Optical vortices in waveguides with discrete and continuous rotational symmetry

Coherent vortex structures are fascinating physical objects that are widespread in nature: from large scale atmospheric phenomena, such as tornadoes and the Great Red Spot of Jupiter to microscopic size topological defects in quantum physics and optics. Unlike classical vortex dynamics in fluids, optical vortices feature new interesting properties. For instance, novel discrete optical vortices can be generated in photonic lattices, leading to new physics. In nonlinear optical media, vortices can be treated as solitons with nontrivial characteristics currently studied under the emerging field of topological photonics. Parallel to theoretical advances, new areas of the engineering applications based on light vortices have emerged. Examples include the possibility of carrying information coded in the vortex orbital angular momentum, understood as a spatial-division-multiplexing scheme, to the creation of optical tweezers for efficient manipulation of small objects. This report presents an overview highlighting some of the recent advances in the field of optical vortices with special attention on discrete vortex systems and related numerical methods for modeling propagation in multi-core fibers.