  We develop a theory of artificial gauge fields in photon fluids for the cases
of both second-order and third-order optical nonlinearities. This applies to
weak excitations in the presence of pump fields carrying orbital angular
momentum, and is thus a type of Bogoliubov theory. The resulting artificial
gauge fields experienced by the weak excitations are an interesting
generalization of previous cases and reflect the PT-symmetry properties of the
underlying non-Hermitian Hamiltonian. We illustrate the observable consequences
of the resulting synthetic magnetic fields for examples involving both
second-order and third-order nonlinearities.
