Polarization (waves)

4332:. 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 2163: 2154: 2173: 2182: 4168: 2191: 4249: 4446:) 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 3568: 241: 3915: 4061:. 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 284: 2287: 4491: 3797: 4401:

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. 90°) will have virtually no impact as the wave at any time can be in any of the 360 degrees.

4155: 4213: 2120: 3612: 2206: 3608:, 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. 1560: 40: 3621:(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 4536:. 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 3991: 1268: 2720: 5201:: in contrast with other authors, this source initially defines ellipticity reciprocally, as the minor-to-major-axis ratio, but then goes on to say that "Although is less than unity, when expressing ellipticity in decibels, the minus sign is frequently omitted for convenience", which essentially reverts to the definition adopted by other authors. 911: 682: 4451:

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.

257:), 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 4507:

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

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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

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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

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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

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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

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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,

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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

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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

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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,

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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.

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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

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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

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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.

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

4324:(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 2685:

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

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when there is more power in one of these streams than the other. At any particular wavelength, partially polarized light can be statistically described as the superposition of a completely unpolarized component and a completely polarized one. One may then describe the light in terms of the

687: 4347:. 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). 3969:

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

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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

461: 2811:. 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 2092:

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

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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

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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.

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and the parameters of the polarized component. That polarized component can be described in terms of a Jones vector or polarization ellipse. However, in order to also describe the degree of polarization, one normally employs Stokes parameters to specify a state of partial

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Paths taken by vectors in the Poincaré sphere under birefringence. The propagation modes (rotation axes) are shown with red, blue, and yellow lines, the initial vectors by thick black lines, and the paths they take by colored ellipses (which represent circles in three

1555:{\displaystyle {\begin{aligned}{\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{aligned}}} 4378:

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.

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Effect of a polarizer on reflection from mud flats. In the picture on the left, the horizontally oriented polarizer preferentially transmits those reflections; rotating the polarizer by 90° (right) as one would view using polarized sunglasses blocks almost all

1211: 2677:. 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. 2724: 2723: 3444: 2227:

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.

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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

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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

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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

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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.

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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

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Similarly, polarization microscopes can be used to aid in the detection of foreign matter in biological tissue slices if it is birefringent; autopsies often mention (a lack of or presence of) "polarizable foreign debris."

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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

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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.

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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

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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

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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

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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

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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

4121:), 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 73:. 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 4364:

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

4478:. 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 906:{\displaystyle {\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)},} 4408:

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

677:{\displaystyle {\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)}} 3328: 1113: 3634:) 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 4373:

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

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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

2145:(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 4404:

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

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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

1832: 1273: 1118: 170:—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. 3641:, 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 4336:

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.

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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

2513: 4079:) 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 4175:

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

1623: 3083: 2384: 2084:, 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 2464: 4083:

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.

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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

158:, 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 1972:

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

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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

3243: 2428: 81:. 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 3519:). 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 5137: 2088:

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

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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

4198:, in conjunction with natural polarization by reflection or scattering. The polarized light from LCD monitors (see below) is extremely conspicuous when these are worn. 3931:

material is thereby observed. Additionally, birefringence is frequently observed due to stresses "frozen in" at the time of manufacture. This is famously observed in

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acts on a polarized beam to create one in which the polarization varies so rapidly across the beam that it may be ignored in the intended applications. Conversely, a

1616:. 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 1976:

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

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One can test whether sunglasses are polarized by looking through two pairs, with one perpendicular to the other. If both are polarized, all light will be blocked.

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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

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In such media, an electromagnetic wave with any given state of polarization may be decomposed into two orthogonally polarized components that encounter different

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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

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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

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being in the plane of incidence. Since there are separate reflection coefficients for the linear polarizations in and orthogonal to the plane of incidence (

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which are always perpendicular to each other; by convention, the "polarization" of electromagnetic waves refers to the direction of the electric field. In

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Even in free space, longitudinal field components can be generated in focal regions, where the plane wave approximation breaks down. An extreme example is

2031: 3663:. Like birefringence, diattenuation can be with respect to linear polarization modes (in a crystal) or circular polarization modes (usually in a liquid). 2470:

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

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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.

2991:. Natural light, like most other common sources of visible light, is produced independently by a large number of atoms or molecules whose emissions are 4579:) 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. 4190:

Wearers of polarized sunglasses will occasionally observe inadvertent polarization effects such as color-dependent birefringent effects, for example in

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Sound waves in solid materials exhibit polarization. Differential propagation of the three polarizations through the earth is a crucial in the field of

3781:. 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 4421:" or AM broadcast tower used as an antenna element (again, for observers horizontally displaced from it) will transmit in the vertical polarization. A 2915:

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

55: 2035: 3588:/retarders and many crystals. If linearly polarized light passes through a birefringent material, its state of polarization will generally change, 3035:

Unpolarized light can be described as a mixture of two independent oppositely polarized streams, each with half the intensity. Light is said to be

6104: 185:. When viewed in this way, the polarization of an electromagnetic wave is determined by a quantum mechanical property of photons called their 4804: 4777: 4747: 4720: 4693: 3707:) exactly half of its initial power is retained. Practical polarizers, especially inexpensive sheet polarizers, have additional loss so that 3290: 3625:

in the Poincaré sphere about the axis defined by the propagation modes. Examples for linear (blue), circular (red), and elliptical (yellow)

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is generally used instead, with the zero azimuth (or position angle, as it is more commonly called in astronomy to avoid confusion with the

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in the sense of polarization), in which only the amplitudes of the two polarizations are affected differentially, may be described using a

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are complex numbers. In the second more compact form, as these equations are customarily expressed, these factors are described using the

4125:. Apart from providing information on sources of radiation and scattering, polarization also probes the interstellar magnetic field via 2238:

axes used in this description is arbitrary. The choice of such a coordinate system and viewing the polarization ellipse in terms of the

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with horizontal conductors, as viewed from a second station toward the horizon, is necessarily horizontally polarized. But a vertical "

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ellipsometry relies on reflection, it is not required for the sample to be transparent to light or for its back side to be accessible.

4360:); a normal diffuse white projection screen causes depolarization of the projected images, making it unsuitable for this application. 1789:). And because the absolute phase of a wave is unimportant in discussing its polarization state, let us stipulate that the phase of 4356:. Projecting such images requires screens that maintain the polarization of the projected light when viewed in reflection (such as 4069:

mixture) then their effects cancel out. However, when there is only one (or a preponderance of one), as is more often the case for

3067:, so that the phase of the wave varies in space and time while the polarization state does not. That is, the electric field vector 1937:{\displaystyle {\begin{aligned}e_{x}&={\sqrt {\frac {1+Q}{2}}}\\e_{y}&={\sqrt {\frac {1-Q}{2}}}\,e^{i\phi },\end{aligned}}} 4912: 4365: 3824:-polarization remaining. This principle is employed in the so-called "pile of plates polarizer" (see figure) in which part of the 5118: 3337:, that is, it will vary as a function of optical frequency (wavelength). In the case of non-birefringent materials, however, the 3251:. When the real or imaginary part of that refractive index is dependent on the polarization state of a wave, properties known as 17: 4470:, a sort of circular birefringence. This is the same mechanism which can rotate the axis of linear polarization by electrons in 5710:

Boyle, Latham A.; Steinhardt, PJ; Turok, N (2006). "Inflationary predictions for scalar and tensor fluctuations reconsidered".

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exploit this effect to reduce glare from reflections by horizontal surfaces, notably the road ahead viewed at a grazing angle.

4001:; upper picture is plane-polarized light, bottom picture is cross-polarized light, scale box at left-center is 0.25 millimeter. 3208:. As noted above, the instantaneous electric field is the real part of the product of the Jones vector times the phase factor 2673:). In general any two orthogonal states can be used, where an orthogonal vector pair is formally defined as one having a zero 5951: 5694: 5616: 5538: 5513: 5488: 5463: 5438: 5270: 5237: 5165: 5131: 5094: 4974: 4922: 4892: 4882: 4857: 4703: 4130: 3847:

In the important special case of reflection at normal incidence (not involving anisotropic materials) there is no particular

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Secrets of the Viking Navigators: How the Vikings used their amazing sunstones and other techniques to cross the open oceans

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of biological molecules on Earth, but chirality selection on inorganic crystals has been proposed as an alternative theory.

3270:. The effect of propagation over a given path on those two components is most easily characterized in the form of a complex 3793:-polarizations. Therefore, the polarization state of reflected light (even if initially unpolarized) is generally changed. 2222:

is produced (fourth and fifth figures). Circular polarization can be created by sending linearly polarized light through a

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if it is circularly polarized (or partially so). In comparison with lower frequencies such as microwaves, the amount of

6434: 4757: 4555:. This pattern is very difficult to see, but with practice one can learn to detect polarized light with the naked eye. 4320:(LCD) technology relies on the rotation of the axis of linear polarization by the liquid crystal array. Light from the 4467: 6350: 6328: 6300: 6281: 6262: 6243: 6224: 6203: 5919: 5413: 5383: 5354: 5192: 5050: 4949: 4814: 4730: 3247:

When an electromagnetic wave interacts with matter, its propagation is altered according to the material's (complex)

2825:, German for 'perpendicular'). Polarized light with its electric field along the plane of incidence is thus denoted 1206:{\displaystyle {\begin{aligned}h_{y}&={\frac {e_{x}}{\eta }}\\h_{x}&=-{\frac {e_{y}}{\eta }}.\end{aligned}}} 3868:

this is specified relative to the direction of propagation. The circular rotation of the electric field around the

2941:. The polarization of the photoluminescence is related to the strain in a material by way of the given material's 6403: 4217: 4207: 3832:-polarization after transmission through many such surfaces. The generally smaller reflection coefficient of the 3523:

between the components which increases the further the waves travel through the material. The Jones matrix is a

3439:{\displaystyle \mathbf {J} =\mathbf {T} {\begin{bmatrix}g_{1}&0\\0&g_{2}\end{bmatrix}}\mathbf {T} ^{-1},} 2262:

polarizations, see below), that choice greatly simplifies the calculation of a wave's reflection from a surface.

2323: 2162: 6444: 5212: 4787: 4597: 4572: 4517: 3844:- (horizontal) polarization, most of the glare due to reflection from a wet street, for instance, is removed. 2153: 6429: 6381: 4229: 1620:

of the light wave is proportional to the sum of the squared magnitudes of the two electric field components:

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is calculated as the fraction of the total power that is carried by the polarized component of the wave.

2432: 3865: 2952: 2611:{\displaystyle \mathbf {e} ={\begin{bmatrix}a_{1}e^{i\theta _{1}}\\a_{2}e^{i\theta _{2}}\end{bmatrix}}.} 4990:

Dorn, R.; Quabis, S. & Leuchs, G. (Dec 2003). "Sharper Focus for a Radially Polarized Light Beam".

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optimize the results of photographing scenes in which reflection or scattering by the sky is involved.

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along with 3 planar projections and a deformation surface of total electric field. The light is always

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or tangentially polarized light, at the focus of which the electric or magnetic field respectively is

305:) is always at right angles to it (blue), and both are perpendicular to the direction of propagation ( 6439: 4463: 4265: 4092: 3010:

light. Conversely, the two constituent linearly polarized states of unpolarized light cannot form an

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polarization components, corresponds to the definition of the Jones vector (below) in terms of those

1072:

each contain up to two nonzero (complex) components describing the amplitude and phase of the wave's

6096: 4167: 3935:

tape whose birefringence is due to the stretching of the material during the manufacturing process.

3212: 344:

are each in some direction perpendicular to (or "transverse" to) the direction of wave propagation;

6449: 2393: 2181: 266: 3747:), when illuminated by unpolarized light the remaining power in the unwanted polarization will be 2669:

vectors used to represent the Jones vector need not represent linear polarization states (i.e. be

2190: 197:

Polarization is an important parameter in areas of science dealing with transverse waves, such as

4612: 2992: 2114: 1995: 1715:{\displaystyle I=\left(\left|e_{x}\right|^{2}+\left|e_{y}\right|^{2}\right)\,{\frac {1}{2\eta }}} 1246: 134: 5608: 5598: 5077:

Sletten, Mark A.; Mc Laughlin, David J. (2005-04-15). "Radar Polarimetry". In Chang, Kai (ed.).

3979: 3191:{\displaystyle \mathbf {e} (z+\Delta z,t+\Delta t)=\mathbf {e} (z,t)e^{ik(c\Delta t-\Delta z)},} 5042: 4317: 4248: 3958: 3718: 3041: 3015: 2988: 2942: 2666: 1249:. The impedance will be complex in a conducting medium. Note that given that relationship, the 5260: 5155: 4387: 4176: 6338: 4617: 4592: 4443: 4325: 4237: 4134: 3274: 3007: 2110: 1999: 1986: 1977: 319: 315: 130: 3033:

acts on an unpolarized beam or arbitrarily polarized beam to create one which is polarized.

2294:

clockwise or counter clockwise. One parameterization of the elliptical figure specifies the

287:

A "vertically polarized" electromagnetic wave of wavelength λ has its electric field vector

6215: 6138: 5990: 5833: 5790: 5729: 5655: 5301: 4999: 4652: 4637: 4607: 4552: 4431: 4414: 4348: 3837: 3267: 3023: 3011: 2896: 2638:

denote the amplitude of the wave in the two components of the electric field vector, while

2281: 2034:

can be launched into a medium whose refractive index has a significant imaginary part (or "

114: 91: 3653:

Media in which transmission of one polarization mode is preferentially reduced are called

3470:

and possibly the amplitude attenuation due to propagation in each of the two polarization

2209:

A circularly polarized wave as a sum of two linearly polarized components 90° out of phase

8: 5554:

Alawi, Faizan; Shields, Bridget E.; Omolehinwa, Temitope; Rosenbach, Misha (2020-10-01).

4657: 4289: 4261: 4241: 4160: 3813: 3642: 3622: 3334: 3248: 3003: 2999: 2214: 2106: 2062: 1617: 178: 144:

Light or other electromagnetic radiation from many sources, such as the sun, flames, and

126: 6409: 6142: 5994: 5837: 5802: 5794: 5733: 5660: 5305: 5111: 5003: 4442:, there are some differences in propagation (and also in reflections responsible for TV 3828:-polarization is removed by reflection at each Brewster angle surface, leaving only the 3515:

substance, electromagnetic waves of different polarizations travel at different speeds (

6167: 6126: 6013: 5980: 5968: 5908: 5849: 5806: 5780: 5753: 5719: 5645: 5372: 5206: 5035: 4939: 4863: 4835: 4662: 4576: 4471: 4439: 4305: 4033: 4018: 2960: 2807: 2223: 218: 148:, consists of short wave trains with an equal mixture of polarizations; this is called 103: 4575:, even of pure circular polarization, compared to the same wave's linear momentum (or 2201:

Animation showing four different polarization states and three orthogonal projections.

435:

of the complex quantities occurring in the following equations. As a function of time

6346: 6324: 6296: 6277: 6258: 6239: 6220: 6199: 6172: 6067: 6059: 6018: 5947: 5915: 5888: 5853: 5745: 5690: 5612: 5575: 5534: 5509: 5484: 5459: 5434: 5409: 5379: 5350: 5266: 5233: 5188: 5161: 5127: 5090: 5056: 5046: 5015: 4970: 4945: 4918: 4888: 4867: 4853: 4810: 4783: 4753: 4726: 4699: 4422: 4122: 4106: 4070: 3778: 2980: 2973: 2938: 2904: 2477:. The special cases of linear and circular polarization correspond to an ellipticity 2073: 995: 431:) notation, the instantaneous physical electric and magnetic fields are given by the 174: 150: 145: 137:, the fields rotate at a constant rate in a plane as the wave travels, either in the 82: 5810: 5757: 5292:

Prakash, Hari; Chandra, Naresh (1971). "Density Operator of Unpolarized Radiation".

4256:

when viewed through a polarizer, due to stress-induced birefringence in the skylight

4137:

is inherently polarized. It has been suggested that astronomical sources caused the

3348:

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

6162: 6154: 6146: 6049: 6008: 5998: 5880: 5841: 5798: 5737: 5665: 5567: 5309: 5082: 5007: 4845: 4568: 4455: 4410: 4333: 4297: 4253: 4126: 4075: 3774: 3722: 3605: 3597: 3556: 3520: 929: 329: 271: 258: 167: 66: 5741: 5011: 3717:. However, in many instances the more relevant figure of merit is the polarizer's 2656:

represent the phases. The product of a Jones vector with a complex number of unit

6392: 6003: 5227: 5182: 4397: 4191: 3263:) respectively, then the polarization state of a wave will generally be altered. 2831:, while light whose electric field is normal to the plane of incidence is called 2247: 2055: 190: 138: 6376: 4352:

head, and is widely used in 3-D movie exhibition today, such as the system from

3345:

and attenuation factor), implying no change in polarization during propagation.

2322:). The ellipticity parameter is an alternative parameterization of an ellipse's 6037: 5594: 4849: 4632: 4567:

in the direction of propagation. In addition, however, light carries a certain

4293: 4180: 3800:

A stack of plates at Brewster's angle to a beam reflects off a fraction of the

3567: 3524: 3516: 3481: 3284: 3064: 2662: 2657: 2505: 2501: 1092: 424: 262: 186: 122: 118: 6414: 5670: 5633: 5571: 5086: 6423: 6063: 5892: 5604: 5579: 5060: 4541: 4533: 4357: 3626: 3506: 3252: 2674: 2266: 2047: 194:

with equal amplitude and phases synchronized to give oscillation in a plane.

159: 78: 4300:

from Asia to Europe in the 12th century. Related to the sky compass is the "

3804:-polarized light at each surface, leaving (after many such plates) a mainly 240: 6176: 6022: 5749: 5313: 5219: 5019: 4418: 3944: 3914: 3631: 3512: 3342: 3260: 2670: 2494: 2089: 2039: 1613: 6127:"Laser-induced rotation and cooling of a trapped microgyroscope in vacuum" 6071: 6054: 6038:"No evidence for polarization sensitivity in the pigeon electroretinogram" 5868: 2119: 154:. Polarized light can be produced by passing unpolarized light through a 6387: 5785: 5724: 4627: 4622: 4563:

It is well known that electromagnetic radiation carries a certain linear

4340: 4301: 4102: 4080: 4062: 4029: 3923: 3467: 2319: 1973: 1612:

component which is necessarily zero for a transverse wave) is known as a

1250: 1054: 325: 70: 4490: 4225: 3666:

Devices that block nearly all of the radiation in one mode are known as

2286: 1944:

where the polarization state is now fully parameterized by the value of

382:

is the speed of light), let us take the direction of propagation as the

283: 43:

Circular polarization on rubber thread, converted to linear polarization

6150: 6125:

Dholakia, Kishan; Mazilu, Michael; Arita, Yoshihiko (August 28, 2013).

5845: 4529: 4479: 4459: 4184: 4058: 4025: 4014: 4010: 3998: 3932: 3744: 3585: 3205: 2500:

phase information can be conveniently represented as a two-dimensional

2250:

polarizations. Axes are selected to suit a particular problem, such as

2094: 2077: 1563: 975: 357: 254: 250: 249:

and polarization in particular, it is easier to just consider coherent

202: 107: 99: 86: 6415:

Animations of Linear, Circular and Elliptical Polarizations on YouTube

6404:

Molecular Expressions: Science, Optics and You — Polarization of Light

6158: 4009:, and indeed was pivotal in the initial discovery of polarization. In 3812:

Any light striking a surface at a special angle of incidence known as

3497:

can be omitted if the coordinate axes have been chosen appropriately.

6397: 6036:

Nuboer, J. F. W.; Coemans, M. a. J. M.; Vos Hzn, J. J. (1995-02-01).

5684: 4830:

Le Tiec, A.; Novak, J. (July 2016). "Theory of Gravitational Waves".

4667: 4647: 4548: 4321: 4154: 4138: 4098: 3954: 3796: 3673: 3655: 3576: 3471: 3256: 3029: 2687: 2318:, the ratio of the ellipse's major to minor axis. (also known as the 2301:, defined as the angle between the major axis of the ellipse and the 2043: 432: 322: 210: 163: 155: 5884: 5824:

Clark, S. (1999). "Polarised starlight and the handedness of Life".

5252: 4881:

Lipson, Stephen G.; Lipson, Henry; Tannhauser, David Stefan (1995).

4212: 4032:) are termed SH and SV, while waves with longitudinal polarization ( 4005:

The property of (linear) birefringence is widespread in crystalline

2197: 2054:

transverse waves, but might be described as an electric or magnetic

5428: 4840: 4564: 4483: 4281: 4233: 3995: 3551: 2815:(parallel) and the component perpendicular to this plane is termed 189:. A photon has one of two possible spins: it can either spin in a 27:

Property of waves that can oscillate with more than one orientation

5985: 5650: 4260:

Sky polarization has been used for orientation in navigation. The

2205: 2038:") such as metals; these fields are also not strictly transverse. 4521: 4344: 4329: 4195: 4066: 4054: 4006: 3638: 3635: 6388:

MathPages: The relationship between photon spin and polarization

4520:. Polarization sensitivity has also been observed in species of 3900: 3611: 3559:(generally multiplied by a common phase factor). In fact, since 293:(red) oscillating in the vertical direction. The magnetic field 5553: 5531:

An Introduction to Seismology, Earthquakes, and Earth Structure

4558: 4537: 4509: 4504: 4285: 4133:

is being used to study the physics of the very early universe.

3601: 3060: 2003: 428: 265:

as a weighted combination of such uncorrelated waves with some

198: 182: 6236:

Fundamentals of Polarized Light: A Statistical Optics Approach

5969:"The secret world of shrimps: polarisation vision at its best" 5340: 5338: 4914:

Introduction to Light: The Physics of Light, Vision, and Color

4692:

Shipman, James; Wilson, Jerry D.; Higgins, Charles A. (2015).

4494:

Circular polarization through an airplane plastic window, 1989

3743:. Since Jones vectors refer to waves' amplitudes (rather than 3687:

unpolarized light is passed through an ideal polarizer (where

3049: 39: 4525: 4447: 4393: 4353: 4277: 4118: 4105:

is of great importance. Although not usually a factor in the

4065:

of such a molecule are present in equal numbers (a so-called

2984: 2955:

representation of a polarized beam. In this representation,

2085: 2081: 253:; these are sinusoidal waves of one particular direction (or 222: 214: 206: 95: 5966: 5771:

Tegmark, Max (2005). "What does inflation really predict?".

4989: 4264:

was used in the 1950s when navigating near the poles of the

3341:

Jones matrix is the identity matrix (multiplied by a scalar

2966: 5528: 5335: 4273: 4110: 4013:, this property is frequently exploited using polarization 3990: 1994:

still obey the above geometry but due to anisotropy in the

1771: 5685:

Hannu Karttunen; Pekka Kröger; Heikki Oja (27 June 2007).

5408:(4th ed.). United States of America: Addison Wesley. 5349:(4th ed.). United States of America: Addison Wesley. 5110:

Schrank, Helmut E.; Evans, Gary E.; Davis, Daniel (1990).

4113:, polarization is also present in radiation from coherent 5232:. Optical Sciences and Applications of Light. CRC Press. 4513: 4269: 2805:

Another coordinate system frequently used relates to the

2136:-plane, along the page, with the wave propagating in the 1580:, one can just as well specify the wave in terms of just 5429:

Dennis Goldstein; Dennis H. Goldstein (3 January 2011).

5363: 4101:, the study of polarized electromagnetic radiation from 3063:, the components of the electric field propagate at the 4028:. Horizontally and vertically polarized seismic waves ( 3820:-polarization is zero, will be reflected with only the 3323:{\displaystyle \mathbf {e'} =\mathbf {J} \mathbf {e} .} 6323:. Translated by Beerling, G. A. Cambridge University. 5422: 4880: 3373: 2530: 2435: 2396: 2331: 1764:; this happens to correspond to an intensity of about 826: 726: 600: 500: 4296:

in the 9th–11th centuries, before the arrival of the

3354: 3293: 3215: 3086: 2516: 1830: 1626: 1594:

describing the electric field. The vector containing

1271: 1116: 690: 464: 59: 6384:: Microscopic images made using polarization effects 6035: 5869:"Chiral selection on inorganic crystalline surfaces" 5709: 5634:"A review of maser polarization and magnetic fields" 5160:. Vol. 2: Applications. Elsevier. p. 177. 4691: 4284:). It has been suggested, controversially, that the 1084:

polarization component for a transverse wave in the

332:, meaning that a plane wave's electric field vector 318:(such as light), traveling in free space or another 235: 6124: 5678: 5638:

Proceedings of the International Astronomical Union

5586: 4937: 4381: 4201: 4194:(e.g., car windows) or items made from transparent 3054: 2895:) is a quantity used to describe the portion of an 2069:longitudinal (along the direction of propagation). 278: 69:which specifies the geometrical orientation of the 5907: 5522: 5371: 5076: 5034: 3438: 3322: 3237: 3190: 2610: 2458: 2422: 2378: 1936: 1714: 1554: 1205: 905: 676: 129:, the fields oscillate in a single direction. In 5109: 4544:, but research indicates this is a popular myth. 1008:. In a more general formulation with propagation 6421: 5910:Electromagnetic Vibrations, Waves, and Radiation 5867:Hazen, Robert M.; Sholl, David S. (2003-06-01). 5503: 5453: 5374:Electromagnetic Vibrations, Waves, and Radiation 4887:. Cambridge University Press. pp. 125–127. 1080:polarization components (again, there can be no 398:fields must then contain components only in the 117:such as light consists of a coupled oscillating 6290: 5592: 5225: 4540:, which was assumed to be one of their aids in 4017:, for the purpose of identifying minerals. See 213:. Especially impacted are technologies such as 5773:Journal of Cosmology and Astroparticle Physics 5529:Seth Stein; Michael Wysession (1 April 2009). 5478: 5447: 5291: 5226:Chipman, R.A.; Lam, W.S.T.; Young, G. (2018). 3982:to control production processes for instance. 3961:, not only are the predicted magnitude of the 3957:layers deposited on a substrate. Due to their 2956: 2948: 2934: 2926: 2920: 2916: 2912: 2908: 2900: 2715:Fresnel equations § S and P polarizations 1566:(at right angles to each other), as expected. 177:, electromagnetic waves can also be viewed as 77:, for example, in a musical instrument like a 5905: 5369: 5326: 5032: 4516:, which use this information to orient their 4292:") in their extensive expeditions across the 4224:Polarization is observed in the light of the 3901:Measurement techniques involving polarization 3881:direction is "left-handed" for a wave in the 3874:axes called "right-handed" for a wave in the 48: 6193: 5941: 5399: 5397: 5395: 5184:Antenna Engineering Handbook, Fourth Edition 5079:Encyclopedia of RF and Microwave Engineering 4964: 4931: 4829: 4771: 4769: 4695:An Introduction to Physical Science, 14th Ed 4559:Angular momentum using circular polarization 4144: 2820: 1728:is only dependent on the (complex) ratio of 1057:, the magnitude of which is the wavenumber. 6257:. SPIE Field Guides. Vol. FG05. SPIE. 5497: 3765:of the power in the intended polarization. 3050:Implications for reflection and propagation 2998:Unpolarized light can be produced from the 2911:of 100%, whereas an unpolarized wave has a 2132:times faster). The field oscillates in the 450:direction the fields have no dependence on 6291:Goldstein, Dennis; Dekker, Marcel (2003). 5937: 5935: 5933: 5931: 5866: 5072: 5070: 4775: 4498: 1810:may be complex. Under these restrictions, 868: 768: 642: 542: 458:) these complex fields can be written as: 6359: 6274:Polarization Optics in Telecommunications 6166: 6053: 6012: 6002: 5984: 5784: 5723: 5669: 5659: 5649: 5631: 5600:Organic Chemistry: Structure and Function 5472: 5392: 4906: 4904: 4839: 4802: 4782:. S. Chand Publishing. pp. 198–199. 4766: 4718: 4426:elevations it is elliptically polarized. 2967:Unpolarized and partially polarized light 2883: 2841:-polarization is commonly referred to as 1913: 1696: 6233: 6212: 6194:Azzam, R. M. A.; Bashara, N. M. (1977). 5126:. McGraw-Hill. pp. 6.30, Fig 6.25. 4796: 4712: 4489: 4247: 4220:(right image) on the sky in a photograph 4211: 4166: 4153: 3989: 3913: 3909: 3795: 3610: 3566: 2963:measured from the center of the sphere. 2933:field in materials when considering the 2718: 2204: 2196: 2118: 282: 239: 38: 6309: 6252: 5967:Sonja Kleinlogel; Andrew White (2008). 5928: 5770: 5764: 5180: 5067: 4958: 4917:. Courier Corporation. pp. 79–80. 4910: 4809:. Pearson Education. pp. 162–163. 4311: 4149: 3816:, where the reflection coefficient for 3571:Color pattern of a plastic box showing 3002:combination of vertical and horizontal 2701: 2379:{\textstyle e={\sqrt {1-b^{2}/a^{2}}},} 2275: 1963: 1018:direction, then the spatial dependence 14: 6422: 6398:Polarization angle in satellite dishes 6318: 6295:(2nd ed.). Taylor & Francis. 6271: 6219:(7th ed.). Cambridge University. 5906:Bekefi, George; Barrett, Alan (1977). 5899: 5370:Bekefi, George; Barrett, Alan (1977). 5258: 4901: 4752:. PHI Learning Pvt. Ltd. p. 453. 4685: 4438:Especially due to the presence of the 3768: 3596:Circular birefringence is also termed 2030:). Even in isotropic media, so-called 1742:. So let us just consider waves whose 1091:direction). For a given medium with a 6382:Polarized Light Digital Image Gallery 6343:Polarised Light in Science and Nature 6186: 5944:Polarised Light in Science and Nature 5823: 5703: 5456:Classical Optics and Its Applications 5431:Polarized Light, Revised and Expanded 5403: 5344: 5153: 4874: 4745: 2466:as is shown in the figure. The angle 2100: 5327:Chandrasekhar, Subrahmanyan (2013). 5033:Chandrasekhar, Subrahmanyan (1960). 4739: 4725:. Nelson Thornes. pp. 465–467. 2459:{\textstyle =\arctan 1/\varepsilon } 261:). Incoherent states can be modeled 6362:Polarized Light, Production and Use 6337: 6097:"'Fastest spinning object' created" 5479:Randy O. Wayne (16 December 2013). 5262:Optics: Principles and Applications 5229:Polarized Light and Optical Systems 4679: 4388:Antenna (radio) § Polarization 4073:, a net circular birefringence (or 3836:-polarization is also the basis of 3777:. These effects are treated by the 3575:when placed in between two crossed 3466:are complex numbers describing the 2907:. A perfectly polarized wave has a 2680: 1569:Knowing the propagation direction ( 24: 5117:. In Skolnik, Merrill Ivan (ed.). 4832:An Overview of Gravitational Waves 4276:were visible (e.g., under daytime 3174: 3165: 3116: 3101: 3014:, even if rotated into alignment ( 2285: 2161: 2152: 1562:indicating that these vectors are 386:axis. Being a transverse wave the 328:medium, are properly described as 25: 6461: 6393:A virtual polarization microscope 6377:Feynman's lecture on polarization 6370: 5942:J. David Pye (13 February 2001). 5265:. Elsevier Science. p. 145. 4779:A Textbook of Engineering Physics 4698:. Cengage Learning. p. 187. 4482:transmissions received following 4288:exploited a similar device (the " 3549:. Media termed diattenuating (or 3006:light, or right- and left-handed 2919:somewhere in between 0 and 100%. 236:Wave propagation and polarization 6196:Ellipsometry and Polarized Light 5632:Vlemmings, W. H. T. (Mar 2007). 5562:. Oral Medicine in Dermatology. 5157:Handbook of Microwave Technology 5143:from the original on 2022-10-09. 4967:Introduction to Nonlinear Optics 4382:Radio transmission and reception 4202:Sky polarization and photography 3725:, which involve a comparison of 3500: 3420: 3364: 3356: 3313: 3308: 3296: 3129: 3088: 3055:Polarization in wave propagation 2972:This section is an excerpt from 2518: 2189: 2180: 2171: 946:is the period of the wave. Here 279:Transverse electromagnetic waves 6118: 6107:from the original on 2019-09-10 6089: 6078:from the original on 2019-08-27 6042:Journal of Experimental Biology 6029: 5960: 5860: 5817: 5625: 5547: 5320: 5285: 5174: 5147: 5103: 5026: 4983: 4944:(3rd ed.). Prentice Hall. 4941:Introduction to Electrodynamics 4208:Polarizing filter (Photography) 3938: 2845:(TM), and has also been termed 2488: 2485:of zero and 45°) respectively. 2213:Now if one were to introduce a 1824:can be represented as follows: 443:(since for a plane wave in the 228: 141:or in the left-hand direction. 6360:Shurcliff, William A. (1962). 5508:. Cambridge University Press. 5458:. Cambridge University Press. 5081:. John Wiley & Sons, Inc. 4969:. Cambridge University Press. 4823: 4749:Fundamentals of Optics, 2nd Ed 4598:Spin angular momentum of light 4475: 3238:{\displaystyle e^{-i\omega t}} 3180: 3159: 3145: 3133: 3122: 3092: 2959:is equal to the length of the 2698:) corresponding to due north. 2423:{\textstyle \chi =\arctan b/a} 1342: 1325: 1299: 1282: 895: 877: 715: 703: 697: 669: 651: 489: 477: 471: 275:), phases, and polarizations. 106:, and transverse sound waves ( 13: 1: 5803:10.1088/1475-7516/2005/04/001 5742:10.1103/PhysRevLett.96.111301 5154:Ishii, T. Koryu, ed. (1995). 5012:10.1103/PhysRevLett.91.233901 4965:Geoffrey New (7 April 2011). 4674: 4228:, as this is due to sunlight 2951:is also visualized using the 2864:-polarization is also called 217:, wireless and optical fiber 6004:10.1371/journal.pone.0002190 5556:"Oral Granulomatous Disease" 4938:Griffiths, David J. (1998). 4484:refraction by the ionosphere 4086: 4048: 3928:stress induced birefringence 3648: 3573:stress-induced birefringence 2987:with a random, time-varying 2729:Electromagnetic vectors for 2696:horizontal coordinate system 2692:equatorial coordinate system 1236:is the refractive index and 364:(light of vacuum wavelength 60: 7: 6406:: Interactive Java tutorial 6255:Field Guide to Polarization 6213:Born, M.; Wolf, E. (1999). 4582: 4131:cosmic microwave background 4117:(e.g. hydroxyl or methanol 2903:can be calculated from the 10: 6466: 5506:Introduction to Seismology 5481:Light and Video Microscopy 5211:: CS1 maint: postscript ( 5187:. McGraw-Hill. Sec. 26.1. 4850:10.1142/9789813141766_0001 4776:Avadhanulu, M. N. (1992). 4643:Polarized light microscopy 4462:, in conjunction with the 4385: 4308:in the late 19th century. 4205: 4129:. The polarization of the 4090: 4039: 3985: 3942: 3897:-polarization components. 3785:and are different for the 3504: 2971: 2858:tangential plane polarized 2795:is the azimuthal angle of 2712: 2492: 2481:of infinity and unity (or 2279: 2123:Electric field oscillation 2104: 2042:or waves propagating in a 2018:) may differ from that of 1219:is real and has the value 29: 6435:Electromagnetic radiation 6321:Polarized Light in Nature 5671:10.1017/s1743921307012549 5572:10.1016/j.det.2020.05.004 5533:. John Wiley & Sons. 5504:Peter M. Shearer (2009). 5454:Masud Mansuripur (2009). 5087:10.1002/0471654507.eme343 4803:Desmarais, Louis (1997). 4719:Muncaster, Roger (1993). 4573:angular momentum in light 4145:Applications and examples 4093:Polarization in astronomy 3918:Stress in plastic glasses 3593:accompanying photograph. 1956:) and the relative phase 1060:Thus the leading vectors 49: 6345:. Institute of Physics. 6253:Collett, Edward (2005). 5593:Vollhardt, K. Peter C.; 4254:Embassy Gardens Sky Pool 3855:-polarization. Both the 2878:sagittal plane polarized 1796:is zero; in other words 1093:characteristic impedance 998:(or "radian frequency") 6272:Damask, Jay N. (2004). 5712:Physical Review Letters 4992:Physical Review Letters 4613:Fluorescence anisotropy 4499:Polarization and vision 4252:Colored fringes in the 3676:". This corresponds to 3073:of a plane wave in the 2929:can be used to map the 2884:Degree of polarization 2230:The orientation of the 2115:Elliptical polarization 1996:electric susceptibility 1803:is a real number while 1247:impedance of free space 135:elliptical polarization 18:Horizontal polarization 6319:Können, G. P. (1985). 6310:Karlsen, Leif (2003). 5404:Hecht, Eugene (2002). 5345:Hecht, Eugene (2002). 5331:. Courier. p. 30. 5314:10.1103/PhysRevA.4.796 5181:Volakis, John (2007). 5112:"6 Reflector Antennas" 4911:Waldman, Gary (2002). 4806:Applied Electro Optics 4746:Singh, Devraj (2015). 4495: 4464:earth's magnetic field 4318:liquid-crystal display 4266:Earth's magnetic field 4257: 4221: 4172: 4164: 4036:) are termed P-waves. 4002: 3919: 3809: 3719:degree of polarization 3617: 3580: 3440: 3324: 3239: 3192: 3042:degree of polarization 2943:photoelasticity tensor 2889:Degree of polarization 2821: 2802: 2778:is the polar angle of 2612: 2460: 2424: 2380: 2290: 2210: 2202: 2166: 2157: 2124: 2036:extinction coefficient 1938: 1716: 1556: 1207: 907: 678: 312: 245: 244:cross linear polarized 44: 6445:Broadcast engineering 6364:. Harvard University. 6234:Brosseau, C. (1998). 6131:Nature Communications 6055:10.1242/jeb.198.2.325 5687:Fundamental Astronomy 5259:Sharma, K.K. (2006). 4593:Plane of polarization 4493: 4326:seven-segment display 4251: 4236:as it passes through 4215: 4206:Further information: 4183:is named. Polarizing 4170: 4157: 4135:Synchrotron radiation 3994:Photomicrograph of a 3993: 3959:reflection properties 3917: 3910:Measurement of stress 3799: 3614: 3570: 3441: 3325: 3268:propagation constants 3240: 3193: 3016:Fresnel–Arago 3rd law 2728: 2613: 2461: 2425: 2381: 2305:-axis along with the 2289: 2220:circular polarization 2208: 2200: 2165: 2156: 2143:state of polarization 2122: 2111:Circular polarization 2105:Further information: 2000:magnetic permeability 1987:magnetic flux density 1978:electric displacement 1939: 1776:in free space (where 1726:state of polarization 1717: 1557: 1208: 908: 679: 439:and spatial position 360:of optical frequency 316:Electromagnetic waves 286: 243: 92:electromagnetic waves 42: 6430:Polarization (waves) 6410:Antenna Polarization 6216:Principles of Optics 5560:Dermatologic Clinics 4653:Polaroid (polarizer) 4638:Polarization rotator 4608:Depolarizer (optics) 4518:communicative dances 4432:satellite television 4415:log-periodic antenna 4349:Polarized 3D glasses 4312:Display technologies 4161:specularly reflected 4150:Polarized sunglasses 4115:astronomical sources 3926:, the phenomenon of 3838:polarized sunglasses 3352: 3291: 3213: 3084: 3012:interference pattern 3008:circularly polarized 2899:which is polarized. 2897:electromagnetic wave 2514: 2433: 2394: 2329: 2282:Polarization ellipse 2276:Polarization ellipse 2058:, or a hybrid mode. 1964:Non-transverse waves 1828: 1724:However, the wave's 1624: 1269: 1114: 688: 462: 269:of frequencies (its 179:streams of particles 115:electromagnetic wave 30:For other uses, see 6143:2013NatCo...4.2374A 5995:2008PLoSO...3.2190K 5838:1999AmSci..87..336C 5795:2005JCAP...04..001T 5734:2006PhRvL..96k1301B 5661:2007IAUS..242...37V 5306:1971PhRvA...4..796P 5004:2003PhRvL..91w3901D 4658:Radial polarization 4177:Étienne-Louis Malus 4034:compressional waves 3769:Specular reflection 3643:Erasmus Bartholinus 3249:index of refraction 3080:direction follows: 3037:partially polarized 2866:transverse-electric 2843:transverse-magnetic 2107:Linear polarization 2032:inhomogeneous waves 2006:, the direction of 406:directions whereas 368:has a frequency of 338:and magnetic field 127:linear polarization 104:gravitational waves 65:) is a property of 6314:. One Earth Press. 6187:General references 6151:10.1038/ncomms3374 5914:. USA: MIT Press. 5846:10.1511/1999.4.336 5826:American Scientist 5483:. Academic Press. 5378:. USA: MIT Press. 5329:Radiative transfer 5037:Radiative Transfer 4663:Rayleigh sky model 4577:radiation pressure 4496: 4472:interstellar space 4343:displays used for 4306:Charles Wheatstone 4258: 4238:Earth's atmosphere 4222: 4173: 4165: 4021:for more details. 4019:optical mineralogy 4003: 3920: 3840:; by blocking the 3810: 3783:angle of incidence 3669:polarizing filters 3618: 3581: 3436: 3412: 3320: 3235: 3188: 3004:linearly polarized 2808:plane of incidence 2803: 2770:-polarized in the 2608: 2599: 2456: 2420: 2376: 2291: 2224:quarter-wave plate 2211: 2203: 2167: 2158: 2125: 2101:Polarization state 2074:longitudinal waves 2002:), now given by a 1934: 1932: 1712: 1576:in this case) and 1552: 1550: 1203: 1201: 1012:restricted to the 924:is the wavelength 903: 862: 762: 674: 636: 536: 313: 246: 219:telecommunications 146:incandescent lamps 83:longitudinal waves 45: 6198:. North-Holland. 5953:978-0-7503-0673-7 5696:978-3-540-34143-7 5618:978-0-7167-4374-3 5540:978-1-4443-1131-0 5515:978-0-521-88210-1 5490:978-0-12-411536-1 5465:978-0-521-88169-2 5440:978-0-203-91158-7 5294:Physical Review A 5272:978-0-08-046391-9 5239:978-1-4987-0057-3 5167:978-0-08-053410-7 5133:978-0-07-057913-2 5096:978-0-471-65450-6 5041:. Dover. p. 4976:978-1-139-50076-0 4924:978-0-486-42118-6 4894:978-0-521-43631-1 4859:978-981-314-175-9 4834:. pp. 1–41. 4705:978-1-305-54467-3 4618:Glan–Taylor prism 4553:Haidinger's brush 4423:turnstile antenna 4316:The principle of 4268:when neither the 4262:Pfund sky compass 4218:polarizing filter 4216:The effects of a 4123:interstellar dust 4107:thermal radiation 4097:In many areas of 4071:organic molecules 3779:Fresnel equations 3255:and polarization 2981:Unpolarized light 2974:Unpolarized light 2939:photoluminescence 2905:Stokes parameters 2868:(TE), as well as 2726: 2388:ellipticity angle 2371: 2296:orientation angle 2147:in the same phase 1911: 1910: 1870: 1869: 1710: 1608:(but without the 1514: 1475: 1345: 1328: 1302: 1285: 1215:In a dielectric, 1194: 1153: 1050: 1041: 1032: 996:angular frequency 809: 796: 700: 583: 570: 474: 175:quantum mechanics 151:unpolarized light 16:(Redirected from 6457: 6440:Antennas (radio) 6365: 6356: 6334: 6315: 6306: 6287: 6268: 6249: 6230: 6209: 6181: 6180: 6170: 6122: 6116: 6115: 6113: 6112: 6093: 6087: 6086: 6084: 6083: 6057: 6033: 6027: 6026: 6016: 6006: 5988: 5964: 5958: 5957: 5939: 5926: 5925: 5913: 5903: 5897: 5896: 5873:Nature Materials 5864: 5858: 5857: 5821: 5815: 5814: 5788: 5786:astro-ph/0410281 5768: 5762: 5761: 5727: 5725:astro-ph/0507455 5707: 5701: 5700: 5682: 5676: 5675: 5673: 5663: 5653: 5629: 5623: 5622: 5603:(4th ed.). 5590: 5584: 5583: 5551: 5545: 5544: 5526: 5520: 5519: 5501: 5495: 5494: 5476: 5470: 5469: 5451: 5445: 5444: 5426: 5420: 5419: 5401: 5390: 5389: 5377: 5367: 5361: 5360: 5342: 5333: 5332: 5324: 5318: 5317: 5289: 5283: 5282: 5280: 5279: 5256: 5250: 5249: 5247: 5246: 5223: 5217: 5216: 5210: 5202: 5178: 5172: 5171: 5151: 5145: 5144: 5142: 5125: 5116: 5107: 5101: 5100: 5074: 5065: 5064: 5040: 5030: 5024: 5023: 4987: 4981: 4980: 4962: 4956: 4955: 4935: 4929: 4928: 4908: 4899: 4898: 4878: 4872: 4871: 4843: 4827: 4821: 4820: 4800: 4794: 4793: 4773: 4764: 4763: 4743: 4737: 4736: 4716: 4710: 4709: 4689: 4680:Cited references 4588:Quantum Physics 4569:angular momentum 4468:Faraday rotation 4396:(and microwave) 4298:magnetic compass 4127:Faraday rotation 4076:optical activity 3887: 3880: 3873: 3862: 3858: 3814:Brewster's angle 3808:-polarized beam. 3775:refractive index 3764: 3742: 3733: 3723:extinction ratio 3716: 3706: 3696: 3685: 3606:Faraday rotation 3600:, especially in 3598:optical activity 3557:Hermitian matrix 3548: 3546: 3537: 3521:phase difference 3517:phase velocities 3496: 3490: 3479: 3465: 3456: 3445: 3443: 3442: 3437: 3432: 3431: 3423: 3417: 3416: 3409: 3408: 3385: 3384: 3367: 3359: 3340: 3329: 3327: 3326: 3321: 3316: 3311: 3303: 3302: 3282: 3273: 3246: 3244: 3242: 3241: 3236: 3234: 3233: 3203: 3197: 3195: 3194: 3189: 3184: 3183: 3132: 3091: 3079: 3072: 2958: 2950: 2936: 2928: 2922: 2918: 2914: 2910: 2902: 2853: 2824: 2800: 2794: 2783: 2777: 2773: 2765: 2746: 2740: 2734: 2727: 2681:Coordinate frame 2655: 2646: 2637: 2628: 2617: 2615: 2614: 2609: 2604: 2603: 2596: 2595: 2594: 2593: 2576: 2575: 2562: 2561: 2560: 2559: 2542: 2541: 2521: 2484: 2480: 2476: 2469: 2465: 2463: 2462: 2457: 2452: 2429: 2427: 2426: 2421: 2416: 2385: 2383: 2382: 2377: 2372: 2370: 2369: 2360: 2355: 2354: 2339: 2317: 2304: 2300: 2253: 2245: 2241: 2237: 2233: 2193: 2184: 2175: 2139: 2135: 2131: 2050:) are generally 2029: 2023: 2017: 2011: 1993: 1984: 1959: 1955: 1947: 1943: 1941: 1940: 1935: 1933: 1926: 1925: 1912: 1906: 1895: 1894: 1885: 1884: 1871: 1865: 1854: 1853: 1844: 1843: 1823: 1816: 1809: 1802: 1795: 1788: 1775: 1769: 1763: 1761: 1752: 1741: 1734: 1721: 1719: 1718: 1713: 1711: 1709: 1698: 1695: 1691: 1690: 1689: 1684: 1680: 1679: 1662: 1661: 1656: 1652: 1651: 1611: 1607: 1600: 1593: 1586: 1579: 1575: 1561: 1559: 1558: 1553: 1551: 1535: 1519: 1515: 1510: 1509: 1500: 1494: 1493: 1481: 1477: 1476: 1471: 1470: 1461: 1451: 1450: 1435: 1431: 1430: 1421: 1420: 1408: 1407: 1398: 1397: 1385: 1384: 1375: 1374: 1358: 1354: 1347: 1346: 1338: 1330: 1329: 1321: 1315: 1311: 1304: 1303: 1295: 1287: 1286: 1278: 1264: 1258: 1244: 1235: 1231: 1218: 1212: 1210: 1209: 1204: 1202: 1195: 1190: 1189: 1180: 1168: 1167: 1154: 1149: 1148: 1139: 1130: 1129: 1109: 1103: 1097: 1090: 1083: 1079: 1075: 1071: 1065: 1052: 1051: 1048: 1043: 1042: 1039: 1033: 1030: 1023: 1017: 1007: 993: 973: 966: 959: 952: 945: 935: 930:refractive index 923: 912: 910: 909: 904: 899: 898: 867: 866: 852: 851: 838: 837: 817: 816: 815: 811: 810: 802: 797: 789: 767: 766: 752: 751: 738: 737: 702: 701: 693: 683: 681: 680: 675: 673: 672: 641: 640: 626: 625: 612: 611: 591: 590: 589: 585: 584: 576: 571: 563: 541: 540: 526: 525: 512: 511: 476: 475: 467: 457: 453: 449: 442: 438: 422: 405: 401: 397: 391: 385: 381: 377: 367: 363: 355: 349: 343: 337: 330:transverse waves 310: 304: 298: 292: 259:angular spectrum 168:optical activity 67:transverse waves 63: 62: 52: 51: 21: 6465: 6464: 6460: 6459: 6458: 6456: 6455: 6454: 6450:Physical optics 6420: 6419: 6373: 6368: 6353: 6331: 6303: 6293:Polarized Light 6284: 6265: 6246: 6227: 6206: 6189: 6184: 6123: 6119: 6110: 6108: 6095: 6094: 6090: 6081: 6079: 6034: 6030: 5965: 5961: 5954: 5940: 5929: 5922: 5904: 5900: 5885:10.1038/nmat879 5865: 5861: 5822: 5818: 5769: 5765: 5708: 5704: 5697: 5683: 5679: 5644:(S242): 37–46. 5630: 5626: 5619: 5595:Schore, Neil E. 5591: 5587: 5552: 5548: 5541: 5527: 5523: 5516: 5502: 5498: 5491: 5477: 5473: 5466: 5452: 5448: 5441: 5427: 5423: 5416: 5402: 5393: 5386: 5368: 5364: 5357: 5343: 5336: 5325: 5321: 5290: 5286: 5277: 5275: 5273: 5257: 5253: 5244: 5242: 5240: 5224: 5220: 5204: 5203: 5195: 5179: 5175: 5168: 5152: 5148: 5140: 5134: 5123: 5114: 5108: 5104: 5097: 5075: 5068: 5053: 5031: 5027: 4988: 4984: 4977: 4963: 4959: 4952: 4936: 4932: 4925: 4909: 4902: 4895: 4884:Optical Physics 4879: 4875: 4860: 4828: 4824: 4817: 4801: 4797: 4790: 4774: 4767: 4760: 4744: 4740: 4733: 4722:A-level Physics 4717: 4713: 4706: 4690: 4686: 4682: 4677: 4672: 4585: 4561: 4501: 4390: 4384: 4314: 4304:", invented by 4210: 4204: 4192:toughened glass 4152: 4147: 4095: 4089: 4051: 4042: 3988: 3947: 3941: 3912: 3903: 3882: 3875: 3869: 3860: 3856: 3771: 3762: 3755: 3748: 3741: 3735: 3732: 3726: 3714: 3708: 3704: 3698: 3694: 3688: 3683: 3677: 3670: 3651: 3545: 3539: 3538:| = | 3536: 3530: 3528: 3509: 3503: 3492: 3486: 3475: 3464: 3458: 3455: 3449: 3424: 3419: 3418: 3411: 3410: 3404: 3400: 3398: 3392: 3391: 3386: 3380: 3376: 3369: 3368: 3363: 3355: 3353: 3350: 3349: 3338: 3312: 3307: 3295: 3294: 3292: 3289: 3288: 3278: 3271: 3220: 3216: 3214: 3211: 3210: 3209: 3201: 3152: 3148: 3128: 3087: 3085: 3082: 3081: 3074: 3068: 3057: 3052: 3047: 3046: 2977: 2969: 2953:Poincaré sphere 2886: 2870:sigma-polarized 2851: 2835: 2829: 2796: 2793: 2785: 2779: 2775: 2771: 2748: 2742: 2736: 2730: 2719: 2717: 2711: 2683: 2654: 2648: 2645: 2639: 2636: 2630: 2627: 2621: 2598: 2597: 2589: 2585: 2581: 2577: 2571: 2567: 2564: 2563: 2555: 2551: 2547: 2543: 2537: 2533: 2526: 2525: 2517: 2515: 2512: 2511: 2497: 2491: 2482: 2478: 2471: 2467: 2448: 2434: 2431: 2430: 2412: 2395: 2392: 2391: 2365: 2361: 2356: 2350: 2346: 2338: 2330: 2327: 2326: 2309: 2302: 2298: 2284: 2278: 2251: 2243: 2239: 2235: 2231: 2195: 2186: 2177: 2168: 2159: 2137: 2133: 2129: 2117: 2103: 2056:transverse mode 2025: 2019: 2013: 2007: 1989: 1980: 1966: 1957: 1949: 1945: 1931: 1930: 1918: 1914: 1896: 1893: 1886: 1880: 1876: 1873: 1872: 1855: 1852: 1845: 1839: 1835: 1831: 1829: 1826: 1825: 1822: 1818: 1815: 1811: 1808: 1804: 1801: 1797: 1794: 1790: 1787: 1777: 1767: 1765: 1759: 1754: 1753:| + | 1750: 1745: 1743: 1740: 1736: 1733: 1729: 1702: 1697: 1685: 1675: 1671: 1667: 1666: 1657: 1647: 1643: 1639: 1638: 1637: 1633: 1625: 1622: 1621: 1609: 1606: 1602: 1599: 1595: 1592: 1588: 1585: 1581: 1577: 1570: 1549: 1548: 1533: 1532: 1505: 1501: 1499: 1495: 1489: 1485: 1466: 1462: 1460: 1456: 1452: 1446: 1442: 1433: 1432: 1426: 1422: 1416: 1412: 1403: 1399: 1393: 1389: 1380: 1376: 1370: 1366: 1359: 1337: 1336: 1335: 1331: 1320: 1319: 1294: 1293: 1292: 1288: 1277: 1276: 1272: 1270: 1267: 1266: 1260: 1254: 1243: 1237: 1233: 1226: 1220: 1216: 1200: 1199: 1185: 1181: 1179: 1169: 1163: 1159: 1156: 1155: 1144: 1140: 1138: 1131: 1125: 1121: 1117: 1115: 1112: 1111: 1105: 1099: 1095: 1085: 1081: 1077: 1073: 1067: 1061: 1047: 1045: 1038: 1029: 1025: 1024:is replaced by 1019: 1013: 999: 992: 978: 972: 968: 965: 961: 958: 954: 951: 947: 937: 933: 918: 914: 873: 869: 861: 860: 854: 853: 847: 843: 840: 839: 833: 829: 822: 821: 801: 788: 787: 783: 773: 769: 761: 760: 754: 753: 747: 743: 740: 739: 733: 729: 722: 721: 692: 691: 689: 686: 685: 647: 643: 635: 634: 628: 627: 621: 617: 614: 613: 607: 603: 596: 595: 575: 562: 561: 557: 547: 543: 535: 534: 528: 527: 521: 517: 514: 513: 507: 503: 496: 495: 466: 465: 463: 460: 459: 455: 451: 444: 440: 436: 419: 412: 407: 403: 399: 393: 387: 383: 379: 369: 365: 361: 351: 345: 339: 333: 326:non-attenuating 306: 300: 294: 288: 281: 238: 231: 35: 28: 23: 22: 15: 12: 11: 5: 6463: 6453: 6452: 6447: 6442: 6437: 6432: 6418: 6417: 6412: 6407: 6401: 6395: 6390: 6385: 6379: 6372: 6371:External links 6369: 6367: 6366: 6357: 6351: 6335: 6329: 6316: 6307: 6301: 6288: 6282: 6269: 6263: 6250: 6244: 6231: 6225: 6210: 6204: 6190: 6188: 6185: 6183: 6182: 6117: 6103:. 2013-08-28. 6088: 6048:(2): 325–335. 6028: 5959: 5952: 5927: 5920: 5898: 5879:(6): 367–374. 5859: 5816: 5763: 5718:(11): 111301. 5702: 5695: 5677: 5624: 5617: 5585: 5566:(4): 429–439. 5546: 5539: 5521: 5514: 5496: 5489: 5471: 5464: 5446: 5439: 5421: 5414: 5391: 5384: 5362: 5355: 5334: 5319: 5300:(2): 796–799. 5284: 5271: 5251: 5238: 5218: 5193: 5173: 5166: 5146: 5132: 5120:Radar Handbook 5102: 5095: 5066: 5051: 5025: 4998:(23): 233901. 4982: 4975: 4957: 4950: 4930: 4923: 4900: 4893: 4873: 4858: 4822: 4815: 4795: 4788: 4765: 4759:978-8120351462 4758: 4738: 4731: 4711: 4704: 4683: 4681: 4678: 4676: 4673: 4671: 4670: 4665: 4660: 4655: 4650: 4645: 4640: 4635: 4633:Pockels effect 4630: 4625: 4620: 4615: 4610: 4601: 4600: 4595: 4586: 4584: 4581: 4560: 4557: 4500: 4497: 4456:free electrons 4454:The effect of 4383: 4380: 4358:silver screens 4313: 4310: 4294:North Atlantic 4203: 4200: 4151: 4148: 4146: 4143: 4091:Main article: 4088: 4085: 4050: 4047: 4041: 4038: 3987: 3984: 3943:Main article: 3940: 3937: 3911: 3908: 3902: 3899: 3770: 3767: 3760: 3753: 3739: 3730: 3712: 3702: 3692: 3681: 3668: 3650: 3647: 3591: 3562: 3543: 3534: 3525:unitary matrix 3505:Main article: 3502: 3499: 3482:unitary matrix 3462: 3453: 3435: 3430: 3427: 3422: 3415: 3407: 3403: 3399: 3397: 3394: 3393: 3390: 3387: 3383: 3379: 3375: 3374: 3372: 3366: 3362: 3358: 3319: 3315: 3310: 3306: 3301: 3298: 3275:transformation 3232: 3229: 3226: 3223: 3219: 3187: 3182: 3179: 3176: 3173: 3170: 3167: 3164: 3161: 3158: 3155: 3151: 3147: 3144: 3141: 3138: 3135: 3131: 3127: 3124: 3121: 3118: 3115: 3112: 3109: 3106: 3103: 3100: 3097: 3094: 3090: 3065:speed of light 3056: 3053: 3051: 3048: 2978: 2970: 2968: 2965: 2885: 2882: 2833: 2827: 2789: 2710: 2700: 2682: 2679: 2663:absolute phase 2652: 2643: 2634: 2625: 2607: 2602: 2592: 2588: 2584: 2580: 2574: 2570: 2566: 2565: 2558: 2554: 2550: 2546: 2540: 2536: 2532: 2531: 2529: 2524: 2520: 2493:Main article: 2490: 2487: 2455: 2451: 2447: 2444: 2441: 2438: 2419: 2415: 2411: 2408: 2405: 2402: 2399: 2375: 2368: 2364: 2359: 2353: 2349: 2345: 2342: 2337: 2334: 2280:Main article: 2277: 2274: 2187: 2178: 2169: 2160: 2151: 2148: 2102: 2099: 2068: 2053: 1965: 1962: 1929: 1924: 1921: 1917: 1909: 1905: 1902: 1899: 1892: 1889: 1887: 1883: 1879: 1875: 1874: 1868: 1864: 1861: 1858: 1851: 1848: 1846: 1842: 1838: 1834: 1833: 1820: 1813: 1806: 1799: 1792: 1785: 1757: 1748: 1738: 1731: 1708: 1705: 1701: 1694: 1688: 1683: 1678: 1674: 1670: 1665: 1660: 1655: 1650: 1646: 1642: 1636: 1632: 1629: 1604: 1597: 1590: 1583: 1547: 1544: 1541: 1538: 1536: 1534: 1531: 1528: 1525: 1522: 1518: 1513: 1508: 1504: 1498: 1492: 1488: 1484: 1480: 1474: 1469: 1465: 1459: 1455: 1449: 1445: 1441: 1438: 1436: 1434: 1429: 1425: 1419: 1415: 1411: 1406: 1402: 1396: 1392: 1388: 1383: 1379: 1373: 1369: 1365: 1362: 1360: 1357: 1353: 1350: 1344: 1341: 1334: 1327: 1324: 1318: 1314: 1310: 1307: 1301: 1298: 1291: 1284: 1281: 1275: 1274: 1265:must be zero: 1241: 1224: 1198: 1193: 1188: 1184: 1178: 1175: 1172: 1170: 1166: 1162: 1158: 1157: 1152: 1147: 1143: 1137: 1134: 1132: 1128: 1124: 1120: 1119: 1104:is related to 1053:is called the 1011: 990: 970: 963: 956: 949: 927: 916: 902: 897: 894: 891: 888: 885: 882: 879: 876: 872: 865: 859: 856: 855: 850: 846: 842: 841: 836: 832: 828: 827: 825: 820: 814: 808: 805: 800: 795: 792: 786: 782: 779: 776: 772: 765: 759: 756: 755: 750: 746: 742: 741: 736: 732: 728: 727: 725: 720: 717: 714: 711: 708: 705: 699: 696: 671: 668: 665: 662: 659: 656: 653: 650: 646: 639: 633: 630: 629: 624: 620: 616: 615: 610: 606: 602: 601: 599: 594: 588: 582: 579: 574: 569: 566: 560: 556: 553: 550: 546: 539: 533: 530: 529: 524: 520: 516: 515: 510: 506: 502: 501: 499: 494: 491: 488: 485: 482: 479: 473: 470: 417: 410: 280: 277: 263:stochastically 237: 234: 230: 227: 123:magnetic field 119:electric field 26: 9: 6: 4: 3: 2: 6462: 6451: 6448: 6446: 6443: 6441: 6438: 6436: 6433: 6431: 6428: 6427: 6425: 6416: 6413: 6411: 6408: 6405: 6402: 6399: 6396: 6394: 6391: 6389: 6386: 6383: 6380: 6378: 6375: 6374: 6363: 6358: 6354: 6352:0-7503-0673-4 6348: 6344: 6340: 6336: 6332: 6330:0-521-25862-6 6326: 6322: 6317: 6313: 6308: 6304: 6302:0-8247-4053-X 6298: 6294: 6289: 6285: 6283:0-387-22493-9 6279: 6275: 6270: 6266: 6264:0-8194-5868-6 6260: 6256: 6251: 6247: 6245:0-471-14302-2 6241: 6237: 6232: 6228: 6226:0-521-64222-1 6222: 6218: 6217: 6211: 6207: 6205:0-444-87016-4 6201: 6197: 6192: 6191: 6178: 6174: 6169: 6164: 6160: 6156: 6152: 6148: 6144: 6140: 6136: 6132: 6128: 6121: 6106: 6102: 6098: 6092: 6077: 6073: 6069: 6065: 6061: 6056: 6051: 6047: 6043: 6039: 6032: 6024: 6020: 6015: 6010: 6005: 6000: 5996: 5992: 5987: 5982: 5978: 5974: 5970: 5963: 5955: 5949: 5946:. CRC Press. 5945: 5938: 5936: 5934: 5932: 5923: 5921:0-262-52047-8 5917: 5912: 5911: 5902: 5894: 5890: 5886: 5882: 5878: 5874: 5870: 5863: 5855: 5851: 5847: 5843: 5839: 5835: 5832:(4): 336–43. 5831: 5827: 5820: 5812: 5808: 5804: 5800: 5796: 5792: 5787: 5782: 5778: 5774: 5767: 5759: 5755: 5751: 5747: 5743: 5739: 5735: 5731: 5726: 5721: 5717: 5713: 5706: 5698: 5692: 5688: 5681: 5672: 5667: 5662: 5657: 5652: 5647: 5643: 5639: 5635: 5628: 5620: 5614: 5610: 5606: 5605:W. H. Freeman 5602: 5601: 5596: 5589: 5581: 5577: 5573: 5569: 5565: 5561: 5557: 5550: 5542: 5536: 5532: 5525: 5517: 5511: 5507: 5500: 5492: 5486: 5482: 5475: 5467: 5461: 5457: 5450: 5442: 5436: 5433:. CRC Press. 5432: 5425: 5417: 5415:0-8053-8566-5 5411: 5407: 5400: 5398: 5396: 5387: 5385:0-262-52047-8 5381: 5376: 5375: 5366: 5358: 5356:0-8053-8566-5 5352: 5348: 5341: 5339: 5330: 5323: 5315: 5311: 5307: 5303: 5299: 5295: 5288: 5274: 5268: 5264: 5263: 5255: 5241: 5235: 5231: 5230: 5222: 5214: 5208: 5200: 5196: 5194:9780071475747 5190: 5186: 5185: 5177: 5169: 5163: 5159: 5158: 5150: 5139: 5135: 5129: 5122: 5121: 5113: 5106: 5098: 5092: 5088: 5084: 5080: 5073: 5071: 5062: 5058: 5054: 5052:0-486-60590-6 5048: 5044: 5039: 5038: 5029: 5021: 5017: 5013: 5009: 5005: 5001: 4997: 4993: 4986: 4978: 4972: 4968: 4961: 4953: 4951:0-13-805326-X 4947: 4943: 4942: 4934: 4926: 4920: 4916: 4915: 4907: 4905: 4896: 4890: 4886: 4885: 4877: 4869: 4865: 4861: 4855: 4851: 4847: 4842: 4837: 4833: 4826: 4818: 4816:0-13-244182-9 4812: 4808: 4807: 4799: 4791: 4785: 4781: 4780: 4772: 4770: 4761: 4755: 4751: 4750: 4742: 4734: 4732:0-7487-1584-3 4728: 4724: 4723: 4715: 4707: 4701: 4697: 4696: 4688: 4684: 4669: 4666: 4664: 4661: 4659: 4656: 4654: 4651: 4649: 4646: 4644: 4641: 4639: 4636: 4634: 4631: 4629: 4626: 4624: 4621: 4619: 4616: 4614: 4611: 4609: 4606: 4605: 4604: 4599: 4596: 4594: 4591: 4590: 4589: 4580: 4578: 4574: 4570: 4566: 4556: 4554: 4550: 4545: 4543: 4539: 4535: 4534:mantis shrimp 4531: 4527: 4523: 4519: 4515: 4511: 4506: 4492: 4488: 4485: 4481: 4477: 4474:as mentioned 4473: 4469: 4465: 4461: 4457: 4452: 4449: 4445: 4441: 4436: 4433: 4427: 4424: 4420: 4416: 4412: 4407: 4402: 4399: 4395: 4389: 4379: 4376: 4372: 4367: 4361: 4359: 4355: 4350: 4346: 4342: 4337: 4335: 4331: 4327: 4323: 4319: 4309: 4307: 4303: 4299: 4295: 4291: 4287: 4283: 4279: 4275: 4271: 4267: 4263: 4255: 4250: 4246: 4243: 4239: 4235: 4231: 4227: 4219: 4214: 4209: 4199: 4197: 4193: 4188: 4186: 4182: 4179:, after whom 4178: 4169: 4162: 4156: 4142: 4140: 4136: 4132: 4128: 4124: 4120: 4116: 4112: 4108: 4104: 4100: 4094: 4084: 4082: 4078: 4077: 4072: 4068: 4064: 4060: 4056: 4046: 4037: 4035: 4031: 4027: 4022: 4020: 4016: 4012: 4008: 4000: 3997: 3992: 3983: 3981: 3977: 3973: 3968: 3964: 3960: 3956: 3951: 3946: 3936: 3934: 3929: 3925: 3916: 3907: 3898: 3896: 3892: 3886: 3879: 3872: 3867: 3854: 3850: 3845: 3843: 3839: 3835: 3831: 3827: 3823: 3819: 3815: 3807: 3803: 3798: 3794: 3792: 3788: 3784: 3780: 3776: 3766: 3759: 3752: 3746: 3738: 3729: 3724: 3720: 3711: 3701: 3691: 3680: 3675: 3671: 3664: 3662: 3661:diattenuating 3658: 3657: 3646: 3644: 3640: 3637: 3633: 3628: 3627:birefringence 3624: 3613: 3609: 3607: 3603: 3599: 3594: 3589: 3587: 3578: 3574: 3569: 3565: 3560: 3558: 3554: 3553: 3542: 3533: 3526: 3522: 3518: 3514: 3508: 3507:Birefringence 3501:Birefringence 3498: 3495: 3489: 3483: 3478: 3473: 3469: 3461: 3452: 3446: 3433: 3428: 3425: 3413: 3405: 3401: 3395: 3388: 3381: 3377: 3370: 3360: 3346: 3344: 3336: 3330: 3317: 3304: 3299: 3286: 3281: 3276: 3269: 3264: 3262: 3261:diattenuation 3258: 3254: 3253:birefringence 3250: 3230: 3227: 3224: 3221: 3217: 3207: 3198: 3185: 3177: 3171: 3168: 3162: 3156: 3153: 3149: 3142: 3139: 3136: 3125: 3119: 3113: 3110: 3107: 3104: 3098: 3095: 3078: 3071: 3066: 3062: 3045:polarization. 3043: 3038: 3034: 3032: 3031: 3026: 3025: 3019: 3017: 3013: 3009: 3005: 3001: 2996: 2994: 2990: 2986: 2982: 2975: 2964: 2962: 2954: 2946: 2944: 2940: 2932: 2924: 2906: 2898: 2894: 2890: 2881: 2879: 2875: 2871: 2867: 2863: 2859: 2855: 2848: 2844: 2840: 2836: 2830: 2823: 2818: 2814: 2810: 2809: 2799: 2792: 2788: 2782: 2769: 2763: 2759: 2755: 2751: 2745: 2739: 2733: 2716: 2708: 2704: 2699: 2697: 2693: 2689: 2678: 2676: 2675:inner product 2672: 2668: 2664: 2659: 2651: 2642: 2633: 2624: 2618: 2605: 2600: 2590: 2586: 2582: 2578: 2572: 2568: 2556: 2552: 2548: 2544: 2538: 2534: 2527: 2522: 2509: 2507: 2503: 2496: 2486: 2475: 2453: 2449: 2445: 2442: 2439: 2436: 2417: 2413: 2409: 2406: 2403: 2400: 2397: 2389: 2373: 2366: 2362: 2357: 2351: 2347: 2343: 2340: 2335: 2332: 2325: 2321: 2316: 2312: 2308: 2297: 2288: 2283: 2273: 2271: 2268: 2263: 2261: 2257: 2249: 2228: 2225: 2221: 2216: 2207: 2199: 2194: 2192: 2185: 2183: 2176: 2174: 2164: 2155: 2150: 2146: 2144: 2121: 2116: 2112: 2108: 2098: 2096: 2091: 2087: 2083: 2079: 2075: 2070: 2066: 2064: 2059: 2057: 2051: 2049: 2048:optical fiber 2045: 2041: 2040:Surface waves 2037: 2033: 2028: 2022: 2016: 2010: 2005: 2001: 1997: 1992: 1988: 1983: 1979: 1975: 1970: 1961: 1953: 1927: 1922: 1919: 1915: 1907: 1903: 1900: 1897: 1890: 1888: 1881: 1877: 1866: 1862: 1859: 1856: 1849: 1847: 1840: 1836: 1784: 1780: 1773: 1760: 1751: 1727: 1722: 1706: 1703: 1699: 1692: 1686: 1681: 1676: 1672: 1668: 1663: 1658: 1653: 1648: 1644: 1640: 1634: 1630: 1627: 1619: 1615: 1574: 1567: 1565: 1545: 1542: 1539: 1537: 1529: 1526: 1523: 1520: 1516: 1511: 1506: 1502: 1496: 1490: 1486: 1482: 1478: 1472: 1467: 1463: 1457: 1453: 1447: 1443: 1439: 1437: 1427: 1423: 1417: 1413: 1409: 1404: 1400: 1394: 1390: 1386: 1381: 1377: 1371: 1367: 1363: 1361: 1355: 1351: 1348: 1339: 1332: 1322: 1316: 1312: 1308: 1305: 1296: 1289: 1279: 1263: 1257: 1252: 1248: 1240: 1230: 1223: 1213: 1196: 1191: 1186: 1182: 1176: 1173: 1171: 1164: 1160: 1150: 1145: 1141: 1135: 1133: 1126: 1122: 1108: 1102: 1094: 1089: 1070: 1064: 1058: 1056: 1037: 1028: 1022: 1016: 1009: 1006: 1002: 997: 989: 985: 981: 977: 944: 940: 931: 926:in the medium 925: 922: 900: 892: 889: 886: 883: 880: 874: 870: 863: 857: 848: 844: 834: 830: 823: 818: 812: 806: 803: 798: 793: 790: 784: 780: 777: 774: 770: 763: 757: 748: 744: 734: 730: 723: 718: 712: 709: 706: 694: 666: 663: 660: 657: 654: 648: 644: 637: 631: 622: 618: 608: 604: 597: 592: 586: 580: 577: 572: 567: 564: 558: 554: 551: 548: 544: 537: 531: 522: 518: 508: 504: 497: 492: 486: 483: 480: 468: 448: 434: 430: 426: 420: 413: 396: 390: 376: 372: 359: 354: 348: 342: 336: 331: 327: 324: 321: 317: 309: 303: 297: 291: 285: 276: 274: 273: 268: 264: 260: 256: 252: 242: 233: 226: 224: 220: 216: 212: 208: 204: 200: 195: 192: 188: 184: 180: 176: 173:According to 171: 169: 165: 161: 160:birefringence 157: 153: 152: 147: 142: 140: 136: 132: 128: 124: 120: 116: 111: 110:) in solids. 109: 105: 101: 97: 93: 88: 84: 80: 79:guitar string 76: 72: 68: 64: 57: 53: 41: 37: 33: 19: 6361: 6342: 6320: 6311: 6292: 6276:. Springer. 6273: 6254: 6235: 6214: 6195: 6134: 6130: 6120: 6109:. Retrieved 6100: 6091: 6080:. Retrieved 6045: 6041: 6031: 5979:(5): e2190. 5976: 5972: 5962: 5943: 5909: 5901: 5876: 5872: 5862: 5829: 5825: 5819: 5776: 5772: 5766: 5715: 5711: 5705: 5689:. Springer. 5686: 5680: 5641: 5637: 5627: 5599: 5588: 5563: 5559: 5549: 5530: 5524: 5505: 5499: 5480: 5474: 5455: 5449: 5430: 5424: 5405: 5373: 5365: 5346: 5328: 5322: 5297: 5293: 5287: 5276:. Retrieved 5261: 5254: 5243:. Retrieved 5228: 5221: 5198: 5183: 5176: 5156: 5149: 5119: 5105: 5078: 5036: 5028: 4995: 4991: 4985: 4966: 4960: 4940: 4933: 4913: 4883: 4876: 4831: 4825: 4805: 4798: 4778: 4748: 4741: 4721: 4714: 4694: 4687: 4602: 4587: 4562: 4546: 4512:, including 4502: 4453: 4437: 4428: 4419:whip antenna 4405: 4403: 4391: 4374: 4370: 4362: 4341:stereoscopic 4338: 4315: 4259: 4223: 4189: 4174: 4096: 4074: 4052: 4043: 4023: 4004: 3975: 3971: 3966: 3962: 3952: 3948: 3945:Ellipsometry 3939:Ellipsometry 3921: 3904: 3894: 3890: 3884: 3877: 3870: 3852: 3848: 3846: 3841: 3833: 3829: 3825: 3821: 3817: 3811: 3805: 3801: 3790: 3786: 3772: 3757: 3750: 3736: 3727: 3709: 3699: 3689: 3678: 3667: 3665: 3660: 3654: 3652: 3619: 3616:dimensions). 3595: 3582: 3550: 3540: 3531: 3513:birefringent 3510: 3493: 3487: 3476: 3459: 3450: 3447: 3347: 3343:phase factor 3331: 3285:Jones matrix 3279: 3265: 3199: 3076: 3069: 3058: 3036: 3028: 3022: 3021:A so-called 3020: 2997: 2993:uncorrelated 2989:polarization 2979: 2947: 2925: 2892: 2888: 2887: 2877: 2873: 2869: 2865: 2861: 2857: 2850: 2847:pi-polarized 2846: 2842: 2838: 2832: 2826: 2816: 2812: 2806: 2804: 2797: 2790: 2786: 2780: 2767: 2761: 2757: 2753: 2749: 2743: 2737: 2731: 2709:designations 2706: 2702: 2684: 2649: 2640: 2631: 2622: 2619: 2510: 2506:Jones vector 2504:vector (the 2498: 2495:Jones vector 2489:Jones vector 2473: 2387: 2324:eccentricity 2314: 2310: 2306: 2295: 2292: 2272: 2265:Any pair of 2264: 2259: 2255: 2229: 2219: 2212: 2188: 2179: 2170: 2142: 2126: 2090:shear stress 2071: 2060: 2046:(such as an 2026: 2020: 2014: 2008: 1990: 1981: 1971: 1967: 1951: 1782: 1778: 1755: 1746: 1725: 1723: 1614:Jones vector 1572: 1568: 1261: 1255: 1238: 1228: 1221: 1214: 1106: 1100: 1087: 1068: 1062: 1059: 1035: 1026: 1020: 1014: 1004: 1000: 987: 983: 979: 942: 938: 920: 446: 415: 408: 394: 388: 374: 370: 352: 346: 340: 334: 314: 307: 301: 295: 289: 270: 267:distribution 247: 232: 229:Introduction 196: 172: 149: 143: 112: 74: 71:oscillations 61:polarisation 58: 50:Polarization 47: 46: 36: 32:Polarization 5607:. pp. 4628:Nicol prism 4623:Kerr effect 4430:is used in 4302:polar clock 4181:Malus's law 4103:outer space 4081:polarimeter 4063:enantiomers 4030:shear waves 4015:microscopes 3924:engineering 3672:or simply " 3604:fluids, or 3586:wave plates 3468:phase delay 3283:known as a 3024:depolarizer 2874:σ-polarized 2834:s-polarized 2828:p-polarized 2320:axial ratio 2307:ellipticity 2215:phase shift 2078:sound waves 1998:(or in the 1974:anisotropic 1948:(such that 1251:dot product 1055:wave vector 320:homogeneous 251:plane waves 108:shear waves 100:radio waves 87:sound waves 75:(see image) 6424:Categories 6339:Pye, David 6159:10023/4019 6111:2019-08-27 6082:2019-08-27 5779:(4): 001. 5278:2023-01-20 5245:2023-01-20 4841:1607.04202 4789:8121908175 4675:References 4547:The naked 4530:cuttlefish 4480:short wave 4460:ionosphere 4386:See also: 4366:convention 4185:sunglasses 4059:mineralogy 4026:seismology 4011:mineralogy 3999:sand grain 3933:cellophane 3866:convention 3674:polarizers 3577:polarizers 3547:| = 1 3472:eigenmodes 3335:dispersive 3206:wavenumber 3000:incoherent 2854:-polarized 2713:See also: 2267:orthogonal 2095:seismology 1762:| = 1 1564:orthogonal 976:wavenumber 433:real parts 358:plane wave 255:wavevector 211:microwaves 203:seismology 191:right hand 139:right-hand 85:, such as 6238:. Wiley. 6064:0022-0949 5986:0804.2162 5893:1476-1122 5854:221585816 5651:0705.0885 5580:0733-8635 5207:cite book 5061:924844798 4868:119283594 4668:Waveplate 4648:Polarizer 4549:human eye 4466:, causes 4345:3D movies 4322:backlight 4242:scattered 4230:scattered 4163:sunlight. 4139:chirality 4099:astronomy 4087:Astronomy 4049:Chemistry 3955:thin film 3745:intensity 3649:Dichroism 3645:in 1669. 3426:− 3257:dichroism 3228:ω 3222:− 3175:Δ 3172:− 3166:Δ 3117:Δ 3102:Δ 3030:polarizer 2822:senkrecht 2688:astronomy 2587:θ 2553:θ 2454:ε 2443:⁡ 2407:⁡ 2398:χ 2344:− 2044:waveguide 1923:ϕ 1901:− 1707:η 1618:intensity 1527:⋅ 1512:η 1473:η 1458:− 1343:→ 1326:→ 1317:⋅ 1300:→ 1283:→ 1192:η 1177:− 1151:η 890:ω 887:− 799:− 794:λ 781:π 698:→ 664:ω 661:− 573:− 568:λ 555:π 472:→ 323:isotropic 164:dichroism 156:polarizer 6341:(2001). 6177:23982323 6137:: 2374. 6105:Archived 6101:BBC News 6076:Archived 6023:18478095 5973:PLOS ONE 5811:17250080 5758:10424288 5750:16605810 5597:(2003). 5138:Archived 5020:14683185 4583:See also 4565:momentum 4444:ghosting 4398:antennas 4290:sunstone 4282:twilight 4234:aerosols 4196:plastics 4007:minerals 3996:volcanic 3656:dichroic 3639:crystals 3623:rotation 3552:dichroic 3300:′ 2774:-plane. 2076:such as 2067:entirely 2063:radially 1950:−1 < 1232:, where 423:. Using 272:spectrum 131:circular 94:such as 6168:3763500 6139:Bibcode 6072:9317897 6014:2377063 5991:Bibcode 5834:Bibcode 5791:Bibcode 5730:Bibcode 5656:Bibcode 5609:169–172 5302:Bibcode 5000:Bibcode 4603:Optics 4538:pigeons 4522:octopus 4510:insects 4505:animals 4458:in the 4375:blocked 4330:helices 4286:Vikings 4067:racemic 4055:geology 4040:Autopsy 3986:Geology 3980:in situ 3636:calcite 3277:matrix 3204:is the 2937:of the 2658:modulus 2502:complex 2386:or the 1245:is the 928:(whose 425:complex 183:photons 181:called 6349: 6327: 6299: 6280: 6261: 6242: 6223: 6202: 6175: 6165: 6070: 6062: 6021: 6011: 5950: 5918: 5891: 5852: 5809: 5756: 5748: 5693: 5615: 5578: 5537: 5512: 5487: 5462: 5437: 5412: 5406:Optics 5382: 5353: 5347:Optics 5269: 5236: 5191: 5164: 5130: 5093: 5059: 5049: 5018: 4973: 4948: 4921: 4891: 4866: 4856: 4813: 4786: 4756: 4729: 4702: 4542:homing 4532:, and 4440:ground 4240:. The 4119:masers 3893:- and 3789:- and 3715:< 1 3602:chiral 3590:unless 3529:| 3448:where 3200:where 3061:vacuum 2961:vector 2931:strain 2819:(from 2817:s-like 2813:p-like 2741:, and 2665:. 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Polarization (waves)

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