also
Also or ALSO may refer to:
*Advanced Life Support in Obstetrics (ALSO), a program developed by the American Academy of Family Physicians (AAFP)
*Alsó-Fehér County, a historic administrative county (comitatus) of the Kingdom of Hungary
* ALSO Gro ...
polarisation) is a property applying to transverse waves that specifies the geometrical orientation of the
oscillation
Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum ...
s. 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
A string is the vibrating element that produces sound in string instruments such as the guitar, harp, piano (piano wire), and members of the violin family. Strings are lengths of a flexible material that a musical instrument holds under tensi ...
. 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 wave
In physics, sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid.
In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by the ...
s 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 wave
In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visib ...
s such as
light
Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 tera ...
and
radio wave
Radio waves are a type of electromagnetic radiation with the longest wavelengths in the electromagnetic spectrum, typically with frequencies of 300 gigahertz (GHz) and below. At 300 GHz, the corresponding wavelength is 1 mm (short ...
s,
gravitational wave
Gravitational waves are waves of the intensity of gravity generated by the accelerated masses of an orbital binary system that propagate as waves outward from their source at the speed of light. They were first proposed by Oliver Heaviside in 1 ...
s, and transverse sound waves ( shear waves) in solids.
An
electromagnetic wave
In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visib ...
such as light consists of a coupled oscillating
electric field
An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field fo ...
and
magnetic field
A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
which are always perpendicular to each other; 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, either in the right-hand or in the left-hand direction.
Light or other electromagnetic radiation from many sources, such as the sun, flames, and
incandescent lamp
An incandescent light bulb, incandescent lamp or incandescent light globe is an electric light with a wire filament heated until it glows. The filament is enclosed in a glass bulb with a vacuum or inert gas to protect the filament from oxid ...
s, consists of short wave trains with an equal mixture of polarizations; this is called ''
unpolarized light Unpolarized light is light with a random, time-varying polarization.
Natural light, like most other common sources of visible light, produced independently by a large number of atoms or molecules whose emissions are uncorrelated.
This term is so ...
''. Polarized light can be produced by passing unpolarized light through a
polarizer
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 ...
, which allows waves of only one polarization to pass through. The most common optical materials do not affect the polarization of light, but some materials—those that exhibit
birefringence
Birefringence is the optical property of a material having a refractive index that depends on the polarization and propagation direction of light. These optically anisotropic materials are said to be birefringent (or birefractive). The birefring ...
,
dichroism
In optics, a dichroic material is either one which causes visible light to be split up into distinct beams of different wavelengths (colours) (not to be confused with dispersion), or one in which light rays having different polarizations are abs ...
, or
optical activity
Optical rotation, also known as polarization rotation or circular birefringence, is the rotation of the orientation of the plane of polarization about the optical axis of linearly polarized light as it travels through certain materials. Circul ...
—affect light differently depending on its polarization. Some of these are used to make polarizing filters. Light also becomes partially polarized when it reflects at an angle from a surface.
According to
quantum mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...
, electromagnetic waves can also be viewed as streams of particles called
photon
A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they always ...
s. When viewed in this way, the polarization of an electromagnetic wave is determined by a quantum mechanical property of photons called their
spin
Spin or spinning most often refers to:
* Spinning (textiles), the creation of yarn or thread by twisting fibers together, traditionally by hand spinning
* Spin, the rotation of an object around a central axis
* Spin (propaganda), an intentionally b ...
. A photon has one of two possible spins: it can either spin in a
right hand
In human biology, handedness is an individual's preferential use of one hand, known as the dominant hand, due to it being stronger, faster or more dextrous. The other hand, comparatively often the weaker, less dextrous or simply less subjecti ...
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
Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviole ...
,
seismology
Seismology (; from Ancient Greek σεισμός (''seismós'') meaning "earthquake" and -λογία (''-logía'') meaning "study of") is the scientific study of earthquakes and the propagation of elastic waves through the Earth or through other ...
,
radio
Radio is the technology of signaling and communicating using radio waves. Radio waves are electromagnetic waves of frequency between 30 hertz (Hz) and 300 gigahertz (GHz). They are generated by an electronic device called a transmit ...
, and
microwave
Microwave is a form of electromagnetic radiation with wavelengths ranging from about one meter to one millimeter corresponding to frequencies between 300 MHz and 300 GHz respectively. Different sources define different frequency ran ...
s. Especially impacted are technologies such as
laser
A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The fir ...
s, wireless and optical fiber
telecommunications
Telecommunication is the transmission of information by various types of technologies over wire, radio, optical, or other electromagnetic systems. It has its origin in the desire of humans for communication over a distance greater than that fe ...
, and
radar
Radar is a detection system that uses radio waves to determine the distance (''ranging''), angle, and radial velocity of objects relative to the site. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, w ...
.
Introduction
Wave propagation and polarization
Most sources of light are classified as incoherent and unpolarized (or only "partially polarized") because they consist of a random mixture of waves having different spatial characteristics, frequencies (wavelengths), phases, and polarization states. However, for understanding electromagnetic waves and polarization in particular, it is easier to just consider coherent
plane wave
In physics, a plane wave is a special case of wave or field: a physical quantity whose value, at any moment, is constant through any plane that is perpendicular to a fixed direction in space.
For any position \vec x in space and any time t, th ...
s; these are sinusoidal waves of one particular direction (or wavevector), frequency, phase, and polarization state. Characterizing an optical system in relation to a plane wave with those given parameters can then be used to predict its response to a more general case, since a wave with any specified spatial structure can be decomposed into a combination of plane waves (its so-called
angular spectrum
The angular spectrum method is a technique for modeling the propagation of a wave field. This technique involves expanding a complex wave field into a summation of infinite number of plane waves of the same frequency and different directions. Its ...
). Incoherent states can be modeled
stochastically
Stochastic (, ) refers to the property of being well described by a randomness, random probability distribution. Although stochasticity and randomness are distinct in that the former refers to a modeling approach and the latter refers to phenome ...
as a weighted combination of such uncorrelated waves with some
distribution Distribution may refer to:
Mathematics
*Distribution (mathematics), generalized functions used to formulate solutions of partial differential equations
* Probability distribution, the probability of a particular value or value range of a vari ...
of frequencies (its ''
spectrum
A spectrum (plural ''spectra'' or ''spectrums'') is a condition that is not limited to a specific set of values but can vary, without gaps, across a continuum. The word was first used scientifically in optics to describe the rainbow of colors i ...
''), phases, and polarizations.
Transverse electromagnetic waves
Electromagnetic waves
In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visible) lig ...
(such as light), traveling in free space or another
homogeneous
Homogeneity and heterogeneity are concepts often used in the sciences and statistics relating to the uniformity of a substance or organism. A material or image that is homogeneous is uniform in composition or character (i.e. color, shape, siz ...
isotropic
Isotropy is uniformity in all orientations; it is derived . Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix ' or ', hence ''anisotropy''. ''Anisotropy'' is also used to describe ...
non-attenuating medium, are properly described as transverse waves, meaning that a plane wave's electric field vector E and magnetic field H are each in some direction perpendicular to (or "transverse" to) the direction of wave propagation; E and H are also perpendicular to each other. By convention, the "polarization" direction of an electromagnetic wave is given by its electric field vector. Considering a monochromatic
plane wave
In physics, a plane wave is a special case of wave or field: a physical quantity whose value, at any moment, is constant through any plane that is perpendicular to a fixed direction in space.
For any position \vec x in space and any time t, th ...
of optical frequency ''f'' (light of vacuum wavelength λ has a frequency of ''f = c/λ'' where ''c'' is the speed of light), let us take the direction of propagation as the ''z'' axis. Being a transverse wave the E and H fields must then contain components only in the ''x'' and ''y'' directions whereas ''Ez = Hz = 0''. Using complex (or
phasor
In physics and engineering, a phasor (a portmanteau of phase vector) is a complex number representing a sinusoidal function whose amplitude (''A''), angular frequency (''ω''), and initial phase (''θ'') are time-invariant. It is related to ...
) notation, the instantaneous physical electric and magnetic fields are given by the real parts of the complex quantities occurring in the following equations. As a function of time ''t'' and spatial position ''z'' (since for a plane wave in the +''z'' direction the fields have no dependence on ''x'' or ''y'') these complex fields can be written as:
:
and
:
where λ = λ/''n'' is the wavelength ''in the medium'' (whose
refractive index
In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium.
The refractive index determines how much the path of light is bent, or ...
is ''n'') and is the period of the wave. Here ''ex'', ''ey'', ''hx'', and ''hy'' are complex numbers. In the second more compact form, as these equations are customarily expressed, these factors are described using the
wavenumber
In the physical sciences, the wavenumber (also wave number or repetency) is the ''spatial frequency'' of a wave, measured in cycles per unit distance (ordinary wavenumber) or radians per unit distance (angular wavenumber). It is analogous to temp ...
and
angular frequency
In physics, angular frequency "''ω''" (also referred to by the terms angular speed, circular frequency, orbital frequency, radian frequency, and pulsatance) is a scalar measure of rotation rate. It refers to the angular displacement per unit tim ...
(or "radian frequency") . In a more general formulation with propagation ''not'' restricted to the ''+z'' direction, then the spatial dependence ''kz'' is replaced by where is called the wave vector, the magnitude of which is the wavenumber.
Thus the leading vectors e and h each contain up to two nonzero (complex) components describing the amplitude and phase of the wave's ''x'' and ''y'' polarization components (again, there can be no ''z'' polarization component for a transverse wave in the +''z'' direction). For a given medium with a
characteristic impedance
The characteristic impedance or surge impedance (usually written Z0) of a uniform transmission line is the ratio of the amplitudes of voltage and current of a single wave propagating along the line; that is, a wave travelling in one direction in ...
, h is related to e by:
:
and
:.
In a dielectric, ''η'' is real and has the value ''η''0/''n'', where ''n'' is the refractive index and ''η''0 is the impedance of free space. The impedance will be complex in a conducting medium. Note that given that relationship, the
dot product
In mathematics, the dot product or scalar productThe term ''scalar product'' means literally "product with a scalar as a result". It is also used sometimes for other symmetric bilinear forms, for example in a pseudo-Euclidean space. is an algebra ...
of E and H must be zero:
:
indicating that these vectors are
orthogonal
In mathematics, orthogonality is the generalization of the geometric notion of ''perpendicularity''.
By extension, orthogonality is also used to refer to the separation of specific features of a system. The term also has specialized meanings in ...
(at right angles to each other), as expected.
So knowing the propagation direction (+''z'' in this case) and η, one can just as well specify the wave in terms of just ''ex'' and ''ey'' describing the electric field. The vector containing ''ex'' and ''ey'' (but without the ''z'' component which is necessarily zero for a transverse wave) is known as a
Jones vector
In optics, polarized light can be described using the Jones calculus, discovered by R. C. Jones in 1941. Polarized light is represented by a Jones vector, and linear optical elements are represented by ''Jones matrices''. When light crosses an op ...
. In addition to specifying the polarization state of the wave, a general Jones vector also specifies the overall magnitude and phase of that wave. Specifically, the
intensity
Intensity may refer to:
In colloquial use
*Strength (disambiguation)
*Amplitude
* Level (disambiguation)
* Magnitude (disambiguation)
In physical sciences
Physics
*Intensity (physics), power per unit area (W/m2)
*Field strength of electric, ma ...
of the light wave is proportional to the sum of the squared magnitudes of the two electric field components:
:
However, the wave's ''state of polarization'' is only dependent on the (complex) ''ratio'' of ''ey'' to ''ex''. So let us just consider waves whose '', ex, 2 + , ey, 2 = 1''; this happens to correspond to an intensity of about .00133
watt
The watt (symbol: W) is the unit of power or radiant flux in the International System of Units (SI), equal to 1 joule per second or 1 kg⋅m2⋅s−3. It is used to quantify the rate of energy transfer. The watt is named after James Wa ...
s per square meter in free space (where ). And since the absolute phase of a wave is unimportant in discussing its polarization state, let us stipulate that the phase of ''ex'' is zero, in other words ''ex'' is a real number while ''ey'' may be complex. Under these restrictions, ''ex'' and ''ey'' can be represented as follows:
:
:
where the polarization state is now fully parameterized by the value of ''Q'' (such that −1 < ''Q'' < 1) and the relative phase .
Non-transverse waves
In addition to transverse waves, there are many wave motions where the oscillation is not limited to directions perpendicular to the direction of propagation. These cases are far beyond the scope of the current article which concentrates on transverse waves (such as most electromagnetic waves in bulk media), but one should be aware of cases where the polarization of a coherent wave cannot be described simply using a Jones vector, as we have just done.
Just considering electromagnetic waves, we note that the preceding discussion strictly applies to plane waves in a homogeneous isotropic non-attenuating medium, whereas in an
anisotropic
Anisotropy () is the property of a material which allows it to change or assume different properties in different directions, as opposed to isotropy. It can be defined as a difference, when measured along different axes, in a material's physic ...
medium (such as birefringent crystals as discussed below) the electric or magnetic field may have longitudinal as well as transverse components. In those cases the
electric displacement
In physics, the electric displacement field (denoted by D) or electric induction is a vector field that appears in Maxwell's equations. It accounts for the effects of free and bound charge within materials. "D" stands for "displacement", as in ...
magnetic permeability
In electromagnetism, permeability is the measure of magnetization that a material obtains in response to an applied magnetic field. Permeability is typically represented by the (italicized) Greek letter ''μ''. The term was coined by William ...
), now given by a
tensor
In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tenso ...
, the direction of ''E'' (or ''H'') may differ from that of ''D'' (or ''B''). Even in isotropic media, so-called
inhomogeneous wave
Homogeneity and heterogeneity are concepts often used in the sciences and statistics relating to the Uniformity (chemistry), uniformity of a Chemical substance, substance or organism. A material or image that is homogeneous is uniform in compos ...
s can be launched into a medium whose refractive index has a significant imaginary part (or " extinction coefficient") such as metals; these fields are also not strictly transverse.
Surface wave
In physics, a surface wave is a mechanical wave that propagates along the Interface (chemistry), interface between differing media. A common example is gravity waves along the surface of liquids, such as ocean waves. Gravity waves can also occu ...
optical fiber
An optical fiber, or optical fibre in Commonwealth English, is a flexible, transparent fiber made by drawing glass (silica) or plastic to a diameter slightly thicker than that of a human hair. Optical fibers are used most often as a means to ...
) are generally ''not'' transverse waves, but might be described as an electric or magnetic
transverse mode
A transverse mode of electromagnetic radiation is a particular electromagnetic field pattern of the radiation in the plane perpendicular (i.e., transverse) to the radiation's propagation direction. Transverse modes occur in radio waves and microwav ...
, or a hybrid mode.
Even in free space, longitudinal field components can be generated in focal regions, where the plane wave approximation breaks down. An extreme example is radially or tangentially polarized light, at the focus of which the electric or magnetic field respectively is ''entirely'' longitudinal (along the direction of propagation).
For longitudinal waves such as
sound wave
In physics, sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid.
In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by the ...
s in
fluid
In physics, a fluid is a liquid, gas, or other material that continuously deforms (''flows'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are substances which cannot resist any shear ...
s, the direction of oscillation is by definition along the direction of travel, so the issue of polarization is normally not even mentioned. On the other hand, sound waves in a bulk
solid
Solid is one of the State of matter#Four fundamental states, four fundamental states of matter (the others being liquid, gas, and Plasma (physics), plasma). The molecules in a solid are closely packed together and contain the least amount o ...
can be transverse as well as longitudinal, for a total of three polarization components. In this case, the transverse polarization is associated with the direction of the
shear stress
Shear stress, often denoted by (Greek: tau), is the component of stress coplanar with a material cross section. It arises from the shear force, the component of force vector parallel to the material cross section. ''Normal stress'', on the ot ...
and displacement in directions perpendicular to the propagation direction, while the longitudinal polarization describes compression of the solid and vibration along the direction of propagation. The differential propagation of transverse and longitudinal polarizations is important in
seismology
Seismology (; from Ancient Greek σεισμός (''seismós'') meaning "earthquake" and -λογία (''-logía'') meaning "study of") is the scientific study of earthquakes and the propagation of elastic waves through the Earth or through other ...
.
Polarization state
Polarization is best understood by initially considering only pure polarization states, and only a coherent sinusoidal wave at some optical frequency. The vector in the adjacent diagram might describe the oscillation of the electric field emitted by a single-mode laser (whose oscillation frequency would be typically 1015 times faster). The field oscillates in the ''x-y'' plane, along the page, with the wave propagating in the ''z'' direction, perpendicular to the page.
The first two diagrams below trace the electric field vector over a complete cycle for linear polarization at two different orientations; these are each considered a distinct ''state of polarization'' (SOP). Note that the linear polarization at 45° can also be viewed as the addition of a horizontally linearly polarized wave (as in the leftmost figure) and a vertically polarized wave of the same amplitude ''in the same phase''.
Now if one were to introduce a phase shift in between those horizontal and vertical polarization components, one would generally obtain elliptical polarization as is shown in the third figure. When the phase shift is exactly ±90°, then ''circular polarization'' is produced (fourth and fifth figures). Thus is circular polarization created in practice, starting with linearly polarized light and employing a
quarter-wave plate
A waveplate or retarder is an optical device that alters the polarization state of a light wave travelling through it. Two common types of waveplates are the ''half-wave plate'', which shifts the polarization direction of linearly polarized ligh ...
to introduce such a phase shift. The result of two such phase-shifted components in causing a rotating electric field vector is depicted in the animation on the right. Note that circular or elliptical polarization can involve either a clockwise or counterclockwise rotation of the field. These correspond to distinct polarization states, such as the two circular polarizations shown above.
Of course the orientation of the ''x'' and ''y'' axes used in this description is arbitrary. The choice of such a coordinate system and viewing the polarization ellipse in terms of the ''x'' and ''y'' polarization components, corresponds to the definition of the Jones vector (below) in terms of those
basis
Basis may refer to:
Finance and accounting
*Adjusted basis, the net cost of an asset after adjusting for various tax-related items
*Basis point, 0.01%, often used in the context of interest rates
*Basis trading, a trading strategy consisting of ...
polarizations. One would typically choose axes to suit a particular problem such as ''x'' being in the plane of incidence. Since there are separate reflection coefficients for the linear polarizations in and orthogonal to the plane of incidence (''p'' and ''s'' polarizations, see below), that choice greatly simplifies the calculation of a wave's reflection from a surface.
Moreover, one can use as basis functions ''any'' pair of
orthogonal
In mathematics, orthogonality is the generalization of the geometric notion of ''perpendicularity''.
By extension, orthogonality is also used to refer to the separation of specific features of a system. The term also has specialized meanings in ...
polarization states, not just linear polarizations. For instance, choosing right and left circular polarizations as basis functions simplifies the solution of problems involving circular birefringence (optical activity) or circular dichroism.
Polarization ellipse
Consider a purely polarized monochromatic wave. If one were to plot the electric field vector over one cycle of oscillation, an ellipse would generally be obtained, as is shown in the figure, corresponding to a particular state of elliptical polarization. Note that linear polarization and circular polarization can be seen as special cases of elliptical polarization.
A polarization state can then be described in relation to the geometrical parameters of the ellipse, and its "handedness", that is, whether the rotation around the ellipse is clockwise or counter clockwise. One parameterization of the elliptical figure specifies the orientation angle ''ψ'', defined as the angle between the major axis of the ellipse and the ''x''-axis along with the ellipticity ''ε'' = ''a/b'', the ratio of the ellipse's major to minor axis. (also known as the axial ratio). The ellipticity parameter is an alternative parameterization of an ellipse's eccentricity or the ellipticity angle, as is shown in the figure. The angle ''χ'' is also significant in that the latitude (angle from the equator) of the polarization state as represented on the Poincaré sphere (see below) is equal to ±2''χ''. The special cases of linear and circular polarization correspond to an ellipticity ''ε'' of infinity and unity (or ''χ'' of zero and 45°) respectively.
Jones vector
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
In optics, polarized light can be described using the Jones calculus, discovered by R. C. Jones in 1941. Polarized light is represented by a Jones vector, and linear optical elements are represented by ''Jones matrices''. When light crosses an op ...
):
:
Here and denote the amplitude of the wave in the two components of the electric field vector, while and represent the phases. 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. 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). To the extent that this standard is accepted by all parties, one can speak of an absolute phase in a particular field of appli ...
. The
basis
Basis may refer to:
Finance and accounting
*Adjusted basis, the net cost of an asset after adjusting for various tax-related items
*Basis point, 0.01%, often used in the context of interest rates
*Basis trading, a trading strategy consisting of ...
vectors used to represent the Jones vector need not represent linear polarization states (i.e. be real). 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 (or, rarely, a Hausdorff space, Hausdorff pre-Hilbert space) is a real vector space or a complex vector space with an operation (mathematics), operation called an inner product. The inner product of two ve ...
. 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.
Coordinate frame
Regardless of whether polarization state is 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
Astronomy () is a natural science that studies astronomical object, celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and chronology of the Universe, evolution. Objects of interest ...
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
The horizontal coordinate system is a celestial coordinate system that uses the observer's local horizon as the fundamental plane to define two angles: altitude and azimuth.
Therefore, the horizontal coordinate system is sometimes called as th ...
) corresponding to due north.
''s'' and ''p'' designations
Another coordinate system frequently used relates to the '' plane of incidence''. This is the plane made by the incoming propagation direction and the vector perpendicular to the plane of an interface, in other words, the plane in which the ray travels before and after reflection or refraction. 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). Polarized light with its electric field along the plane of incidence is thus denoted ''p-polarized'', while light whose electric field is normal to the plane of incidence is called ''s-polarized''. ''P'' polarization is commonly referred to as ''transverse-magnetic'' (TM), and has also been termed ''pi-polarized'' or ''tangential plane polarized''. ''S'' polarization is also called ''transverse-electric'' (TE), as well as ''sigma-polarized'' or ''sagittal plane polarized''.
Degree of polarization
Degree of polarization (DOP) is a quantity used to describe the portion of an
electromagnetic wave
In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visib ...
which is polarized. A perfectly polarized wave has a DOP of 100%, whereas an unpolarized wave has a DOP of 0%. A wave which is partially polarized, and therefore can be represented by a superposition of a polarized and unpolarized component, will have a DOP somewhere in between 0 and 100%. DOP is calculated as the fraction of the total power that is carried by the polarised component of the wave.
DOP can be used to map the strain field in materials when considering the DOP of the
photoluminescence
Photoluminescence (abbreviated as PL) is light emission from any form of matter after the absorption of photons (electromagnetic radiation). It is one of many forms of luminescence (light emission) and is initiated by photoexcitation (i.e. photon ...
. The polarization of the photoluminescence is related to the strain in a material by way of the given material's
photoelasticity tensor
Photoelasticity describes changes in the optical properties of a material under mechanical deformation. It is a property of all dielectric media and is often used to experimentally determine the stress distribution in a material, where it gives ...
.
DOP is also visualized using the Poincaré sphere representation of a polarized beam. In this representation, DOP is equal to the length of the vector measured from the center of the sphere.
Unpolarized and partially polarized light
Implications for reflection and propagation
Polarization in wave propagation
In a
vacuum
A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicists often dis ...
, the components of the electric field propagate at the
speed of light
The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
, so that the phase of the wave varies in space and time while the polarization state does not. That is, the electric field vector e of a plane wave in the +''z'' direction follows:
:
where ''k'' is the
wavenumber
In the physical sciences, the wavenumber (also wave number or repetency) is the ''spatial frequency'' of a wave, measured in cycles per unit distance (ordinary wavenumber) or radians per unit distance (angular wavenumber). It is analogous to temp ...
. As noted above, the instantaneous electric field is the real part of the product of the Jones vector times the phase factor . When an electromagnetic wave interacts with matter, its propagation is altered according to the material's (complex)
index of refraction
In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium.
The refractive index determines how much the path of light is bent, or ...
. When the real or imaginary part of that refractive index is dependent on the polarization state of a wave, properties known as
birefringence
Birefringence is the optical property of a material having a refractive index that depends on the polarization and propagation direction of light. These optically anisotropic materials are said to be birefringent (or birefractive). The birefring ...
and polarization
dichroism
In optics, a dichroic material is either one which causes visible light to be split up into distinct beams of different wavelengths (colours) (not to be confused with dispersion), or one in which light rays having different polarizations are abs ...
(or
diattenuation
In optics, a dichroic material is either one which causes visible light to be split up into distinct beams of different wavelengths (colours) (not to be confused with dispersion), or one in which light rays having different polarizations are abs ...
) respectively, then the polarization state of a wave will generally be altered.
In such media, an electromagnetic wave with any given state of polarization may be decomposed into two orthogonally polarized components that encounter different propagation constants. The effect of propagation over a given path on those two components is most easily characterized in the form of a complex 2×2
transformation
Transformation may refer to:
Science and mathematics
In biology and medicine
* Metamorphosis, the biological process of changing physical form after birth or hatching
* Malignant transformation, the process of cells becoming cancerous
* Trans ...
matrix J known as a
Jones matrix
In optics, polarized light can be described using the Jones calculus, discovered by R. C. Jones in 1941. Polarized light is represented by a Jones vector, and linear optical elements are represented by ''Jones matrices''. When light crosses an op ...
:
:
The Jones matrix due to passage through a transparent material is dependent on the propagation distance as well as the birefringence. The birefringence (as well as the average refractive index) will generally be dispersive, that is, it will vary as a function of optical frequency (wavelength). In the case of non-birefringent materials, however, the 2×2 Jones matrix is the identity matrix (multiplied by a scalar phase factor and attenuation factor), implying no change in polarization during propagation.
For propagation effects in two orthogonal modes, the Jones matrix can be written as
:
where ''g''1 and ''g''2 are complex numbers
describing the phase delay and possibly the amplitude attenuation due to propagation in each of the two polarization eigenmodes. T is a unitary matrix representing a change of basis from these propagation modes to the linear system used for the Jones vectors; in the case of linear birefringence or diattenuation the modes are themselves linear polarization states so T and T−1 can be omitted if the coordinate axes have been chosen appropriately.
Birefringence
In a birefringent substance, electromagnetic waves of different polarizations travel at different speeds (
phase velocities
The phase velocity of a wave is the rate at which the wave propagates in any medium. This is the velocity at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave (for example, ...
). As a result when unpolarized waves travel through a plate of birefringent material, one polarization component has a shorter wavelength than the other, resulting in a phase difference between the components which increases the further the waves travel through the material. The Jones matrix is a unitary matrix: , ''g''1, = , ''g''2, = 1. Media termed diattenuating (or ''
dichroic
In optics, a dichroic material is either one which causes visible light to be split up into distinct beams of different wavelengths (colours) (not to be confused with dispersion), or one in which light rays having different polarizations are abs ...
'' in the sense of polarization), in which only the amplitudes of the two polarizations are affected differentially, may be described using a Hermitian matrix (generally multiplied by a common phase factor). In fact, since ''any'' matrix may be written as the product of unitary and positive Hermitian matrices, light propagation through any sequence of polarization-dependent optical components can be written as the product of these two basic types of transformations.
In birefringent media there is no attenuation, but two modes accrue a differential phase delay. Well known manifestations of linear birefringence (that is, in which the basis polarizations are orthogonal linear polarizations) appear in optical wave plates/retarders and many crystals. If linearly polarized light passes through a birefringent material, its state of polarization will generally change, ''unless'' its polarization direction is identical to one of those basis polarizations. Since the phase shift, and thus the change in polarization state, is usually wavelength-dependent, such objects viewed under white light in between two polarizers may give rise to colorful effects, as seen in the accompanying photograph.
Circular birefringence is also termed
optical activity
Optical rotation, also known as polarization rotation or circular birefringence, is the rotation of the orientation of the plane of polarization about the optical axis of linearly polarized light as it travels through certain materials. Circul ...
Faraday rotation
The Faraday effect or Faraday rotation, sometimes referred to as the magneto-optic Faraday effect (MOFE), is a physical magneto-optical phenomenon. The Faraday effect causes a polarization rotation which is proportional to the projection of the m ...
, when due to the presence of a magnetic field along the direction of propagation. When linearly polarized light is passed through such an object, it will exit still linearly polarized, but with the axis of polarization rotated. A combination of linear and circular birefringence will have as basis polarizations two orthogonal elliptical polarizations; however, the term "elliptical birefringence" is rarely used.
One can visualize the case of linear birefringence (with two orthogonal linear propagation modes) with an incoming wave linearly polarized at a 45° angle to those modes. As a differential phase starts to accrue, the polarization becomes elliptical, eventually changing to purely circular polarization (90° phase difference), then to elliptical and eventually linear polarization (180° phase) perpendicular to the original polarization, 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
Rotation, or spin, is the circular movement of an object around a '' central axis''. A two-dimensional rotating object has only one possible central axis and can rotate in either a clockwise or counterclockwise direction. A three-dimensional ...
in the Poincaré sphere about the axis defined by the propagation modes. Examples for linear (blue), circular (red), and elliptical (yellow)
birefringence
Birefringence is the optical property of a material having a refractive index that depends on the polarization and propagation direction of light. These optically anisotropic materials are said to be birefringent (or birefractive). The birefring ...
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, the two polarization components of a collimated beam (or
ray
Ray may refer to:
Fish
* Ray (fish), any cartilaginous fish of the superorder Batoidea
* Ray (fish fin anatomy), a bony or horny spine on a fin
Science and mathematics
* Ray (geometry), half of a line proceeding from an initial point
* Ray (g ...
) can exit the material with a positional offset, even though their final propagation directions will be the same (assuming the entrance face and exit face are parallel). This is commonly viewed using
calcite
Calcite is a Carbonate minerals, carbonate mineral and the most stable Polymorphism (materials science), polymorph of calcium carbonate (CaCO3). It is a very common mineral, particularly as a component of limestone. Calcite defines hardness 3 on ...
crystal
A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macros ...
s, which present the viewer with two slightly offset images, in opposite polarizations, of an object behind the crystal. It was this effect that provided the first discovery of polarization, by
Erasmus Bartholinus
Rasmus Bartholin (; Latinized: ''Erasmus Bartholinus''; 13 August 1625 – 4 November 1698) was a Danish physician and grammarian.
Biography
Bartholin was born in Roskilde. He was the son of Caspar Bartholin the Elder (1585–1629) and Anna ...
in 1669.
Dichroism
Media in which transmission of one polarization mode is preferentially reduced are called ''
dichroic
In optics, a dichroic material is either one which causes visible light to be split up into distinct beams of different wavelengths (colours) (not to be confused with dispersion), or one in which light rays having different polarizations are abs ...
'' or ''diattenuating''. Like birefringence, diattenuation can be with respect to linear polarization modes (in a crystal) or circular polarization modes (usually in a liquid).
Devices that block nearly all of the radiation in one mode are known as ''polarizing filters'' or simply "
polarizer
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 ...
s". This corresponds to ''g''2=0 in the above representation of the Jones matrix. The output of an ideal polarizer is a specific polarization state (usually linear polarization) with an amplitude equal to the input wave's original amplitude in that polarization mode. Power in the other polarization mode is eliminated. Thus if unpolarized light is passed through an ideal polarizer (where ''g''1=1 and ''g''2=0) exactly half of its initial power is retained. Practical polarizers, especially inexpensive sheet polarizers, have additional loss so that
''g''1 < 1. However, in many instances the more relevant figure of merit is the polarizer's
degree of polarization
Degree of polarization (DOP) is a quantity used to describe the portion of an electromagnetic wave which is polarized. A perfectly polarized wave has a DOP of 100%, whereas an unpolarized wave has a DOP of 0%. A wave which is partially polarize ...
or
extinction ratio
In telecommunications, extinction ratio (''r''e) is the ratio of two optical Power (physics), power levels of a Digital signal (electronics), digital signal generated by an optical source, e.g., a laser diode. The extinction ratio may be expressed ...
, which involve a comparison of ''g''1 to ''g''2. Since Jones vectors refer to waves' amplitudes (rather than
intensity
Intensity may refer to:
In colloquial use
*Strength (disambiguation)
*Amplitude
* Level (disambiguation)
* Magnitude (disambiguation)
In physical sciences
Physics
*Intensity (physics), power per unit area (W/m2)
*Field strength of electric, ma ...
), when illuminated by unpolarized light the remaining power in the unwanted polarization will be (''g''2/''g''1)2 of the power in the intended polarization.
Specular reflection
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
In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium.
The refractive index determines how much the path of light is bent, or ...
. These effects are treated by the Fresnel equations. Part of the wave is transmitted and part is reflected; for a given material those proportions (and also the phase of reflection) are dependent on the angle of incidence and are different for the ''s'' and ''p'' polarizations. Therefore, the polarization state of reflected light (even if initially unpolarized) is generally changed.
Any light striking a surface at a special angle of incidence known as Brewster's angle, where the reflection coefficient for ''p'' polarization is zero, will be reflected with only the ''s''-polarization remaining. This principle is employed in the so-called "pile of plates polarizer" (see figure) in which part of the ''s'' polarization is removed by reflection at each Brewster angle surface, leaving only the ''p'' polarization after transmission through many such surfaces. The generally smaller reflection coefficient of the ''p'' polarization is also the basis of
polarized sunglasses
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 th ...
; by blocking the ''s'' (horizontal) polarization, most of the glare due to reflection from a wet street, for instance, is removed.
In the important special case of reflection at normal incidence (not involving anisotropic materials) there is no particular ''s'' or ''p'' polarization. Both the ''x'' and ''y'' polarization components are reflected identically, and therefore the polarization of the reflected wave is identical to that of the incident wave. However, in the case of circular (or elliptical) polarization, the handedness of the polarization state is thereby reversed, since by
convention
Convention may refer to:
* Convention (norm), a custom or tradition, a standard of presentation or conduct
** Treaty, an agreement in international law
* Convention (meeting), meeting of a (usually large) group of individuals and/or companies in a ...
this is specified relative to the direction of propagation. The circular rotation of the electric field around the ''x-y'' axes called "right-handed" for a wave in the ''+z'' direction is "left-handed" for a wave in the ''-z'' direction. But in the general case of reflection at a nonzero angle of incidence, no such generalization can be made. For instance, right-circularly polarized light reflected from a dielectric surface at a grazing angle, will still be right-handed (but elliptically) polarized. Linear polarized light reflected from a metal at non-normal incidence will generally become elliptically polarized. These cases are handled using Jones vectors acted upon by the different Fresnel coefficients for the ''s'' and ''p'' polarization components.
Measurement techniques involving polarization
Some optical measurement techniques are based on polarization. In many other optical techniques polarization is crucial or at least must be taken into account and controlled; such examples are too numerous to mention.
Measurement of stress
In
engineering
Engineering is the use of scientific method, scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad rang ...
, the phenomenon of stress induced birefringence allows for stresses in transparent materials to be readily observed. As noted above and seen in the accompanying photograph, the chromaticity of birefringence typically creates colored patterns when viewed in between two polarizers. As external forces are applied, internal stress induced in the material is thereby observed. Additionally, birefringence is frequently observed due to stresses "frozen in" at the time of manufacture. This is famously observed in cellophane tape whose birefringence is due to the stretching of the material during the manufacturing process.
Ellipsometry
Ellipsometry is a powerful technique for the measurement of the optical properties of a uniform surface. It involves measuring the polarization state of light following specular reflection from such a surface. This is typically done as a function of incidence angle or wavelength (or both). Since ellipsometry relies on reflection, it is not required for the sample to be transparent to light or for its back side to be accessible.
Ellipsometry can be used to model the (complex) refractive index of a surface of a bulk material. It is also very useful in determining parameters of one or more
thin film
A thin film is a layer of material ranging from fractions of a nanometer (monolayer) to several micrometers in thickness. The controlled synthesis of materials as thin films (a process referred to as deposition) is a fundamental step in many ap ...
layers deposited on a substrate. Due to their reflection properties, not only are the predicted magnitude of the ''p'' and ''s'' polarization components, but their relative phase shifts upon reflection, compared to measurements using an ellipsometer. A normal ellipsometer does not measure the actual reflection coefficient (which requires careful photometric calibration of the illuminating beam) but the ratio of the ''p'' and ''s'' reflections, as well as change of polarization ellipticity (hence the name) induced upon reflection by the surface being studied. In addition to use in science and research, ellipsometers are used in situ to control production processes for instance.
Geology
The property of (linear) birefringence is widespread in crystalline
mineral
In geology and mineralogy, a mineral or mineral species is, broadly speaking, a solid chemical compound with a fairly well-defined chemical composition and a specific crystal structure that occurs naturally in pure form.John P. Rafferty, ed. ( ...
s, and indeed was pivotal in the initial discovery of polarization. In
mineralogy
Mineralogy is a subject of geology specializing in the scientific study of the chemistry, crystal structure, and physical (including optical) properties of minerals and mineralized artifacts. Specific studies within mineralogy include the proces ...
, this property is frequently exploited using polarization
microscope
A microscope () is a laboratory instrument used to examine objects that are too small to be seen by the naked eye. Microscopy is the science of investigating small objects and structures using a microscope. Microscopic means being invisibl ...
s, for the purpose of identifying minerals. See optical mineralogy for more details.
Sound waves in solid materials exhibit polarization. Differential propagation of the three polarizations through the earth is a crucial in the field of
seismology
Seismology (; from Ancient Greek σεισμός (''seismós'') meaning "earthquake" and -λογία (''-logía'') meaning "study of") is the scientific study of earthquakes and the propagation of elastic waves through the Earth or through other ...
. Horizontally and vertically polarized seismic waves (
shear waves
In physics, a transverse wave is a wave whose oscillations are perpendicular to the direction of the wave's advance. This is in contrast to a longitudinal wave which travels in the direction of its oscillations. Water waves are an example of t ...
) are termed SH and SV, while waves with longitudinal polarization (
compressional wave
Longitudinal waves are waves in which the vibration of the medium is parallel ("along") to the direction the wave travels and displacement of the medium is in the same (or opposite) direction of the wave propagation. Mechanical longitudinal wav ...
s) are termed P-waves.
Chemistry
We have seen (above) that the birefringence of a type of crystal is useful in identifying it, and thus detection of linear birefringence is especially useful in
geology
Geology () is a branch of natural science concerned with Earth and other astronomical objects, the features or rocks of which it is composed, and the processes by which they change over time. Modern geology significantly overlaps all other Ear ...
and
mineralogy
Mineralogy is a subject of geology specializing in the scientific study of the chemistry, crystal structure, and physical (including optical) properties of minerals and mineralized artifacts. Specific studies within mineralogy include the proces ...
. Linearly polarized light generally has its polarization state altered upon transmission through such a crystal, making it stand out when viewed in between two crossed polarizers, as seen in the photograph, above. Likewise, in chemistry, rotation of polarization axes in a liquid solution can be a useful measurement. In a liquid, linear birefringence is impossible, but there may be circular birefringence when a chiral molecule is in solution. When the right and left handed
enantiomers
In chemistry, an enantiomer ( /ɪˈnænti.əmər, ɛ-, -oʊ-/ ''ih-NAN-tee-ə-mər''; from Ancient Greek ἐνάντιος ''(enántios)'' 'opposite', and μέρος ''(méros)'' 'part') – also called optical isomer, antipode, or optical anti ...
of such a molecule are present in equal numbers (a so-called racemic mixture) then their effects cancel out. However, when there is only one (or a preponderance of one), as is more often the case for
organic molecules
In chemistry, organic compounds are generally any chemical compounds that contain carbon-hydrogen or carbon-carbon bonds. Due to carbon's ability to catenate (form chains with other carbon atoms), millions of organic compounds are known. The s ...
, a net circular birefringence (or ''
optical activity
Optical rotation, also known as polarization rotation or circular birefringence, is the rotation of the orientation of the plane of polarization about the optical axis of linearly polarized light as it travels through certain materials. Circul ...
'') is observed, revealing the magnitude of that imbalance (or the concentration of the molecule itself, when it can be assumed that only one enantiomer is present). This is measured using a
polarimeter
A polarimeter is a scientific instrument used to measure the angle of rotation caused by passing polarized light through an optically active substance.
Astronomy
In many areas of
astronomy
Astronomy () is a natural science that studies astronomical object, celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and chronology of the Universe, evolution. Objects of interest ...
, the study of polarized electromagnetic radiation from
outer space
Outer space, commonly shortened to space, is the expanse that exists beyond Earth and its atmosphere and between celestial bodies. Outer space is not completely empty—it is a near-perfect vacuum containing a low density of particles, pred ...
is of great importance. Although not usually a factor in the
thermal radiation
Thermal radiation is electromagnetic radiation generated by the thermal motion of particles in matter. Thermal radiation is generated when heat from the movement of charges in the material (electrons and protons in common forms of matter) is ...
of
star
A star is an astronomical object comprising a luminous spheroid of plasma (physics), plasma held together by its gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked ...
s, polarization is also present in radiation from coherent
astronomical source
Astronomy () is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution. Objects of interest include planets, moons, stars, nebulae, galaxies, ...
s (e.g. hydroxyl or methanol
maser
A maser (, an acronym for microwave amplification by stimulated emission of radiation) is a device that produces coherent electromagnetic waves through amplification by stimulated emission. The first maser was built by Charles H. Townes, Ja ...
s), 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
Cosmic dust, also called extraterrestrial dust, star dust or space dust, is dust which exists in outer space, or has fallen on Earth. Most cosmic dust particles measure between a few molecules and 0.1 mm (100 micrometers). Larger particles are c ...
. Apart from providing information on sources of radiation and scattering, polarization also probes the interstellar magnetic field via
Faraday rotation
The Faraday effect or Faraday rotation, sometimes referred to as the magneto-optic Faraday effect (MOFE), is a physical magneto-optical phenomenon. The Faraday effect causes a polarization rotation which is proportional to the projection of the m ...
. The polarization of the
cosmic microwave background
In Big Bang cosmology the cosmic microwave background (CMB, CMBR) is electromagnetic radiation that is a remnant from an early stage of the universe, also known as "relic radiation". The CMB is faint cosmic background radiation filling all spac ...
is being used to study the physics of the very early universe.
Synchrotron radiation
Synchrotron radiation (also known as magnetobremsstrahlung radiation) is the electromagnetic radiation emitted when relativistic charged particles are subject to an acceleration perpendicular to their velocity (). It is produced artificially in ...
is inherently polarized. It has been suggested that astronomical sources caused the
chirality
Chirality is a property of asymmetry important in several branches of science. The word ''chirality'' is derived from the Greek (''kheir''), "hand", a familiar chiral object.
An object or a system is ''chiral'' if it is distinguishable from ...
of biological molecules on Earth.
Applications and examples
Polarized sunglasses
Unpolarized light, after being reflected by a specular (shiny) surface, generally obtains a degree of polarization. This phenomenon was observed in 1808 by the mathematician Étienne-Louis Malus, after whom
Malus's law
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 ...
is named. Polarizing
sunglasses
Sunglasses or sun glasses (informally called shades or sunnies; more names below) are a form of protective eyewear designed primarily to prevent bright sunlight and high-energy visible light from damaging or discomforting the eyes. They can s ...
exploit this effect to reduce glare from reflections by horizontal surfaces, notably the road ahead viewed at a grazing angle.
Wearers of polarized sunglasses will occasionally observe inadvertent polarization effects such as color-dependent birefringent effects, for example in toughened glass (e.g., car windows) or items made from transparent
plastic
Plastics are a wide range of synthetic or semi-synthetic materials that use polymers as a main ingredient. Their plasticity makes it possible for plastics to be moulded, extruded or pressed into solid objects of various shapes. This adaptab ...
s, in conjunction with natural polarization by reflection or scattering. The polarized light from LCD monitors (see below) is very conspicuous when these are worn.
Sky polarization and photography
Polarization is observed in the light of the
sky
The sky is an unobstructed view upward from the surface of the Earth. It includes the atmosphere and outer space. It may also be considered a place between the ground and outer space, thus distinct from outer space.
In the field of astronomy, ...
, as this is due to sunlight
scattered
Scattered may refer to:
Music
* ''Scattered'' (album), a 2010 album by The Handsome Family
* "Scattered" (The Kinks song), 1993
* "Scattered", a song by Ace Young
* "Scattered", a song by Lauren Jauregui
* "Scattered", a song by Green Day from ' ...
by
aerosols
An aerosol is a suspension of fine solid particles or liquid droplets in air or another gas. Aerosols can be natural or anthropogenic. Examples of natural aerosols are fog or mist, dust, forest exudates, and geyser steam. Examples of anthrop ...
as it passes through
Earth's atmosphere
The atmosphere of Earth is the layer of gases, known collectively as air, retained by Earth's gravity that surrounds the planet and forms its planetary atmosphere. The atmosphere of Earth protects life on Earth by creating pressure allowing for ...
. The
scattered
Scattered may refer to:
Music
* ''Scattered'' (album), a 2010 album by The Handsome Family
* "Scattered" (The Kinks song), 1993
* "Scattered", a song by Ace Young
* "Scattered", a song by Lauren Jauregui
* "Scattered", a song by Green Day from ' ...
light produces the brightness and color in clear skies. This partial polarization of scattered light can be used to darken the sky in photographs, increasing the contrast. This effect is most strongly observed at points on the sky making a 90° angle to the Sun. Polarizing filters use these effects to optimize the results of photographing scenes in which reflection or scattering by the sky is involved.
Sky polarization has been used for orientation in navigation. The Pfund sky compass was used in the 1950s when navigating near the poles of the
Earth's magnetic field
Earth's magnetic field, also known as the geomagnetic field, is the magnetic field that extends from Earth's interior out into space, where it interacts with the solar wind, a stream of charged particles emanating from the Sun. The magnetic f ...
star
A star is an astronomical object comprising a luminous spheroid of plasma (physics), plasma held together by its gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked ...
s were visible (e.g., under daytime
cloud
In meteorology, a cloud is an aerosol consisting of a visible mass of miniature liquid droplets, frozen crystals, or other particles suspended in the atmosphere of a planetary body or similar space. Water or various other chemicals may co ...
or
twilight
Twilight is light produced by sunlight scattering in the upper atmosphere, when the Sun is below the horizon, which illuminates the lower atmosphere and the Earth's surface. The word twilight can also refer to the periods of time when this il ...
). It has been suggested, controversially, that the
Viking
Vikings ; non, víkingr is the modern name given to seafaring people originally from Scandinavia (present-day Denmark, Norway and Sweden),
who from the late 8th to the late 11th centuries raided, pirated, traded and se ...
s exploited a similar device (the " sunstone") in their extensive expeditions across the
North Atlantic
The Atlantic Ocean is the second-largest of the world's five oceans, with an area of about . It covers approximately 20% of Earth's surface and about 29% of its water surface area. It is known to separate the "Old World" of Africa, Europe and ...
in the 9th–11th centuries, before the arrival of the magnetic compass from Asia to Europe in the 12th century. Related to the sky compass is the "
polar clock
Sir Charles Wheatstone Fellow of the Royal Society, FRS FRSE Doctor of Civil Law, DCL LLD (6 February 1802 – 19 October 1875), was an English scientist and inventor of many scientific breakthroughs of the Victorian era, including the Engli ...
liquid-crystal display
A liquid-crystal display (LCD) is a flat-panel display
A flat-panel display (FPD) is an electronic display used to display visual content such as text or images. It is present in consumer, medical, transportation, and industrial equipmen ...
(LCD) technology relies on the rotation of the axis of linear polarization by the liquid crystal array. Light from the backlight (or the back reflective layer, in devices not including or requiring a backlight) first passes through a linear polarizing sheet. That polarized light passes through the actual liquid crystal layer which may be organized in pixels (for a TV or computer monitor) or in another format such as a
seven-segment display
A seven-segment display is a form of electronic display device for displaying decimal numerals that is an alternative to the more complex dot matrix displays.
Seven-segment displays are widely used in digital clocks, electronic meters, basic ...
or one with custom symbols for a particular product. The liquid crystal layer is produced with a consistent right (or left) handed chirality, essentially consisting of tiny
helices
A helix () is a shape like a corkscrew or spiral staircase. It is a type of smooth space curve with tangent lines at a constant angle to a fixed axis. Helices are important in biology, as the DNA molecule is formed as two intertwined helices, ...
. This causes circular birefringence, and is engineered so that there is a 90 degree rotation of the linear polarization state. However, when a voltage is applied across a cell, the molecules straighten out, lessening or totally losing the circular birefringence. On the viewing side of the display is another linear polarizing sheet, usually oriented at 90 degrees from the one behind the active layer. Therefore, when the circular birefringence is removed by the application of a sufficient voltage, the polarization of the transmitted light remains at right angles to the front polarizer, and the pixel appears dark. With no voltage, however, the 90 degree rotation of the polarization causes it to exactly match the axis of the front polarizer, allowing the light through. Intermediate voltages create intermediate rotation of the polarization axis and the pixel has an intermediate intensity. Displays based on this principle are widespread, and now are used in the vast majority of televisions, computer monitors and video projectors, rendering the previous
CRT
CRT or Crt may refer to:
Science, technology, and mathematics Medicine and biology
* Calreticulin, a protein
*Capillary refill time, for blood to refill capillaries
*Cardiac resynchronization therapy and CRT defibrillator (CRT-D)
* Catheter-re ...
technology essentially obsolete. The use of polarization in the operation of LCD displays is immediately apparent to someone wearing polarized sunglasses, often making the display unreadable.
In a totally different sense, polarization encoding has become the leading (but not sole) method for delivering separate images to the left and right eye in
stereoscopic
Stereoscopy (also called stereoscopics, or stereo imaging) is a technique for creating or enhancing the depth perception, illusion of depth in an image by means of stereopsis for binocular vision. The word ''stereoscopy'' derives . Any stere ...
displays used for
3D movies
3D films are motion pictures made to give an illusion of three-dimensional solidity, usually with the help of special glasses worn by viewers. They have existed in some form since 1915, but had been largely relegated to a niche in the motion pict ...
. This involves separate images intended for each eye either projected from two different projectors with orthogonally oriented polarizing filters or, more typically, from a single projector with time multiplexed polarization (a fast alternating polarization device for successive frames). Polarized 3D glasses with suitable polarizing filters ensure that each eye receives only the intended image. Historically such systems used linear polarization encoding because it was inexpensive and offered good separation. However, circular polarization makes separation of the two images insensitive to tilting of the head, and is widely used in 3-D movie exhibition today, such as the system from
RealD
RealD Inc. is a private company known for its RealD 3D system, which is used for projecting 3-D film, films in stereoscopic 3D using circularly polarized light. The company was founded in 2003 by Michael Lewis (entrepreneur), Michael V. Lewis an ...
. Projecting such images requires screens that maintain the polarization of the projected light when viewed in reflection (such as silver screens); a normal diffuse white projection screen causes depolarization of the projected images, making it unsuitable for this application.
Although now obsolete, CRT computer displays suffered from reflection by the glass envelope, causing glare from room lights and consequently poor contrast. Several anti-reflection solutions were employed to ameliorate this problem. One solution utilized the principle of reflection of circularly polarized light. A circular polarizing filter in front of the screen allows for the transmission of (say) only right circularly polarized room light. Now, right circularly polarized light (depending on the
convention
Convention may refer to:
* Convention (norm), a custom or tradition, a standard of presentation or conduct
** Treaty, an agreement in international law
* Convention (meeting), meeting of a (usually large) group of individuals and/or companies in a ...
used) has its electric (and magnetic) field direction rotating clockwise while propagating in the +z direction. Upon reflection, the field still has the same direction of rotation, but now propagation is in the −z direction making the reflected wave ''left'' circularly polarized. With the right circular polarization filter placed in front of the reflecting glass, the unwanted light reflected from the glass will thus be in very polarization state that is ''blocked'' by that filter, eliminating the reflection problem. The reversal of circular polarization on reflection and elimination of reflections in this manner can be easily observed by looking in a mirror while wearing 3-D movie glasses which employ left- and right-handed circular polarization in the two lenses. Closing one eye, the other eye will see a reflection in which it cannot see itself; that lens appears black. However, the other lens (of the closed eye) will have the correct circular polarization allowing the closed eye to be easily seen by the open one.
Radio transmission and reception
All
radio
Radio is the technology of signaling and communicating using radio waves. Radio waves are electromagnetic waves of frequency between 30 hertz (Hz) and 300 gigahertz (GHz). They are generated by an electronic device called a transmit ...
(and microwave) antennas used for transmitting or receiving are intrinsically polarized. They transmit in (or receive signals from) a particular polarization, being totally insensitive to the opposite polarization; in certain cases that polarization is a function of direction. Most antennas are nominally linearly polarized, but elliptical and circular polarization is a possibility. As is the convention in optics, the "polarization" of a radio wave is understood to refer to the polarization of its electric field, with the magnetic field being at a 90 degree rotation with respect to it for a linearly polarized wave.
The vast majority of antennas are linearly polarized. In fact it can be shown from considerations of symmetry that an antenna that lies entirely in a plane which also includes the observer, can ''only'' have its polarization in the direction of that plane. This applies to many cases, allowing one to easily infer such an antenna's polarization at an intended direction of propagation. So a typical rooftop Yagi or log-periodic antenna with horizontal conductors, as viewed from a second station toward the horizon, is necessarily horizontally polarized. But a vertical "
whip antenna
A whip antenna is an antenna consisting of a straight flexible wire or rod. The bottom end of the whip is connected to the radio receiver or transmitter. A whip antenna is a form of monopole antenna. The antenna is designed to be flexible so th ...
" or AM broadcast tower used as an antenna element (again, for observers horizontally displaced from it) will transmit in the vertical polarization. A turnstile antenna with its four arms in the horizontal plane, likewise transmits horizontally polarized radiation toward the horizon. However, when that same turnstile antenna is used in the "axial mode" (upwards, for the same horizontally-oriented structure) its radiation is circularly polarized. At intermediate elevations it is elliptically polarized.
Polarization is important in radio communications because, for instance, if one attempts to use a horizontally polarized antenna to receive a vertically polarized transmission, the signal strength will be substantially reduced (or under very controlled conditions, reduced to nothing). This principle is used in
satellite television
Satellite television is a service that delivers television programming to viewers by relaying it from a communications satellite orbiting the Earth directly to the viewer's location. The signals are received via an outdoor parabolic antenna comm ...
in order to double the channel capacity over a fixed frequency band. The same frequency channel can be used for two signals broadcast in opposite polarizations. By adjusting the receiving antenna for one or the other polarization, either signal can be selected without interference from the other.
Especially due to the presence of the
ground
Ground may refer to:
Geology
* Land, the surface of the Earth not covered by water
* Soil, a mixture of clay, sand and organic matter present on the surface of the Earth
Electricity
* Ground (electricity), the reference point in an electrical c ...
, there are some differences in propagation (and also in reflections responsible for TV ghosting) between horizontal and vertical polarizations. AM and FM broadcast radio usually use vertical polarization, while television uses horizontal polarization. At low frequencies especially, horizontal polarization is avoided. That is because the phase of a horizontally polarized wave is reversed upon reflection by the ground. A distant station in the horizontal direction will receive both the direct and reflected wave, which thus tend to cancel each other. This problem is avoided with vertical polarization. Polarization is also important in the transmission of
radar
Radar is a detection system that uses radio waves to determine the distance (''ranging''), angle, and radial velocity of objects relative to the site. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, w ...
pulses and reception of radar reflections by the same or a different antenna. For instance, back scattering of radar pulses by rain drops can be avoided by using circular polarization. Just as specular reflection of circularly polarized light reverses the handedness of the polarization, as discussed above, the same principle applies to scattering by objects much smaller than a wavelength such as rain drops. On the other hand, reflection of that wave by an irregular metal object (such as an airplane) will typically introduce a change in polarization and (partial) reception of the return wave by the same antenna.
The effect of free electrons in the
ionosphere
The ionosphere () is the ionized part of the upper atmosphere of Earth, from about to above sea level, a region that includes the thermosphere and parts of the mesosphere and exosphere. The ionosphere is ionized by solar radiation. It plays an ...
, in conjunction with the
earth's magnetic field
Earth's magnetic field, also known as the geomagnetic field, is the magnetic field that extends from Earth's interior out into space, where it interacts with the solar wind, a stream of charged particles emanating from the Sun. The magnetic f ...
, causes
Faraday rotation
The Faraday effect or Faraday rotation, sometimes referred to as the magneto-optic Faraday effect (MOFE), is a physical magneto-optical phenomenon. The Faraday effect causes a polarization rotation which is proportional to the projection of the m ...
, a sort of circular birefringence. This is the same mechanism which can rotate the axis of linear polarization by electrons in interstellar space as mentioned
below
Below may refer to:
*Earth
*Ground (disambiguation)
*Soil
*Floor
*Bottom (disambiguation)
Bottom may refer to:
Anatomy and sex
* Bottom (BDSM), the partner in a BDSM who takes the passive, receiving, or obedient role, to that of the top or ...
. The magnitude of Faraday rotation caused by such a plasma is greatly exaggerated at lower frequencies, so at the higher microwave frequencies used by satellites the effect is minimal. However, medium or
short wave
Shortwave radio is radio transmission using shortwave (SW) radio frequencies. There is no official definition of the band, but the range always includes all of the High frequency, high frequency band (HF), which extends from 3 to 30 MHz (10 ...
transmissions received following refraction by the ionosphere are strongly affected. Since a wave's path through the ionosphere and the earth's magnetic field vector along such a path are rather unpredictable, a wave transmitted with vertical (or horizontal) polarization will generally have a resulting polarization in an arbitrary orientation at the receiver.
Polarization and vision
Many
animal
Animals are multicellular, eukaryotic organisms in the Kingdom (biology), biological kingdom Animalia. With few exceptions, animals Heterotroph, consume organic material, Cellular respiration#Aerobic respiration, breathe oxygen, are Motilit ...
s are capable of perceiving some of the components of the polarization of light, e.g., linear horizontally polarized light. This 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
insect
Insects (from Latin ') are pancrustacean hexapod invertebrates of the class Insecta. They are the largest group within the arthropod phylum. Insects have a chitinous exoskeleton, a three-part body ( head, thorax and abdomen), three pairs ...
s, including
bee
Bees are winged insects closely related to wasps and ants, known for their roles in pollination and, in the case of the best-known bee species, the western honey bee, for producing honey. Bees are a monophyly, monophyletic lineage within the ...
s, which use this information to orient their communicative dances. Polarization sensitivity has also been observed in species of
octopus
An octopus ( : octopuses or octopodes, see below for variants) is a soft-bodied, eight- limbed mollusc of the order Octopoda (, ). The order consists of some 300 species and is grouped within the class Cephalopoda with squids, cuttle ...
,
squid
True squid are molluscs with an elongated soft body, large eyes, eight arms, and two tentacles in the superorder Decapodiformes, though many other molluscs within the broader Neocoleoidea are also called squid despite not strictly fitting t ...
,
cuttlefish
Cuttlefish or cuttles are marine molluscs of the order Sepiida. They belong to the class Cephalopoda which also includes squid, octopuses, and nautiluses. Cuttlefish have a unique internal shell, the cuttlebone, which is used for control of ...
, and
mantis shrimp
Mantis shrimp, or stomatopods, are carnivorous marine crustaceans of the order Stomatopoda (). Stomatopods branched off from other members of the class Malacostraca around 340 million years ago. Mantis shrimp typically grow to around in lengt ...
. In the latter case, one species measures all six orthogonal components of polarization, and is believed to have optimal polarization vision. 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 naked
human eye
The human eye is a sensory organ, part of the sensory nervous system, that reacts to visible light and allows humans to use visual information for various purposes including seeing things, keeping balance, and maintaining circadian rhythm.
...
is weakly sensitive to polarization, without the need for intervening filters. Polarized light creates a very faint pattern near the center of the visual field, called
Haidinger's brush
Haidinger's brush, more commonly known as Haidinger's brushes is an image produced by the eye, an entoptic phenomenon, first described by Austrian physicist Wilhelm Karl von Haidinger in 1844. Haidinger saw it when he looked through various mine ...
. This pattern is very difficult to see, but with practice one can learn to detect polarized light with the naked eye.
Angular momentum using circular polarization
It is well known that electromagnetic radiation carries a certain linear
momentum
In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass an ...
in the direction of propagation. In addition, however, light carries a certain
angular momentum
In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity—the total angular momentum of a closed syst ...
if it is circularly polarized (or partially so). In comparison with lower frequencies such as microwaves, the amount of angular momentum in light, even of pure circular polarization, compared to the same wave's linear momentum (or radiation pressure) is very small and difficult to even measure. However, it was utilized in an experiment to achieve speeds of up to 600 million revolutions per minute.
See also
*
Depolarizer (optics) A depolarizer or depolariser is an optical device used to scramble the photon polarization, polarization of light. An ideal depolarizer would output randomly polarized light whatever its input, but all practical depolarizers produce pseudo-random ou ...
*
Fluorescence anisotropy
Fluorescence anisotropy or fluorescence polarization is the phenomenon where the light emitted by a fluorophore has unequal intensities along different axes of polarization. Early pioneers in the field include Aleksander Jablonski, Gregorio Web ...
*
Glan–Taylor prism
A Glan–Taylor prism is a type of prism (optics), prism which is used as a polarizer or Polarization (waves), polarizing beam splitter. It is one of the most common types of modern polarizing prism. It was first described by Archard and Taylor i ...
*
Kerr effect
The Kerr effect, also called the quadratic electro-optic (QEO) effect, is a change in the refractive index of a material in response to an applied electric field. The Kerr effect is distinct from the Pockels effect in that the induced index chang ...
*
Nicol prism
A Nicol prism is a type of polarizer, an optical device made from calcite crystal used to produce and analyse plane polarized light. It is made in such a way that it eliminates one of the rays by total internal reflection, i.e. the ordinary ray ...
*
Plane of polarization
The term ''plane of polarization'' refers to the direction of polarization of '' linearly-polarized'' light or other electromagnetic radiation. Unfortunately the term is used with two contradictory meanings. As originally defined by Étienne-Lou ...
Polarization rotator
A polarization rotator is an optical device that rotates the polarization axis of a linearly polarized light beam by an angle of choice. Such devices can be based on the Faraday effect, on birefringence, or on total internal reflection. F. J. ...
*
Polarized light microscopy
Polarized light microscopy can mean any of a number of optical microscopy techniques involving polarized light. Simple techniques include illumination of the sample with polarized light. Directly transmitted light can, optionally, be blocked wit ...
*
Polarizer
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 ...
*
Polaroid (polarizer)
A Polaroid synthetic plastic sheet is a brand name product trademarked and produced by the Polaroid Corporation used as a polarizer or polarizing filter. The term “Polaroid” entered the common vocabulary with the early 1960s introduction of pa ...
*
Radial polarization
A beam of light has radial polarization if at every position in the beam the polarization (electric field) vector points towards the centre of the beam. In practice, an array of waveplates may be used to provide an approximation to a radially pol ...
Principles of Optics
''Principles of Optics'', colloquially known as ''Born and Wolf'', is an optics textbook written by Max Born and Emil Wolf that was initially published in 1959 by Pergamon Press. After going through six editions with Pergamon Press, the book wa ...
'', 7th edition, M. Born & E. Wolf, Cambridge University, 1999, .
* ''Fundamentals of polarized light: a statistical optics approach'', C. Brosseau, Wiley, 1998, .
* ''Polarized Light, second edition'', Dennis Goldstein, Marcel Dekker, 2003, .
* ''Field Guide to Polarization'', Edward Collett, SPIE Field Guides vol. FG05, SPIE, 2005, .
* ''Polarization Optics in Telecommunications'', Jay N. Damask, Springer 2004, .
* ''Polarized Light in Nature'', G. P. Können, Translated by G. A. Beerling, Cambridge University, 1985, .
* ''Polarised Light in Science and Nature'', D. Pye, Institute of Physics, 2001, .
* ''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, .
* ''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.