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

Control of spatio-temporal and spectral characteristics of optical waves using nonlinear and quantum properties of matter is an important, research area. Two prominent, examples of such control are the techniques developed for the generation of ultrashort, pulses [1] and of optical vortices [2]. 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 solitoli 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. So that, the strong coupling between the temporal and spatial degrees of freedom is induced in such a process. The most, interesting case is obviously when the FWM develops in a cascaded manner so that, many temporal and angular harmonics are generated and strong compression effects can be expected. The most, prominent, system, where cascaded FWM has been observed in the non-guided geometry, is the Raman active molecular gases excited by the two frequency pump at, the tail of Raman line, so that, the parametric FWM dominates over the Raman gain [1]. Therefore we focus on the Raman model to verify our ideas. Similar effects in the systems based on the Kerr-like nonlinearities are under the current, investigation.