Exciton-polariton X-waves in a microcavity

We investigate the possibility of creating X-waves, or localized wave packets, in resonantly excited exciton-polariton superfluids. We demonstrate the existence of X-wave traveling solutions in the coupled exciton-photon system past the inflection point, where the effective mass of lower polaritons is negative in the direction perpendicular to the wavevector of the pumping beam. Contrary to the case of bright solitons, X-waves do not require nonlinearity for sustaining their shape. Nevertheless, we show that nonlinearity is important for their dynamics, as it allows for their spontaneous formation from an initial Gaussian wave packet. Unique properties of exciton-polaritons may lead to applications of their X-waves in long-distance signal propagation inside novel integrated optoelectronic circuits based on excitons.