Generation of multiply charged optical vortices and spatiotemporal helical beams using cascaded four-wave mixing

In this work, we suggest a method for simultaneous manipulation by the frequency and angular harmonics of light opening new opportunities for spatio-temporal shaping of optical waves. Amongst others, we demonstrate the effect of cascaded vortex generation, describe the counter-intuitive process of strong spatial compression induced by self-defocusing nonlinearity and generation of spatio-temporal helical beams in the soliton and non-soliton regimes. Our approach is based on the observation that the four-wave mixing (FWM) process in nonlinear materials imposes a selection rules not only on the frequency spacing between the interacting waves but also on their orbital angular momentum also called topological charge. The strong coupling between the temporal and spatial degrees of freedom is induced in such a process.