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Polarization (waves)

Polarization (also polarisation) is a property of transverse waves which specifies the geometrical orientation of the oscillations. In a transverse wave, the direction of the oscillation is perpendicular to the direction of motion of the wave. A simple example of a polarized transverse wave is vibrations traveling along a taut string (see image); for example, in a musical instrument like a guitar string. Depending on how the string is plucked, the vibrations can be in a vertical direction, horizontal direction, or at any angle perpendicular to the string. In contrast, in longitudinal waves, such as sound waves in a liquid or gas, the displacement of the particles in the oscillation is always in the direction of propagation, so these waves do not exhibit polarization. Transverse waves that exhibit polarization include electromagnetic waves such as light and radio waves, gravitational waves, and transverse sound waves (shear waves) in solids.

An electromagnetic wave such as light consists of a coupled oscillating electric field and magnetic field 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 lamps, consists of short wave trains with an equal mixture of polarizations; this is called unpolarized light. Polarized light can be produced by passing unpolarized light through a polarizer, which allows waves of only one polarization to pass through. The most common optical materials do not affect the polarization of light, but some materials—those that exhibit birefringence, dichroism, or optical activity—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, electromagnetic waves can also be viewed as streams of particles called photons. When viewed in this way, the polarization of an electromagnetic wave is determined by a quantum mechanical property of photons called their spin. A photon has one of two possible spins: it can either spin in a right hand sense or a left hand sense about its direction of travel. Circularly polarized electromagnetic waves are composed of photons with only one type of spin, either right- or left-hand. Linearly polarized waves consist of photons that are in a superposition of right and left circularly polarized states, with equal amplitude and phases synchronized to give oscillation in a plane.

Polarization is an important parameter in areas of science dealing with transverse waves, such as optics, seismology, radio, and microwaves. Especially impacted are technologies such as lasers, wireless and optical fiber telecommunications, and radar.

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 waves; 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). Incoherent states can be modeled stochastically as a weighted combination of such uncorrelated waves with some distribution of frequencies (its spectrum), phases, and polarizations.

Transverse electromagnetic waves

Electromagnetic waves (such as light), traveling in free space or another homogeneous isotropic non-attenuating medium, are properly described as transverse waves, meaning that a plane wave's electric field vector $E$ and magnetic field $B$ are each in some direction perpendicular to (or "transverse" to) the direction of wave propagation; $H$ and $z$ 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 of optical frequency $f$ (light of vacuum wavelength $λ$ has a frequency of $E$ where $c$ is the speed of light), let us take the direction of propagation as the $z$ axis. Being a transverse wave the $H$ and $E$ fields must then contain components only in the $x$ and $y$ directions whereas $H$. Using complex (or phasor) 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 $f = c/λ$ direction the fields have no dependence on $x$ or $y$) these complex fields can be written as: $$\vec{E}(z, t) = \begin{bmatrix} e_x \\ e_y \\ 0 \end{bmatrix}\; e^{i2\pi \left(\frac{z}{\lambda} - \frac{t}{T}\right)} = \begin{bmatrix} e_x \\ e_y \\ 0 \end{bmatrix}\; e^{i(kz - \omega t)}$$ and $$\vec{H}(z, t) = \begin{bmatrix} h_x \\ h_y \\ 0 \end{bmatrix}\; e^{i2\pi \left(\frac{z}{\lambda} - \frac{t}{T}\right)} = \begin{bmatrix} h_x \\ h_y \\ 0 \end{bmatrix}\; e^{i(kz - \omega t)},$$ where $E$ is the wavelength (whose refractive index is $n$) and $H$ is the period of the wave. Here $e_{x}$, $e_{y}$, $h_{x}$, and $h_{y}$ are complex numbers. In the second more compact form, as these equations are customarily expressed, these factors are described using the wavenumber $E_{z} = H_{z} = 0$ and angular frequency (or "radian frequency") $+z$. In a more general formulation with propagation restricted to the $λ = λ0/n$ direction, then the spatial dependence $T = 1/f$ is replaced by $k = 2πn/λ0$ where $k$ is called the wave vector, the magnitude of which is the wavenumber.

Thus the leading vectors $ω = 2πf$ and $+z$ 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 $kz$ direction). For a given medium with a characteristic impedance $η$, $k ∙ r$ is related to $e$ by: $$\begin{align} h_y &= \frac{e_x}{\eta} \\ h_x &= -\frac{e_y}{\eta}. \end{align}$$

In a dielectric, $η$ is real and has the value $h$, where $n$ is the refractive index and $+z$ is the impedance of free space. The impedance will be complex in a conducting medium. Note that given that relationship, the dot product of $h$ and $e$ must be zero: $$\begin{align} \vec{E}\left(\vec{r}, t\right) \cdot \vec{H}\left(\vec{r}, t\right) &= e_x h_x + e_y h_y + e_z h_z \\ &= e_x \left(-\frac{e_y}{\eta}\right) + e_y \left(\frac{e_x}{\eta}\right) + 0 \cdot 0 \\ &= 0, \end{align}$$ indicating that these vectors are orthogonal (at right angles to each other), as expected.

Knowing the propagation direction ($η_{0}/n$ in this case) and $η$, one can just as well specify the wave in terms of just $e_{x}$ and $e_{y}$ describing the electric field. The vector containing $e_{x}$ and $e_{y}$ (but without the $z$ component which is necessarily zero for a transverse wave) is known as a Jones vector. 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 of the light wave is proportional to the sum of the squared magnitudes of the two electric field components: $$ I = \left(\left|e_x\right|^2 + \left|e_y\right|^2\right) \, \frac{1}{2\eta} $$

However, the wave's state of polarization is only dependent on the (complex) ratio of $e_{y}$ to $e_{x}$. So let us just consider waves whose $η_{0}$; this happens to correspond to an intensity of about $0.001 W$ in free space (where $E$). And because the absolute phase of a wave is unimportant in discussing its polarization state, let us stipulate that the phase of $e_{x}$ is zero; in other words $e_{x}$ is a real number while $e_{y}$ may be complex. Under these restrictions, $e_{x}$ and $e_{y}$ can be represented as follows: $$\begin{align} e_x &= \sqrt{\frac{1 + Q}{2}} \\ e_y &= \sqrt{\frac{1 - Q}{2}}\, e^{i\phi}, \end{align}$$ where the polarization state is now fully parameterized by the value of $Q$ (such that $H$) and the relative phase $ϕ$.

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 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 D and magnetic flux density B still obey the above geometry but due to anisotropy in the electric susceptibility (or in the magnetic permeability), now given by a tensor, the direction of E (or H) may differ from that of D (or B). Even in isotropic media, so-called inhomogeneous waves 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 waves or waves propagating in a waveguide (such as an optical fiber) are generally not transverse waves, but might be described as an electric or magnetic transverse mode, 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 waves in fluids, 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 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 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.

Polarization state
Polarization can be defined in terms of pure polarization states with only a coherent sinusoidal wave at one 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). 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°, and the amplitudes are the same, then circular polarization is produced (fourth and fifth figures). Circular polarization can be created by sending linearly polarized light through a quarter-wave plate oriented at 45° to the linear polarization to create two components of the same amplitude with the required phase shift. The superposition of the original and phase-shifted components causes a rotating electric field vector, which 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, depending on the relative phases of the components. These correspond to distinct polarization states, such as the two circular polarizations shown above.

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 polarizations. Axes are selected 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.

Any pair of orthogonal polarization states may be used as basis functions, 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
For a purely polarized monochromatic wave the electric field vector over one cycle of oscillation traces out an ellipse. 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 $e=\sqrt{1 - b^2/a^2},$ or the ellipticity angle, $\chi=\arctan b/a$  $=\arctan 1/\varepsilon$  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 ±2χ. 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):

 * $$ \mathbf{e} = \begin{bmatrix}

a_1 e^{i\theta_1} \\ a_2 e^{i\theta_2} \end{bmatrix}.$$

Here $$a_1$$ and $$a_2$$ denote the amplitude of the wave in the two components of the electric field vector, while $$\theta_1$$ and $$\theta_2$$ 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. The basis 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. 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 the equatorial coordinate system is generally used instead, with the zero azimuth (or position angle, as it is more commonly called in astronomy to avoid confusion with the horizontal coordinate system) corresponding to due north.

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 which is polarized. DOP can be calculated from the Stokes parameters. 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 polarized component of the wave.

DOP can be used to map the strain field in materials when considering the DOP of the photoluminescence. The polarization of the photoluminescence is related to the strain in a material by way of the given material's photoelasticity tensor.

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.

Polarization in wave propagation
In a vacuum, the components of the electric field propagate at the speed of light, so that the phase of the wave varies in space and time while the polarization state does not. That is, the electric field vector e of a plane wave in the +z direction follows:
 * $$\mathbf{e}(z + \Delta z, t + \Delta t) = \mathbf{e}(z, t) e^{ik (c\Delta t - \Delta z)},$$

where k is the wavenumber. As noted above, the instantaneous electric field is the real part of the product of the Jones vector times the phase factor $$e^{-i\omega t}$$. When an electromagnetic wave interacts with matter, its propagation is altered according to the material's (complex) index of refraction. When the real or imaginary part of that refractive index is dependent on the polarization state of a wave, properties known as birefringence and polarization dichroism (or diattenuation) 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 matrix J known as a Jones matrix:
 * $$\mathbf{e'} = \mathbf{J}\mathbf{e}.$$

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

 * $$\mathbf{J} = \mathbf{T}\begin{bmatrix}

g_1 & 0 \\ 0 & g_2 \end{bmatrix}\mathbf{T}^{-1},$$

where g1 and g2 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). 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: |g1| = |g2| = 1. Media termed diattenuating (or dichroic 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, especially in chiral fluids, or Faraday rotation, 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 in the Poincaré sphere about the axis defined by the propagation modes. Examples for linear (blue), circular (red), and elliptical (yellow) birefringence are shown in the figure on the left. The total intensity and degree of polarization are unaffected. If the path length in the birefringent medium is sufficient, the two polarization components of a collimated beam (or ray) 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 crystals, 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 in 1669.

Dichroism
Media in which transmission of one polarization mode is preferentially reduced are called dichroic 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 "polarizers". This corresponds to g2=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 g1=1 and g2=0) exactly half of its initial power is retained. Practical polarizers, especially inexpensive sheet polarizers, have additional loss so that g1 < 1. However, in many instances the more relevant figure of merit is the polarizer's degree of polarization or extinction ratio, which involve a comparison of g1 to g2. Since Jones vectors refer to waves' amplitudes (rather than intensity), when illuminated by unpolarized light the remaining power in the unwanted polarization will be (g2/g1)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. 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; 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 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, 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 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 minerals, and indeed was pivotal in the initial discovery of polarization. In mineralogy, this property is frequently exploited using polarization microscopes, 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. Horizontally and vertically polarized seismic waves (shear waves) are termed SH and SV, while waves with longitudinal polarization (compressional waves) 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 and mineralogy. 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 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, a net circular birefringence (or optical activity) 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 in which polarized light is passed through a tube of the liquid, at the end of which is another polarizer which is rotated in order to null the transmission of light through it.

Astronomy
In many areas of astronomy, the study of polarized electromagnetic radiation from outer space is of great importance. Although not usually a factor in the thermal radiation of stars, polarization is also present in radiation from coherent astronomical sources (e.g. hydroxyl or methanol masers), and incoherent sources such as the large radio lobes in active galaxies, and pulsar radio radiation (which may, it is speculated, sometimes be coherent), and is also imposed upon starlight by scattering from interstellar dust. Apart from providing information on sources of radiation and scattering, polarization also probes the interstellar magnetic field via Faraday rotation. The polarization of the cosmic microwave background is being used to study the physics of the very early universe. Synchrotron radiation is inherently polarized. It has been suggested that astronomical sources caused the chirality of biological molecules on Earth, but chirality selection on inorganic crystals has been proposed as an alternative theory.

Polarized sunglasses
Unpolarized light, after being reflected by a specular (shiny) surface, generally obtains a degree of polarization. This phenomenon was observed in the early 1800s by the mathematician Étienne-Louis Malus, after whom Malus's law is named. Polarizing sunglasses 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 plastics, in conjunction with natural polarization by reflection or scattering. The polarized light from LCD monitors (see below) is extremely conspicuous when these are worn.

Sky polarization and photography

Polarization is observed in the light of the sky, as this is due to sunlight scattered by aerosols as it passes through Earth's atmosphere. The scattered 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 when neither the sun nor stars were visible (e.g., under daytime cloud or twilight). It has been suggested, controversially, that the Vikings exploited a similar device (the "sunstone") in their extensive expeditions across the North Atlantic in the 9th–11th centuries, before the arrival of the magnetic compass from Asia to Europe in the 12th century. Related to the sky compass is the "polar clock", invented by Charles Wheatstone in the late 19th century.

Display technologies
The principle of liquid-crystal display (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 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. 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 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 displays used for 3D movies. 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. 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 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 (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. In the case of linear polarization, the same kind of filtering as described above, is possible. In the case of elliptical polarization (circular polarization is in reality just a kind of elliptical polarization where the length of both elasticity factors is the same), filtering out a single angle (e.g. 90deg) will have virtually no impact as the wave at any time can be in any of the 360deg.

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" 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 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, 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 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, in conjunction with the earth's magnetic field, causes Faraday rotation, 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. 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 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 animals 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 insects, including bees, which use this information to orient their communicative dances. Polarization sensitivity has also been observed in species of octopus, squid, cuttlefish, and mantis shrimp. 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 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. 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 the direction of propagation. In addition, however, light carries a certain angular momentum 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.

title: Polarization (waves)


text:
Polarization-maintaining optical fiber

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

Polarization crosstalk
In an ordinary (non-polarization-maintaining) fiber, two polarization modes (say vertical and horizontal polarization) have the same nominal phase velocity due to the fiber's circular symmetry. However tiny amounts of random birefringence in such a fiber, or bending in the fiber, will cause a tiny amount of crosstalk from the vertical to the horizontal polarization mode. And since even a short portion of fiber, over which a tiny coupling coefficient may apply, is many thousands of wavelengths long, even that small coupling between the two polarization modes, applied coherently, can lead to a large power transfer to the horizontal mode, completely changing the wave's net state of polarization. Since that coupling coefficient was unintended and a result of arbitrary stress or bending applied to fiber, the output state of polarization will itself be random, and will vary as those stresses or bends vary; it will also vary with wavelength.

Principle of operation
Polarization-maintaining fibers work by intentionally introducing a systematic linear birefringence in the fiber, so that there are two well defined polarization modes which propagate along the fiber with very distinct phase velocities. The beat length Lb of such a fiber (for a particular wavelength) is the distance (typically a few millimeters) over which the wave in one mode will experience an additional delay of one wavelength compared to the other polarization mode. Thus a length Lb /2 of such fiber is equivalent to a half-wave plate. Now consider that there might be a random coupling between the two polarization states over a significant length of such fiber. At point 0 along the fiber, the wave in polarization mode 1 induces an amplitude into mode 2 at some phase. However at point 1/2 Lb  along the fiber, the same coupling coefficient between the polarization modes induces an amplitude into mode 2 which is now 180 degrees out of phase with the wave coupled at point zero, leading to cancellation. At point Lb along the fiber the coupling is again in the original phase, but at 3/2 Lb it is again out of phase and so on. The possibility of coherent addition of wave amplitudes through crosstalk over distances much larger than Lb is thus eliminated. Most of the wave's power remains in the original polarization mode, and exits the fiber in that mode's polarization as it is oriented at the fiber end. Optical fiber connectors used for PM fibers are specially keyed so that the two polarization modes are aligned and exit in a specific orientation.

Note that a polarization-maintaining fiber does not polarize light as a polarizer does. Rather, PM fiber maintains the linear polarization of linearly polarized light provided that it is launched into the fiber aligned with one of the fiber's polarization modes. Launching linearly polarized light into the fiber at a different angle will excite both polarization modes, conducting the same wave at slightly different phase velocities. At most points along the fiber the net polarization will be an elliptically polarized state, with a return to the original polarization state after an integer number of beat lengths. Consequently, if visible laser light is launched into the fiber exciting both polarization modes, scattering of propagating light viewed from the side, is observed with a light and dark pattern periodic over each beat length, since scattering is preferentially perpendicular to the polarization direction.

Designs
Several different designs are used to create birefringence in a fiber. The fiber may be geometrically asymmetric or have a refractive index profile which is asymmetric such as the design using an elliptical cladding as shown in the diagram. Alternatively, stress permanently induced in the fiber will produce stress birefringence; this may be accomplished using rods of another material included within the cladding. Several different shapes of rod are used, and the resulting fiber is sold under brand names such as "PANDA" and "Bow-tie". ("PANDA" refers to the resemblance of the fiber's cross-section to the face of a panda, and is also an acronym for "Polarization-maintaining AND Absorption-reducing".)

It is possible to create a circularly birefringent optical fiber just using an ordinary (circularly symmetric) single-mode fiber and twisting it, thus creating internal torsional stress. That causes the phase velocity of right and left hand circular polarizations to significantly differ. Thus the two circular polarizations propagate with little crosstalk in between them

Applications
Polarization-maintaining optical fibers are used in special applications, such as in fiber optic sensing, interferometry and quantum key distribution. They are also commonly used in telecommunications for the connection between a source laser and a modulator, since the modulator requires polarized light as input. They are rarely used for long-distance transmission, because PM fiber is expensive and has higher attenuation than single-mode fiber. Another important application is fiber-optic gyroscopes, which are widely used in the aerospace industry.

The output of a PM fiber is typically characterized by its polarization extinction ratio (PER)—the ratio of correctly to incorrectly polarized light, expressed in decibels. The quality of PM patchcords and pigtails can be characterized with a PER meter. Good PM fibers have extinction ratios in excess of 20 dB.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Polarization-maintaining optical fiber


text:
Polling, Mühldorf

Polling is a municipality in the district of Mühldorf in Bavaria in Germany. It lies on the river Inn.

title: Polling, Mühldorf


text:
Power factor

In electrical engineering, the power factor of an AC power system is defined as the ratio of the real power absorbed by the load to the apparent power flowing in the circuit. Real power is the average of the instantaneous product of voltage and current and represents the capacity of the electricity for performing work. Apparent power is the product of root mean square (RMS) current and voltage. Due to energy stored in the load and returned to the source, or due to a non-linear load that distorts the wave shape of the current drawn from the source, the apparent power may be greater than the real power, so more current flows in the circuit than would be required to transfer real power alone. A power factor magnitude of less than one indicates the voltage and current are not in phase, reducing the average product of the two. A negative power factor occurs when the device (which is normally the load) generates real power, which then flows back towards the source.

In an electric power system, a load with a low power factor draws more current than a load with a high power factor for the same amount of useful power transferred. The larger currents increase the energy lost in the distribution system and require larger wires and other equipment. Because of the costs of larger equipment and wasted energy, electrical utilities will usually charge a higher cost to industrial or commercial customers where there is a low power factor.

Power-factor correction increases the power factor of a load, improving efficiency for the distribution system to which it is attached. Linear loads with a low power factor (such as induction motors) can be corrected with a passive network of capacitors or inductors. Non-linear loads, such as rectifiers, distort the current drawn from the system. In such cases, active or passive power factor correction may be used to counteract the distortion and raise the power factor. The devices for correction of the power factor may be at a central substation, spread out over a distribution system, or built into power-consuming equipment.

General case
The general expression for power factor is given by

 * $$ \mbox{power factor} = P/P_a $$
 * $$ P_a = I_{rms} V_{rms} $$

where $$P$$ is the real power measured by an ideal wattmeter, $$I_{rms}$$ is the rms current measured by an ideal ammeter, and $$V_{rms}$$ is the rms voltage measured by an ideal voltmeter. Apparent power, $$P_a$$, is the product of the rms current and the rms voltage.

If the load is sourcing power back toward the generator, then $$P$$ and $$ \mbox{power factor} $$ will be negative.

Periodic waveforms
If the waveforms are periodic with the same period which is much shorter than the averaging time of the physical meters, then the power factor can be computed by the following

 * $$ \mbox{power factor} = P/P_a $$
 * $$ P_a = I_{rms} V_{rms} $$
 * $$ P =\frac 1 T \int_{t'}^{t'+T} i(t)v(t) dt $$
 * $$ I_{rms}^2 =\frac 1 T \int_{t'}^{t'+T} {i(t)}^2 dt $$
 * $$ V_{rms}^2 =\frac 1 T \int_{t'}^{t'+T} {v(t)}^2 dt $$

where $$i(t)$$ is the instantaneous current, $$v(t)$$ is the instantaneous voltage, $$t'$$ is an arbitrary starting time, and $$T$$ is the period of the waveforms.

Nonperiodic waveforms
If the waveforms are not periodic and the physical meters have the same averaging time, then the equations for the periodic case can be used with the exception that $$T$$ is the averaging time of the meters instead of the waveform period.

Linear time-invariant circuits

Linear time-invariant circuits (referred to simply as linear circuits for the rest of this article), for example, circuits consisting of combinations of resistors, inductors and capacitors have a sinusoidal response to the sinusoidal line voltage. A linear load does not change the shape of the input waveform but may change the relative timing (phase) between voltage and current, due to its inductance or capacitance.

In a purely resistive AC circuit, voltage and current waveforms are in step (or in phase), changing polarity at the same instant in each cycle. All the power entering the load is consumed (or dissipated).

Where reactive loads are present, such as with capacitors or inductors, energy storage in the loads results in a phase difference between the current and voltage waveforms. During each cycle of the AC voltage, extra energy, in addition to any energy consumed in the load, is temporarily stored in the load in electric or magnetic fields then returned to the power grid a fraction of the period later.

Electrical circuits containing predominantly resistive loads (incandescent lamps, heating elements) have a power factor of almost 1, but circuits containing inductive or capacitive loads (electric motors, solenoid valves, transformers, fluorescent lamp ballasts, and others) can have a power factor well below 1.

In the electric power grid, reactive loads cause a continuous ebb and flow of nonproductive power. A circuit with a low power factor will use a greater amount of current to transfer a given quantity of real power than a circuit with a high power factor thus causing increased losses due to resistive heating in power lines, and requiring the use of higher-rated conductors and transformers.

Definition and calculation
AC power has two components:
 * Real power or active power ($$P$$) (sometimes called average power ), expressed in watts (W)
 * Reactive power ($$Q$$), usually expressed in reactive volt-amperes (var)

Together, they form the complex power ($$S$$) expressed as volt-amperes (VA). The magnitude of the complex power is the apparent power ($$|S|$$), also expressed in volt-amperes (VA).

The VA and var are non-SI units mathematically identical to the watt, but are used in engineering practice instead of the watt to state what quantity is being expressed. The SI explicitly disallows using units for this purpose or as the only source of information about a physical quantity as used.

The power factor is defined as the ratio of real power to apparent power. As power is transferred along a transmission line, it does not consist purely of real power that can do work once transferred to the load, but rather consists of a combination of real and reactive power, called apparent power. The power factor describes the amount of real power transmitted along a transmission line relative to the total apparent power flowing in the line.

The power factor can also be computed as the cosine of the angle θ by which the current waveform lags or leads the voltage waveform,.

Power triangle

One can relate the various components of AC power by using the power triangle in vector space. Real power extends horizontally in the real axis and reactive power extends in the direction of the imaginary axis. Complex power (and its magnitude, apparent power) represents a combination of both real and reactive power, and therefore can be calculated by using the vector sum of these two components. We can conclude that the mathematical relationship between these components is:

 * $$\begin{align}

S &= P + jQ \\ |S| &= \sqrt{P^2 + Q^2} \\ \text{pf} &= \cos{\theta} = \frac{P}{|S|} = \cos{ \left( \arctan{ \left( \frac{Q}{P} \right) } \right) } \\ Q &= P \, \tan(\arccos(\text{pf})) \end{align}$$

As the angle θ increases with fixed total apparent power, current and voltage are further out of phase with each other. Real power decreases, and reactive power increases.

Lagging, leading and unity power factors
Power factor is described as leading if the current waveform is advanced in phase with respect to voltage, or lagging when the current waveform is behind the voltage waveform. A lagging power factor signifies that the load is inductive, as the load will consume reactive power. The reactive component $$Q$$ is positive as reactive power travels through the circuit and is consumed by the inductive load. A leading power factor signifies that the load is capacitive, as the load supplies reactive power, and therefore the reactive component $$Q$$ is negative as reactive power is being supplied to the circuit.

If θ is the phase angle between the current and voltage, then the power factor is equal to the cosine of the angle, $$\cos\theta$$:
 * $$|P| = |S| \cos\theta$$

Since the units are consistent, the power factor is by definition a dimensionless number between -1 and 1. When power factor is equal to 0, the energy flow is entirely reactive and stored energy in the load returns to the source on each cycle. When the power factor is 1, referred to as unity power factor, all the energy supplied by the source is consumed by the load. Power factors are usually stated as leading or lagging to show the sign of the phase angle. Capacitive loads are leading (current leads voltage), and inductive loads are lagging (current lags voltage).

If a purely resistive load is connected to a power supply, current and voltage will change polarity in step, the power factor will be 1, and the electrical energy flows in a single direction across the network in each cycle. Inductive loads such as induction motors (any type of wound coil) consume reactive power with the current waveform lagging the voltage. Capacitive loads such as capacitor banks or buried cables generate reactive power with the current phase leading the voltage. Both types of loads will absorb energy during part of the AC cycle, which is stored in the device's magnetic or electric field, only to return this energy back to the source during the rest of the cycle.

For example, to get 1 kW of real power, if the power factor is unity, 1 kVA of apparent power needs to be transferred (1 kW ÷ 1 = 1 kVA). At low values of power factor, more apparent power needs to be transferred to get the same real power. To get 1 kW of real power at 0.2 power factor, 5 kVA of apparent power needs to be transferred (1 kW ÷ 0.2 = 5 kVA). This apparent power must be produced and transmitted to the load and is subject to losses in the production and transmission processes.

Electrical loads consuming alternating current power consume both real power and reactive power. The vector sum of real and reactive power is the complex power, and its magnitude is the apparent power. The presence of reactive power causes the real power to be less than the apparent power, and so, the electric load has a power factor of less than 1.

A negative power factor (0 to −1) can result from returning active power to the source, such as in the case of a building fitted with solar panels when surplus power is fed back into the supply.

Power factor correction of linear loads
A high power factor is generally desirable in a power delivery system to reduce losses and improve voltage regulation at the load. Compensating elements near an electrical load will reduce the apparent power demand on the supply system. Power factor correction may be applied by an electric power transmission utility to improve the stability and efficiency of the network. Individual electrical customers who are charged by their utility for low power factor may install correction equipment to increase their power factor so as to reduce costs.

Power factor correction brings the power factor of an AC power circuit closer to 1 by supplying or absorbing reactive power, adding capacitors or inductors that act to cancel the inductive or capacitive effects of the load, respectively. In the case of offsetting the inductive effect of motor loads, capacitors can be locally connected. These capacitors help to generate reactive power to meet the demand of the inductive loads. This will keep that reactive power from having to flow all the way from the utility generator to the load. In the electricity industry, inductors are said to consume reactive power and capacitors are said to supply it, even though reactive power is just energy moving back and forth on each AC cycle.

The reactive elements in power factor correction devices can create voltage fluctuations and harmonic noise when switched on or off. They will supply or sink reactive power regardless of whether there is a corresponding load operating nearby, increasing the system's no-load losses. In the worst case, reactive elements can interact with the system and with each other to create resonant conditions, resulting in system instability and severe overvoltage fluctuations. As such, reactive elements cannot simply be applied without engineering analysis.

An automatic power factor correction unit consists of a number of capacitors that are switched by means of contactors. These contactors are controlled by a regulator that measures power factor in an electrical network. Depending on the load and power factor of the network, the power factor controller will switch the necessary blocks of capacitors in steps to make sure the power factor stays above a selected value.

In place of a set of switched capacitors, an unloaded synchronous motor can supply reactive power. The reactive power drawn by the synchronous motor is a function of its field excitation. It is referred to as a synchronous condenser. It is started and connected to the electrical network. It operates at a leading power factor and puts vars onto the network as required to support a system's voltage or to maintain the system power factor at a specified level.

The synchronous condenser's installation and operation are identical to those of large electric motors. Its principal advantage is the ease with which the amount of correction can be adjusted; it behaves like a variable capacitor. Unlike with capacitors, the amount of reactive power furnished is proportional to voltage, not the square of voltage; this improves voltage stability on large networks. Synchronous condensers are often used in connection with high-voltage direct-current transmission projects or in large industrial plants such as steel mills.

For power factor correction of high-voltage power systems or large, fluctuating industrial loads, power electronic devices such as the static VAR compensator or STATCOM are increasingly used. These systems are able to compensate sudden changes of power factor much more rapidly than contactor-switched capacitor banks and, being solid-state, require less maintenance than synchronous condensers.

Non-linear loads
Examples of non-linear loads on a power system are rectifiers (such as used in a power supply), and arc discharge devices such as fluorescent lamps, electric welding machines, or arc furnaces. Because current in these systems is interrupted by a switching action, the current contains frequency components that are multiples of the power system frequency. Distortion power factor is a measure of how much the harmonic distortion of a load current decreases the average power transferred to the load.

Non-sinusoidal components
In linear circuits having only sinusoidal currents and voltages of one frequency, the power factor arises only from the difference in phase between the current and voltage. This is displacement power factor.

Non-linear loads change the shape of the current waveform from a sine wave to some other form. Non-linear loads create harmonic currents in addition to the original (fundamental frequency) AC current. This is of importance in practical power systems that contain non-linear loads such as rectifiers, some forms of electric lighting, electric arc furnaces, welding equipment, switched-mode power supplies, variable speed drives and other devices. Filters consisting of linear capacitors and inductors can prevent harmonic currents from entering the supplying system.

To measure the real power or reactive power, a wattmeter designed to work properly with non-sinusoidal currents must be used.

Distortion power factor
The distortion power factor is the distortion component associated with the harmonic voltages and currents present in the system.

\begin{align} \mbox{distortion power factor} & = \frac{ I_1}{I_{rms}} \\ & = \frac{I_1} {\sqrt{I_1^2+I_2^2+I_3^2+I_4^2+\cdots}} \\ & = \frac{1} { \sqrt{1+ \frac{I_2^2+I_3^2+I_4^2+\cdots}{I_1^2}}} \\ & = \frac{1} {\sqrt{ 1+THD_i^2}} \\ \end{align} $$

$$\mbox{THD}_i$$ is the total harmonic distortion of the load current.
 * $$THD_i = \frac{\sqrt{\displaystyle\sum_{h=2}^\infty I_h^2}} {I_1}= \frac{\sqrt{I_2^2+I_3^2+I_4^2+\cdots}} {I_1}$$

$$I_1$$ is the fundamental component of the current, $$I_{rms}$$ is the total current, and $$I_h$$ is the current on the hth harmonic; all are root mean square values (distortion power factor can also be used to describe individual order harmonics, using the corresponding current in place of total current). This definition with respect to total harmonic distortion assumes that the voltage stays undistorted (sinusoidal, without harmonics). This simplification is often a good approximation for stiff voltage sources (not being affected by changes in load downstream in the distribution network). Total harmonic distortion of typical generators from current distortion in the network is on the order of 1–2%, which can have larger scale implications but can be ignored in common practice.

The result when multiplied with the displacement power factor is the overall, true power factor or just power factor (PF):
 * $$\mbox{PF} = \frac{\cos{\varphi}} {\sqrt{ 1+THD_i^2}}$$

Distortion in three-phase networks
In practice, the local effects of distortion current on devices in a three-phase distribution network rely on the magnitude of certain order harmonics rather than the total harmonic distortion.

For example, the triplen, or zero-sequence, harmonics (3rd, 9th, 15th, etc.) have the property of being in-phase when compared line-to-line. In a delta-wye transformer, these harmonics can result in circulating currents in the delta windings and result in greater resistive heating. In a wye-configuration of a transformer, triplen harmonics will not create these currents, but they will result in a non-zero current in the neutral wire. This could overload the neutral wire in some cases and create error in kilowatt-hour metering systems and billing revenue. The presence of current harmonics in a transformer also result in larger eddy currents in the magnetic core of the transformer. Eddy current losses generally increase as the square of the frequency, lowering the transformer's efficiency, dissipating additional heat, and reducing its service life.

Negative-sequence harmonics (5th, 11th, 17th, etc.) combine 120 degrees out of phase, similarly to the fundamental harmonic but in a reversed sequence. In generators and motors, these currents produce magnetic fields which oppose the rotation of the shaft and sometimes result in damaging mechanical vibrations.

Switched-mode power supplies
A particularly important class of non-linear loads is the millions of personal computers that typically incorporate switched-mode power supplies (SMPS) with rated output power ranging from a few watts to more than 1 kW. Historically, these very-low-cost power supplies incorporated a simple full-wave rectifier that conducted only when the mains instantaneous voltage exceeded the voltage on the input capacitors. This leads to very high ratios of peak-to-average input current, which also lead to a low distortion power factor and potentially serious phase and neutral loading concerns.

A typical switched-mode power supply first converts the AC mains to a DC bus by means of a bridge rectifier. The output voltage is then derived from this DC bus. The problem with this is that the rectifier is a non-linear device, so the input current is highly non-linear. That means that the input current has energy at harmonics of the frequency of the voltage. This presents a problem for power companies, because they cannot compensate for the harmonic current by adding simple capacitors or inductors, as they could for the reactive power drawn by a linear load. Many jurisdictions are beginning to require power factor correction for all power supplies above a certain power level.

Regulatory agencies such as the EU have set harmonic limits as a method of improving power factor. Declining component cost has hastened implementation of two different methods. To comply with current EU standard EN61000-3-2, all switched-mode power supplies with output power more than 75 W must at least include passive power factor correction. 80 Plus power supply certification requires a power factor of 0.9 or more.

Passive PFC
The simplest way to control the harmonic current is to use a filter that passes current only at line frequency (50 or 60 Hz). The filter consists of capacitors or inductors and makes a non-linear device look more like a linear load. An example of passive PFC is a valley-fill circuit.

A disadvantage of passive PFC is that it requires larger inductors or capacitors than an equivalent power active PFC circuit. Also, in practice, passive PFC is often less effective at improving the power factor.

Active PFC

Active PFC is the use of power electronics to change the waveform of current drawn by a load to improve the power factor. Some types of the active PFC are buck, boost, buck-boost and synchronous condenser. Active power factor correction can be single-stage or multi-stage.

In the case of a switched-mode power supply, a boost converter is inserted between the bridge rectifier and the main input capacitors. The boost converter attempts to maintain a constant voltage at its output while drawing a current that is always in phase with and at the same frequency as the line voltage. Another switched-mode converter inside the power supply produces the desired output voltage from the DC bus. This approach requires additional semiconductor switches and control electronics but permits cheaper and smaller passive components. It is frequently used in practice.

For a three-phase SMPS, the Vienna rectifier configuration may be used to substantially improve the power factor.

SMPSs with passive PFC can achieve power factor of about 0.7–0.75, SMPSs with active PFC, up to 0.99 power factor, while a SMPS without any power factor correction have a power factor of only about 0.55–0.65.

Due to their very wide input voltage range, many power supplies with active PFC can automatically adjust to operate on AC power from about 100 V (Japan) to 240 V (Europe). That feature is particularly welcome in power supplies for laptops.

Dynamic PFC
Dynamic power factor correction (DPFC), sometimes referred to as real-time power factor correction, is used for electrical stabilization in cases of rapid load changes (e.g. at large manufacturing sites). DPFC is useful when standard power factor correction would cause over or under correction. DPFC uses semiconductor switches, typically thyristors, to quickly connect and disconnect capacitors or inductors to improve power factor.

Importance in distribution systems
Power factors below 1.0 require a utility to generate more than the minimum volt-amperes necessary to supply the real power (watts). This increases generation and transmission costs. For example, if the load power factor were as low as 0.7, the apparent power would be 1.4 times the real power used by the load. Line current in the circuit would also be 1.4 times the current required at 1.0 power factor, so the losses in the circuit would be doubled (since they are proportional to the square of the current). Alternatively, all components of the system such as generators, conductors, transformers, and switchgear would be increased in size (and cost) to carry the extra current. When the power factor is close to unity, for the same kVA rating of the transformer more load current can be supplied.

Utilities typically charge additional costs to commercial customers who have a power factor below some limit, which is typically 0.9 to 0.95. Engineers are often interested in the power factor of a load as one of the factors that affect the efficiency of power transmission.

With the rising cost of energy and concerns over the efficient delivery of power, active PFC has become more common in consumer electronics. Current Energy Star guidelines for computers call for a power factor of ≥ 0.9 at 100% of rated output in the PC's power supply. According to a white paper authored by Intel and the U.S. Environmental Protection Agency, PCs with internal power supplies will require the use of active power factor correction to meet the ENERGY STAR 5.0 Program Requirements for Computers.

In Europe, EN 61000-3-2 requires power factor correction be incorporated into consumer products.

Small customers, such as households, are not usually charged for reactive power and so power factor metering equipment for such customers will not be installed.

Measurement techniques
The power factor in a single-phase circuit (or balanced three-phase circuit) can be measured with the wattmeter-ammeter-voltmeter method, where the power in watts is divided by the product of measured voltage and current. The power factor of a balanced polyphase circuit is the same as that of any phase. The power factor of an unbalanced polyphase circuit is not uniquely defined.

A direct reading power factor meter can be made with a moving coil meter of the electrodynamic type, carrying two perpendicular coils on the moving part of the instrument. The field of the instrument is energized by the circuit current flow. The two moving coils, A and B, are connected in parallel with the circuit load. One coil, A, will be connected through a resistor and the second coil, B, through an inductor, so that the current in coil B is delayed with respect to current in A. At unity power factor, the current in A is in phase with the circuit current, and coil A provides maximum torque, driving the instrument pointer toward the 1.0 mark on the scale. At zero power factor, the current in coil B is in phase with circuit current, and coil B provides torque to drive the pointer towards 0. At intermediate values of power factor, the torques provided by the two coils add and the pointer takes up intermediate positions.

Another electromechanical instrument is the polarized-vane type. In this instrument a stationary field coil produces a rotating magnetic field, just like a polyphase motor. The field coils are connected either directly to polyphase voltage sources or to a phase-shifting reactor if a single-phase application. A second stationary field coil, perpendicular to the voltage coils, carries a current proportional to current in one phase of the circuit. The moving system of the instrument consists of two vanes that are magnetized by the current coil. In operation, the moving vanes take up a physical angle equivalent to the electrical angle between the voltage source and the current source. This type of instrument can be made to register for currents in both directions, giving a four-quadrant display of power factor or phase angle.

Digital instruments exist that directly measure the time lag between voltage and current waveforms. Low-cost instruments of this type measure the peak of the waveforms. More sophisticated versions measure the peak of the fundamental harmonic only, thus giving a more accurate reading for phase angle on distorted waveforms. Calculating power factor from voltage and current phases is only accurate if both waveforms are sinusoidal.

Power Quality Analyzers, often referred to as Power Analyzers, make a digital recording of the voltage and current waveform (typically either one phase or three phase) and accurately calculate true power (watts), apparent power (VA) power factor, AC voltage, AC current, DC voltage, DC current, frequency, IEC61000-3-2/3-12 Harmonic measurement, IEC61000-3-3/3-11 flicker measurement, individual phase voltages in delta applications where there is no neutral line, total harmonic distortion, phase and amplitude of individual voltage or current harmonics, etc.

Mnemonics
English-language power engineering students are advised to remember: ELI the ICE man or ELI on ICE – the voltage E, leads the current I, in an inductor L. The current I leads the voltage E in a capacitor C.

Another common mnemonic is CIVIL – in a capacitor (C) the current (I) leads voltage (V), voltage (V) leads current (I) in an inductor (L).

title: Power factor


text:
Power-law index profile

For optical fibers, a power-law index profile is an index of refraction profile characterized by

 * $$ n(r) =

\begin{cases} n_1 \sqrt{1-2\Delta\left({r \over \alpha}\right)^g} & r \le \alpha\\ n_1 \sqrt{1-2\Delta} & r \ge \alpha \end{cases}$$ where $$\Delta = {n_1^2 - n_2^2 \over 2 n_1^2},$$

and $$ n(r)$$ is the nominal refractive index as a function of distance from the fiber axis, $$n_1$$ is the nominal refractive index on axis, $$n_2$$ is the refractive index of the cladding, which is taken to be homogeneous ($$n(r)=n_2 \mathrm{\ for\ } r \ge \alpha$$), $$\alpha$$ is the core radius, and $$g$$ is a parameter that defines the shape of the profile. $$\alpha$$ is often used in place of $$g$$. Hence, this is sometimes called an alpha profile.

For this class of profiles, multimode distortion is smallest when $$g$$ takes a particular value depending on the material used. For most materials, this optimum value is approximately 2. In the limit of infinite $$g$$, the profile becomes a step-index profile.

title: Power-law index profile


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Power margin

In telecommunication, the power margin is the difference between available signal power and the minimum signal power needed to overcome system losses and still satisfy the minimum input requirements of the receiver for a given performance level.

System power margin reflects the excess signal level, present at the input of the receiver, that is available to compensate for (a) the effects of component aging in the transmitter, receiver, or physical transmission medium, and (b) a deterioration in propagation conditions. Synonym system power margin.

title: Power margin


text:
Precision

Precision, precise or precisely may refer to:

Arts and media

 * Precision (march), the official marching music of the Royal Military College of Canada
 * "Precision" (song), by Big Sean
 * Precisely (sketch), a dramatic sketch by the English playwright Harold Pinter

Mathematics and computing (general)

 * Accuracy and precision, measurement deviation from true value and its scatter
 * Significant figures, the number of digits that carry real information about a measurement
 * Precision and recall, in information retrieval: the proportion of relevant documents returned
 * Precision (computer science), a measure of the detail in which a quantity is expressed
 * Precision (statistics), a model parameter or a quantification of precision

Computing products

 * Dell Precision, a line of Dell workstations
 * Precision Architecture, former name for PA-RISC, a reduced instruction set architecture developed by Hewlett-Packard
 * Ubuntu 12.04 "Precise Pangolin", Canonical's sixteenth release of Ubuntu

Companies

 * Precision Air, an airline based in Tanzania
 * Precision Castparts Corp., a casting company based in Portland, Oregon, in the United States
 * Precision Drilling, the largest drilling-rig contractor in Canada
 * Precision Monolithics, an American company that produced linear semiconductors
 * Precision Talent, a voice-over talent-management company
 * F. E. Baker Ltd, maker of Precision motorcycle and cycle-car engines pre-WW1
 * Precisely (company), formerly Syncsort

Other uses

 * Precision Club, a bidding system in the game of contract bridge
 * Precision 15, a self-bailing dinghy
 * Fender Precision Bass, by Fender Musical Instruments Corporation

title: Precision


text:
Preemphasis improvement

In FM broadcasting, preemphasis improvement is the improvement in the signal-to-noise ratio of the high-frequency portion of the baseband, i.e., modulating signal, which improvement results from passing the modulating signal through a preemphasis network before transmission.

The reason that preemphasis is needed is that the process of detecting a frequency-modulated signal in a receiver produces a noise spectrum that rises in frequency (a so-called triangular spectrum). Without preemphasis, the received audio would sound unacceptably noisy at high frequencies, especially under conditions of low carrier-to-noise ratio, i.e., during fringe reception conditions. Preemphasis increases the magnitude of the higher signal frequencies, thereby improving the signal-to-noise ratio. At the output of the discriminator in the FM receiver, a deemphasis network restores the original signal power distribution.

FM improvement factor is the quotient obtained by dividing the signal-to-noise ratio (SNR) at the output of an FM receiver by the carrier-to-noise ratio (CNR) at the input of the receiver. When the FM improvement factor is greater than unity, the improvement in the SNR is always obtained at the expense of an increased bandwidth in the receiver and the transmission path.

FM improvement threshold is the point in an FM (frequency modulation) receiver at which the peaks in the RF signal equal the peaks of the thermal noise generated in the receiver. A baseband signal-to-noise ratio of about 30 dB is typical at the improvement threshold, and this ratio improves 1 dB for each decibel of increase in the signal above the threshold.

title: Preemphasis improvement


text:
Primary channel

In telecommunication, the term primary channel has the following meanings:

 * 1) The communication channel that is designated as a prime transmission channel and is used as the first choice in restoring priority circuits.
 * 2) In a communications network, the channel that has the highest data rate of all the channels sharing a common interface.
 * 3) The main Television channel of several operated by a broadcaster.

A primary channel may support the transfer of information in one direction only, either direction alternately, or both directions simultaneously.

 * 1) On a computer motherboard, it is the first physical connector for an IDE or ATA drive.

title: Primary channel


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Primary Rate Interface

The Primary Rate Interface (PRI) is a telecommunications interface standard used on an Integrated Services Digital Network (ISDN) for carrying multiple DS0 voice and data transmissions between the network and a user.

PRI is the standard for providing telecommunication services to enterprises and offices. It is based on T-carrier (T1) transmission in the US, Canada, and Japan, while the E-carrier (E1) is common in Europe and Australia. The T1 line consists of 23 bearer (B) channels and one data (D) channel for control purposes, for a total bandwidth of 24x64-kbit/s or 1.544 Mbit/s. The E1 carrier provides 30 B- and one D-channel for a bandwidth of 2.048 Mbit/s. The first timeslot on the E1 is used for synchronization purposes and is not considered to be a B- or D-channel. The D-channel typically uses timeslot 16 on an E1, while it is timeslot 24 for a T1. Fewer active bearer channels, sometimes called user channels, may be used in fractional T1 or E1 services.

ISDN service types
The Integrated Services Digital Network (ISDN) prescribes two levels of service:
 * Basic Rate Interface (BRI): one 16-kbit/s D channel with two 64-kbit/s B channels, intended for small enterprises and residential service.
 * Primary Rate Interface (PRI): one 64-kbit/s D channel with 23 (1.544 Mbit/s T1, a.k.a. "23B + D") or 30 (2.048 Mbit/s E1, a.k.a. "30B + D") 64-kbit/s B channels, intended for large organizations.

Each B-channel carries data, voice, and other services. The D-channel carries control and signaling information. Larger connections are possible using PRI pairing. A dual T1-PRI could have 24 + 23 = 47 B-channels and 1 D-channel (often called "47B + D"), but more commonly has 46 B-channels and 2 D-channels thus providing a backup signaling channel. The concept applies to E1s as well and both can include more than 2 PRIs. When configuring multiple T1's as ISDN-PRI's, it's possible to use NFAS (non-facility associated signaling) to enable one or two D-channels to support additional B-channels on separate T1 circuits.

Application
The Primary Rate Interface channels are typically used by medium to large enterprises with digital private branch exchange (PBX) telephone systems to provide digital access to the public switched telephone network (PSTN). The B-channels may be used flexibly and reassigned when necessary to meet special needs such as video conferences.

PRI channels and direct inward dialing are also common as a means of delivering inbound calls to voice over IP gateways from the PSTN.

title: Primary Rate Interface


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Primary station

In a data communication network, the primary station is the station responsible for unbalanced control of a data link.

The primary station generates commands and interprets responses, and is responsible for initialization of data and control information interchange, organization and control of data flow, retransmission control, and all recovery functions at the link level.

title: Primary station


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Primary time standard

In telecommunications, a primary time standard is a time standard that does not require calibration against another time standard.

Examples of primary time, (i.e., frequency standards) are caesium standards and hydrogen masers.

The international second is based on the microwave frequency (9,192,631,770 Hz) associated with the atomic resonance of the hyperfine ground state levels of the caesium-133 atom in a magnetically neutral environment. Realizable caesium frequency standards use a strong electromagnet to deliberately introduce a magnetic field which overwhelms that of the Earth. The presence of this strong magnetic field introduces a slight, but known, increase in the atomic resonance frequency. However, very small variations in the calibration of the electric current in the electromagnet introduce minuscule frequency variations among different caesium oscillators.

title: Primary time standard


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Priority

Prioritization is an action that arranges items or activities in order of importance.

Priority may refer specifically to:

Law

 * Priority or right of way on the road, see Traffic § Priority (right of way)
 * Priority signs, a traffic sign that specifies which route has the right of way
 * Priority date, a concept of establishing waiting times in the immigration process by United States Department of State
 * Priority right, a time-limited right, triggered by the first filing of an application for a patent
 * Subordination (finance), the order of priorities in claims for ownership or interest in various assets

Music

 * Priority (Pointer Sisters album)
 * Priority (Imperials album), 1980
 * Priorities, the debut album by Bedfordshire-based rock band Don Broco
 * "Priority", a song by Jolin Tsai from the 2004 album Castle
 * "Priority", a song by SM Town from the 2022 album 2022 Winter SM Town: SMCU Palace
 * Priority Records, a record label started in 1985 and acquired by Capitol Records

Science and technology

 * Scheduling priority, the way computing processes are assigned priorities in a run queue
 * Priority, a tag or attribute of a requirement in software or systems engineering
 * Priority of the scientific names of organisms, including:
 * Principle of priority, the principle that the oldest available name for a biological taxon is the valid one
 * In botanical nomenclature
 * In zoological nomenclature
 * Priority number, given to each functional group in IUPAC organic nomenclature
 * Scientific priority, the priority of scientific ideas

Other uses

 * Priority (fencing), a scoring criterion in the sport of fencing
 * Priority level, the priority of emergency communications
 * Priority mail, a service of the US Postal Service

title: Priority


text:
Priority level

Priority level or priority, in the Telecommunications Service Priority system, is the level that may be assigned to an NS/EP telecommunications service, which level specifies the order in which provisioning or restoration of the service is to occur relative to other NS/EP or non-NS/EP telecommunication services.

Priority levels authorized are designated (highest to lowest) "E," "1," "2," "3," "4," and "5" for provisioning and "1," "2," "3," "4," and "5" for restoration.

title: Priority level


text:
Private line

In telecommunication, a private line is typically a telephone company service that uses a dedicated, usually unswitched point-to-point circuit, but it may involve private switching arrangements, or predefined transmission physical or virtual paths. Most private lines connect only two locations, but some have multiple drop points. If the circuit is used for interconnecting switching systems, including manual switchboards, it is often called a tie line.

Among subscribers to the public switched telephone network, the term private line is often erroneously used to describe an individual telephone line for service for only one subscriber, as opposed to a party line with multiple stations connected.

In radio or wireless telephony, Private Line is a term trademarked by Motorola to describe an implementation of a Continuous Tone-Coded Squelch System (CTCSS), a method of using low-frequency subaudible tones to share a single radio channel among multiple users. Each user group would use a different low frequency tone. Motorola's trade name, especially the abbreviation PL, has become a genericized trademark for the method. General Electric used the term Channel Guard to describe the same system and other manufacturers used other terms.

A later digital version of a private line is called digital private line (DPL).

Advantages of private lines are:
 * High security as one dedicated link is provided
 * Always available
 * Instant data transmission

Types

 * PLNA - Private Line No Apparatus
 * PLNE - Private Line No Equipment
 * PLAR - Private Line Automatic Ringdown (think the "Red Phone")

title: Private line


text:
Proceed-to-select

In telecommunications, proceed-to-select is a signal or event in the call-access phase of a data call, which signal or event confirms the reception of a call-request signal and advises the calling data terminal equipment to proceed with the transmission of the selection signals.

Examples of proceed-to-select pertain to a dial tone in a telephone system.

title: Proceed-to-select