  Propagation of coherent light in a Kerr nonlinear medium can be mapped onto a
flow of an equivalent fluid. Here we use this mapping to model the conditions
in the vicinity of a rotating black hole as a Laguerre-Gauss vortex beam. We
describe weak fluctuations of the phase and amplitude of the electric field by
wave equations in curved space, with a metric that is similar to the Kerr
metric. We find the positions of event horizons and ergoregion boundaries, and
the conditions for the onset of superradiance, which are simultaneously the
conditions for a resonance in the analogue Hawking radiation. The resonance
strongly enhances the otherwise exponentially weak Hawking radiation at certain
frequencies, and makes its experimental observation feasible.
