Pulse shaping and compression by second-harmonic generation with quasi-phase-matching gratings in the presence of arbitrary dispersion

A theoretical treatment of group-velocity dispersion and higher-order dispersion effects on the second-harmonic-generation (SHG) process with longitudinally nonuniform quasi-phase-matching (QPM) gratings is presented. We show how these dispersion terms can be accounted for in the design of a QPM-SHG pulse shaper. Our numerical simulation results show that, if the proper dispersion correction is included in the QPM grating design, one can generate sub-10-fs transform-limited pulses at 400 nm by doubling the output of a Ti:sapphire oscillator.