Optical phase singularities: Physical nature, manifestations and applications

Over the past 30 years, physical optics has been enriched by the appearance of singular optics as a new branch approved in scientific classifiers. This review briefly outlines the main concepts of the singular optics, their role in physical research and applications, and prospects of further development. The wave singularities are considered as a sort of structured-light elements and analyzed based on the generic example of screw wavefront dislocation (optical vortex). Their specific topological and mechanical properties associated with the transverse energy circulation are discussed. Peculiar features of the non-linear optical phenomena with singular fields are exhibited, with the special attention to generation of multidimensional entangled quantum states of photons. Optical fields with multiple singularities, especially, the stochastic speckle fields, are discussed in the context of optical diagnostics of random scattering objects. The exact and approximate correspondences between characteristic parameters of the optical-field intensity and phase distributions are analyzed with the aim of recovering phase information from the intensity measurements ( "phase problem " solution). Rational singularity-based approaches to informative measurements of the scattered-field distribution are discussed, as well as their employment for the objects' diagnostics. In particular, the practical instruments are described for the high-precision rough-surface testing. Possible enhancements of the singular-optics ideas and concepts in a wider context, including the transformation optics, near-field optics (surface waves), partially-coherent fields, and wave fields of other physical nature, are briefly exposed.