# What is the degree of polarization

The polarization is a property of transverse waves that describes the direction of the amplitude vector. No polarization phenomenon can occur with longitudinal waves, since the oscillation takes place in the direction of propagation. A transverse wave is characterized by two directions: the wave vector, which points in the direction of propagation, and the amplitude vector, which in the case of transverse waves is always perpendicular to the wave vector. However, this still leaves one degree of freedom open in three-dimensional space, namely the rotation around the wave vector. A distinction is made between three types of polarization, which can be described by the direction and magnitude of the amplitude vector in a fixed point in space:

• linear polarization: The amplitude vector always points in a fixed direction and the deflection changes its magnitude and sign periodically (with a fixed amplitude) as the wave progresses.
• circular polarization (also known as rotating polarization): The amplitude vector rotates around the wave vector at a constant angular velocity as the wave advances and does not change its magnitude.
• elliptical polarization: The amplitude vector rotates around the wave vector and periodically changes its magnitude. The tip of the field vector describes an ellipse.

Linear and circular polarization can also be understood as borderline cases of elliptical polarization, but conversely any elliptical polarization can also be described as a superposition of a linear and a circularly polarized wave.

The background to this fact is that the polarization of any transverse wave is fully described by three quantities. These are the projection of the amplitude vector onto two orthogonal axes perpendicular to the wave vector and the phase difference between these two projections. The two orthogonal axes can be fixed in space (e.g. 'horizontal' or 'vertical'), but they can also rotate around the wave vector (right or left circular).

### Overlay

Any polarization can be represented as a superposition of two basic polarizations. The following two variants are often used:

1. Two linearly polarized waves whose polarization directions are perpendicular to each other are superimposed. Depending on the phase relationship and the intensity ratio of the two waves, the following initial polarizations result:
• with a vanishing phase difference (or a phase difference that corresponds to a multiple of π) and different amplitudes, the output polarization is linear and the direction depends on the amplitude ratio.
• with a phase difference of π / 2 and the same intensities, the output polarization is circular.
• in any other case the output polarization is elliptical.
2. Two circularly polarized waves, one clockwise and one counterclockwise, are superimposed. Depending on the phase relationship and the intensity ratio of the two waves, the following initial polarizations result:
• With the same intensities and variable phase difference, the initial polarization is linear and the direction depends on the phase position of the base polarizations.
• if one of the base polarizations has a vanishing amplitude, the output polarization is the other circular polarization.
• in any other case the output polarization is elliptical.

### Polarization of electromagnetic waves

Electromagnetic waves, including light waves, are transverse waves. To describe their polarization one usually refers to the electric field and disregards the magnetic one, which is perpendicular to the electric one. In circularly polarized light, the spins of all photons point in the same direction. Nevertheless, a single photon can also be linearly polarized by superimposing two oppositely circularly polarized states.

Unpolarized light cannot be generated by superimposing coherent polarized waves.

### Generation of polarized microwaves e.g. B. for satellite radio

News and television satellites use either two different linear polarization planes (horizontal / vertical) or two circular polarization directions (left or right) in order to be able to better utilize the scarce frequency bands available for satellite radio.

• In the Ku band (10.7 - 12.75 GHz), linear polarization is used almost exclusively today. At the beginning of the 1990s, however, pure television satellites were supposed to transmit circularly polarized (see: BSS Band).
• In the C-band (3.7-4.2 GHz), on the other hand, almost all satellites were transmitting circularly polarized until recently, but linear polarization has also been used more frequently in the C-band recently.
• It is known from the Mercury probe MESSENGER that its antennas send the signals circularly polarized in the X-band.

Linearly polarized microwaves are generated by aligning the transmitting dipole either “horizontally” or “vertically”. The microwaves generated in this way are polarized in the plane in which the transmitting dipole is located. To receive the linearly polarized signals, the receiving dipole must be in the plane in which the wave to be received oscillates.

Radio waves of lower frequencies are almost always radiated polarized. The type of polarization depends on the orientation of the antenna. Transmitters in the UHF / VHF range work - apart from mobile radio transmitters - as a rule with horizontal polarization, since less interference occurs here. Both horizontal and vertical polarization are common in the short wave range. Transmitters in the long, long and medium wave range almost always work with vertical polarization, as this enables the ground wave to propagate better.

Circular polarization is rarely used for broadcast purposes. It is sometimes used for steep beam antennas in the medium wave range.

### Mathematical description of polarization

The polarization state can be described by the four-dimensional real-valued Stokes vectors or by the two-dimensional complex-valued Jones vectors. As an alternative, quasi-monochromatic light can also be described by the coherence matrix. The description of the effect of a polarization-changing optical element is then carried out by multiplication with a corresponding Müller matrix or a Jones matrix.