Spin-orbit coupling in photonic graphene

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.