Four-wave mixing and secondary radiations generated by nonharmonic two-color filaments in air: Influence of the Kerr and plasma nonlinearities
Four-wave mixing (FWM) is an efficient source of light waves emitted at various frequencies, usually associated with third-order optical nonlinearities. Whereas attention has mostly been paid in the past to the generation of Stokes (e.g., visible) modes by mixing two nonharmonic frequencies in degenerate FWM, the present work aims to analyze the weaker components, i.e., the anti-Stokes (resp. mid-IR) radiation and cascaded satellites, and characterize their conversion efficiency and tunability. Here we report the production of tunable mid-infrared radiation around 3.3 $\mu$m delivered by two-color femtosecond filaments in air combining $\sim 800$ nm fundamental and $\sim 1.3$ $\mu$m seed waves. Although the Kerr response of air plays a key role in creating both visible and mid-IR radiations, we show that plasma nonlinearities also contribute by broadening and mixing the pump frequencies. Two experimental setups are exploited to focus, separately, on the production of FWM modes and cascaded satellites - called secondary radiations. A first filamentation setup employing different focal lengths for the two colors displays an ionization-induced broadening of the mid-IR radiation during the plasma stage. A second setup focusing the two pump components over equal propagation distances allows us to unveil the secondary radiations emerging at lower intensity levels when plasma occurs. We examine which player, among the plasma- or Kerr-induced FWM, is the most active in the conversion process. Numerical simulations based on a local-current model and a unidirectional solver highlight the role of the Kerr stage in amplifying the FWM radiations prior to the development of the weaker satellites in plasma regime. Their results, agreeing well with the experimental data, demonstrate that a broad visible emission is needed to trigger secondary radiations.