Illustrations of optical vortices in three dimensions

Optical vortices (phase singularities) arise from interference and are threads of darkness embedded within light fields. Although usually visualised in terms of their points of intersection with an observation plane, appreciation of their true form requires a view in three dimensions. Through numerical simulation we re-examine three situations where optical vortex lines evolve as an additional parameter is varied. Our specific examples are: the addition of a fourth plane wave of varying amplitude into a superposition of three plane waves, the increase of height of a non-integer spiral phase step, and finally the perturbation that creates, and then dissolves, a vortex link in a specific combination of Laguerre-Gauss modes.