In modern optics, we understand fields of light through their geometrical singularities. These are different at different levels of description. The coarsest level is geometrical optics, where the singularities are caustics: focal lines and surfaces. These singularities of bright light are classified by the mathematics of catastrophe theory. Wave optics smooths these singularities and decorates them with rich and ubiquitous interference patterns. Wave optics also introduces phase, which has its own singularities. These are optical vortices, a.k.a nodes or wavefront dislocations. Geometrically, these singularities of dark light are lines in space, or points in the plane. They occur in all types of quantum or classical waves. Incorporating the vector nature of light leads to polarisation singularities, also geometrical, describing lines where the polarisation is purely circular or linear. With hindsight, it is clear that singular optics started in the 1830s. The levels form a hierarchy, leading to predictions of phenomena at the quantum level.
Reference Berry, M.V. “The singularities of light: intensity, phase, polarisation,” Light, Science and Applications, Vol. 12, 1-4, 2023.
About the speaker: Sir Michael Berry is a theoretical physicist at the University of Bristol, where he has been for more than twice as long as he has not. His research centres on the relations between physical theories at different levels of description (classical and quantum physics, ray optics and wave optics…). In addition to these deeply mathematical, often geometric, studies, he also delights in finding familiar phenomena illustrating deep concepts – the arcane in the mundane: rainbows, the sparkling of the sun on the sea, twinkling starlight, polarised light in the sky, tidal bores... (for more, see https://michaelberryphysics.wordpress.com)
This lecture is part of the discussion meeting "Phases, Caustics and Chaos: Classical and Quantum Aspects".