Noninstantaneous femtosecond phase shift in second order cascading process

In this paper, we have studied the nonlinear propagation of femtosecond pulse in a χ (2) medium. We investigated the self-phase modulation induced by cascaded processes in type I BBO crystal. In particular, we measured precisely the temporal phase shift versus time as a function of the phase matching by two techniques: frequency direct phase measurement technique and linear spectral interferometry technique. These experimental outcomes are compared to numerical calculations from the coupled nonlinear wave equation.