Efficiency of short-pulse type-I second-harmonic generation with simultaneous spatial walk-off, temporal walk-off, and pump depletion

We have developed a theory which for the first time predicts the efficiency of type-I second-harmonic generation (SHG) with simultaneous spatial and temporal walk-offs and with pump depletion. In order to validate our theory, we have compared its predictions with a numerical solver. We also have measured the conversion efficiency for type-I SHG in experiments with ∼120--fs laser pulses in BBO and LBO crystals long enough that both temporal and spatial walk-off are important. Comparison supports our theoretical analysis. Our theory provides a useful tool for estimating SHG efficiency with pulsed sources in both nondepletion and depletion regions.