Polarization (Brit. polarisation) is a property of transverse waves which describes the orientation of the oscillations in the plane perpendicular to the wave's direction of travel. British English or UK English ( BrE, BE, en-GB) is the broad term used to distinguish the forms of the English language used in the A transverse wave is a moving Wave that consists of oscillations occurring perpendicular to the direction of energy transfer This concept is used in areas of science and technology dealing with wave propagation, such as optics, seismology, and telecommunications. Wave propagation is any of the ways in which waves travel through a Waveguide. Seismology (from Greek grc σεισμός seismos, "earthquake" and grc -λογία -logia) is the scientific study of Earthquakes In electrodynamics, polarization characterizes electromagnetic waves, such as light, by specifying the direction of the wave's electric field. Classical electromagnetism (or classical electrodynamics) is a theory of Electromagnetism that was developed over the course of the 19th century most prominently Electromagnetic radiation takes the form of self-propagating Waves in a Vacuum or in Matter. Light, or visible light, is Electromagnetic radiation of a Wavelength that is visible to the Human eye (about 400–700 In Physics, the space surrounding an Electric charge or in the presence of a time-varying Magnetic field has a property called an electric field (that can Longitudinal waves such as sound waves in liquids and gases do not exhibit polarization, because for these waves the direction of oscillation is along (and thus is uniquely determined by) the direction of wave's travel. Longitudinal waves are waves that have vibrations along or parallel to their direction of travel that is waves in which the motion of the medium is in the same direction as the motion An acoustic wave is a weak compression wave (meaning a small pressure change that moves at the Speed of sound. Liquid is one of the principal States of matter. A liquid is a Fluid that has the particles loose and can freely form a distinct surface at the boundaries of This page is about the physical properties of gas as a state of matter In contrast, the direction of the (electric field) oscillation in electromagnetic waves is not uniquely determined by the direction of propagation. Similarly, the direction of shear stress in a transverse sound wave in a solid can have any orientation in the plane that is perpendicular to the propagation direction. A shear stress, denoted \tau\ ( Tau) is defined as a stress which is applied Parallel or tangential to a face of a material A transverse wave is a moving Wave that consists of oscillations occurring perpendicular to the direction of energy transfer The term polarization thus describes the possible orientations of the oscillatory process in the plane perpendicular to the transverse wave's path.

Theory

Basics: plane waves

The simplest manifestation of polarization to visualize is that of a plane wave, which is a good approximation of most light waves (a plane wave is a wave with infinitely long and wide wavefronts). In the Physics of Wave propagation (especially Electromagnetic waves, a plane wave (also spelled planewave) is a constant-frequency wave whose In Optics and Physics, a wavefront is the locus (a line, or in a Wave propagating in 3 dimensions a Surface) of All electromagnetic waves propagating in free space or in a uniform material of infinite extent have electric and magnetic fields perpendicular to the direction of propagation. In Physics, the space surrounding an Electric charge or in the presence of a time-varying Magnetic field has a property called an electric field (that can In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges Conventionally, when considering polarization, the electric field vector is described and the magnetic field is ignored since it is perpendicular to the electric field and proportional to it. In Geometry, two lines or planes (or a line and a plane are considered perpendicular (or orthogonal) to each other if they form congruent The electric field vector may be arbitrarily divided into two perpendicular components labeled x and y (with z indicating the direction of travel). For a simple harmonic wave, where the amplitude of the electric vector varies in a sinusoidal manner, the two components have exactly the same frequency. Simple harmonic motion is the motion of a simple harmonic oscillator, a motion that is neither driven nor damped. However, these components have two other defining characteristics that can differ. First, the two components may not have the same amplitude. Amplitude is the magnitude of change in the oscillating variable with each Oscillation, within an oscillating system Second, the two components may not have the same phase, that is they may not reach their maxima and minima at the same time. The phase of an oscillation or wave is the fraction of a complete cycle corresponding to an offset in the displacement from a specified reference point at time t = 0 The shape traced out in a fixed plane by the electric vector as such a plane wave passes over it (a Lissajous figure) is a description of the polarization state. In Mathematics, a Lissajous curve ( Lissajous figure or Bowditch curve) is the graph of the system of Parametric equations The following figures show some examples of the evolution of the electric field vector (blue) with time (the vertical axes), along with its x and y components (red/left and green/right), and the path traced by the tip of the vector in the plane (purple):

Linear

Circular

Elliptical

In the leftmost figure above, the two orthogonal (perpendicular) components are in phase. In this case the ratio of the strengths of the two components is constant, so the direction of the electric vector (the vector sum of these two components) is constant. Since the tip of the vector traces out a single line in the plane, this special case is called linear polarization. In Electrodynamics, linear polarization or plane polarization of Electromagnetic radiation is a confinement of the Electric field vector or The direction of this line depends on the relative amplitudes of the two components.

In the middle figure, the two orthogonal components have exactly the same amplitude and are exactly ninety degrees out of phase. In this case one component is zero when the other component is at maximum or minimum amplitude. There are two possible phase relationships that satisfy this requirement: the x component can be ninety degrees ahead of the y component or it can be ninety degrees behind the y component. In this special case the electric vector traces out a circle in the plane, so this special case is called circular polarization. In Electrodynamics, circular polarization (also circular polarisation) of Electromagnetic radiation is a Polarization such that the tip of the The direction the field rotates in depends on which of the two phase relationships exists. These cases are called right-hand circular polarization and left-hand circular polarization, depending on which way the electric vector rotates.

In all other cases, where the two components are not in phase and either do not have the same amplitude and/or are not ninety degrees out of phase, the polarization is called elliptical polarization because the electric vector traces out an ellipse in the plane (the polarization ellipse). In Electrodynamics, elliptical polarization is the Polarization of Electromagnetic radiation such that the tip of the Electric field vector In Mathematics, an ellipse (from the Greek ἔλλειψις literally absence) is a Conic section, the locus of points in a This is shown in the above figure on the right.

The "Cartesian" decomposition of the electric field into x and y components is, of course, arbitrary. Plane waves of any polarization can be described instead by combining waves of opposite circular polarization, for example. The Cartesian polarization decomposition is natural when dealing with reflection from surfaces, birefringent materials, or synchrotron radiation. Birefringence, or double refraction, is the decomposition of a ray of Light into two rays (the ordinary ray and the extraordinary ray This article concerns the physical phenomenon of synchrotron radiation The circularly polarized modes are a more useful basis for the study of light propagation in stereoisomers. Stereoisomers are isomeric molecules that have the same molecular formula and sequence of bonded atoms (constitution but which differ in the three dimensional orientations

Incoherent radiation

In nature, electromagnetic radiation is often produced by a large number of individual sources, producing waves independently of each other. This type of light is described as incoherent. In Physics, coherence is a property of waves that enables stationary (i In general there is no single frequency but rather a spectrum of different frequencies present, and even if filtered to an arbitrarily narrow frequency range, there may not be a consistent state of polarization. A spectrum (plural spectra or spectrums) is a condition that is not limited to a specific set of values but can vary infinitely within a continuum. However, this does not mean that polarization is only a feature of coherent radiation. Incoherent radiation may show statistical correlation between the components of the electric field, which can be interpreted as partial polarization. In Probability theory and Statistics, correlation, (often measured as a correlation coefficient) indicates the strength and direction of a linear In general it is possible to describe an observed wave field as the sum of a completely incoherent part (no correlations) and a completely polarized part. One may then describe the light in terms of the degree of polarization, and the parameters of the polarization ellipse.

Parameterizing polarization

For ease of visualization, polarization states are often specified in terms of the polarization ellipse, specifically its orientation and elongation. A common parameterization uses the azimuth angle, ψ (the angle between the major semi-axis of the ellipse and the x-axis) and the ellipticity, ε (the ratio of the two semi-axes). An ellipticity of zero corresponds to linear polarization and an ellipticity of 1 corresponds to circular polarization. The arctangent of the ellipticity, χ = arctan ε (the "ellipticity angle"), is also commonly used. An example is shown in the diagram to the right. An alternative to the ellipticity or ellipticity angle is the eccentricity, however unlike the azimuth angle and ellipticity angle, the latter has no obvious geometrical interpretation in terms of the Poincaré sphere (see below). In Mathematics, the eccentricity, denoted e or \varepsilon is a parameter associated with every conic section.

Full information on a completely polarized state is also provided by the amplitude and phase of oscillations in two components of the electric field vector in the plane of polarization. This representation was used above to show how different states of polarization are possible. The amplitude and phase information can be conveniently represented as a two-dimensional complex vector (the Jones vector):

Here a₁ and a₂ denote the amplitude of the wave in the two components of the electric field vector, while θ₁ and θ₂ represent the phases. Complex plane In Mathematics, the complex numbers are an extension of the Real numbers obtained by adjoining an Imaginary unit, denoted In Optics one can describe Polarization using the Jones calculus, invented by R The product of a Jones vector with a complex number of unit modulus gives a different Jones vector representing the same ellipse, and thus the same state of polarization. In Mathematics, the absolute value (or modulus) of a Real number is its numerical value without regard to its sign. The physical electric field, as the real part of the Jones vector, would be altered but the polarization state itself is independent of absolute phase. Absolute phase refers to the phase of a Waveform relative to some standard (strictly speaking phase is always relative The basis vectors used to represent the Jones vector need not represent linear polarization states (i. Basis vector redirects here For basis vector in the context of crystals see Crystal structure. e. be real). In Mathematics, the real numbers may be described informally in several different ways In general any two orthogonal states can be used, where an orthogonal vector pair is formally defined as one having a zero inner product. In Mathematics, an inner product space is a Vector space with the additional Structure of inner product. A common choice is left and right circular polarizations, for example to model the different propagation of waves in two such components in circularly birefringent media (see below) or signal paths of coherent detectors sensitive to circular polarization.

Reflection of a plane wave from a surface perpendicular to the page. The p-components of the waves are in the plane of the page, while the s components are perpendicular to it.

Regardless of whether polarization ellipses are represented using geometric parameters or Jones vectors, implicit in the parameterization is the orientation of the coordinate frame. This permits a degree of freedom, namely rotation about the propagation direction. When considering light that is propagating parallel to the surface of the Earth, the terms "horizontal" and "vertical" polarization are often used, with the former being associated with the first component of the Jones vector, or zero azimuth angle. On the other hand, in astronomy the equatorial coordinate system is generally used instead, with the zero azimuth (or position angle, as it is more commonly called in astronomy to avoid confusion with the horizontal coordinate system) corresponding to due north. Astronomy (from the Greek words astron (ἄστρον "star" and nomos (νόμος "law" is the scientific study The equatorial coordinate system is probably the most widely used Celestial coordinate system, whose equatorial coordinates are Declination (\delta The horizontal coordinate system is a Celestial coordinate system that uses the observer's local Horizon as the fundamental plane. Another coordinate system frequently used relates to the plane made by the propagation direction and a vector normal to the plane of a reflecting surface. This is known as the plane of incidence. The rays in this plane are illustrated in the diagram to the right. The component of the electric field parallel to this plane is termed p-like (parallel) and the component perpendicular to this plane is termed s-like (from senkrecht, German for perpendicular). The German language (de ''Deutsch'') is a West Germanic language and one of the world's major languages. Light with a p-like electric field is said to be p-polarized, pi-polarized, tangential plane polarized, or is said to be a transverse-magnetic (TM) wave. Light with an s-like electric field is s-polarized, also known as sigma-polarized or sagittal plane polarized, or it can be called a transverse-electric (TE) wave.

In the case of partially-polarized radiation, the Jones vector varies in time and space in a way that differs from the constant rate of phase rotation of monochromatic, purely-polarized waves. In this case, the wave field is likely stochastic, and only statistical information can be gathered about the variations and correlations between components of the electric field. Stochastic (from the Greek "Στόχος" for "aim" or "guess" means Random. Statistics is a mathematical science pertaining to the collection analysis interpretation or explanation and presentation of Data. This information is embodied in the coherency matrix:

where angular brackets denote averaging over many wave cycles. In Mathematics, a matrix (plural matrices) is a rectangular table of elements (or entries) which may be Numbers or more generally Several variants of the coherency matrix have been proposed: the Wiener coherency matrix and the spectral coherency matrix of Richard Barakat measure the coherence of a spectral decomposition of the signal, while the Wolf coherency matrix averages over all time/frequencies. Norbert Wiener ( November 26, 1894, Columbia Missouri – March 18, 1964, Stockholm, Sweden) was an American In Mathematics, particularly Linear algebra and Functional analysis, the spectral theorem is any of a number of results about Linear operators Emil Wolf (born July 30, 1922) is a Czech born American Physicist who made advancements in physical Optics, including Diffraction,

The coherency matrix contains all of the information on polarization that is obtainable using second order statistics. It can be decomposed into the sum of two idempotent matrices, corresponding to the eigenvectors of the coherency matrix, each representing a polarization state that is orthogonal to the other. Idempotence ˌaɪdɨmˈpoʊtəns describes the property of operations in Mathematics and Computer science which means that multiple applications of the operation In Mathematics, given a Linear transformation, an of that linear transformation is a nonzero vector which when that transformation is applied to it changes An alternative decomposition is into completely polarized (zero determinant) and unpolarized (scaled identity matrix) components. In either case, the operation of summing the components corresponds to the incoherent superposition of waves from the two components. The latter case gives rise to the concept of the "degree of polarization"; i. e. , the fraction of the total intensity contributed by the completely polarized component.

The coherency matrix is not easy to visualize, and it is therefore common to describe incoherent or partially polarized radiation in terms of its total intensity (I), (fractional) degree of polarization (p), and the shape parameters of the polarization ellipse. An alternative and mathematically convenient description is given by the Stokes parameters, introduced by George Gabriel Stokes in 1852. The Stokes parameters are a set of values that describe the Polarization state of Electromagnetic radiation (including Visible light) Sir George Gabriel Stokes 1st Baronet FRS ( 13 August 1819 &ndash 1 February 1903) was a mathematician and physicist Year 1852 ( MDCCCLII) was a Leap year starting on Thursday (link will display the full calendar of the Gregorian calendar (or a Leap year The relationship of the Stokes parameters to intensity and polarization ellipse parameters is shown in the equations and figure below.

Here Ip, 2ψ and 2χ are the spherical coordinates of the polarization state in the three-dimensional space of the last three Stokes parameters. In Mathematics, the spherical coordinate system is a Coordinate system for representing geometric figures in three dimensions using three coordinates the radial Note the factors of two before ψ and χ corresponding respectively to the facts that any polarization ellipse is indistinguishable from one rotated by 180°, or one with the semi-axis lengths swapped accompanied by a 90° rotation. The Stokes parameters are sometimes denoted I, Q, U and V.

The Stokes parameters contain all of the information of the coherency matrix, and are related to it linearly by means of the identity matrix plus the three Pauli matrices:

Mathematically, the factor of two relating physical angles to their counterparts in Stokes space derives from the use of second-order moments and correlations, and incorporates the loss of information due to absolute phase invariance. The Pauli matrices are a set of 2 × 2 complex Hermitian and unitary matrices.

The figure above makes use of a convenient representation of the last three Stokes parameters as components in a three-dimensional vector space. This space is closely related to the Poincaré sphere, which is the spherical surface occupied by completely polarized states in the space of the vector

All four Stokes parameters can also be combined into the four-dimensional Stokes vector, which can be interpreted as four-vectors of Minkowski space. The Stokes parameters are a set of values that describe the Polarization state of Electromagnetic radiation (including Visible light) In relativity, a four-vector is a vector in a four-dimensional real Vector space, called Minkowski space. In Physics and Mathematics, Minkowski space (or Minkowski spacetime) is the mathematical setting in which Einstein's theory of Special relativity In this case, all physically realizable polarization states correspond to time-like, future-directed vectors.

Propagation, reflection and scattering

In a vacuum, the components of the electric field propagate at the speed of light, so that the phase of the wave varies in space in time while the polarization state does not. This vacuum means "absence of matter" or "an empty area or space" for the cleaning appliance see Vacuum cleaner. That is,

where k is the wavenumber and positive z is the direction of propagation. Wavenumber in most physical sciences is a Wave property inversely related to Wavelength, having SI units of reciprocal meters As noted above, the physical electric vector is the real part of the Jones vector. When electromagnetic waves interact with matter, their propagation is altered. If this depends on the polarization states of the waves, then their polarization may also be altered.

In many types of media, electromagnetic waves may be decomposed into two orthogonal components that encounter different propagation effects. A similar situation occurs in the signal processing paths of detection systems that record the electric field directly. Such effects are most easily characterized in the form of a complex 2×2 transformation matrix called the Jones matrix:

In general the Jones matrix of a medium depends on the frequency of the waves. In Mathematics, a linear map (also called a linear transformation, or linear operator) is a function between two Vector spaces that In Optics one can describe Polarization using the Jones calculus, invented by R

For propagation effects in two orthogonal modes, the Jones matrix can be written as

where g₁ and g₂ are complex numbers representing the change in amplitude and phase caused in each of the two propagation modes, and T is a unitary matrix representing a change of basis from these propagation modes to the linear system used for the Jones vectors. In Mathematics, a unitary matrix is an n by n complex matrix U satisfying the condition U^* U = UU^* For those media in which the amplitudes are unchanged but a differential phase delay occurs, the Jones matrix is unitary, while those affecting amplitude without phase have Hermitian Jones matrices. A number of Mathematical entities are named Hermitian, after the Mathematician Charles Hermite: Hermitian adjoint In fact, since any matrix may be written as the product of unitary and positive Hermitian matrices, any sequence of linear propagation effects, no matter how complex, can be written as the product of these two basic types of transformations.

Paths taken by vectors in the Poincaré sphere under birefringence. In Algebraic topology, a homology sphere is an n -manifold X having the Homology groups of an n - Sphere, for some integer The propagation modes (rotation axes) are shown with red, blue, and yellow lines, the initial vectors by thick black lines, and the paths they take by colored ellipses (which represent circles in three dimensions).

Media in which the two modes accrue a differential delay are called birefringent. Birefringence, or double refraction, is the decomposition of a ray of Light into two rays (the ordinary ray and the extraordinary ray Well known manifestations of this effect appear in optical wave plates/retarders (linear modes) and in Faraday rotation/optical rotation (circular modes). A wave plate or retarder is an optical device that alters the Polarization state of a Light wave travelling through it In Physics, the Faraday effect or Faraday rotation is a Magneto-optical phenomenon or an interaction between Light and a Magnetic Optical rotation or optical activity is the rotation of linearly polarized Light as it travels through certain materials An easily visualized example is one where the propagation modes are linear, and the incoming radiation is linearly polarized at a 45° angle to the modes. As the phase difference starts to appear, the polarization becomes elliptical, eventually changing to purely circular polarization (90° phase difference), then to elliptical and eventually linear polarization (180° phase) with an azimuth angle perpendicular to the original direction, then through circular again (270° phase), then elliptical with the original azimuth angle, and finally back to the original linearly polarized state (360° phase) where the cycle begins anew. In general the situation is more complicated and can be characterized as a rotation in the Poincaré sphere about the axis defined by the propagation modes (this is a consequence of the isomorphism of SU(2) with SO(3)). In Geometry and Linear algebra, a rotation is a transformation in a plane or in space that describes the motion of a Rigid body around a fixed In Abstract algebra, an isomorphism ( Greek: ἴσος isos "equal" and μορφή morphe "shape" is a bijective Special Unit 2In Mathematics, the special unitary group of degree n, denoted SU( n) is the group of n × n This article is about rotations in three-dimensional Euclidean space Examples for linear (blue), circular (red), and elliptical (yellow) birefringence are shown in the figure on the left. The total intensity and degree of polarization are unaffected. If the path length in the birefringent medium is sufficient, plane waves will exit the material with a significantly different propagation direction, due to refraction. Refraction is the change in direction of a Wave due to a change in its Speed. For example, this is the case with macroscopic crystals of calcite, which present the viewer with two offset, orthogonally polarized images of whatever is viewed through them. In Materials science, a crystal is a Solid in which the constituent Atoms Molecules or Ions are packed in a regularly ordered repeating Calcite is a carbonate mineral and the most stable polymorph of Calcium carbonate ( Ca[[carbon C]] O 3 It was this effect that provided the first discovery of polarization, by Erasmus Bartholinus in 1669. Rasmus Bartholin (Latinized Erasmus Bartholinus; August 13, 1625, Roskilde - † November 4, 1698, Kopenhagen In addition, the phase shift, and thus the change in polarization state, is usually frequency dependent, which, in combination with dichroism, often gives rise to bright colors and rainbow-like effects. Dichroic redirects here For the filter see Dichroic filter. For the glass see Dichroic glass.

Media in which the amplitude of waves propagating in one of the modes is reduced are called dichroic. Dichroic redirects here For the filter see Dichroic filter. For the glass see Dichroic glass. Devices that block nearly all of the radiation in one mode are known as polarizing filters or simply "polarizers". A polarizer is a device that converts an unpolarized or mixed- Polarization beam of Electromagnetic waves (e In terms of the Stokes parameters, the total intensity is reduced while vectors in the Poincaré sphere are "dragged" towards the direction of the favored mode. Mathematically, under the treatment of the Stokes parameters as a Minkowski 4-vector, the transformation is a scaled Lorentz boost (due to the isomorphism of SL(2,C) and the restricted Lorentz group, SO(3,1)). In Physics, the Lorentz transformation converts between two different observers' measurements of space and time where one observer is in constant motion with respect to In Mathematics, the special linear group of degree n over a field F is the set of n × n matrices with In Physics (and mathematics the Lorentz group is the group of all Lorentz transformations of Minkowski spacetime, the classical setting Just as the Lorentz transformation preserves the proper time, the quantity det Ψ = S₀²-S₁²-S₂²-S₃² is invariant within a multiplicative scalar constant under Jones matrix transformations (dichroic and/or birefringent). In relativity, proper time is Time measured by a single Clock between events that occur at the same place as the clock

In birefringent and dichroic media, in addition to writing a Jones matrix for the net effect of passing through a particular path in a given medium, the evolution of the polarization state along that path can be characterized as the (matrix) product of an infinite series of infinitesimal steps, each operating on the state produced by all earlier matrices. In a uniform medium each step is the same, and one may write

where J is an overall (real) gain/loss factor. Here D is a traceless matrix such that αDe gives the derivative of e with respect to z. In Linear algebra, the trace of an n -by- n Square matrix A is defined to be the sum of the elements on the Main diagonal If D is Hermitian the effect is dichroism, while a unitary matrix models birefringence. The matrix D can be expressed as a linear combination of the Pauli matrices, where real coefficients give Hermitian matrices and imaginary coefficients give unitary matrices. The Jones matrix in each case may therefore be written with the convenient construction

where σ is a 3-vector composed of the Pauli matrices (used here as generators for the Lie group SL(2,C)) and n and m are real 3-vectors on the Poincaré sphere corresponding to one of the propagation modes of the medium. In Mathematics, a Lie group (ˈliː sounds like "Lee" is a group which is also a Differentiable manifold, with the property that the group The effects in that space correspond to a Lorentz boost of velocity parameter 2β along the given direction, or a rotation of angle 2φ about the given axis. These transformations may also be written as biquaternions (quaternions with complex elements), where the elements are related to the Jones matrix in the same way that the Stokes parameters are related to the coherency matrix. The biquaternions are the numbers w + xi + yj + zk \ \! where w x y and z are complex numbers and the elements of {1 i j k} multiply as in the Quaternion group Quaternions, in Mathematics, are a non-commutative extension of Complex numbers They were first described by the Irish Mathematician They may then be applied in pre- and post-multiplication to the quaternion representation of the coherency matrix, with the usual exploitation of the quaternion exponential for performing rotations and boosts taking a form equivalent to the matrix exponential equations above. (See Quaternion rotation)

In addition to birefringence and dichroism in extended media, polarization effects describable using Jones matrices can also occur at (reflective) interface between two materials of different refractive index. Unit quaternions provide a convenient mathematical notation for representing Orientations and Rotations of objects in three dimensions The refractive index (or index of Refraction) of a medium is a measure for how much the speed of light (or other waves such as sound waves is reduced inside the medium These effects are treated by the Fresnel equations. Part of the wave is transmitted and part is reflected, with the ratio depending on angle of incidence and the angle of refraction. In addition, if the plane of the reflecting surface is not aligned with the plane of propagation of the wave, the polarization of the two parts is altered. In general, the Jones matrices of the reflection and transmission are real and diagonal, making the effect similar to that of a simple linear polarizer. In Linear algebra, a diagonal matrix is a Square matrix in which the entries outside the Main diagonal (↘ are all zero For unpolarized light striking a surface at a certain optimum angle of incidence known as Brewster's angle, the reflected wave will be completely s-polarized. Brewster's angle (also known as the polarization angle) is an Angle of incidence at which light with a particular Polarization is perfectly transmitted

Certain effects do not produce linear transformations of the Jones vector, and thus cannot be described with (constant) Jones matrices. For these cases it is usual instead to use a 4×4 matrix that acts upon the Stokes 4-vector. Such matrices were first used by Paul Soleillet in 1929, although they have come to be known as Mueller matrices. Year 1929 ( MCMXXIX) was a Common year starting on Tuesday (link will display the full calendar of the Gregorian calendar. Mueller calculus is a matrix method for manipulating Stokes vectors, which represent the Polarization of incoherent light While every Jones matrix has a Mueller matrix, the reverse is not true. Mueller matrices are frequently used to study the effects of the scattering of waves from complex surfaces or ensembles of particles. Scattering is a general physical process whereby some forms of Radiation, such as Light, Sound or moving particles for example are forced to deviate from

Polarization in nature, science, and technology

Polarization effects in everyday life

See also: Photographic filter#Polarizer

Effect of a polarizer on reflection from mud flats. In Photography, a filter is a Camera accessory consisting of an optical filter that can be inserted in the optical path In the picture on the left, the polarizer is rotated to transmit the reflections as well as possible; by rotating the polarizer by 90° (picture on the right) almost all specularly reflected sunlight is blocked. Specular reflection is the perfect Mirror -like reflection of light (or sometimes other kinds of Wave) from a surface in which light from a single incoming

The effects of a polarizing filter on the sky in a photograph. In Photography, a filter is a Camera accessory consisting of an optical filter that can be inserted in the optical path The picture on the right uses the filter.

Light reflected by shiny transparent materials is partly or fully polarized, except when the light is normal (perpendicular) to the surface. It was through this effect that polarization was first discovered in 1808 by the mathematician Etienne Louis Malus. Etienne-Louis Malus (23 July 1775 &ndash 24 February 1812 was a French officer, Engineer, Physicist, and Mathematician. A polarizing filter, such as a pair of polarizing sunglasses, can be used to observe this effect by rotating the filter while looking through it at the reflection off of a distant horizontal surface. Sunglasses or sun glasses are a visual aid variously termed Spectacles or Glasses, which feature lenses that are coloured or darkened to prevent strong At certain rotation angles, the reflected light will be reduced or eliminated. Polarizing filters remove light polarized at 90° to the filter's polarization axis. If two polarizers are placed atop one another at 90° angles to one another, there is minimal light transmission.

Polarization by scattering is observed as light passes through the atmosphere. Temperature and layers The temperature of the Earth's atmosphere varies with altitude the mathematical relationship between temperature and altitude varies among five The scattered light produces the brightness and color in clear skies. Rayleigh scattering (named after Lord Rayleigh) is the elastic Scattering of Light or other electromagnetic radiation by particles much smaller The sky is the part of the Atmosphere or of Outer space visible from the surface of any Astronomical object. This partial polarization of scattered light can be used to darken the sky in photographs, increasing the contrast. This effect is easiest to observe at sunset, on the horizon at a 90° angle from the setting sun. Sunset, also called sundown in some American English Dialects is the instant when the trailing edge of the Sun 's disk disappears below Another easily observed effect is the drastic reduction in brightness of images of the sky and clouds reflected from horizontal surfaces, which is the main reason polarizing filters are often used in sunglasses. Also frequently visible through polarizing sunglasses are rainbow-like patterns caused by color-dependent birefringent effects, for example in toughened glass (e. A rainbow is an optical and meteorological phenomenon that causes a spectrum of Light to appear in the Sky when the Sun Toughened or tempered glass is Glass that has been processed by controlled thermal or chemical treatments to increase its strength compared with normal glass g. car windows) or items made from transparent plastics. Plastic is the general common term for a wide range of synthetic or semisynthetic organic solid materials suitable for the manufacture of industrial products The role played by polarization in the operation of liquid crystal displays (LCD's) is also frequently apparent to the wearer of polarizing sunglasses, which may reduce the contrast or even make the display unreadable.

Polarizing sunglasses reveal stress in car window (see text for explanation. )

The photograph on the right was taken through polarizing sunglasses and through the rear window of a car. Light from the sky is reflected by the windshield of the other car at an angle, making it mostly horizontally polarized. The rear window is made of tempered glass. Toughened or tempered glass is Glass that has been processed by controlled thermal or chemical treatments to increase its strength compared with normal glass Stress in the glass, left from its heat treatment, causes it to alter the polarization of light passing through it, like a wave plate. A wave plate or retarder is an optical device that alters the Polarization state of a Light wave travelling through it Without this effect, the sunglasses would block the horizontally polarized light reflected from the other car's window. The stress in the rear window, however, changes some of the horizontally polarized light into vertically polarized light that can pass through the glasses. As a result, the regular pattern of the heat treatment becomes visible.

Biology

Many animals are apparently capable of perceiving the polarization of light, which is generally used for navigational purposes, since the linear polarization of sky light is always perpendicular to the direction of the sun. This ability is very common among the insects, including bees, which use this information to orient their communicative dances. Insects ( Class Insecta) are a major group of Arthropods and the most diverse group of Animals on the Earth with over a million described Bees are flying Insects closely related to Wasps and Ants Bees are a Monophyletic lineage within the superfamily Apoidea Honey bees learn and communicate in order to find food sources and for other means Polarization sensitivity has also been observed in species of octopus, squid, cuttlefish, and mantis shrimp. The Squid are marine Cephalopods of the order Teuthida, which comprises around 300 species Cuttlefish are marine animals of the order Sepiida belonging to the Cephalopoda class (which also includes Squid, Octopuses Mantis shrimp or stomatopods are marine Crustaceans the members of the order Stomatopoda. The rapidly changing, vividly colored skin patterns of cuttlefish, used for communication, also incorporate polarization patterns, and mantis shrimp are known to have polarization selective reflective tissue. Sky polarization was thought to be perceived by pigeons, which was assumed to be one of their aids in homing, but research indicates this is a popular myth. The homing pigeon is a variety of domesticated Rock Pigeon ( Columba livia domestica) that has been selectively ^[1]

The naked human eye is weakly sensitive to polarization, without the need for intervening filters. Eyes are organs that detect Light, and send signals along the Optic nerve to the visual areas of the brain Polarized light creates a very faint pattern near the center of the visual field, called Haidinger's brush. Haidinger's brush is an Entoptic phenomenon first described by Austrianphysicist Wilhelm Karl von Haidinger in 1844 This pattern is very difficult to see, but with practice one can learn to detect polarized light with the naked eye.

Geology

The property of (linear) birefringence is widespread in crystalline minerals, and indeed was pivotal in the initial discovery of polarization. A mineral is a naturally occurring substance formed through geological processes that has a characteristic chemical composition a highly ordered atomic structure and specific In mineralogy, this property is frequently exploited using polarization microscopes, for the purpose of identifying minerals. Mineralogy is an Earth Science focused around the Chemistry, Crystal structure, and physical (including optical) properties of Minerals A microscope ( Greek: ( micron) = small + ( skopein) = to look or see is an instrument for viewing objects that are See pleochroism. Pleochroism is an Optical phenomenon in which grains of a rock appear to be different colors when observed at different angles under a Petrographic microscope.

Chemistry

Polarization is principally of importance in chemistry due to the circular dichroism and "optical rotation" (circular birefringence) exhibited by optically active (chiral) molecules. Chemistry (from Egyptian kēme (chem meaning "earth") is the Science concerned with the composition structure and properties Circular dichroism (CD is a form of Spectroscopy based on the differential absorption of left- and right-handed circularly polarized Light. Optical rotation or optical activity is the rotation of linearly polarized Light as it travels through certain materials The term chiral (pronounced /ˈkaɪɹ(əl̩/ is used to describe an object that is non- superimposable on its mirror image In Chemistry, a molecule is defined as a sufficiently stable electrically neutral group of at least two Atoms in a definite arrangement held together by It may be measured using a polarimeter. Polarimetry is the measurement and interpretation of the Polarization of Transverse waves, most notably electromagnetic waves such as radio waves and Light

Polarization may also refer to the through-bond (inductive or resonant effect) or through-space influence of a nearby functional group on the electronic properties (e. The inductive effect in Chemistry is an experimentally observable effect of the transmission of charge through a chain of Atoms in a Molecule Resonance in Chemistry is a theory used to represent and model certain types of non-classical Molecular structures Resonance is a key component g. dipole moment) of a covalent bond or atom.

Astronomy

Main article: Polarization in astronomy

In many areas of astronomy, the study of polarized electromagnetic radiation from outer space is of great importance. Polarization is an important phenomenon in Astronomy. The polarization of Starlight was first observed by the Astronomers William Hiltner and Astronomy (from the Greek words astron (ἄστρον "star" and nomos (νόμος "law" is the scientific study Outer space, often simply called space, comprises the relatively empty regions of the Universe outside the escape velocities of Celestial bodies. Although not usually a factor in the thermal radiation of stars, polarization is also present in radiation from coherent astronomical sources (e. Thermal radiation is Electromagnetic radiation emitted from the surface of an object which is due to the object's Temperature. A star is a massive luminous ball of plasma. The nearest star to Earth is the Sun, which is the source of most of the Energy on Earth g. hydroxyl or methanol masers), and incoherent sources such as the large radio lobes in active galaxies, and pulsar radio radiation (which may, it is speculated, sometimes be coherent), and is also imposed upon starlight by scattering from interstellar dust. A maser is a device that produces coherent Electromagnetic waves through amplification due to Stimulated emission. Apart from providing information on sources of radiation and scattering, polarization also probes the interstellar magnetic field via Faraday rotation. In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges In Physics, the Faraday effect or Faraday rotation is a Magneto-optical phenomenon or an interaction between Light and a Magnetic The polarization of the cosmic microwave background is being used to study the physics of the very early universe. Synchrotron radiation is inherently polarised. This article concerns the physical phenomenon of synchrotron radiation

Technology

Technological applications of polarization are extremely widespread. Perhaps the most commonly encountered examples are liquid crystal displays and polarized sunglasses. Sunglasses or sun glasses are a visual aid variously termed Spectacles or Glasses, which feature lenses that are coloured or darkened to prevent strong

All radio transmitting and receiving antennas are intrinsically polarized, special use of which is made in radar. Radio is the transmission of signals by Modulation of electromagnetic waves with frequencies below those of visible Light. An antenna is a Transducer designed to transmit or Receive electromagnetic waves In other words antennas convert electromagnetic waves into Radar is a system that uses electromagnetic waves to identify the range altitude direction or speed of both moving and fixed objects such as Aircraft, ships Most antennas radiate either horizontal, vertical, or circular polarization although elliptical polarization also exists. The electric field or E-plane determines the polarization or orientation of the radio wave. The E-plane and H-plane are reference planes for linearly polarized antennas. Vertical polarization is most often used when it is desired to radiate a radio signal in all directions such as widely distributed mobile units. AM and FM radio uses vertical polarization. Television uses horizontal polarization. Alternating vertical and horizontal polarization is used on satellite communications (including television satellites), to reduce interference between programs on the same frequency band transmitted from adjacent satellites (one uses vertical, the next horizontal, and so on), allowing for reduced angular separation between the satellites. A communications satellite (sometimes abbreviated to comsat) is an artificial Satellite stationed in space for the purposes of Telecommunications. Frequency is a measure of the number of occurrences of a repeating event per unit Time.

Strain in Glass

In engineering, the relationship between strain and birefringence motivates the use of polarization in characterizing the distribution of stress and strain in prototypes. Engineering is the Discipline and Profession of applying technical and scientific Knowledge and Stress is a measure of the average amount of Force exerted per unit Area. Electronically controlled birefringent devices are used in combination with polarizing filters as modulators in fiber optics. An optical fiber (or fibre) is a Glass or Plastic fiber that carries Light along its length Polarizing filters are also used in photography. Photography (fә'tɒgrәfi or fә'tɑːgrәfi (from Greek φωτο and γραφία is the process and Art of recording pictures by means of capturing They can deepen the color of a blue sky and eliminate reflections from windows and standing water.

Sky polarization has been exploited in the "sky compass", which was used in the 1950s when navigating near the poles of the Earth's magnetic field when neither the sun nor stars were visible (e. The 1950s Decade refers to the years of 1950 to 1959 inclusive Earth 's magnetic field (and the surface magnetic field) is approximately a Magnetic dipole, with one pole near the North pole (see The Sun (Sol is the Star at the center of the Solar System. A star is a massive luminous ball of plasma. The nearest star to Earth is the Sun, which is the source of most of the Energy on Earth g. under daytime cloud or twilight). A cloud is a visible mass of droplets or frozen crystals floating in the atmosphere above the surface of the Earth or another Planetary body Twilight is the time before Sunrise, called Dawn, and the time after Sunset, called Dusk. It has been suggested, controversially, that the Vikings exploited a similar device (the "sunstone") in their extensive expeditions across the North Atlantic in the 9th–11th centuries, before the arrival of the magnetic compass in Europe in the 12th century. A Viking is one of the Norse ( Scandinavian Explorers Warriors Merchants, and pirates who raided and colonized wide areas Iceland spar, formerly known as Iceland crystal, is a transparent variety of Calcite, or crystallized Calcium carbonate, originally brought from Iceland The 9th century is the period from 801 to 900 in accordance with the Julian calendar in the Christian / Common Era. A compass, magnetic compass or mariner's compass is a navigational instrument for determining direction relative to the earth's Magnetic poles It consists Related to the sky compass is the "polar clock", invented by Charles Wheatstone in the late 19th century. Sir Charles Wheatstone FRS (6 February 1802 - 19 October 1875 was a British Scientist and Inventor of many scientific breakthroughs The 19th century of the Common Era began on January 1, 1801 and ended on December 31, 1900, according to the Gregorian calendar

Polarization is also used for some 3D movies, in which the images intended for each eye are either projected from two different projectors with orthogonally oriented polarizing filters or from a single projector with time multiplexed polarization (a fast alternating polarization device for successive frames). See also [[stereoscopy]] In film the term 3-D (or 3D) is used to describe any visual presentation system that attempts to maintain or recreate moving images Filter glasses with similarly oriented polarized filters ensure that each eye receives only the correct image. Typical stereoscopic projection displays use linear polarization encoding, because it is not very expensive and offers high contrast. Stereoscopy, stereoscopic imaging or 3-D (three-dimensional imaging is any technique capable of recording three-dimensional visual In environments where the viewer is moving, such as in simulators, circular polarization is sometimes used. This makes the channel separation insensitive to the viewing orientation. The 3-D effect only works on a silver screen since it maintains polarization, whereas the scattering in a normal projection screen would void the effect. A silver screen, also known as a silver lenticular screen, is a type of projection screen that was popular in the early years of the Motion picture industry and is

Art

Several visual artists have worked with polarized light and birefringent materials to create colorful, sometimes changing images. Birefringence, or double refraction, is the decomposition of a ray of Light into two rays (the ordinary ray and the extraordinary ray Most notable is contemporary artist Austine Wood Comarow, whose "Polage" art works have been exhibited at the Museum of Science, Boston, the New Mexico Museum of Natural History and Science in Albuquerque, NM, and la Cité des Sciences et de l'Industrie (the City of Science and Industry) in Paris. The Museum of Science ( MoS) is a Boston Massachusetts landmark located in Science Park a plot of land spanning the Charles River. The New Mexico Museum of Natural History and Science is a Natural history and Science museum in Albuquerque New Mexico near Old Town Albuquerque Cité des Sciences et de l'Industrie is the biggest Science museum in Europe. Paris (ˈpærɨs in English; in French) is the Capital of France and the country's largest city The artist works by cutting hundreds of small pieces of cellophane and other birefringent films and laminating them between plane polarizing filters. Cellophane is a thin transparent sheet made of regenerated Cellulose.

Other examples of polarization

• Shear waves in elastic materials exhibit polarization. A transverse wave is a moving Wave that consists of oscillations occurring perpendicular to the direction of energy transfer A material is said to be elastic if it deforms under stress (e These effects are studied as part of the field of seismology, where horizontal and vertical polarizations are termed SH and SV, respectively. Seismology (from Greek grc σεισμός seismos, "earthquake" and grc -λογία -logia) is the scientific study of Earthquakes

See also

Notes and references

• Austine Wood Comarow: Paintings in Polarized Light, James Mann, Wasabi Publishing, 2005, ISBN 0-9768198-0-5. A polarizer is a device that converts an unpolarized or mixed- Polarization beam of Electromagnetic waves (e An antenna is a Transducer designed to transmit or Receive electromagnetic waves In other words antennas convert electromagnetic waves into Birefringence, or double refraction, is the decomposition of a ray of Light into two rays (the ordinary ray and the extraordinary ray Circular dichroism (CD is a form of Spectroscopy based on the differential absorption of left- and right-handed circularly polarized Light. Electromagnetic radiation takes the form of self-propagating Waves in a Vacuum or in Matter. The E-plane and H-plane are reference planes for linearly polarized antennas. A Nicol prism is a type of Polarizer, an optical device used to generate a beam of polarized light. Photon polarization is the quantum mechanical description of the classical polarized sinusoidal plane electromagnetic wave A satellite dish is a type of Parabolic antenna that receives or transmits electromagnetic signals to and from another location typically a satellite The Stokes parameters are a set of values that describe the Polarization state of Electromagnetic radiation (including Visible light)
• Principles of Optics, 7th edition, M. Born & E. Wolf, Cambridge University, 1999, ISBN 0-521-64222-1.
• Fundamentals of polarized light : a statistical optics approach, C. Brosseau, Wiley, 1998, ISBN 0-471-14302-2.
• Polarized Light, second edition, Dennis Goldstein, Marcel Dekker, 2003, ISBN 0-8247-4053-X
• Field Guide to Polarization, Edward Collett, SPIE Field Guides vol. FG05, SPIE, 2005, ISBN 0-8194-5868-6.
• Polarization Optics in Telecommunications, Jay N. Damask, Springer 2004, ISBN 0-387-22493-9.
• Optics, 4th edition, Eugene Hecht, Addison Wesley 2002, ISBN 0-8053-8566-5.
• Polarized Light in Nature, G. P. Können, Translated by G. A. Beerling, Cambridge University, 1985, ISBN 0-521-25862-6.
• Polarised Light in Science and Nature, D. Pye, Institute of Physics, 2001, ISBN 0-7503-0673-4.
• Polarized Light, Production and Use, William A. Shurcliff, Harvard University, 1962.
• Ellipsometry and Polarized Light, R. M. A. Azzam and N. M. Bashara, North-Holland, 1977, ISBN 0-444-87016-4
• Secrets of the Viking Navigators—How the Vikings used their amazing sunstones and other techniques to cross the open oceans, Leif Karlsen, One Earth Press, 2003.

1. ^ "No evidence for polarization sensitivity in the pigeon electroretinogram", J. J. Vos Hzn, M. A. J. M. Coemans & J. F. W. Nuboer, The Journal of Experimental Biology, 1995.

External links

• Polarized Light in Nature and Technology
• Polarized Light Digital Image Gallery: Microscopic images made using polarization effects
• Polarization by the University of Colorado Physics 2000: Animated explanation of polarization
• MathPages: The relationship between photon spin and polarization
• A virtual polarization microscope
• Polarization angle in satellite dishes.
• Using polarizers in photography
• Molecular Expressions: Science, Optics and You — Polarization of Light: Interactive Java tutorial
• Electromagnetic waves and circular dichroism: an animated tutorial
• HyperPhysics: Polarization concepts
• Tutorial on rotating polarization through waveplates (retarders)
• SPIE technical group on polarization