We present ab initio calculations using the $R$-matrix with time dependence method for high-order harmonic generation (HHG) in argon in a short, intense pulse regime. The calculations employ a six-cycle ${sin}^2$ pulse at 850 nm with peak intensity $2.3\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$ and, for comparison with the experiment by Guo et al. [J. Phys. B: At. Mol. Opt. Phys. 51, 034006 (2018)], a Gaussian pulse with the same frequency and peak intensity. Both pulse shapes yield the expected harmonic structure in the region above the ionization threshold (approximately 15.82 eV in $LS$ coupling). The spectra exhibit strong carrier-envelope-phase sensitivity. The energy region leading up to the ionization threshold contains spectral features arising from residual coherent dipole oscillations (free-induction decay) that strongly depend on spectral windowing and the post-pulse propagation time. We show that the HHG spectrum, particularly below the ionization threshold, is a defined quantity that depends on analysis choices rather than being a uniquely determined observable. Comparison between theoretical predictions and experimental observations in this energy regime, therefore, requires explicit specification of these parameters.

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• Atomic & molecular processes in external fields
• High-order harmonic generation
• Pulse shaping
• Ultrafast phenomena
• XUV generation
• Atoms
• Dipole approximation
• Nonperturbative methods
• Schroedinger equation