Topology of singularaties and umbilic points in dynamic random optical fields

Abstract

Singularities are realized in variety of physical systems from optics to the Bose-Einstein condensates [1]. Optical singularities (optical vortices, circularly polarized C points, etc.) possess quit new properties against classical optics with smooth wave fields. Their discovery [2, 3] and investigation has created appearance of the singular optics as a new rapidly developing chapter of modern optics [3 5], etc. Most of papers in singular optics are devoted to realization and investigation of static optical fields. Quit new phenomena and regularities are realized in the dynamic optical fields [6–7]. We have shown also that very important and quite unusual topological role in singular optics play umbilic points, where wavefront is locally spherical one and possess special morphology [4].