Phase singularities and optical vortices in photonics

Since the second half of the 20th century, ideas to develop methods for the formation of optical vortices (OVs) or OV beams <SIC> regions of circular motion of energy flow in an electromagnetic wave around so-called phase singularity points <SIC> have become widespread. Such optical beams are unique because of the special spiral shape of the wave front, endowing them with orbital angular momentum (OAM) that can be transferred to matter and cause rotation of nano- and micro-objects. Presently, OV beams are actively used to solve both applied and fundamental problems in optics and photonics. We systematically discuss the development stages and the main advantages and disadvantages of methods for the formation of OV beams, from the appearance of phase singularities in light scattering in inhomogeneous media to the latest developments in vortex microlasers for controlled generation of light fields with a predefined OAM on nano-and microscales.