Negative-frequency dispersive wave generation in quadratic media

Abstract: We show that the extremely blue-shifted dispersive wave emitted in Kerr media owing to the coupling with the negative-frequency branch [Phys. Rev. Lett. {\bf 108}, 253901 (2012)] can be observed in quadratic media via second-harmonic generation. Not only such phenomenon is thus independent on the specific nonlinear mechanism, but it is shown to occur regardless of the fact that the process is pumped by a pulse which exhibits soliton-like features or, viceversa, undergoes wave-breaking. A simple unified formula gives the frequencies of the emitted dispersive waves in both cases.