$\textit{Ab Initio}$ Theoretical Investigation of the Frequency Comb Structure in the XUV Regime via High Harmonic Generation

We present an $\textit{ab initio}$ quantum investigation of the frequency comb structure formed within each high harmonic generation (HHG) power spectrum driven by a train of equal- spacing short laser pulses. The HHG power spectrum of atomic hydrogen is calculated by solving the time-dependent Schr\"{o} dinger equation accurately and efficiently by means of the time- dependent generalized pseudospectral method. We found that the frequency comb structure is preserved within each harmonic. In addition, the repetition frequency of the comb laser depends upon the pulse separation $\tau$ and the spectral width of each individual comb fringe is inversely proportional to the number of pulses $(n)$ used. However, the global HHG power spectrum pattern depends only upon the laser frequency and intensity used and is not sensitive to the $\tau$ and $n$ parameters. Finally, the frequency comb structure persists even in the presence of appreciable ionization.