Abstract

Control of spatio-temporal and spectral characteristics of optical waves using nonlinear and quantum properties of matter is an active 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 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. The most interesting case is 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. Frequencies are chosen so that the excitation is done at the tail of Raman line and 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. A dimensionless model describing the evolution of the Raman sidebands: i∂_zE_n−1/2·ΔE_n = β_nE_n + q^*E_n−1 + qE_n+1, where q is the Raman coherence dependent on the side-band amplitudes E_n. β_n are the wavenumber mismatches.

© 2007 IEEE