Polarization (
also
polarisation) is a property of
waves that describes the orientation of their
oscillations.
Electromagnetic waves such as
light, along with other types of wave, exhibit
polarization.
By convention, the polarization of light is described by specifying
the direction of the wave's
electric
field. When light travels in free space, in most cases it
propagates as a
transverse wave—the
polarization is perpendicular to the wave's direction of travel. In
this case, the electric field may be oriented in a single direction
(
linear polarization), or it may
rotate as the wave travels (
circular or
elliptical polarization). In the
latter cases, the oscillations can rotate rightward or leftward in
the direction of travel, and which of those two rotations is
present in a wave is called the wave's
chirality or handedness. In general the
polarization of an
electromagnetic
wave is a complex issue. For instance in a
waveguide such as an
optical fiber, or for
radially polarized beams in free space,
the description of the wave's polarization is more complicated, as
the fields can have longitudinal as well as transverse components.
Such EM waves are either
TM or hybrid
modes.
For
longitudinal waves such as
sound waves in
fluids, the direction of oscillation is by definition
along the direction of travel, so there is no polarization. In a
solid medium, however, sound waves can be
transverse. In this case, the polarization is associated with the
direction of the
shear stress in the
plane perpendicular to the propagation direction. This is important
in
seismology.
Polarization is significant in areas of science and technology
dealing with
wave propagation, such
as
optics,
seismology,
telecommunications and
radar science. The polarization of light can be
measured with a
polarimeter.
Theory
Basics: plane waves
The simplest manifestation of polarization to visualize is that of
a
plane wave, which is a good
approximation of most light waves (a plane wave is a wave with
infinitely long and wide
wavefronts). For
plane waves
Maxwell's equations,
specifically
Gauss's laws,
impose the transversality requirement that the
electric and
magnetic field be perpendicular to the
direction of propagation and to each other. Conventionally, when
considering polarization, the electric field
vector is described and the magnetic field
is ignored since it is
perpendicular
to the electric field and proportional to it. The electric field
vector of a plane wave may be arbitrarily divided into two
perpendicular components labeled
x and
y (with
z indicating the direction of travel). For a
simple harmonic wave, where
the amplitude of the electric vector varies in a
sinusoidal manner in time, the two components have
exactly the same frequency. However, these components have two
other defining characteristics that can differ. First, the two
components may not have the same
amplitude. Second, the two components may not have
the same
phase, that is they may not
reach their maxima and minima at the same time. Mathematically, the
electric field of a plane wave can be written as,
- \vec{E}(\vec{r},t) = \mathrm{Re} \left[\left(A_{x}, A_{y}\cdot
e^{i\phi}, 0 \right) e^{i(kz - \omega t)} \right]
or alternatively,
- \vec{E}(\vec{r},t) = (A_{x}\cdot \cos(kz - \omega t),
A_{y}\cdot \cos(kz - \omega t + \phi), 0)
where A_{x} and A_{y} are the amplitudes of the x and y directions
and \phi is the relative phase between the two components.
Polarization state
The shape traced out in a fixed plane by the electric vector as
such a plane wave passes over it (a
Lissajous figure) is a description of the
polarization state. The following figures show
some examples of the evolution of the electric field vector (blue),
with time(the vertical axes), at a particular point in space, along
with its
x and
y components (red/left and
green/right), and the path traced by the tip of the vector in the
plane (purple): The same evolution would occur when looking at the
electric field at a particular time while evolving the point in
space, along the direction opposite to propagation.
Linear
Circular
Elliptical
In the leftmost figure above, the two orthogonal (perpendicular)
components are in phase. In this case the ratio of the strengths of
the two components is constant, so the direction of the electric
vector (the vector sum of these two components) is constant. Since
the tip of the vector traces out a single line in the plane, this
special case is called
linear
polarization. The direction of this line depends on the
relative amplitudes of the two components.
In the middle figure, the two orthogonal components have exactly
the same amplitude and are exactly ninety degrees out of phase. In
this case one component is zero when the other component is at
maximum or minimum amplitude. There are two possible phase
relationships that satisfy this requirement: the
x
component can be ninety degrees ahead of the
y component
or it can be ninety degrees behind the
y component. In
this special case the electric vector traces out a circle in the
plane, so this special case is called
circular polarization. The direction
the field rotates in, depends on which of the two phase
relationships exists. These cases are called
right-hand
circular polarization and
left-hand circular
polarization, depending on which way the electric vector
rotates.
Another case is when the two components are not in phase and either
do not have the same amplitude or are not ninety degrees out of
phase, though their phase offset and their amplitude ratio are
constant. This kind of polarization is called
elliptical polarization because the
electric vector traces out an
ellipse in the
plane (the
polarization ellipse). This is shown in the
above figure on the right.
The "Cartesian" decomposition of the electric field into
x
and
y components is, of course, arbitrary. Plane waves of
any polarization can be described instead by combining any two
orthogonally polarized waves, for
instance waves of opposite circular polarization. The Cartesian
polarization decomposition is natural when dealing with reflection
from surfaces,
birefringent materials,
or
synchrotron radiation. The
circularly polarized modes are a more useful basis for the study of
light propagation in
stereoisomers.
Though this section discusses polarization for idealized plane
waves, all the above is a very accurate description for most
practical optical experiments which use
TEM modes, including Gaussian optics.
Unpolarized light
Most sources of
electromagnetic radiation contain
a large number of atoms or molecules that emit light. The
orientation of the electric fields produced by these emitters may
not be
correlated, in which
case the light is said to be
unpolarized. If there is
partial correlation between the emitters, the light is
partially polarized. If the polarization is consistent
across the spectrum of the source, partially polarized light can be
described as a superposition of a completely unpolarized component,
and a completely polarized one. One may then describe the light in
terms of the
degree of
polarization, and the parameters of the polarization
ellipse.
Parameterization
For ease of visualization, polarization states are often specified
in terms of the polarization ellipse, specifically its orientation
and elongation. A common parameterization uses the
azimuth
angle, ψ (the angle between the major semi-axis of the
ellipse and the
x-axis) and the
ellipticity, ε (the major-to-minor-axis ratio),
also known as the
axial ratio. An
ellipticity of infinity corresponds to linear polarization and an
ellipticity of 1 corresponds to circular polarization. The
arccotangent of the ellipticity,
χ = arccot ε (the "
ellipticity
angle"), is also commonly used. An example is shown in the
diagram to the right. An alternative to the ellipticity or
ellipticity angle is the
eccentricity, however unlike the
azimuth angle and ellipticity angle, the latter has no obvious
geometrical interpretation in terms of the Poincaré sphere (see
below).
Full information on a completely polarized state is also provided
by the amplitude and phase of oscillations in two components of the
electric field vector in the plane of polarization. This
representation was used above to show how different states of
polarization are possible. The amplitude and phase information can
be conveniently represented as a two-dimensional
complex vector (the
Jones vector):
- \mathbf{e} = \begin{bmatrix}
a_1 e^{i \theta_1} \\ a_2 e^{i \theta_2} \end{bmatrix} .
Here a_1 and a_2 denote the amplitude of the wave in the two
components of the electric field vector, while \theta_1 and
\theta_2 represent the phases. The product of a Jones vector with a
complex number of unit
modulus gives
a different Jones vector representing the same ellipse, and thus
the same state of polarization. The physical electric field, as the
real part of the Jones vector, would be altered but the
polarization state itself is independent of
absolute phase. The
basis vectors used to represent the
Jones vector need not represent linear polarization states (i.e. be
real). In general any two
orthogonal states can be used, where an orthogonal
vector pair is formally defined as one having a zero
inner product. A common choice is left and
right circular polarizations, for example to model the different
propagation of waves in two such components in circularly
birefringent media (see below) or signal paths of coherent
detectors sensitive to circular polarization.
Reflection of a plane wave from a
surface perpendicular to the page.
The p-components of the waves are in the
plane of the page, while the s components are
perpendicular to it.
Regardless of whether polarization ellipses are represented using
geometric parameters or Jones vectors, implicit in the
parameterization is the orientation of the coordinate frame. This
permits a degree of freedom, namely rotation about the propagation
direction. When considering light that is propagating parallel to
the surface of the Earth, the terms "horizontal" and "vertical"
polarization are often used, with the former being associated with
the first component of the Jones vector, or zero azimuth angle. On
the other hand, in
astronomy the
equatorial coordinate system is
generally used instead, with the zero azimuth (or position angle,
as it is more commonly called in astronomy to avoid confusion with
the
horizontal coordinate
system) corresponding to due north. Another coordinate system
frequently used relates to the plane made by the propagation
direction and a vector normal to the plane of a reflecting surface.
This is known as the
plane of incidence. The rays in this
plane are illustrated in the diagram to the right. The component of
the electric field parallel to this plane is termed
p-like
(parallel) and the component perpendicular to this plane is termed
s-like (from
senkrecht,
German for perpendicular). Light with a
p-like electric field is said to be
p-polarized,
pi-polarized,
tangential plane polarized, or is
said to be a
transverse-magnetic (TM) wave. Light with an
s-like electric field is
s-polarized, also known as
sigma-polarized or
sagittal plane polarized, or
it can be called a
transverse-electric (TE) wave.
In the case of partially-polarized radiation, the Jones vector
varies in time and space in a way that differs from the constant
rate of phase rotation of monochromatic, purely-polarized waves. In
this case, the wave field is likely
stochastic, and only
statistical information can be gathered about
the variations and correlations between components of the electric
field. This information is embodied in the
coherency
matrix:
- \mathbf{\Psi} = \left\langle\mathbf{e} \mathbf{e}^\dagger
\right\rangle\,
- :=\left\langle\begin{bmatrix}
e_1 e_1^* & e_1 e_2^* \\e_2 e_1^* & e_2 e_2^*\end{bmatrix}
\right\rangle
- :=\left\langle\begin{bmatrix}
a_1^2 & a_1 a_2 e^{i (\theta_1-\theta_2)} \\a_1 a_2 e^{-i
(\theta_1-\theta_2)}& a_2^2\end{bmatrix} \right\rangle
where angular brackets denote averaging over many wave cycles.
Several variants of the coherency matrix have been proposed: the
Wiener coherency matrix and the
spectral coherency matrix of
Richard
Barakat measure the coherence of a
spectral decomposition of the signal,
while the
Wolf coherency matrix averages
over all time/frequencies.
The coherency matrix contains all of the information on
polarization that is obtainable using second order statistics. It
can be decomposed into the sum of two
idempotent matrices, corresponding to the
eigenvectors of the coherency matrix,
each representing a polarization state that is orthogonal to the
other. An alternative decomposition is into completely polarized
(zero determinant) and unpolarized (scaled identity matrix)
components. In either case, the operation of summing the components
corresponds to the incoherent superposition of waves from the two
components. The latter case gives rise to the concept of the
"degree of polarization"; i.e., the fraction of the total intensity
contributed by the completely polarized component.
The coherency matrix is not easy to visualize, and it is therefore
common to describe incoherent or partially polarized radiation in
terms of its total intensity (
I), (fractional) degree of
polarization (
p), and the shape parameters of the
polarization ellipse. An alternative and mathematically convenient
description is given by the
Stokes
parameters, introduced by
George Gabriel Stokes in 1852. The
relationship of the Stokes parameters to intensity and polarization
ellipse parameters is shown in the equations and figure
below.
- S_0 = I \,
- S_1 = I p \cos 2\psi \cos 2\chi\,
- S_2 = I p \sin 2\psi \cos 2\chi\,
- S_3 = I p \sin 2\chi\,
Here
Ip, 2ψ and 2χ are the
spherical coordinates of the
polarization state in the three-dimensional space of the last three
Stokes parameters. Note the factors of two before ψ and χ
corresponding respectively to the facts that any polarization
ellipse is indistinguishable from one rotated by 180°, or one with
the semi-axis lengths swapped accompanied by a 90° rotation. The
Stokes parameters are sometimes denoted
I,
Q,
U and
V.
The Stokes parameters contain all of the information of the
coherency matrix, and are related to it linearly by means of the
identity matrix plus the three
Pauli
matrices:
- \mathbf{\Psi} = \frac{1}{2}\sum_{j=0}^3 S_j
\mathbf{\sigma}_j,\;\mbox{where}
- \begin{matrix}
\mathbf{\sigma}_0 &=& \begin{bmatrix} 1 & 0 \\ 0 &
1 \end{bmatrix} &\mathbf{\sigma}_1 &=& \begin{bmatrix}
1 & 0 \\ 0 & -1 \end{bmatrix} \\\\\mathbf{\sigma}_2
&=& \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}
&\mathbf{\sigma}_3 &=& \begin{bmatrix} 0 & -i \\ i
& 0 \end{bmatrix}\end{matrix}
Mathematically, the factor of two relating physical angles to their
counterparts in Stokes space derives from the use of second-order
moments and correlations, and incorporates the loss of information
due to absolute phase invariance.
The figure above makes use of a convenient representation of the
last three Stokes parameters as components in a three-dimensional
vector space. This space is closely related to the
Poincaré
sphere, which is the spherical surface occupied by
completely polarized states in the space of the vector
\mathbf{u} = \frac{1}{S_0}\begin{bmatrix}
S_1\\S_2\\S_3\end{bmatrix}.
All four Stokes parameters can also be combined into the
four-dimensional
Stokes vector, which
can be interpreted as
four-vectors of
Minkowski space. In this case, all
physically realizable polarization states correspond to time-like,
future-directed vectors.
Propagation, reflection and scattering
In a
vacuum, the components of the electric
field propagate at the
speed of
light, so that the phase of the wave varies in space and time
while the polarization state does not. That is,
- \mathbf{e}(z+\Delta z,t+\Delta t) = \mathbf{e}(z, t) e^{i k
(c\Delta t - \Delta z)},
where
k is the
wavenumber and
positive
z is the direction of propagation. As noted
above, the physical electric vector is the real part of the Jones
vector. When electromagnetic waves interact with matter, their
propagation is altered. If this depends on the polarization states
of the waves, then their polarization may also be altered.
In many types of media, electromagnetic waves may be decomposed
into two orthogonal components that encounter different propagation
effects. A similar situation occurs in the signal processing paths
of detection systems that record the electric field directly. Such
effects are most easily characterized in the form of a complex 2×2
transformation matrix called
the
Jones matrix:
- \mathbf{e'} = \mathbf{J}\mathbf{e}.
In general the Jones matrix of a medium depends on the frequency of
the waves.
For propagation effects in two orthogonal modes, the Jones matrix
can be written as
- \mathbf{J} = \mathbf{T}
\begin{bmatrix} g_1 & 0 \\ 0 & g_2 \end{bmatrix}
\mathbf{T}^{-1},
where
g_{1} and
g_{2} are complex
numbers representing the change in amplitude and phase caused in
each of the two propagation modes, and
T is a
unitary matrix representing a change
of basis from these propagation modes to the linear system used for
the Jones vectors. For those media in which the amplitudes are
unchanged but a differential phase delay occurs, the Jones matrix
is unitary, while those affecting amplitude without phase have
Hermitian Jones matrices. In fact, since
any matrix may be written as the product of unitary and
positive Hermitian matrices, any sequence of linear propagation
effects, no matter how complex, can be written as the product of
these two basic types of transformations.
Paths taken by vectors in the
Poincaré sphere under birefringence. The propagation modes
(rotation axes) are shown with red, blue, and yellow lines, the
initial vectors by thick black lines, and the paths they take by
colored ellipses (which represent circles in three
dimensions).
Media in which the two modes accrue a differential delay are called
birefringent. Well known
manifestations of this effect appear in optical
wave plates/retarders (linear modes) and in
Faraday rotation/
optical rotation (circular modes). An
easily visualized example is one where the propagation modes are
linear, and the incoming radiation is linearly polarized at a 45°
angle to the modes. As the phase difference starts to appear, the
polarization becomes elliptical, eventually changing to purely
circular polarization (90° phase difference), then to elliptical
and eventually linear polarization (180° phase) with an azimuth
angle perpendicular to the original direction, then through
circular again (270° phase), then elliptical with the original
azimuth angle, and finally back to the original linearly polarized
state (360° phase) where the cycle begins anew. In general the
situation is more complicated and can be characterized as a
rotation in the Poincaré sphere
about the axis defined by the propagation modes (this is a
consequence of the
isomorphism of
SU with
SO). Examples for
linear (blue), circular (red), and elliptical (yellow)
birefringence are shown in the figure on the
left. The total intensity and degree of polarization are
unaffected. If the path length in the birefringent medium is
sufficient, plane waves will exit the material with a significantly
different propagation direction, due to
refraction. For example, this is the case with
macroscopic
crystals of
calcite, which present the viewer with two offset,
orthogonally polarized images of whatever is viewed through them.
It was this effect that provided the first discovery of
polarization, by
Erasmus
Bartholinus in 1669. In addition, the phase shift, and thus the
change in polarization state, is usually frequency dependent,
which, in combination with
dichroism,
often gives rise to bright colors and rainbow-like effects.
Media in which the amplitude of waves propagating in one of the
modes is reduced are called
dichroic. Devices that block nearly all of
the radiation in one mode are known as
polarizing filters
or simply "
polarizers". In terms of the
Stokes parameters, the total intensity is reduced while vectors in
the Poincaré sphere are "dragged" towards the direction of the
favored mode. Mathematically, under the treatment of the Stokes
parameters as a Minkowski 4-vector, the transformation is a scaled
Lorentz boost (due to the isomorphism
of
SL and the restricted
Lorentz group, SO(3,1)). Just as the
Lorentz transformation preserves the
proper
time, the quantity det
Ψ =
S
_{0}^{2}-S
_{1}^{2}-S
_{2}^{2}-S
_{3}^{2}
is invariant within a multiplicative scalar constant under Jones
matrix transformations (dichroic and/or birefringent).
In birefringent and dichroic media, in addition to writing a Jones
matrix for the net effect of passing through a particular path in a
given medium, the evolution of the polarization state along that
path can be characterized as the (matrix) product of an infinite
series of infinitesimal steps, each operating on the state produced
by all earlier matrices. In a uniform medium each step is the same,
and one may write
- \mathbf{J} = Je^{\mathbf{D}},
where
J is an overall (real) gain/loss factor. Here
D is a
traceless matrix
such that
αDe gives the derivative of
e with respect to
z. If
D is Hermitian the effect is dichroism, while a
unitary matrix models birefringence. The matrix
D
can be expressed as a linear combination of the Pauli matrices,
where real coefficients give Hermitian matrices and imaginary
coefficients give unitary matrices. The Jones matrix in each case
may therefore be written with the convenient construction
- \begin{matrix}
\mathbf{J_b} &=& J_be^{\beta
\mathbf{\sigma}\cdot\mathbf{\hat{n}}} & \mbox{and}
&\mathbf{J_r} &=& J_re^{\phi
i\mathbf{\sigma}\cdot\mathbf{\hat{m}}},\end{matrix}
where σ is a 3-vector composed of the Pauli matrices (used here as
generators for the
Lie group SL(2,C)) and
n and
m are real 3-vectors on the
Poincaré sphere corresponding to one of the propagation modes of
the medium. The effects in that space correspond to a Lorentz boost
of velocity parameter 2β along the given direction, or a rotation
of angle 2φ about the given axis. These transformations may also be
written as
biquaternions (
quaternions with complex elements), where the
elements are related to the Jones matrix in the same way that the
Stokes parameters are related to the coherency matrix. They may
then be applied in pre- and post-multiplication to the quaternion
representation of the coherency matrix, with the usual exploitation
of the quaternion exponential for performing rotations and boosts
taking a form equivalent to the matrix exponential equations above.
(
See Quaternion
rotation)
In addition to birefringence and dichroism in extended media,
polarization effects describable using Jones matrices can also
occur at (reflective) interface between two materials of different
refractive index. These effects are
treated by the
Fresnel equations.
Part of the wave is transmitted and part is reflected, with the
ratio depending on angle of incidence and the angle of refraction.
In addition, if the plane of the reflecting surface is not aligned
with the plane of propagation of the wave, the polarization of the
two parts is altered. In general, the Jones matrices of the
reflection and transmission are real and
diagonal, making the effect similar to that
of a simple linear polarizer. For unpolarized light striking a
surface at a certain optimum angle of incidence known as
Brewster's angle, the reflected wave will
be completely
s-polarized.
Certain effects do not produce linear transformations of the Jones
vector, and thus cannot be described with (constant) Jones
matrices. For these cases it is usual instead to use a 4×4 matrix
that acts upon the Stokes 4-vector. Such matrices were first used
by
Paul Soleillet in 1929, although
they have come to be known as
Mueller
matrices. While every Jones matrix has a Mueller matrix, the
reverse is not true. Mueller matrices are frequently used to study
the effects of the
scattering of waves
from complex surfaces or ensembles of particles.
Polarization in nature, science, and technology
Polarization effects in everyday life
Light reflected by shiny transparent materials is partly or fully
polarized, except when the light is
normal (perpendicular) to the surface. It was
through this effect that polarization was first discovered in 1808
by the mathematician
Etienne Louis
Malus. A polarizing filter, such as a pair of polarizing
sunglasses, can be used to observe this
effect by rotating the filter while looking through it at the
reflection off of a distant horizontal surface. At certain rotation
angles, the reflected light will be reduced or eliminated.
Polarizing filters remove light polarized at 90° to the filter's
polarization axis. If two polarizers are placed atop one another at
90° angles to one another, there is minimal light
transmission.
Polarization by scattering is observed as light passes through the
atmosphere. The
scattered light produces the brightness
and color in clear
skies. This partial
polarization of scattered light can be used to darken the sky in
photographs, increasing the contrast. This effect is easiest to
observe at
sunset, on the horizon at a 90°
angle from the setting sun. Another easily observed effect is the
drastic reduction in brightness of images of the sky and clouds
reflected from horizontal surfaces (see
Brewster's angle), which is the main reason
polarizing filters are often used in sunglasses. Also frequently
visible through polarizing sunglasses are
rainbow-like patterns caused by color-dependent
birefringent effects, for example in
toughened glass (e.g., car windows) or items
made from transparent
plastics. The role
played by polarization in the operation of
liquid crystal displays (LCDs) is
also frequently apparent to the wearer of polarizing sunglasses,
which may reduce the contrast or even make the display
unreadable.
Polarizing sunglasses reveal stress in
car window (see text for explanation.)
The photograph on the right was taken through polarizing sunglasses
and through the rear window of a car. Light from the sky is
reflected by the windshield of the other car at an angle, making it
mostly horizontally polarized. The rear window is made of
tempered glass. Stress in the glass, left
from its heat treatment, causes it to alter the polarization of
light passing through it, like a
wave
plate. Without this effect, the sunglasses would block the
horizontally polarized light reflected from the other car's window.
The stress in the rear window, however, changes some of the
horizontally polarized light into vertically polarized light that
can pass through the glasses. As a result, the regular pattern of
the heat treatment becomes visible.
Biology
Many
animals are apparently capable of
perceiving some of the components of the polarization of light,
e.g. linear horizontally-polarized light. This is generally used
for navigational purposes, since the linear polarization of sky
light is always perpendicular to the direction of the sun. This
ability is very common among the
insects,
including
bees, which use this information to
orient their
communicative dances.
Polarization sensitivity has also been observed in species of
octopus,
squid,
cuttlefish, and
mantis shrimp. In the latter case, one species
measures all six orthogonal components of polarization, and is
believed to have optimal polarization vision. The rapidly changing,
vividly colored skin patterns of cuttlefish, used for
communication, also incorporate polarization patterns, and mantis
shrimp are known to have polarization selective reflective tissue.
Sky polarization was thought to be perceived by
pigeons, which was assumed to be one of their aids in
homing, but research indicates this is
a popular myth.
The naked
human eye is weakly sensitive to
polarization, without the need for intervening filters. Polarized
light creates a very faint pattern near the center of the visual
field, called
Haidinger's brush.
This pattern is very difficult to see, but with practice one can
learn to detect polarized light with the naked eye.
Geology
The property of (linear) birefringence is widespread in crystalline
minerals, and indeed was pivotal in the
initial discovery of polarization. In
mineralogy, this property is frequently exploited
using polarization
microscopes, for the
purpose of identifying minerals. See
pleochroism.
Chemistry
Polarization is principally of importance in
chemistry due to
circular dichroism and "optical rotation"
(circular birefringence) exhibited by
optically active (
chiral)
molecules. It may be measured using
polarimetry.
The term 'polarization' may also refer to the through-bond
(
inductive or
resonant effect) or through-space
influence of a nearby functional group on the electronic properties
(e.g.
dipole moment) of a
covalent bond or atom. This concept is based
on the formation of an electric
dipole
within a molecule, which is generally not related to the
polarization of electromagnetic waves.
Polarized light does interact with
anisotropic materials, which is the basis for
birefringence. This is usually seen in
crystalline materials and is especially useful in
geology (see above). The polarized light is 'double
refracted', as the refractive index is different for horizontally
and vertically polarized light in these materials. This is to say,
the
polarizability of
anisotropic materials is not equivalent in all
directions. This anisotropy causes changes in the polarization of
the incident beam, and is easily observable using cross-polar
microscopy or
polarimetry. The optical
rotation of chiral compounds (as opposed to achiral compounds that
form anisotropic crystals), is derived from circular birefringence.
Like linear birefringence described above, circular birefringence
is the 'double refraction' of
circular polarized light.
Astronomy
In many areas of
astronomy, the study of
polarized electromagnetic radiation from
outer space is of great importance. Although not
usually a factor in the
thermal
radiation of
stars, polarization is also
present in radiation from coherent astronomical sources (e.g.
hydroxyl or methanol
masers), and incoherent
sources such as the large radio lobes in active galaxies, and
pulsar radio radiation (which may, it is speculated, sometimes be
coherent), and is also imposed upon starlight by scattering from
interstellar dust. Apart from
providing information on sources of radiation and scattering,
polarization also probes the interstellar
magnetic field via
Faraday rotation. The polarization of the
cosmic microwave
background is being used to study the physics of the very early
universe.
Synchrotron
radiation is inherently polarised.
Technology
Technological applications of polarization are extremely
widespread. Perhaps the most commonly encountered examples are
liquid crystal displays and
polarized
sunglasses.
All
radio transmitting and receiving
antennas are intrinsically polarized,
special use of which is made in
radar. Most
antennas radiate either horizontal, vertical, or circular
polarization although elliptical polarization also exists. The
electric field or
E-plane determines the
polarization or orientation of the radio wave. Vertical
polarization is most often used when it is desired to radiate a
radio signal in all directions such as widely distributed mobile
units. AM and FM radio uses vertical polarization. Television uses
horizontal polarization. Alternating vertical and horizontal
polarization is used on
satellite communications (including
television satellites), to allow the satellite to carry two
separate transmissions on a given frequency, thus doubling the
number of customers a single satellite can serve.
Strain in Glass
engineering, the relationship between
strain and birefringence
motivates the use of polarization in characterizing the
distribution of
stress and strain
in prototypes. Electronically controlled birefringent devices are
used in combination with polarizing filters as modulators in
fiber optics. Polarizing filters are
also used in
photography. They can
deepen the color of a blue sky and eliminate reflections from
windows and standing water.
Sky polarization has been exploited in the "
sky compass", which was used in the 1950s when
navigating near the poles of the
Earth's magnetic field when neither
the
sun nor
stars were
visible (e.g. under daytime
cloud or
twilight).
It has been suggested, controversially, that
the Vikings exploited a similar device (the
"sunstone") in their extensive
expeditions across the North Atlantic in the 9th–11th centuries, before the arrival of
the magnetic compass in Europe in
the 12th century. Related to the sky compass is the
"
polar clock", invented by
Charles Wheatstone in the late 19th
century.
Polarization is also used for some
3D
movies, in which the images intended for each eye are either
projected from two different projectors with orthogonally oriented
polarizing filters or from a single projector with time multiplexed
polarization (a fast alternating polarization device for successive
frames). Filter glasses with similarly oriented polarized filters
ensure that each eye receives only the correct image. Typical
stereoscopic projection displays use
linear polarization encoding, because it is not very expensive and
offers high contrast. In environments where the viewer is moving,
such as in simulators, circular polarization is sometimes used.
This makes the channel separation insensitive to the viewing
orientation. The 3-D effect only works on a
silver screen since it maintains polarization,
whereas the scattering in a normal projection screen would void the
effect.
Art
Several visual artists have worked with polarized light and
birefringent materials to create
colorful, sometimes changing images.
One example is
contemporary artist Austine Wood
Comarow, whose "Polage" art works have been exhibited at the
Museum of
Science, Boston,[6774] the New Mexico Museum of Natural History and
Science in Albuquerque, NM, and the Cité des
Sciences et de l'Industrie (the City of Science and Industry) in Paris. The
artist works by cutting hundreds of small pieces of
cellophane and other birefringent films and
laminating them between plane polarizing filters.
3-D films make use of
polarized light and polarization filters in order to generate the
3D effect.
Other examples of polarization
- Shear waves in elastic materials exhibit
polarization. These effects are studied as part of the field of
seismology, where horizontal and vertical
polarizations are termed SH and SV, respectively.
See also
Notes and references
- Principles of Optics, 7th edition, M. Born & E.
Wolf, Cambridge University, 1999, ISBN 0-521-64222-1.
- Fundamentals of polarized light: a statistical optics
approach, C. Brosseau, Wiley, 1998, ISBN 0-471-14302-2.
- Polarized Light, second edition, Dennis Goldstein,
Marcel Dekker, 2003, ISBN 0-8247-4053-X
- Field Guide to Polarization, Edward Collett, SPIE
Field Guides vol. FG05, SPIE, 2005, ISBN
0-8194-5868-6.
- Polarization Optics in Telecommunications, Jay N.
Damask, Springer 2004, ISBN 0-387-22493-9.
- Optics, 4th edition, Eugene Hecht, Addison Wesley
2002, ISBN 0-8053-8566-5.
- Polarized Light in Nature, G. P. Können, Translated by
G. A. Beerling, Cambridge University, 1985, ISBN
0-521-25862-6.
- Polarised Light in Science and Nature, D. Pye,
Institute of Physics, 2001, ISBN 0-7503-0673-4.
- Polarized Light, Production and Use, William A.
Shurcliff, Harvard University, 1962.
- Ellipsometry and Polarized Light, R. M. A. Azzam and
N. M. Bashara, North-Holland, 1977, ISBN 0-444-87016-4
- Secrets of the Viking Navigators—How the Vikings used their
amazing sunstones and other techniques to cross the open
oceans, Leif Karlsen, One Earth Press, 2003.
- Subrahmanyan Chandrasekhar (1960) Radiative transfer, p.27
- Merrill Ivan Skolnik (1990) Radar Handbook, Fig. 6.52,
sec. 6.60.
- Hamish Meikle (2001) Modern Radar Systems, eq.
5.83.
- T. Koryu Ishii (Editor), 1995, Handbook of Microwave
Technology. Volume 2, Applications, p. 177.
- John Volakis (ed) 2007 Antenna Engineering Handbook, Fourth
Edition, sec. 26.1. Note: 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
[it] is less than unity, when expressing ellipticity in decibels,
the minus sign is frequently omitted for convenience", which
essentially reverts back to the definition adopted by other
authors.
- "No evidence for polarization sensitivity in the pigeon
electroretinogram", J. J. Vos Hzn, M. A. J. M. Coemans & J. F.
W. Nuboer, The Journal of Experimental Biology, 1995.
External links