Photon Polarization

A calcite crystal laid upon a paper with some letters showing the double refraction

A recent paper on double-slit trajectories tilted

Watching Photons Interfere: "Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer"

is featured at Chad Orzel's highly educational and entertaining weblog, Uncertain Principles, here

It's entertaining as well as informative, but not overly so if one refreshes and bones up or learns for the first time what "photon polarization" is.

The mathematics of Photon Polarization are not difficult, and Photon Polarization is an important field. Its entry in Wikipedia is quite long, so I leave with the introduction and contents of the Wiki article and wish you all great joy exploring on your own:

Photon polarization is the quantum mechanical description of the classical polarized sinusoidal plane electromagnetic wave. Individual photons are completely polarized. Their polarization state can be linear or circular, or it can be elliptical, which is anywhere in between of linear and circular polarization.

The description 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, and 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 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 two pairs (or one broken pair) ofpolaroid sunglasses.

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 (calledspin), as well as energy, with the photon.

Contents  [hide] 1 Polarization of classical electromagnetic waves 1.1 A polarization state vector 1.1.1 Jones vector 1.1.2 Dual of the Jones vector 1.1.3 Normalization of the Jones vector 1.2 Polarization states 1.2.1 Linear polarization 1.2.2 Circular polarization 1.2.3 Elliptical polarization 1.2.4 Physical interpretation of an arbitrary polarization state 2 Energy, momentum, and angular momentum of a classical electromagnetic wave 2.1 Energy density of classical electromagnetic waves 2.1.1 Energy in a plane wave 2.1.2 Fraction of energy in each component 2.2 Momentum density of classical electromagnetic waves 2.3 Angular momentum density of classical electromagnetic waves 3 Optical filters and crystals 3.1 Passage of a classical wave through a polaroid filter 3.2 Example of energy conservation: Passage of a classical wave through a birefringent crystal 3.2.1 Initial and final states 3.2.2 Dual of the final state 3.2.3 Unitary operators and energy conservation 3.2.4 Hermitian operators and energy conservation 4 Photons: The connection to quantum mechanics 4.1 Energy, momentum, and angular momentum of photons 4.1.1 Energy 4.1.2 Momentum 4.1.3 Angular momentum and spin 4.1.3.1 Spin operator 4.1.3.2 Spin states 4.1.3.3 Spin and angular momentum operators in differential form 4.2 The nature of probability in quantum mechanics 4.2.1 Probability for a single photon 4.2.2 Probability amplitudes 4.3 Uncertainty principle 4.3.1 Mathematical preparation 4.3.2 Application to angular momentum 4.4 States, probability amplitudes, unitary and Hermitian operators, and eigenvectors 5 See also 6 References