Limiting factors for frequency doubling of a Ti:Sapphire laser with a femtosecond pulse

The second-harmonic generation for a Ti:Sapphire laser (790 nm) is simulated with a femtosecond pulse. KDP type I and type II crystals are used for the second-harmonic generator. To discuss the phase mismatching in the second-harmonic generation, we simulated the wave equations, including group velocity, group-velocity dispersion, and third-order nonlinear susceptibility, for a femtosecond pulse. The results of the simulation show that the conversion efficiency is decreased mainly by the third-order nonlinear susceptibility at the KDP type I crystal and by the group-velocity mismatch at the KDP type II crystal. The optimum efficiency is 22.9 % at the KDP type I crystal and 9.2 % at the KDP type II crystal with a time delay of 80 fs under an input intensity of 500 GW/cm(2).