  We investigate the two-dimensional motion of polaritons injected into a
planar microcavity by a continuous wave optical pump in presence of a static
perturbation, e.g. a point defect. By finding the stationary solutions of the
nonlinear mean-field equations (away from any parametric instability), we show
how the spectrum of the polariton Bogoliubov-like excitations reflects onto the
shape and intensity of the resonant Rayleigh scattering emission pattern in
both momentum and real space. We find a superfluid regime in the sense of the
Landau criterion, in which the Rayleigh scattering ring in momentum space
collapses as well as its normalized intensity. More generally, we show how
collective excitation spectra having no analog in equilibrium systems can be
observed by tuning the excitation angle and frequency. Predictions with
realistic semiconductor microcavity parameters are given.
