Optical vortices and vortex solitons

Optical vortices are phase singularities in electromagnetic waves that constitute a unique and fascinating class of phenomena within the context of the physics of light. We present a brief overview of the recent advances in the study of optical vortices propagating in nonlinear media. We demonstrate that self-focusing nonlinearity leads, in general, to the azimuthal instability of a vortex-carrying beam, but it can support novel types of stable (or quasi-stable) self-trapped beams carrying nonzero angular momentum, such as vortex solitons, necklace beams, and soliton clusters. We also describe the properties of the discrete vortex solitons in periodic photonic lattices.