Relative strengths of sum and difference frequency generation in perturbative high harmonic wave mixing

Abstract

High harmonic generation (HHG) modulated by a weak laser field allows the perturbative wave mixing process which involves sum and difference frequency generations (SFG and DFG). The relative strengths of SFG and DFG have been extensively discussed in the literature but are still ambiguous. Here we experimentally study the relative strengths between SFG and DFG channels by applying a frequency-offset second-harmonic perturbing laser field collinearly in a thin gaseous nonlinear medium. It shows that SFG is favored for low harmonic orders, but DFG dominates for high-energy photons, when only short trajectories of high harmonics are considered. A semi-classical model incorporating both modulations to the tunneling ionization and the electron propagation steps by the perturbing laser field for a train of attosecond pulses explains the experimental results.