  We show that nonparaxial polarized light beams propagating in a bulk
nonlinear Kerr medium naturally exhibit a coupling between the motional and the
polarization degrees of freedom, realizing a spin-orbit-coupled mixture of
fluids of light. We investigate the impact of this mechanism on the Bogoliubov
modes of the fluid, using a suitable density-phase formalism built upon a
linearization of the exact Helmholtz equation. The Bogoliubov spectrum is found
to be anisotropic, and features both low-frequency gapless branches and
high-frequency gapped ones. We compute the amplitudes of these modes and
propose a couple of experimental protocols to study their excitation
mechanisms. This allows us to highlight a phenomenon of hybridization between
density and spin modes, which is absent in the paraxial description and
represents a typical fingerprint of spin-orbit coupling.
