\displaystyle {\alpha }_x}$ and the x amplitude equals the y amplitude, the wave is circularly polarized. The Jones vector is:

${\displaystyle |\psi ⟩=\frac{1}{\sqrt{2}}\left(\begin{array}{c}1\\ \pm i\end{array}\right)\exp \left(i{\alpha }_x\right)}$

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 thex-y plane.

If basis vectors are defined such that:

${\displaystyle |\mathrm{R}⟩\stackrel{\mathrm{d}\mathrm{e}\mathrm{f}}{=}\frac{1}{\sqrt{2}}\left(\begin{array}{c}1\\ -i\end{array}\right)}$

and:

${\displaystyle |\mathrm{L}⟩\stackrel{\mathrm{d}\mathrm{e}\mathrm{f}}{=}\frac{1}{\sqrt{2}}\left(\begin{array}{c}1\\ i\end{array}\right)}$

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

${\displaystyle |\psi ⟩={\psi }_{\mathrm{R}}|\mathrm{R}⟩+{\psi }_{\mathrm{L}}|\mathrm{L}⟩}$

where:

and:

${\displaystyle \delta ={\alpha }_y-{\alpha }_x.}$

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A number of different types of antenna elements can be used to produce circularly polarized (or nearly so) radiation; followingBalanis,^[16] one can usedipole 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;

orhelical elements:

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

orpatch 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.

In thequantum mechanical view, light is composed ofphotons. Polarization is a manifestation of thespin angular momentum of light. More specifically, in quantum mechanics, the direction of spin of a photon is tied to the handedness of the circularly polarized light, and the spin of a beam of photons is similar to the spin of a beam of particles, such as electrons.^[17] In thephysics convention (from the point of view of the source), a right-handed circular polarization corresponds to a positive spin (denoted${\displaystyle {\sigma }^{+}}$), whereas a left-handed circular polarization corresponds to a negative spin (denoted${\displaystyle {\sigma }^{-}}$).^[18]

Only a few mechanisms in nature are known to systematically produce circularly polarizedlight. In 1911,Albert Abraham Michelson discovered that light reflected from the golden scarab beetleChrysina resplendens is preferentially left-polarized. Since then, circular polarization has been measured in several otherscarab beetles such asChrysina gloriosa,^[19] as well as somecrustaceans such as themantis shrimp. In these cases, the underlying mechanism is the molecular-level helicity of thechitinouscuticle.^[20]

Thebioluminescence of thelarvae offireflies is also circularly polarized, as reported in 1980 for the speciesPhoturis lucicrescens andPhoturis 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 alinear polarization due to inhomogeneities inside alignedphotocytes, and it picks up circular polarization while passing through linearlybirefringent tissue.^[21]

Circular polarization has been detected in light reflected from leaves and photosynthetic microbes.^[22]

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 thentotally internally reflected back down, its vertical component undergoes a phase shift. To an underwater observer looking up, the faint light outsideSnell's window therefore is (partially) circularly polarized.^[23]

Weaker sources of circular polarization in nature include multiple scattering by linear polarizers^{[dubious –discuss]}, as in the circular polarization of starlight, and selective absorption bycircularly dichroic media.

Radio emission from pulsars can be strongly circularly polarized.^[24]

Two species ofmantis shrimp have been reported to be able to detect circular polarized light.^[25][26]

• Polarizer
• 3D film
• Chirality
• Sinusoidal plane-wave solutions of the electromagnetic wave equation
• Starlight polarization
• Waveplate

• 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.

• Circularly polarized light: beetles and displays
• Article on the mantis shrimp and circular polarization
• Animation of Circular Polarization (on YouTube)
• Comparison of Circular Polarization with Linear and Elliptical Polarizations (YouTube Animation)
• Reversal of handedness of circularly polarized light by mirror. A demonstration – simple, cheap & instructive

• Concepts in astrophysics
• Polarization (waves)
• Stellar astronomy

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