Singular optics and topological photonics

For centuries, singularities in wave fields have been a mainstay of interest in multiple areas of physics, ranging from plasma physics, fluid dynamics and atmospheric physics to optics and photonics [1]. In optics, energy and momentum flow around singularities in the interference field can twist to form vortices, which carry angular momentum [2–4]. Singular Optics is the branch of physics that encompasses studies of structured light with localized and extended singularities, such as optical vortices in scalar optical fields and polarization singularities in vector fields [2, 5, 6]. It has been pioneered by the publication of a seminal paper of Nye and Berry 'Dislocations in wave trains' in 1974 [7], and has recently celebrated its 40th anniversary