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. See polarization and plane of polarization for more information.

The orientation of a linearly polarized electromagnetic wave is defined by the direction of the electric field vector.[1] For example, if the electric field vector is vertical (alternately up and down as the wave travels) the radiation is said to be vertically polarized.

Linear polarization schematic
Diagram of the electric field of a light wave (blue), linear-polarized along a plane (purple line), and consisting of two orthogonal, in-phase components (red and green waves)

Mathematical description of linear polarization

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

for the magnetic field, where k is the wavenumber,

is the angular frequency of the wave, and is the speed of light.

Here is the amplitude of the field and

is the Jones vector in the x-y plane.

The wave is linearly polarized when the phase angles are equal,


This represents a wave polarized at an angle with respect to the x axis. In that case, the Jones vector can be written


The state vectors for linear polarization in x or y are special cases of this state vector.

If unit vectors are defined such that


then the polarization state can be written in the "x-y basis" as


See also


  • Jackson, John D. (1998). Classical Electrodynamics (3rd ed.). Wiley. ISBN 0-471-30932-X.
  1. ^ Shapira, Joseph; Shmuel Y. Miller (2007). CDMA radio with repeaters. Springer. p. 73. ISBN 0-387-26329-2.

External links

 This article incorporates public domain material from the General Services Administration document "Federal Standard 1037C".

B(e) star

A B[e] star, frequently called a B[e]-type star, is a B-type star with distinctive forbidden neutral or low ionisation emission lines in its spectrum. The designation results from combining the spectral class B, the lowercase e denoting emission in the spectral classification system, and the surrounding square brackets signifying forbidden lines. These stars frequently also show strong hydrogen emission lines, but this feature is present in a variety of other stars and is not sufficient to classify a B[e] object. Other observational characteristics include optical linear polarization and often infrared radiation that is much stronger than in ordinary B-class stars, called infrared excess. As the B[e] nature is transient, B[e]-type stars might exhibit a normal B-type spectrum at times, and hitherto normal B-type stars may become B[e]-type stars.


COSMOSOMAS is a circular scanning astronomical microwave experiment to investigate the Cosmic Microwave Background anisotropy and diffuse emission from the Galaxy on angular scales from 1 to 5 degrees. It was designed and built by the Instituto de Astrofísica de Canarias (IAC) in Tenerife, Spain, in 1998. Its name comes from "COSMOlogical Structures On Medium Angular Scales" referring to CMB fluctuations. This experiment grew out experience of the previous Tenerife Experiment with the need to go to smaller angular scales with greater sensitivity.

The experiment consists of two instruments, COSMO15 (three channels at 12.7, 14.7 and 16.3 GHz) and COSMO11 (two hands of linear polarization at 10.9 GHz). Both instruments are based on a circular scanning sky strategy, consisting of a 60 rpm spinning flat mirror directing the sky radiation into an off-axis paraboloidal antenna, whose size is 1.8-m in the COSMO15 and 2.4-m in the COSMO11. These antennas focus the radiation on to cryogenically cooled HEMT-based receivers, both at an operating temperature of 20K (-253 C) and in the frequency range of 10–12 GHz for COSMO11, and 12–18 GHz for COSMO15. In the COSMO15 instrument, the signal is split by a set of three filters, allowing simultaneous observations at 13, 15 and 17 GHz. Thus, four 1-degree resolution sky maps complete in right ascension and covering 20 degrees in declination are obtained every day at these frequencies.

The most important result to come from this experiment is the cleanest detection of "spinning dust" in the Perseus molecular cloud. These are very small dust grains which can spin thousands of million times a second. If they have an asymmetrical electrical charge they can radiate like a lot of tiny dipole antennas. This cloud is very bright at infra-red wavelengths due to thermal emission from the large dust grains, but very little emission would be expected at microwave wavelengths by this type of dust. Instead there is a broad bump of signal centered on 22 GHz, a factor of 50 above the expected level of signal.

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.

Diffuse Infrared Background Experiment

Diffuse Infrared Background Experiment (DIRBE) was an experiment on NASA's COBE mission, to survey the diffuse infrared sky. Measurements were made with a reflecting telescope with 19 cm diameter aperture. The goal was to obtain brightness maps of the universe at ten frequency bands ranging from the near to far infrared (1.25 to 240 micrometer). Also, linear polarization was measured at 1.25, 2.2, and 3.5 micrometers. During the mission, the instrument could sample half the celestial sphere each day.

Domain wall (optics)

A domain wall is a term used in physics which can have similar meanings in optics, magnetism, or string theory. These phenomena can all be generically described as topological solitons which occur whenever a discrete symmetry is spontaneously broken.As of 2009, a phase-locked dark-dark vector soliton was observed only in fiber lasers of positive dispersion while a phase-locked dark-bright vector soliton was obtained in fiber lasers of either positive or negative dispersion. Numerical simulations confirmed the experimental observations, and further showed that the observed vector solitons are the two types of phase-locked polarization domain-wall solitons theoretically predicted. Another novel type of domain wall soliton is the vector dark domain wall, consisting of stable localized structures separating the two orthogonal linear polarization eigenstates of the laser emission, with a dark structure that is visible only when the total laser emission is measured.

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. An elliptically polarized wave may be resolved into two linearly polarized waves in phase quadrature, with their polarization planes at right angles to each other. Since the electric field can rotate clockwise or counterclockwise as it propagates, elliptically polarized waves exhibit chirality.

Other forms of polarization, such as circular and linear polarization, can be considered to be special cases of elliptical polarization.

Faraday effect

In physics, the Faraday effect or Faraday rotation is a magneto-optical phenomenon—that is, an interaction between light and a magnetic field in a medium. The Faraday effect causes a rotation of the plane of polarization which is linearly proportional to the component of the magnetic field in the direction of propagation. Formally, it is a special case of gyroelectromagnetism obtained when the dielectric permittivity tensor is diagonal.Discovered by Michael Faraday in 1845, the Faraday effect was the first experimental evidence that light and electromagnetism are related. The theoretical basis of electromagnetic radiation (which includes visible light) was completed by James Clerk Maxwell in the 1860s and 1870s. This effect occurs in most optically transparent dielectric materials (including liquids) under the influence of magnetic fields.

The Faraday effect is caused by left and right circularly polarized waves propagating at slightly different speeds, a property known as circular birefringence. Since a linear polarization can be decomposed into the superposition of two equal-amplitude circularly polarized components of opposite handedness and different phase, the effect of a relative phase shift, induced by the Faraday effect, is to rotate the orientation of a wave's linear polarization.

The Faraday effect has applications in measuring instruments. For instance, the Faraday effect has been used to measure optical rotatory power and for remote sensing of magnetic fields (such as fiber optic current sensors). The Faraday effect is used in spintronics research to study the polarization of electron spins in semiconductors. Faraday rotators can be used for amplitude modulation of light, and are the basis of optical isolators and optical circulators; such components are required in optical telecommunications and other laser applications.

GRB 160625B

GRB 160625B is a gamma-ray burst (GRB) detected by NASA's Fermi Gamma-ray Space Telescope on 25 June 2016 and, three minutes later, by the Large Area Telescope. This was followed by a bright prompt optical flash, during which variable linear polarization was measured This is the first time that these observations are made when the GRB is still bright and active. The source of the GRB was a possible black hole, within the Delphinus constellation, about 9 billion light-years (light travel distance) away (a redshift of z = 1.406).

Linear dichroism

Linear dichroism (LD) or diattenuation is the difference between absorption of light polarized parallel and polarized perpendicular to an orientation axis. It is the property of a material whose transmittance depends on the orientation of linearly polarized light incident upon it. As a technique, it is primarily used to study the functionality and structure of molecules. LD measurements are based on the interaction between matter and light and thus are a form of electromagnetic spectroscopy.

This effect has been applied across the EM spectrum, where different wavelengths of light can probe a host of chemical systems. The predominant use of LD currently is in the study of bio-macromolecules (e.g. DNA) as well as synthetic polymers.

Optical rotation

Optical rotation or optical activity (sometimes referred to as rotary polarization) is the rotation of the plane of polarization of linearly polarized light as it travels through certain materials. Optical activity occurs only in chiral materials, those lacking microscopic mirror symmetry. Unlike other sources of birefringence which alter a beam's state of polarization, optical activity can be observed in fluids. This can include gases or solutions of chiral molecules such as sugars, molecules with helical secondary structure such as some proteins, and also chiral liquid crystals. It can also be observed in chiral solids such as certain crystals with a rotation between adjacent crystal planes (such as quartz) or metamaterials. Rotation of light's plane of polarization may also occur through the Faraday effect which involves a static magnetic field, however this is a distinct phenomenon that is not usually classified under "optical activity."

The rotation of the plane of polarization may be either clockwise, to the right (dextrorotary — d-rotary), or to the left (levorotary — l-rotary) depending on which stereoisomer is present (or dominant). For instance, sucrose and camphor are d-rotary whereas cholesterol is l-rotary. For a given substance, the angle by which the polarization of light of a specified wavelength is rotated is proportional to the path length through the material and (for a solution) proportional to its concentration. The rotation is not dependent on the direction of propagation, unlike the Faraday effect where the rotation is dependent on the relative direction of the applied magnetic field.

Optical activity is measured using a polarized source and polarimeter. This is a tool particularly used in the sugar industry to measure the sugar concentration of syrup, and generally in chemistry to measure the concentration or enantiomeric ratio of chiral molecules in solution. Modulation of a liquid crystal's optical activity, viewed between two sheet polarizers, is the principle of operation of liquid-crystal displays (used in most modern televisions and computer monitors).

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.


PlanetPol was a ground-based, high sensitivity polarimeter based at the William Herschel Telescope on the island of La Palma in the Canary Islands, Spain that has now been decommissioned. It was the most sensitive astronomical visual polarimeter ever built in fractional polarisation, a mantle that since its decommissioning now belongs to HIPPI. Although the device could be used for a wide range of astronomy, its primary use was the detection of extrasolar planets.

Polarization-maintaining optical fiber

In fiber optics, polarization-maintaining optical fiber (PMF or PM fiber) is a single-mode optical fiber in which linearly polarized light, if properly launched into the fiber, maintains a linear polarization during propagation, exiting the fiber in a specific linear polarization state; there is little or no cross-coupling of optical power between the two polarization modes. Such fiber is used in special applications where preserving polarization is essential.

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.

Polarization controller

A polarization controller is an optical device which allows one to modify the polarization state of light.


A polarizer or polariser is an optical filter that lets light waves of a specific polarization pass through while blocking light waves of other polarizations. It can filter a beam of light of undefined or mixed polarization into a beam of well-defined polarization, that is polarized light. The common types of polarizers are linear polarizers and circular polarizers. Polarizers are used in many optical techniques and instruments, and polarizing filters find applications in photography and LCD technology. Polarizers can also be made for other types of electromagnetic waves besides light, such as radio waves, microwaves, and X-rays.

Second solar spectrum

The second solar spectrum is an electromagnetic spectrum of the Sun that shows the degree of linear polarization. The term was coined by V. V. Ivanov in 1991. The polarization is at a maximum close to the limb (edge) of the Sun, thus the best place to observe such a spectrum is from just inside the limb. It is also possible to get polarized light from outside the limb, but since this is much dimmer compared to the disk of the Sun, it is very easily polluted by scattered light.

The second solar spectrum differs significantly from the solar spectrum determined by the intensity of light.

Large effects come around the Ca II K and H line. These have broad effects 200 Å wide and show a sign reversal at their centres. Molecular lines with stronger polarization than the background due to MgH and C2 are common. Rare-earth elements stand out far more than expected from the intensity spectrum.Other odd lines include Li I at 6708 Å which has 0.005% more polarization at its peak, but is almost unobservable in the intensity spectrum. The Ba II 4554 Å appears as a triplet in the second solar spectrum. This is due to differing isotopes and hyperfine structure.Two lines at 5896 Å 4934 Å being the D1 lines of sodium and barium were predicted not to be polarized, but nevertheless are present in this spectrum.

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.

Umov effect

The Umov effect, also known as Umov's law, is a relationship between the albedo of an astronomical object, and the degree of polarization of light reflecting off it. The effect was discovered by the Russian physicist Nikolay Umov in 1905, and can be observed for celestial objects such as the surface of the Moon and the asteroids.

The degree of linear polarization of light P is defined by

where and are the intensities of light in the directions perpendicular and parallel to the plane of a polarizer aligned in the plane of reflection. Values of P are zero for unpolarized light, and ±1 for linearly polarized light.

Umov's law states

where α is the albedo of the object. Thus, highly reflective objects tend to reflect mostly unpolarized light, and dimly reflective objects tend to reflect polarized light. The law is only valid for large phase angles (angles between the incident light and the reflected light).

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