High-harmonic generation (HHG) in gaseous media is a workhorse tool in attosecond science. Its description originates from the microscopic scale of a single atom or molecule interacting with a driving IR-laser pulse. A complete macroscopic picture corresponding to usual experimental realizations aggregates all the microscopic emitters and brings novel physical mechanisms that drive the generation. One of the key mechanisms within the macroscopic scale is the shaping of the driving pulse due to the non-linear response of the medium.
We present a comprehensive numerical model describing and coupling the physics on both scales. The model consists of different modules that provide different levels of approximation to choose an optimal trade-off between accuracy and computational cost. We then use it to address two generation schemes, for which we provide a detailed picture together with experimental realizations. The first scheme uses a long medium homogeneously pre-ionized by an electrical discharge to optimize the phase-matching of the harmonic signal. This scheme allows, in particular, for optimizing HHG in long media where the control is difficult because the driving pulse undergoes strong re-shaping and defocusing due to the non-linear response after the entrance to the medium. The second scheme is based on the driving-pulse-wavefront shaping that is imprinted in the HHG beam and used to control the harmonic-beam divergence. This mechanism is harmonic dependent and may provide a tunable spectral filter of the harmonic spectrum. The proposed scheme is optics-free and dodges unavoidable losses inherent to the use of optics in the XUV region.
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