Designing phase compensation for coherent control of frequency combs via high-order harmonic generation

We present a phase-compensation rule for achieving coherent control of frequency combs via high-order harmonic generation (HHG). The phase-compensation rule is illustrated by performing the generation of frequency combs via HHG from a hydrogen atom subjected to an intense laser pulse train. The numerical technique involves accurate and efficient solution of the time-dependent Schrödinger equation by means of the time-dependent generalized pseudospectral method. The results indicate that the frequency combs are fully optimized by employing the proposed phase-compensation rule, allowing direct control and generation of frequency combs with either the regular structure or the denser repetition combs. The performance of phase compensation is evaluated by analyzing the dynamical evolution of the harmonic spectra driven by several phase-compensation schemes. We believe that our findings serve as a guide for the experimental realization of phase coherent control of frequency combs via HHG at extremely high repetition frequencies.