Second-harmonic generation of weak femtosecond pulses under the condition of vanishing group-velocity mismatch

In this paper we theoretically study second-harmonic generation (SHG) of weak femtosecond pulses at the wavelength with vanished group-velocity mismatch (GVM) where group-velocity dispersion (GVD) plays a major role. While the principles behind the modelling are general, the simulations of SHG for Nd: glass laser pulses using the actual dispersion of a partially deuterated KDP are included. We demonstrate that both the proper pre-chirping of the pump pulse and optimization of the phase-matching condition may improve the conversion efficiency. The defined optimum dispersing parameter is calculated for several typical cases, and the results are compared with those obtained by Boyd and Kleinman in the space domain. The dependence of the SH spectrum on the phase-matching condition, GVDs and crystal length are evaluated respectively, and shows that optimum phase matching may enhance while strong GVDs and/or long crystal length narrow the SH bandwidth.