|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"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.