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:
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
4249:
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
3568:
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.
241:
3915:
284:
2287:
4491:
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.
3797:
1560:
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
4155:
4213:
2120:
3612:
2206:
40:
1268:
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:
3991:
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
4244:
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
1968:
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
4450:
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
4429:
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
4400:
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,
3888:
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
3620:
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
193:
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,
4486:
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.
4351:
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
248:
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
4434:
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.
2499:
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
4425:
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
4377:
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
3949:
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
4363:
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
3930:
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
2293:
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
2226:
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
3686:
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
2127:
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
3039:
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
3592:
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
3863:
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
2269:
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.
1942:
3044:
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
3615:
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.
4158:
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.
3444:
2198:
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.
4368:
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
2720:
2616:
3583:
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
2686:
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
3563:
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.
1720:
3196:
2660:
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
4044:
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."
2217:
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
3905:
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.
3629:
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
3484:
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
1827:
2140:
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
3332:
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
89:
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
3351:
3978:
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
3889:
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.
3773:
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
2724:
2723:
2725:
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.
356:
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
4328:
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
55:
4551:
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.
2722:
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
3027:
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
4171:
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.
3953:
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
3266:
In such media, an electromagnetic wave with any given state of polarization may be decomposed into two orthogonally polarized components that encounter different
4053:
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
4339:
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
2254:
being in the plane of incidence. Since there are separate reflection coefficients for the linear polarizations in and orthogonal to the plane of incidence (
125:
which are always perpendicular to each other; by convention, the "polarization" of electromagnetic waves refers to the direction of the electric field. In
2061:
Even in free space, longitudinal field components can be generated in focal regions, where the plane wave approximation breaks down. An extreme example is
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
1969:
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
4024:
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
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:
5951:
5694:
5616:
5538:
5513:
5488:
5463:
5438:
5270:
5237:
5165:
5131:
5094:
4974:
4922:
4892:
4857:
4703:
4130:
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)
2694:
is generally used instead, with the zero azimuth (or position angle, as it is more commonly called in astronomy to avoid confusion with the
3555:
in the sense of polarization), in which only the amplitudes of the two polarizations are affected differentially, may be described using a
2162:
974:
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
2153:
4417:
with horizontal conductors, as viewed from a second station toward the horizon, is necessarily horizontally polarized. But a vertical "
3950:
ellipsometry relies on reflection, it is not required for the sample to be transparent to light or for its back side to be accessible.
2721:
6434:
4757:
4360:); a normal diffuse white projection screen causes depolarization of the projected images, making it unsuitable for this application.
6350:
6328:
6300:
6281:
6262:
6243:
6224:
6203:
5919:
5413:
5383:
5354:
5192:
5050:
4949:
4814:
4730:
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:
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
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".
4217:
4207:
4187:
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.
2172:
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
6444:
5212:
4882:
4787:
4597:
4572:
4517:
3847:
In the important special case of reflection at normal incidence (not involving anisotropic materials) there is no particular
6312:
Secrets of the Viking
Navigators: How the Vikings used their amazing sunstones and other techniques to cross the open oceans
4141:
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
4167:
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
6429:
6075:
4229:
2181:
31:
4571:
if it is circularly polarized (or partially so). In comparison with lower frequencies such as microwaves, the amount of
2695:
2691:
2190:
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
3782:
2035:
3247:
When an electromagnetic wave interacts with matter, its propagation is altered according to the material's (complex)
2952:
4248:
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}}}
4642:
3868:
this is specified relative to the direction of propagation. The circular rotation of the electric field around the
2930:
2323:
2941:. The polarization of the photoluminescence is related to the strain in a material by way of the given material's
6439:
6403:
4463:
4265:
4092:
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.
6449:
266:
3844:- (horizontal) polarization, most of the glare due to reflection from a wet street, for instance, is removed.
6381:
1620:
of the light wave is proportional to the sum of the squared magnitudes of the two electric field components:
4612:
2992:
2328:
2114:
1995:
1246:
134:
3015:
5555:
4317:
4176:
3958:
3718:
3041:
2988:
2942:
2666:
4617:
4114:
2923:
is calculated as the fraction of the total power that is carried by the polarized component of the wave.
2432:
6338:
4592:
4443:
4365:
4325:
4134:
3865:
3274:
3007:
2611:{\displaystyle \mathbf {e} ={\begin{bmatrix}a_{1}e^{i\theta _{1}}\\a_{2}e^{i\theta _{2}}\end{bmatrix}}.}
2110:
2031:
1999:
1986:
1977:
319:
315:
130:
4990:
Dorn, R.; Quabis, S. & Leuchs, G. (Dec 2003). "Sharper Focus for a
Radially Polarized Light Beam".
4245:
optimize the results of photographing scenes in which reflection or scattering by the sky is involved.
4237:
2766:
along with 3 planar projections and a deformation surface of total electric field. The light is always
2065:
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 (
6215:
6138:
5990:
5833:
5790:
5729:
5655:
5301:
4999:
4652:
4637:
4607:
4552:
4431:
4414:
4348:
3837:
3267:
3023:
3011:
3010:
light. Conversely, the two constituent linearly polarized states of unpolarized light cannot form an
2896:
2281:
2246:
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
114:
91:
6096:
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;
4657:
4289:
4261:
4241:
4160:
3813:
3642:
3622:
3334:
3248:
3003:
2999:
2393:
2106:
2062:
1617:
178:
126:
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
197:
Polarization is an important parameter in areas of science dealing with transverse waves, such as
5980:
5849:
5806:
5780:
5753:
5719:
5645:
5206:
4863:
4835:
4662:
4576:
4471:
4305:
4033:
4018:
2960:
2807:
2223:
1715:{\displaystyle I=\left(\left|e_{x}\right|^{2}+\left|e_{y}\right|^{2}\right)\,{\frac {1}{2\eta }}}
218:
103:
5608:
5598:
5077:
Sletten, Mark A.; Mc
Laughlin, David J. (2005-04-15). "Radar Polarimetry". In Chang, Kai (ed.).
3191:{\displaystyle \mathbf {e} (z+\Delta z,t+\Delta t)=\mathbf {e} (z,t)e^{ik(c\Delta t-\Delta z)},}
5042:
3567:
1249:. The impedance will be complex in a conducting medium. Note that given that relationship, the
6346:
6324:
6296:
6277:
6258:
6239:
6220:
6199:
6172:
6067:
6059:
6018:
5947:
5915:
5888:
5745:
5690:
5612:
5575:
5534:
5509:
5484:
5459:
5434:
5409:
5379:
5350:
5266:
5260:
5233:
5188:
5161:
5155:
5127:
5090:
5056:
5046:
5015:
4970:
4945:
4918:
4888:
4853:
4810:
4783:
4753:
4726:
4699:
4422:
4122:
4106:
4070:
3778:
2980:
2973:
2938:
2904:
2714:
2073:
995:
174:
150:
145:
82:
6162:
6154:
6146:
6049:
6008:
5998:
5880:
5841:
5798:
5737:
5665:
5567:
5309:
5082:
5007:
4845:
4568:
4467:
4455:
4410:
4333:
4297:
4253:
4126:
4075:
3774:
3722:
3605:
3597:
3556:
3520:
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
929:
329:
287:
A "vertically polarized" electromagnetic wave of wavelength λ has its electric field vector
271:
258:
167:
66:
2638:
denote the amplitude of the wave in the two components of the electric field vector, while
2034:
can be launched into a medium whose refractive index has a significant imaginary part (or "
240:
4397:
4387:
4191:
3914:
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
2247:
2209:
A circularly polarized wave as a sum of two linearly polarized components 90° out of phase
2055:
190:
138:
5554:
Alawi, Faizan; Shields, Bridget E.; Omolehinwa, Temitope; Rosenbach, Misha (2020-10-01).
144:
Light or other electromagnetic radiation from many sources, such as the sun, flames, and
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 (
2119:
6167:
6126:
6013:
5968:
5908:
5594:
5372:
5035:
4939:
4632:
4293:
4180:
3524:
3516:
3481:
3284:
3064:
2662:
2657:
2505:
2501:
1092:
424:
262:
186:
148:, consists of short wave trains with an equal mixture of polarizations; this is called
122:
118:
4575:, even of pure circular polarization, compared to the same wave's linear momentum (or
4490:
2286:
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
283:
6423:
5853:
5604:
4867:
4541:
4533:
4357:
3927:
3626:
3572:
3506:
3252:
2674:
2477:. The special cases of linear and circular polarization correspond to an ellipticity
2266:
2214:
2047:
431:) notation, the instantaneous physical electric and magnetic fields are given by the
159:
137:, the fields rotate at a constant rate in a plane as the wave travels, either in the
78:
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
17:
4439:
4418:
3979:
3944:
3631:
3512:
3342:
3260:
2670:
2494:
2089:
2039:
1613:
5741:
5011:
4154:
3796:
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:
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
6376:
4627:
4622:
4352:
head, and is widely used in 3-D movie exhibition today, such as the system from
4340:
4301:
4212:
4102:
4080:
4062:
4029:
3923:
3467:
3345:
and attenuation factor), implying no change in polarization during propagation.
2322:). The ellipticity parameter is an alternative parameterization of an ellipse's
2319:
2197:
1973:
1250:
1054:
325:
70:
6037:
4849:
4567:
in the direction of propagation. In addition, however, light carries a certain
3800:
A stack of plates at
Brewster's angle to a beam reflects off a fraction of the
6414:
5670:
5633:
5571:
5086:
4529:
4479:
4459:
4184:
4058:
4025:
4014:
4010:
3998:
3932:
3744:
3585:
3205:
2205:
2094:
2077:
1563:
975:
357:
254:
250:
202:
107:
99:
86:
6063:
5892:
5579:
5060:
194:
with equal amplitude and phases synchronized to give oscillation in a plane.
4667:
4647:
4548:
4321:
4300:
from Asia to Europe in the 12th century. Related to the sky compass is the "
4138:
4098:
3954:
3804:-polarized light at each surface, leaving (after many such plates) a mainly
3673:
3655:
3576:
3471:
3256:
3029:
2687:
2043:
432:
322:
210:
163:
155:
6176:
6022:
5749:
5313:
5019:
3611:
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:
154:. Polarized light can be produced by passing unpolarized light through a
6387:
5785:
5724:
4564:
4563:
It is well known that electromagnetic radiation carries a certain linear
4483:
4281:
4233:
3995:
3551:
1612:
component which is necessarily zero for a transverse wave) is known as a
3666:
Devices that block nearly all of the radiation in one mode are known as
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
43:
Circular polarization on rubber thread, converted to linear polarization
39:
6150:
6125:
Dholakia, Kishan; Mazilu, Michael; Arita, Yoshihiko (August 28, 2013).
5845:
4521:
4344:
4329:
4195:
4066:
4054:
4006:
3638:
3635:
2500:
phase information can be conveniently represented as a two-dimensional
2250:
polarizations. Axes are selected to suit a particular problem, such as
249:
and polarization in particular, it is easier to just consider coherent
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).
4830:
Le Tiec, A.; Novak, J. (July 2016). "Theory of Gravitational Waves".
4537:
4509:
4504:
4285:
3601:
3060:
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
2003:
428:
198:
182:
5884:
5824:
Clark, S. (1999). "Polarised starlight and the handedness of Life".
4881:
Lipson, Stephen G.; Lipson, Henry; Tannhauser, David Stefan (1995).
4032:) are termed SH and SV, while waves with longitudinal polarization (
4005:
The property of (linear) birefringence is widespread in crystalline
3990:
2054:
transverse waves, but might be described as an electric or magnetic
4840:
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:
4525:
4489:
4447:
4393:
4353:
4277:
4260:
Sky polarization has been used for orientation in navigation. The
4247:
4211:
4166:
4153:
4118:
3989:
3913:
3795:
3610:
3566:
2984:
2718:
2204:
2196:
2118:
2085:
2081:
2038:") such as metals; these fields are also not strictly transverse.
282:
239:
222:
214:
206:
95:
38:
6388:
MathPages: The relationship between photon spin and polarization
4520:. Polarization sensitivity has also been observed in species of
4273:
4110:
3559:(generally multiplied by a common phase factor). In fact, since
1771:
293:(red) oscillating in the vertical direction. The magnetic field
5531:
An Introduction to Seismology, Earthquakes, and Earth Structure
4133:
is being used to study the physics of the very early universe.
265:
as a weighted combination of such uncorrelated waves with some
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).
4513:
4494:
Circular polarization through an airplane plastic window, 1989
4269:
4225:
3743:. Since Jones vectors refer to waves' amplitudes (rather than
3687:
unpolarized light is passed through an ideal polarizer (where
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
2955:
representation of a polarized beam. In this representation,
253:; these are sinusoidal waves of one particular direction (or
5771:
Tegmark, Max (2005). "What does inflation really predict?".
4264:
was used in the 1950s when navigating near the poles of the
3341:
Jones matrix is the identity matrix (multiplied by a scalar
2285:
2161:
2152:
4013:, this property is frequently exploited using polarization
1994:
still obey the above geometry but due to anisotropy in the
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.
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).
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.
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
5869:"Chiral selection on inorganic crystalline surfaces"
5634:"A review of maser polarization and magnetic fields"
5160:. Vol. 2: Applications. Elsevier. p. 177.
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
5638:
Proceedings of the International Astronomical Union
4194:(e.g., car windows) or items made from transparent
2895:) is a quantity used to describe the portion of an
2069:longitudinal (along the direction of propagation).
69:which specifies the geometrical orientation of the
5907:
5371:
5034:
3438:
3322:
3237:
3190:
2610:
2458:
2422:
2378:
1936:
1714:
1554:
1205:
905:
676:
129:, the fields oscillate in a single direction. In
4544:, but research indicates this is a popular myth.
1008:. In a more general formulation with propagation
5910:Electromagnetic Vibrations, Waves, and Radiation
5867:Hazen, Robert M.; Sholl, David S. (2003-06-01).
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
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).
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
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:
8:
5399:
5397:
5395:
5184:Antenna Engineering Handbook, Fourth Edition
5079:Encyclopedia of RF and Microwave Engineering
4771:
4769:
4695:An Introduction to Physical Science, 14th Ed
4559:Angular momentum using circular polarization
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.
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:
5072:
5070:
1810:may be complex. Under these restrictions,
868:
768:
642:
542:
458:) these complex fields can be written as:
6274:Polarization Optics in Telecommunications
6166:
6053:
6012:
6002:
5984:
5784:
5723:
5669:
5659:
5649:
5600:Organic Chemistry: Structure and Function
4906:
4904:
4839:
4782:. S. Chand Publishing. pp. 198–199.
4426:elevations it is elliptically polarized.
3424:
3419:
3404:
3380:
3368:
3363:
3355:
3353:
3312:
3307:
3294:
3292:
3220:
3214:
3152:
3128:
3087:
3085:
2967:Unpolarized and partially polarized light
2841:-polarization is commonly referred to as
2589:
2581:
2571:
2555:
2547:
2537:
2525:
2517:
2515:
2448:
2434:
2412:
2395:
2365:
2356:
2350:
2338:
2330:
1918:
1913:
1893:
1880:
1852:
1839:
1831:
1829:
1697:
1696:
1685:
1675:
1657:
1647:
1625:
1505:
1499:
1489:
1466:
1460:
1446:
1426:
1416:
1403:
1393:
1380:
1370:
1337:
1336:
1320:
1319:
1294:
1293:
1277:
1276:
1272:
1270:
1185:
1179:
1163:
1144:
1138:
1125:
1117:
1115:
873:
847:
833:
821:
801:
788:
773:
747:
733:
721:
692:
691:
689:
647:
621:
607:
595:
575:
562:
547:
521:
507:
495:
466:
465:
463:
6194:Azzam, R. M. A.; Bashara, N. M. (1977).
5126:. McGraw-Hill. pp. 6.30, Fig 6.25.
4220:(right image) on the sky in a photograph
2963:measured from the center of the sphere.
2933:field in materials when considering the
5967:Sonja Kleinlogel; Andrew White (2008).
4917:. Courier Corporation. pp. 79–80.
4809:. Pearson Education. pp. 162–163.
4684:
3816:, where the reflection coefficient for
3571:Color pattern of a plastic box showing
3002:combination of vertical and horizontal
2379:{\textstyle e={\sqrt {1-b^{2}/a^{2}}},}
1018:direction, then the spatial dependence
6398:Polarization angle in satellite dishes
6295:(2nd ed.). Taylor & Francis.
6219:(7th ed.). Cambridge University.
5906:Bekefi, George; Barrett, Alan (1977).
5370:Bekefi, George; Barrett, Alan (1977).
5204:
4752:. PHI Learning Pvt. Ltd. p. 453.
4438:Especially due to the presence of the
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
5944:Polarised Light in Science and Nature
5456:Classical Optics and Its Applications
5431:Polarized Light, Revised and Expanded
2466:as is shown in the figure. The angle
7:
5327:Chandrasekhar, Subrahmanyan (2013).
5033:Chandrasekhar, Subrahmanyan (1960).
4725:. Nelson Thornes. pp. 465–467.
2459:{\textstyle =\arctan 1/\varepsilon }
261:). Incoherent states can be modeled
6362:Polarized Light, Production and Use
6097:"'Fastest spinning object' created"
5479:Randy O. Wayne (16 December 2013).
5262:Optics: Principles and Applications
5229:Polarized Light and Optical Systems
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
1569:Knowing the propagation direction (
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 (
1562:indicating that these vectors are
386:axis. Being a transverse wave the
328:medium, are properly described as
25:
6393:A virtual polarization microscope
6377:Feynman's lecture on polarization
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
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
6107:from the original on 2019-09-10
6078:from the original on 2019-08-27
6042:Journal of Experimental Biology
4944:(3rd ed.). Prentice Hall.
4941:Introduction to Electrodynamics
4208:Polarizing filter (Photography)
2845:(TM), and has also been termed
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
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.
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 (
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).
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
3928:stress induced birefringence
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:
6406:: Interactive Java tutorial
6255:Field Guide to Polarization
6213:Born, M.; Wolf, E. (1999).
4131:cosmic microwave background
4117:(e.g. hydroxyl or methanol
2903:can be calculated from the
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:
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
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
18:Polarisation (waves)
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:
6359:
6353:
6337:
6331:
6318:
6309:
6303:
6293:Polarized Light
6290:
6284:
6271:
6265:
6252:
6246:
6233:
6227:
6212:
6206:
6193:
6189:
6184:
6124:
6123:
6119:
6110:
6108:
6095:
6094:
6090:
6081:
6079:
6035:
6034:
6030:
5966:
5965:
5961:
5954:
5941:
5940:
5929:
5922:
5905:
5904:
5900:
5885:10.1038/nmat879
5866:
5865:
5861:
5823:
5822:
5818:
5770:
5769:
5765:
5709:
5708:
5704:
5697:
5684:
5683:
5679:
5644:(S242): 37–46.
5631:
5630:
5626:
5619:
5595:Schore, Neil E.
5592:
5591:
5587:
5553:
5552:
5548:
5541:
5528:
5527:
5523:
5516:
5503:
5502:
5498:
5491:
5478:
5477:
5473:
5466:
5453:
5452:
5448:
5441:
5428:
5427:
5423:
5416:
5403:
5402:
5393:
5386:
5369:
5368:
5364:
5357:
5344:
5343:
5336:
5326:
5325:
5321:
5291:
5290:
5286:
5277:
5275:
5273:
5258:
5257:
5253:
5244:
5242:
5240:
5225:
5224:
5220:
5203:
5195:
5180:
5179:
5175:
5168:
5153:
5152:
5148:
5140:
5134:
5123:
5114:
5109:
5108:
5104:
5097:
5076:
5075:
5068:
5053:
5032:
5031:
5027:
4989:
4988:
4984:
4977:
4964:
4963:
4959:
4952:
4937:
4936:
4932:
4925:
4910:
4909:
4902:
4895:
4884:Optical Physics
4880:
4879:
4875:
4860:
4829:
4828:
4824:
4817:
4802:
4801:
4797:
4790:
4775:
4774:
4767:
4760:
4745:
4744:
4740:
4733:
4722:A-level Physics
4718:
4717:
4713:
4706:
4691:
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:
3418:
3411:
3410:
3400:
3398:
3392:
3391:
3386:
3376:
3369:
3350:
3349:
3338:
3295:
3289:
3288:
3278:
3271:
3216:
3211:
3210:
3209:
3201:
3148:
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:
2585:
2577:
2567:
2564:
2563:
2551:
2543:
2533:
2526:
2512:
2511:
2497:
2491:
2482:
2478:
2471:
2467:
2431:
2430:
2392:
2391:
2361:
2346:
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:
1914:
1896:
1886:
1876:
1873:
1872:
1855:
1845:
1835:
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:
1671:
1667:
1666:
1643:
1639:
1638:
1637:
1633:
1622:
1621:
1609:
1606:
1602:
1599:
1595:
1592:
1588:
1585:
1581:
1577:
1570:
1549:
1548:
1533:
1532:
1501:
1495:
1485:
1462:
1456:
1452:
1442:
1433:
1432:
1422:
1412:
1399:
1389:
1376:
1366:
1359:
1335:
1331:
1292:
1288:
1267:
1266:
1260:
1254:
1243:
1237:
1233:
1226:
1220:
1216:
1200:
1199:
1181:
1169:
1159:
1156:
1155:
1140:
1131:
1121:
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:
869:
861:
860:
854:
853:
843:
840:
839:
829:
822:
787:
783:
769:
761:
760:
754:
753:
743:
740:
739:
729:
722:
686:
685:
643:
635:
634:
628:
627:
617:
614:
613:
603:
596:
561:
557:
543:
535:
534:
528:
527:
517:
514:
513:
503:
496:
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:
6461:
6453:
6452:
6447:
6442:
6437:
6432:
6422:
6421:
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:
24:
14:
13:
10:
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:
6370:
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:
6186:
6178:
6174:
6169:
6164:
6160:
6156:
6152:
6148:
6144:
6140:
6136:
6132:
6128:
6121:
6118:
6106:
6102:
6098:
6092:
6089:
6077:
6073:
6069:
6065:
6061:
6056:
6051:
6047:
6043:
6039:
6032:
6029:
6024:
6020:
6015:
6010:
6005:
6000:
5996:
5992:
5987:
5982:
5978:
5974:
5970:
5963:
5960:
5955:
5949:
5946:. CRC Press.
5945:
5938:
5936:
5934:
5932:
5928:
5923:
5921:0-262-52047-8
5917:
5912:
5911:
5902:
5899:
5894:
5890:
5886:
5882:
5878:
5874:
5870:
5863:
5860:
5855:
5851:
5847:
5843:
5839:
5835:
5832:(4): 336–43.
5831:
5827:
5820:
5817:
5812:
5808:
5804:
5800:
5796:
5792:
5787:
5782:
5778:
5774:
5767:
5764:
5759:
5755:
5751:
5747:
5743:
5739:
5735:
5731:
5726:
5721:
5717:
5713:
5706:
5703:
5698:
5692:
5688:
5681:
5678:
5672:
5667:
5662:
5657:
5652:
5647:
5643:
5639:
5635:
5628:
5625:
5620:
5614:
5610:
5606:
5605:W. H. Freeman
5602:
5601:
5596:
5589:
5586:
5581:
5577:
5573:
5569:
5565:
5561:
5557:
5550:
5547:
5542:
5536:
5532:
5525:
5522:
5517:
5511:
5507:
5500:
5497:
5492:
5486:
5482:
5475:
5472:
5467:
5461:
5457:
5450:
5447:
5442:
5436:
5433:. CRC Press.
5432:
5425:
5422:
5417:
5415:0-8053-8566-5
5411:
5407:
5400:
5398:
5396:
5392:
5387:
5385:0-262-52047-8
5381:
5376:
5375:
5366:
5363:
5358:
5356:0-8053-8566-5
5352:
5348:
5341:
5339:
5335:
5330:
5323:
5320:
5315:
5311:
5307:
5303:
5299:
5295:
5288:
5285:
5274:
5268:
5264:
5263:
5255:
5252:
5241:
5235:
5231:
5230:
5222:
5219:
5214:
5208:
5200:
5196:
5194:9780071475747
5190:
5186:
5185:
5177:
5174:
5169:
5163:
5159:
5158:
5150:
5147:
5139:
5135:
5129:
5122:
5121:
5113:
5106:
5103:
5098:
5092:
5088:
5084:
5080:
5073:
5071:
5067:
5062:
5058:
5054:
5052:0-486-60590-6
5048:
5044:
5039:
5038:
5029:
5026:
5021:
5017:
5013:
5009:
5005:
5001:
4997:
4993:
4986:
4983:
4978:
4972:
4968:
4961:
4958:
4953:
4951:0-13-805326-X
4947:
4943:
4942:
4934:
4931:
4926:
4920:
4916:
4915:
4907:
4905:
4901:
4896:
4890:
4886:
4885:
4877:
4874:
4869:
4865:
4861:
4855:
4851:
4847:
4842:
4837:
4833:
4826:
4823:
4818:
4816:0-13-244182-9
4812:
4808:
4807:
4799:
4796:
4791:
4785:
4781:
4780:
4772:
4770:
4766:
4761:
4755:
4751:
4750:
4742:
4739:
4734:
4732:0-7487-1584-3
4728:
4724:
4723:
4715:
4712:
4707:
4701:
4697:
4696:
4688:
4685:
4679:
4674:
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:
4582:
4580:
4578:
4574:
4570:
4566:
4558:
4556:
4554:
4550:
4545:
4543:
4539:
4535:
4534:mantis shrimp
4531:
4527:
4523:
4519:
4515:
4511:
4506:
4498:
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:
4381:
4379:
4376:
4372:
4367:
4361:
4359:
4355:
4350:
4346:
4342:
4337:
4335:
4331:
4327:
4323:
4319:
4311:
4309:
4307:
4303:
4299:
4295:
4291:
4287:
4283:
4279:
4275:
4271:
4267:
4263:
4255:
4250:
4246:
4243:
4239:
4235:
4231:
4227:
4219:
4214:
4209:
4201:
4199:
4197:
4193:
4188:
4186:
4182:
4179:, after whom
4178:
4169:
4162:
4156:
4149:
4144:
4142:
4140:
4136:
4132:
4128:
4124:
4120:
4116:
4112:
4108:
4104:
4100:
4094:
4086:
4084:
4082:
4078:
4077:
4072:
4068:
4064:
4060:
4056:
4048:
4046:
4039:
4037:
4035:
4031:
4027:
4022:
4020:
4016:
4012:
4008:
4000:
3997:
3992:
3985:
3983:
3981:
3977:
3973:
3968:
3964:
3960:
3956:
3951:
3946:
3938:
3936:
3934:
3929:
3925:
3916:
3909:
3907:
3900:
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:
3768:
3766:
3759:
3752:
3746:
3738:
3729:
3724:
3720:
3711:
3701:
3691:
3680:
3675:
3671:
3664:
3662:
3661:diattenuating
3658:
3657:
3648:
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
3500:
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:
3054:
3049:
3045:polarization.
3043:
3038:
3034:
3032:
3031:
3026:
3025:
3019:
3017:
3013:
3009:
3005:
3001:
2996:
2994:
2990:
2986:
2982:
2975:
2966:
2964:
2962:
2954:
2946:
2944:
2940:
2932:
2924:
2906:
2898:
2894:
2890:
2883:
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:
2701:
2699:
2697:
2693:
2689:
2680:
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:
2488:
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:
2275:
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:
2100:
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:
1963:
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:
278:
276:
274:
273:
268:
264:
260:
256:
252:
242:
235:
233:
228:
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:. The
2440:arctan
2404:arctan
2113:, and
2082:fluids
2004:tensor
1954:< 1
1770:
1744:|
1044:where
967:, and
936:) and
913:where
429:phasor
378:where
221:, and
215:lasers
209:, and
199:optics
5981:arXiv
5850:S2CID
5807:S2CID
5781:arXiv
5754:S2CID
5720:arXiv
5646:arXiv
5141:(PDF)
5124:(PDF)
5115:(PDF)
4864:S2CID
4836:arXiv
4526:squid
4503:Many
4476:below
4448:radar
4394:radio
4354:RealD
4278:cloud
4274:stars
4111:stars
3851:- or
3511:In a
3480:is a
3339:2 × 2
3272:2 × 2
3059:In a
2985:light
2876:, or
2856:, or
2747:with
2667:basis
2620:Here
2248:basis
2086:solid
1766:0.001
915:λ = λ
223:radar
207:radio
166:, or
96:light
6347:ISBN
6325:ISBN
6297:ISBN
6278:ISBN
6259:ISBN
6240:ISBN
6221:ISBN
6200:ISBN
6173:PMID
6068:PMID
6060:ISSN
6019:PMID
5948:ISBN
5916:ISBN
5889:ISSN
5777:0504
5746:PMID
5691:ISBN
5613:ISBN
5576:ISSN
5535:ISBN
5510:ISBN
5485:ISBN
5460:ISBN
5435:ISBN
5410:ISBN
5380:ISBN
5351:ISBN
5267:ISBN
5234:ISBN
5213:link
5199:Note
5189:ISBN
5162:ISBN
5128:ISBN
5091:ISBN
5057:OCLC
5047:ISBN
5016:PMID
4971:ISBN
4946:ISBN
4919:ISBN
4889:ISBN
4854:ISBN
4811:ISBN
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