In this work we experimentally demonstrate the generation ofexciton-polariton X-waves and study their dynamics in time. X-waves belong tothe category of localized packets, a class of states able to sustain theirshape without the need of any nonlinearity. This allows to keep the packetshape for very low densities and very long times compared, for instance, tosoliton waves which, on the contrary, always need nonlinearity to compensatethe diffusion. The use of polaritons in microcavities is paramount since it isthe unique system that allows the formation of an X-wave starting from aGaussian spot profile. A weak four wave mixing process together with thestructured non-parabolic dispersion drives the initial shaping alongpreferential directions that ultimately leads to the formation of a spatialX-wave front. This is the first time that such an X-wave is spontaneouslygenerated in a 2D spatial geometry via the characteristic polariton dispersionand their nonlinearities. We also show the crucial parameters driving thephenomena, observe the redistribution by means of ultrafast imaging experimentsand compare our results with numerical simulations.
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