Trapping of ultrashort pulses in nondegenerate parametric conversion

Parametric conversion of ultrashort pulses is a versatile tool in nonlinear and quantum optics. Here, we present a detailed theory and numerical investigation of the phenomenon of the signal and idler trapping by the ultrashort pump pulse in a material with second- and third-order nonlinearities. The trapping regime becomes possible by balancing the characteristic length scales associated with the group-velocity mismatch and second-order nonlinearity, ensuring that signal, idler, and pump pulses propagate with the pump group velocity. We have derived analytical solutions for the trapped states and found that the transition between the broadband coherent and in-coherent signal and idler spectra accompanies the changeover between the trapping and no-trapping regimes. We have also demonstrated the higher-order trapped states, reported a significant boost to conversion efficiency in the trapping regime and considered in detail a particular case of the pump pulse being an optical soliton.