Think of a photon as a sphere that spins around an axis as it tumbles through space. The polarization literally is the orientation of this axis. In technical terms, the axis is the B component (magnetic); the plane orthogonal to it is the E component (electric) a.k.a the plane of polarization.
Polarization of visible light can be observed using a polarizing filter (the lenses of polaroid sunglasses will work). While viewing through the filter, rotate it, and if linearly polarized light is present the degree of illumination will change. An easy first phenomenon to observe is at sunset to view the horizon at a 90° angle from the sunset.
Common sources of light, such as the Sun and the electric light bulb emit what is known as unpolarized light. More specialised sources, such as certain kinds of discharge tubes and lasers, produce polarized light. The difference between these two types of light is caused by the behaviour of the electromagnetic fields that make up the light.
As described by Maxwell's equations, light is a transverse wave made up of an interacting electric field E and a magnetic field B. The oscillations of these two interacting fields cause the fields to self-propagate in a certain direction, at the speed of light. In most cases, the directions of the electric field, the magnetic field, and the direction of propagation of the light are all mutually perpendicular. That is, both the E and B fields oscillate in a direction at right angles to the direction that the light is moving, and also at right angles to each other.
(In optics, it is usual to define the polarization in terms of the direction of the electric field, and disregard the magnetic field since it is almost always perpendicular to the electric field.)
If the direction of oscillation of the electric field E is fixed, the light wave is said to be linearly polarized. There are two possible linear polarization states, with their E fields orthogonal to one another. Any other angle of linear polarisation can be constructed as a superposition of these two states.
The direction of polarization is arbitrary with respect to the light itself. It is usual to label the two linear polarization states in accordance with some other external reference. For example, the terms horizontally and vertically polarized are generally used when light is propagating in free space. If the light is interacting with a surface, such as a mirror, lens or some other interface between two media, the terms s- and p-polarized are used. For example, consider the following:
reflecting off a mirror at some angle. If the electric field of the light is oscillating perpendicular to the plane of the diagram, the light is termed s-polarized. If it is oscillating in the plane of the diagram, it is termed p-polarized. Other terms used for s-polarization are sigma-polarized and sagittal plane polarised. Similarly, p-polarized light is also referred to as pi-polarised and tangential plane polarized.
If the direction of the electric field E is not fixed, but rotates as the light propagates, the light is said to be circularly polarized. Two possible independent circular polarization states exist, termed left-hand or right-hand circularly polarized depending on whether the electric field is rotating in a counter-clockwise or clockwise sense, respectively, when looking in the direction of the light propagation. Elliptical polarization can be thought of as a combination of circular and linear polarization.
If the light consists of many incoherent waves with randomly varying polarisation, the light is said to be unpolarized. It is possible to convert unpolarised light to polarised light by using a polarizer. One such device is Polaroid® sheet. This is a sheet of plastic with molecules that are arranged such that they absorb any light passing through it which has an electric field oscillating in a given direction; this has the effect of linearly polarizing the light. Other devices can split an unpolarised beam into two beams of orthogonal linear polarization; They are generally constructed from certain arrangements of prisms and optical coatings.
The angle of polarization of linearly polarised light can be rotated using a device known as a half-wave plate. Similarly, linear polarization can be converted to circular polarization and vice versa with the use of a quarter-wave plate.
The possible polarization states can be mapped to a sphere, with left circular at +z, right circular at -z, horizontal at +x, vertical at -x, and the diagonals at +y and -y. Passing through a dichroic wave plate is equivalent to a rotation of the sphere. The amount of amplitude of polarization x that passes through a polarizer that passes y is 1/2 the distance between x and the antipode of y; the intensity is (x·y+1)/2.
In electrostatics, the polarization is the vector field that results from permanent or induced dipole moments in a dielectric material. The polarization vector P is defined as the dipole moment per unit volume.
If the polarization P is not proportional to the electric field E, the medium is termed nonlinear and is described by the field of nonlinear optics. If the direction of P is not aligned with E, as in many crystals, the medium is anisotropic and is described by crystal optics.