Negative-frequency resonant radiation in quadratic media

The aim of this contribution is twofold: (i) to assess the universal nature of negative frequency resonant radiation (NRR) by showing that it can be predicted to occur also via pure quadratic nonlinearities, under experimentally viable conditions of second harmonic generation (SHG); (ii) to generalize the concept of radiation by showing that in fact one does not necessarily need a soliton-like excitation, since RR and NRR can be produced also in the opposite regime where the nonlinearity, instead of compensating the action of group-velocity dispersion (GVD), is such to strongly enforce it leading to wave-breaking (shock formation). This regime investigated recently in experiments performed in the spatial domain features dispersive shock wave (DSW), as predicted in a seminal work by Gurevich and Pitaevskii.