The paper deals with the scattering of linear polaritons on the incoherently excited stationary states. By direct numerical simulations it is shown that the vorticity of the stationary nonlinear polariton state can be probed by propagating polaritons of low intensity. It is discussed how the influence of the vorticity of the nonlinear state on the probe signal can be used for the characterization of the polariton states and for the design of polariton interferometers.

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