Duality between phase vortices and Argand-plane caustics

Singularities in the mappings of complex two-dimensional vortical wavefields to Argand space are used here to investigate the duality between vortices in the physical field and caustic-like structures in the Argand plane. Such map singularities are exemplified via a method of optical vortex generation based on low-pass filtering of two-dimensional noise. The presence of Argand-plane fold caustics crossing the Argand-plane origin is tied to changes in vortex numbers in the physical wavefield. Increasing the low-pass filter cutoff leads to higher-order Argand-plane caustic singularities, such as the hyperbolic umbilic catastrophe. This work presents a duality between vortices and caustics, explores the Argand plane as a tool in analysing optical wavefields, and provides a new environment for studying catastrophes.