Linear polarizers can be divided into two general categories: absorptive polarizers, where the unwanted polarization states are
absorbed by the device, and beam-splitting polarizers, where the unpolarized beam is split into two beams with opposite polarization states. Polarizers which maintain the same axes of polarization with varying angles of incidence are often called
Cartesian polarizers, since the polarization vectors can be described with simple
Cartesian coordinates (for example, horizontal vs. vertical) independent from the orientation of the polarizer surface. When the two polarization states are relative to the direction of a surface (usually found with Fresnel reflection), they are usually termed
s and
p. This distinction between Cartesian and
s–
p polarization can be negligible in many cases, but it becomes significant for achieving high contrast and with wide angular spreads of the incident light.
Absorptive polarizers Certain
crystals, due to the effects described by
crystal optics, show
dichroism, preferential absorption of light which is polarized in particular directions. They can therefore be used as linear polarizers. The best known crystal of this type is
tourmaline. However, this crystal is seldom used as a polarizer, since the dichroic effect is strongly wavelength dependent and the crystal appears coloured.
Herapathite is also dichroic, and is not strongly coloured, but is difficult to grow in large crystals. A
Polaroid polarizing filter functions similarly on an atomic scale to the wire-grid polarizer. It was originally made of microscopic herapathite crystals. Its current
H-sheet form is made from
polyvinyl alcohol (PVA) plastic with an
iodine doping. Stretching of the sheet during manufacture causes the PVA chains to align in one particular direction.
Valence electrons from the iodine dopant are able to move linearly along the polymer chains, but not transverse to them. So incident light polarized parallel to the chains is absorbed by the sheet; light polarized perpendicularly to the chains is transmitted. The durability and practicality of Polaroid makes it the most common type of polarizer in use, for example for
sunglasses,
photographic filters, and
liquid crystal displays. It is also much cheaper than other types of polarizer. A modern type of absorptive polarizer is made of elongated
silver nano-particles embedded in thin (≤0.5 mm) glass plates. These polarizers are more durable, and can polarize light much better than plastic Polaroid film, achieving polarization ratios as high as 100,000:1 and absorption of correctly polarized light as low as 1.5%. Such glass polarizers perform best for long-wavelength
infrared light, and are widely used in
fiber-optic communication.
Beam-splitting polarizers Beam-splitting polarizers split the incident beam into two beams of differing
linear polarization. For an ideal polarizing beamsplitter these would be fully polarized, with orthogonal polarizations. For many common beam-splitting polarizers, however, only one of the two output beams is fully polarized. The other contains a mixture of polarization states. Unlike absorptive polarizers, beam splitting polarizers do not need to absorb and dissipate the energy of the rejected polarization state, and so they are more suitable for use with high intensity beams such as
laser light. True polarizing beamsplitters are also useful where the two polarization components are to be analyzed or used simultaneously.
Polarization by Fresnel reflection to a beam reflects off a fraction of the
s-polarized light at each surface, leaving a
p-polarized beam. Full polarization at Brewster's angle requires many more plates than shown. The arrows indicate the direction of the electrical field, not the magnetic field, which is perpendicular to the electric field. When light reflects (by Fresnel reflection) at an angle from an interface between two transparent materials, the reflectivity is different for light polarized in the
plane of incidence and light polarized perpendicular to it. Light polarized in the plane is said to be
p-polarized, while that polarized perpendicular to it is
s-polarized. At a special angle known as
Brewster's angle, no
p-polarized light is reflected from the surface, thus all reflected light must be
s-polarized, with an electric field perpendicular to the plane of incidence. A simple linear polarizer can be made by tilting a stack of glass plates at Brewster's angle to the beam. Some of the
s-polarized light is reflected from each surface of each plate. For a stack of plates, each reflection depletes the incident beam of
s-polarized light, leaving a greater fraction of
p-polarized light in the transmitted beam at each stage. For visible light in air and typical glass, Brewster's angle is about 57°, and about 16% of the
s-polarized light present in the beam is reflected for each air-to-glass or glass-to-air transition. It takes many plates to achieve even mediocre polarization of the transmitted beam with this approach. For a stack of 10 plates (20 reflections), about 3% (= (1 − 0.16)20) of the
s-polarized light is transmitted. The reflected beam, while fully polarized, is spread out and may not be very useful. A more useful polarized beam can be obtained by tilting the pile of plates at a steeper angle to the incident beam. Counterintuitively, using incident angles greater than Brewster's angle yields a higher degree of polarization of the
transmitted beam, at the expense of decreased overall transmission. For angles of incidence steeper than 80° the polarization of the transmitted beam can approach 100% with as few as four plates, although the transmitted intensity is very low in this case. Adding more plates and reducing the angle allows a better compromise between transmission and polarization to be achieved. beam into one with a single
linear polarization. Coloured arrows depict the electric field vector. The diagonally polarized waves also contribute to the transmitted polarization. Their vertical components are transmitted (shown), while the horizontal components are absorbed and reflected (not shown). Because their polarization vectors depend on incidence angle, polarizers based on Fresnel reflection inherently tend to produce
s–
p polarization rather than Cartesian polarization, which limits their use in some applications.
Birefringent polarizers Other linear polarizers exploit the
birefringent properties of crystals such as
quartz and
calcite. In these crystals, a beam of unpolarized light incident on their surface is split by
refraction into two rays.
Snell's law holds for both of these rays, the
ordinary or
o-ray, and the
extraordinary or
e-ray, with each ray experiencing a different
index of refraction (this is called double refraction). In general the two rays will be in different polarization states, though not in linear polarization states except for certain propagation directions relative to the crystal axis. A
Nicol prism was an early type of birefringent polarizer, that consists of a crystal of calcite which has been split and rejoined with
Canada balsam. The crystal is cut such that the
o- and
e-rays are in orthogonal linear polarization states.
Total internal reflection of the
o-ray occurs at the balsam interface, since it experiences a larger refractive index in calcite than in the balsam, and the ray is deflected to the side of the crystal. The
e-ray, which sees a smaller refractive index in the calcite, is transmitted through the interface without deflection. Nicol prisms produce a very high purity of polarized light, and were extensively used in
microscopy, though in modern use they have been mostly replaced with alternatives such as the
Glan–Thompson prism,
Glan–Foucault prism, and
Glan–Taylor prism. These prisms are not true polarizing beamsplitters since only the transmitted beam is fully polarized. A
Wollaston prism is another birefringent polarizer consisting of two triangular calcite prisms with orthogonal crystal axes that are cemented together. At the internal interface, an unpolarized beam splits into two linearly polarized rays which leave the prism at a divergence angle of 15°–45°. The
Rochon and
Sénarmont prisms are similar, but use different
optical axis orientations in the two prisms. The Sénarmont prism is air spaced, unlike the Wollaston and Rochon prisms. These prisms truly split the beam into two fully polarized beams with perpendicular polarizations. The
Nomarski prism is a variant of the Wollaston prism, which is widely used in
differential interference contrast microscopy.
Thin film polarizers Thin-film linear polarizers (also known as TFPN) are glass substrates on which a special
optical coating is applied. Either Brewster's angle reflections or
interference effects in the film cause them to act as beam-splitting polarizers. The substrate for the film can either be a plate, which is inserted into the beam at a particular angle, or a wedge of glass that is cemented to a second wedge to form a cube with the film cutting diagonally across the center (one form of this is the very common MacNeille cube). Thin-film polarizers generally do not perform as well as Glan-type polarizers, but they are inexpensive and provide two beams that are about equally well polarized. The cube-type polarizers generally perform better than the plate polarizers. The former are easily confused with Glan-type birefringent polarizers.
Wire-grid polarizers One of the simplest linear polarizers is the
wire-grid polarizer (WGP), which consists of many fine parallel metallic wires placed in a plane. WGPs mostly reflect the non-transmitted polarization and can thus be used as polarizing beam splitters. The parasitic absorption is relatively high compared to most of the dielectric polarizers though much lower than in absorptive polarizers. Electromagnetic waves that have a component of their
electric fields aligned parallel to the wires will induce the movement of
electrons along the length of the wires. Since the electrons are free to move in this direction, the polarizer behaves in a similar manner to the surface of a
metal when reflecting light, and the wave is reflected backwards along the incident beam (minus a small amount of energy lost to
Joule heating of the wire). For waves with electric fields perpendicular to the wires, the electrons cannot move very far across the width of each wire. Therefore, little energy is reflected and the incident wave is able to pass through the grid. In this case the grid behaves like a
dielectric material. Overall, this causes the transmitted wave to be
linearly polarized with an electric field completely perpendicular to the wires. The hypothesis that the waves "slip through" the gaps between the wires is incorrect. == Malus's law and other properties ==