Theory of backward second-harmonic and third-harmonic generation using laser pulses in quasi-phase-matched second-order nonlinear medium

Recently, we have observed backward second-harmonic generation (SHG) using subpicosecond and nanosecond laser pulses in periodically poled lithium niobate crystals. The conversion efficiency in terms of energy density per pulse measured in the experiments agrees well with that based on our theory. In this paper, we present our theoretical investigation of this process in detail. Although the temporal behaviors of the second-harmonic radiation are determined by the same functions as those for the forward SHG, the amounts of pulse broadening and conversion efficiencies are quite different for the two configurations. In addition, we have investigated saturation of the conversion efficiencies. We have also considered effective third-harmonic generation based on cascaded second-order nonlinear processes. For a few optimized spatial periods of the domains, we have estimated the conversion efficiencies