Manipulation of double-four-wave mixing in an atomic system under vortex-beam illumination

Here we study systematically the double-channel four-wave mixing (FWM) processing in an atomic medium by adjusting azimuthal and radial indices (i.e., l and p ) of the Laguerre–Gaussian (LG) beams in the presence and absence of an elliptically polarized beam. It is found that there are ∣ l 1 - l 2 ∣ periods of phase jumps from - π to π as well as ∣ p 1 - p 2 ∣ raised phase surface and p min ( p min = min { p 1 , p 2 } ) convex rings in the phase profile of the FWM-generated field under the combined action of two LG beams and two circularly polarized components of the elliptically polarized light. In such a case, there are p max + 1 ( p max = max { p 1 , p 2 } ) concentric bright rings with a dark hollow center in the intensity distribution. However, the phase profile of the FWM field becomes twisted and displays petal-like structures under the action of four LG vortex beams. Compared with the situation of vortex and elliptically polarized beams illumination, the intensity pattern of the FWM field is distorted and multiple singularities occur at the transverse plane accompanied by zero-intensity regions. Our investigation shows the possibility of manipulating the intensity and phase profiles of the FWM-generated field, by purposely choosing appropriate azimuthal and radial mode indices of LG beams. Graphical abstract