### Light Polarization

For other uses, see Polarization.

Polarization (also polarisation) is a property of waves that can oscillate with more than one orientation. Electromagnetic waves, such as light, and gravitational waves exhibit polarization; sound waves in a gas or liquid do not have polarization because the medium vibrates only along the direction in which the waves are travelling.

By convention, the polarization of light is described by specifying the orientation of the wave's electric field at a point in space over one period of the oscillation. 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 case, the field may rotate in either direction. The direction in which the field rotates is the wave's chirality or handedness.

The polarization of an electromagnetic (EM) wave can be more complicated in certain cases. For instance, in a waveguide such as an optical fiber or for radially polarized beams in free space, 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. A polarizer is a device that affects polarization.

## 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,

$\vec\left\{E\right\}\left(\vec\left\{r\right\},t\right) = \mathrm\left\{Re\right\} \left\left[\left\left(A_\left\{x\right\}, A_\left\{y\right\}\cdot e^\left\{i\phi\right\}, 0 \right\right) e^\left\{i\left(kz - \omega t\right)\right\} \right\right]$

or alternatively,

$\vec\left\{E\right\}\left(\vec\left\{r\right\},t\right) = \left(A_\left\{x\right\}\cdot \cos\left(kz - \omega t\right), A_\left\{y\right\}\cdot \cos\left(kz - \omega t + \phi\right), 0\right)$

where $A_\left\{x\right\}$ and $A_\left\{y\right\}$ 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 (black), with time (the vertical axes), at a particular point in space, along with its x and y components (red/left and blue/right), and the path traced by the tip of the vector in the plane (yellow in figure 1&3, purple in figure 2): 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 and the chosen convention.

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.