Photon polarization is the quantum mechanical description of the classical polarized sinusoidal plane electromagnetic wave. An individual photon can be described as having right or left circular polarization, or a superposition of the two. Equivalently, a photon can be described as having horizontal or vertical linear polarization, or a superposition of the two.

The description of photon polarization contains many of the physical concepts and much of the mathematical machinery of more involved quantum descriptions, such as the quantum mechanics of an electron in a potential well. Polarization is an example of a qubit degree of freedom, which forms a fundamental basis for an understanding of more complicated quantum phenomena. Much of the mathematical machinery of quantum mechanics, such as state vectors, probability amplitudes, unitary operators, and Hermitian operators, emerge naturally from the classical Maxwell's equations in the description. The quantum polarization state vector for the photon, for instance, is identical with the Jones vector, usually used to describe the polarization of a classical wave. Unitary operators emerge from the classical requirement of the conservation of energy of a classical wave propagating through lossless media that alter the polarization state of the wave. Hermitian operators then follow for infinitesimal transformations of a classical polarization state.

Many of the implications of the mathematical machinery are easily verified experimentally. In fact, many of the experiments can be performed with polaroid sunglass lenses.

The connection with quantum mechanics is made through the identification of a minimum packet size, called a photon, for energy in the electromagnetic field. The identification is based on the theories of Planck and the interpretation of those theories by Einstein. The correspondence principle then allows the identification of momentum and angular momentum (called spin), as well as energy, with the photon.

Polarization of classical electromagnetic waves

This section duplicates the scope of other articles, specifically Sinusoidal plane-wave solutions of the electromagnetic wave equation. Please discuss this issue and help introduce a summary style to the section by replacing the section with a link and a summary or by splitting the content into a new article. (July 2014)

Polarization states

Linear polarization

The wave is linearly polarized (or plane polarized) when the phase angles ${\displaystyle \alpha _{x}\,,\;\alpha _{y}}$ are equal,

$${\displaystyle \alpha _{x}=\alpha _{y}\ {\stackrel {\mathrm {def} }{=}}\ \alpha .}$$

This represents a wave with phase ${\displaystyle \alpha }$ polarized at an angle ${\displaystyle \theta }$ with respect to the x axis. In this case the Jones vector

$${\displaystyle |\psi \rangle ={\begin{pmatrix}\cos \theta \exp \left(i\alpha _{x}\right)\\\sin \theta \exp \left(i\alpha _{y}\right)\end{pmatrix}}}$$

can be written with a single phase:

$${\displaystyle |\psi \rangle ={\begin{pmatrix}\cos \theta \\\sin \theta \end{pmatrix}}\exp \left(i\alpha \right).}$$

The state vectors for linear polarization in x or y are special cases of this state vector.

If unit vectors are defined such that

$${\displaystyle |x\rangle \ {\stackrel {\mathrm {def} }{=}}\ {\begin{pmatrix}1\\0\end{pmatrix}}}$$

and

$${\displaystyle |y\rangle \ {\stackrel {\mathrm {def} }{=}}\ {\begin{pmatrix}0\\1\end{pmatrix}}}$$

then the linearly polarized polarization state can be written in the "x-y basis" as

$${\displaystyle |\psi \rangle =\cos \theta \exp \left(i\alpha \right)|x\rangle +\sin \theta \exp \left(i\alpha \right)|y\rangle =\psi _{x}|x\rangle +\psi _{y}|y\rangle .}$$

Circular polarization

If the phase angles ${\displaystyle {\mathrm{\alpha <!--\; \alpha \; -->}}_x}$Zdroj:https://en.wikipedia.org?pojem=Photon_polarization
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