Dispersive waves in fs cascaded second-harmonic generation

Here we study second-harmonic generation (SHG) for soliton compression in detail by modelling an intense fs pulse propagating in a quadratic nonlinear crystal, where phase mismatched (cascaded) SHG takes place. As the pump pulse propagates, a huge nonlinear phase shift - and thus a chirp - is created on it due to cascaded SHG. In presence of proper dispersion this strongly chirped pulse can through the soliton effect be compressed using to duration of just a few cycles. The physics behind this is that the pump pulse may propagate as a Kerr-like soliton: if the cascaded SHG process has a negative phase mismatch, then a self-focusing Kerr-like nonlinearity is created and solitons are therefore supported with anomalous group-velocity dispersion (GVD). However, if the pump feels the cascaded SHG as a self-defocusing Kerr-like nonlinearity and solitons are supported with normal GVD.