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We used a high-energy femtosecond fundamental IR (centered at λ0 = 800 nm) pulse, and spatially filtered the laser beam before compression. Spatial filtering was performed under vacuum with a 250-μm pinhole after clipping the incoming beam with an iris and focusing it with a f = 1.3 m lens. The beam was afterward collimated with a spherical mirror located 1.5 m after the pinhole. The overall transmission of the spatial filtering was 50%, and output pulses with maximum energies of 50 mJ after compression could be used. When the spatial chirp was introduced, the pulse energy was limited to 2.5 mJ to limit nonlinear effects in the wedge.

The IR wavefront was corrected after compression under vacuum by a deformable mirror (High Power Active Mirror, Hipao, ISP Systems) that was specifically designed for high-energy ultrashort lasers. This active mirror is equipped with a thick glass membrane with multilayer dielectric coating that allows smooth correction and stable operation. The corrected IR wavefront, measured with an HASO (Imagine Optics), showed a residual error smaller than 8 nm rms (λ/100), and the Strehl ratio was larger than 0.95. Controlling the wavefront with such a high precision is crucial, since it ensures good XUV spatial coherence even when the harmonics are generated far from the IR focus position. Wavefront control was also used here to precompensate for the astigmatism induced by the spherical mirror used to focus the IR beam in the gas jet.

After corrections, we observed that the intensity profile of the fundamental beam was close to a Gaussian beam in the far field and near focus with a small asymmetry. The measured laser beam factor (M2) was slightly different in the horizontal and vertical directions (see the Supplementary Materials), and we used a value of M2 = 1.04 in the simulations. We measured a beam profile and size evolution with z that was close to a perfect Gaussian beam (see the Supplementary Materials), and we assumed in the simulations that the fundamental beam propagates (waist and wavefront dependence with z) as a Gaussian beam. The ability to control the IR wavefront with the deformable mirror has a large impact on the XUV beam, since it directly affects the XUV wavefront. It also ensures that the transverse evolution of the IR wavefront is regular even if far from the IR focus, while this is not always the case with a laser beam having a large M2 factor that can exhibit complex phase evolution and additional spatial structures off-focus.

We used a 40-fs fundamental pulse with energy of ~2 to 5 mJ to generate high-order harmonics by focusing the input beam (Wx = 6.7 mm and Wy = 7.6 mm) truncated by a 20-mm-diameter iris with a f = 2 m spherical mirror to a focal spot size of W0 ≈ 83 μm. The iris transmits most of the beam power and improves the beam symmetry near focus. HHG occurs at 10 Hz in a pulsed neon jet with a 250-μm nozzle diameter that could be moved by 7.5 cm before and after the IR focus. We analyzed the spatial profile of each harmonic in the far field with a flat field spectrometer. It is equipped with a 500-μm-wide entrance slit, a grazing incidence grating with 1200 grooves/mm (Hitachi aberration-corrected concave grating), and a 40-mm-diameter microchannel plate detector that was located 2.9 m after the IR focus position.

When HHG was performed with a spatially chirped beam, the fundamental beam was transmitted through a single fused silica 2.5° wedge used near normal incidence and located ~1.5 m before the focusing mirror. The wedge was located near a motorized folding mirror used to compensate for the average beam deviation introduced by the wedge and to maintain the same optical axis after the wedge.

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