Polarization shaping for control of nonlinear propagation

We study the nonlinear optical propagation of two different classes of{light beams with space varying polarization -- radially symmetric vector beams and Poincar\'e beams with lemon and star topologies -- in a rubidium vapour cell. Unlike Laguerre-Gauss and other types of beams that quickly experience instabilities, we observe that their propagation is not marked by beam breakup while still exhibiting traits such as nonlinear confinement and self-focusing. Our results suggest that by tailoring the spatial structure of the polarization, the effects of nonlinear propagation can be effectively controlled. These findings provide a novel approach to transport high-power light beams in nonlinear media with controllable distortions to their spatial structure and polarization properties.