Anomalous multi-ramp fractional vortex beams with arbitrary topological charge jumps

Traditional fractional vortex beams are well-known "jump" beams: that is, their net topological charge jumps by unity as the effective topological charge of the source passes a half-integer value. Here, we propose an anomalous multi-ramp fractional vortex (AMRFV) beam. Unlike the traditional fractional vortex beams, an AMRFV beam can be designed to have arbitrary jumps in topological charge at any critical threshold of the source charge. We walk through some examples of AMRFV beams using simulations and present a clear interpretation of the multi-jump characteristic based on the evolution of phase singularities.