Nonlinear phase shift experienced by ultrafast optical pulses propagating in quadratic medium

Self-phase modulation (SPM) due to the second order cascading effect has been studied extensively because of their potential for all-optical switching applications. In second harmonic generation (SHG), for example, a large nonlinear phase shift can accumulate in the fundamental wave (FW) when light is upconverted to its second harmonic (SH) and then is subsequently downconverted back. Such an effect is known to be at least two orders of magnitude larger than the Kerr-type SPM. However, problems such as temporal and spectral broadening exist in dealing with ultrafast optical pulses propagating in dispersive quadratic media. Among these, the temporal walk-off between the FW and the SH pulses caused by the group velocity mismatch (GVM) is the most significant hurdle, which results in a poor cascading efficiency. On the other hand, spatial solitary waves were observed in a KTP crystal, in which both of the diffraction and the spatial walk-off were compensated by the cascaded self-focusing effect. As a temporal analogue, one can consider the possibility of temporal solitons in the context that the GVM and the group velocity dispersion (GVD) are properly balanced by the cascaded SPM. In the present work, we numerically study ultrafast pulse propagation in a medium with both GVD and GVM near phase matching condition for SHG. We also propose novel methods for reducing these effects for ultrafast all-optical switching applications.