Geometry of phase and polarization singularities.
Michael Berry (Department of Physics, Bristol University)

Jeudi 28 mars 2002

At a zero of a complex scalar wave, the phase is singular. This happens along lines in space, or at points in the plane. Although the occurrence of phase singularities as a generic feature of waves was appreciated only in 1974, they were almost discovered in edge diffraction by Newton in 1727, and actually discovered in the tides by Whewell in 1833.

Now they are familiar as quantized flux lines in superconductors and quantized vortices in superfluids, and as optical vortices (also called wavefront dislocation lines or topological charges) in interfering beam of light. Phase singularities are complementary to the caustic singularities of geometrical optics.

In random waves (e.g. black-body radiation or chaotic quantum billiards) they have interesting statistics, and they can be constructed explicitly in the form of knots and links.

In complex vector waves there are no phase singularities, but there exist other line singularities, where the polarization is purely linear or purely circular, with an interesting interpretation in terms of photon spin.