  We propose a four wave mixing experiment to probe the elementary excitation
spectrum of a non-equilibrium Bose-Einstein condensate of exciton-polaritons
under non-resonant pumping. Analytical calculations based on mean-field theory
show that this method is able to reveal the characteristic negative energy
feature of the Bogoliubov dispersion. Numerical simulations including the
finite spatial profile of the excitation laser spot and a weak disorder confirm
the practical utility of the method for realistic condensates.
