  We generate experimentally a honeycomb refractive index pattern in an atomic
vapor cell using electromagnetically-induced transparency. We study
experimentally and theoretically the propagation of polarized light beams in
such "photonic graphene". We demonstrate that an effective spin-orbit coupling
appears as a correction to the paraxial beam equations because of the strong
spatial gradients of the permittivity. It leads to the coupling of spin and
angular momentum at the Dirac points of the graphene lattice. Our results
suggest that the polarization degree plays an important role in many
configurations where it has been previously neglected.
