In this thesis, we investigate ultrafast second harmonic generations (SHG). The pump laser is a mode-locked fiber laser at 1.56 □m with a 0.6 ps pulse width and 1.5 kW peak powers, so the walk-off problems also need to be considered in our study In order to satisfy phase matching condition and compensate group velocity walk-off, the quasi-phase technique was a possible method to design an engineerable nonlinear optics crystal. The nonlinear crystal in these experiments was a type-I (ooe), 30-mm long Mg:PPLN crystal with a 20.6 □m period. The phase and group mismatches of the mixing waves at 1560 and 780 nm were simultaneously compensated in this crystal.
Since the phase matching acceptance bandwidth of our design is about 30 nm, therefore, the phase matching conditions of other □□ nonlinear processes, such as sum-frequency generation (SFG), difference-frequency generation (DFG), and cascaded SHG/DFG, are also satisfied near the broad pump spectrum. The first evidence of cascaded nonlinear processes was that the spectral bandwidth of the fundamental wave was 1.08 times the original one. The second evidence of cascaded nonlinear processes was shown in a dual continuous-wave diode lasers pumped SHG The side band spectra provide evidence on the presence of cascading nonlinear processes simultaneously. Therefore, the cascaded processes are experimentally and numerically confirmed as a mechanism to limit the conversion efficiency of the ultrafast SHG to about 30 %.

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