Fig. 1. Schematic view of HHG driven by OAM beams. An intense IR vortex beam carrying OAM (with $\ell =1$ in this case), is focused into an argon gas jet. The near-field coordinates are ($\unicode[STIX]{x1D70C},\unicode[STIX]{x1D719}$). Each atom emits HHG radiation that, upon propagation, results in the far-field emission of XUV vortices with some divergence and azimuth ($\unicode[STIX]{x1D6FD},\unicode[STIX]{x1D711}$). In the bottom we show the near-field amplitude (left) and phase (right) of the $LG_{1,0}$ IR mode, with beam waist of $30~\unicode[STIX]{x03BC}\text{m}$.

Fig. 2. Spatial intensity profile of the emitted 19th harmonic for a slab placed at seven near-field positions, from $z_{t}=-3~\text{mm}$ (left) to $z_{t}=3~\text{mm}$ (right), calculated with the TSM considering (a) short$+$long, (b) short and (c) long quantum-path contributions. Whereas short quantum-path contributions exhibit similar intensity and structure independently of the near-field slab location, long ones are more intense if the slab is placed before the focus position. As a consequence, a rich vortex structure profile is obtained depending on the relative position between the gas jet and the beam focus.

Fig. 3. Radial intensity profile of the emitted 19th harmonic as a function of the near-field slab position, calculated with the TSM considering (a) short$+$long, (b) short and (c) long quantum-path contributions. As depicted in Figure 2, the dependence of the profile of short quantum-path contributions with the slab position is almost symmetric with respect to the focus, whereas that of the long ones is completely asymmetric. As a consequence, the relative position between the gas jet and the beam focus serves as a knob control to select harmonic vortices with short or long quantum-path contributions.

Fig. 4. Attosecond twisted beam structures of the emitted harmonic radiation obtained with the 3D SFA quantum model for a multi-cycle driving laser pulse of $\unicode[STIX]{x1D70F}_{P}=15.4~\text{fs}$ (a, b) and a few-cycle driver of $\unicode[STIX]{x1D70F}_{P}=3.8~\text{fs}$ (c, d). The harmonics are generated in a $500~\unicode[STIX]{x03BC}\text{m}$ argon gas jet placed 2 mm before (a, c) and after (b, d) the focus position. On the left we show the attosecond twisted beam structure, whereas on the right we show transverse intensity snapshots at four different time instants within a half-cycle, $0.12T,0.25T,0.38T$ and $0.5T$ (where $T$ is the laser period). The contribution from long quantum-path contributions is indicated in yellow.