Nonlinear X waves: a spontaneous localization in spatio-temporal domain

X waves, known in linear optics, acoustic and microwave physics for their unique non-dispersive and non-diffracting features, appear as the normal propagation mode of a wide class of nonlinear systems. Here we demonstrate how these apparently exotic objects represent the normal mode of propagation for a wide class of nonlinear systems, i. e. in the presence of normal dispersion and self-focusing phase modulation. The experiment is made in regime of second-harmonic generation (SHG), which allowed us to exploit a very strong temporal-broadening effect due to the group-velocity mismatch between the fundamental and the second harmonic.