We experimentally investigate the frequency conversion of vector beams with four-wave-mixing (FWM) in rubidium vapor. The conversion of vector beams from the probe beam to the conjugate beam is realized. In FWM experiments, the pump and the probe beam have orthogonal polarizations because of the polarization sensitivity of the FWM process and detection convenience. In order to satisfy the polarization sensitive phase matching condition and realize the nonlinear frequency conversion of vector beams, a Sagnac interferometer is used to form two FWM processes in the same rubidium cell, and two generated conjugate beams are combined with a polarizing beam splitter to form a conjugate vector beam. The experimental results agree well with our theoretical simulation. Compared with nonlinear optical crystals, the atomic vapor provides another platform to control and manipulate the vector beams nonlinearly.
The orbital angular momentum (OAM) of light is a quantity explored for communication and quantum technology, its key strength being a wide set of values offering a large basis for quantum working. In this context we have studied the vortex conversion from a red optical vortex to a blue one, for OAMs ranging $\ensuremath{-}30$ to
+30. The conversion is realized in a rubidium vapor, via the $5{S}_{1/2}\ensuremath{-}5{D}_{5/2}\phantom{\rule{0.16em}{0ex}}^{85}\mathrm{Rb}$ two-photon transition done with a Gaussian beam at
780nm plus a Laguerre-Gaussian beam at
776nm with the OAM $\ensuremath{\ell}$, producing a radiation at
420nm. With copropagating input beams, we demonstrate a conversion from red to blue for high-$\ensuremath{\ell}$ input vortices. We show that the output blue vortex respects the azimuthal phase matching, has a size determined by the product of the input beams, and a power decreasing with $\ensuremath{\ell}$, in agreement with their overlap. Its propagation indicates that the generated blue wave is a nearly pure Laguerre-Gaussian mode. The vortex converter thus permits a correct OAM transmission.