Radial-angular coupling in self-phase-modulation with structured light

In this work we study the evolution of an optical vortex undergoing self-phase modulation inside a nonlinear Kerr medium. The intensity-dependent phase evolution couples the angular and radial degrees of freedom of the input vortex, giving rise to a rich dynamics where new radial modes are created. In the short propagation range, this dynamics is well described by a perturbative approach, predicting the generation of modes with radial numbers between zero and the absolute value of the vortex topological charge. This prediction is confirmed by numerical simulations of the nonlinear propagation equation.