Abstract
Studies on the singular optics of scalar wave fields carried out in the world and at V.E. Zuev Institute of Atmospheric Optics, Siberian Branch, Russian Academy of Sciences (IAO SB RAS) are reviewed. The study results of the processes of origination and annihilation of phase singularities are generalized. The methods for singular phase reconstruction and their applicability to the problems of adaptive focusing of radiation in randomly inhomogeneous media are examined. The energy, statistical, and topological properties of vortex optical beams propagating through a turbulent atmosphere are analyzed. The results of the synthesis of vortex beams with quickly controllable orbital angular momentum by the matrix approach developed at IAO SB RAS are described.
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