A beam with an angular-dependant phase Φ = ℓϕ about the beam axis carries an orbital angular momentum of ℓℏ per photon. Such beams are exploited to provide superresolution in microscopy. Creating extreme ultraviolet or soft-x-ray beams with controllable orbital angular momentum is a critical step towards extending superresolution to much higher spatial resolution. We show that orbital angular momentum is conserved during high-harmonic generation. Experimentally, we use a fundamental beam with |ℓ| = 1 and interferometrically determine that the harmonics each have orbital angular momentum equal to their harmonic number. Theoretically, we show how any small value of orbital angular momentum can be coupled to any harmonic in a controlled manner. Our results open a route to microscopy on the molecular, or even submolecular, scale.

Attosecond extreme-ultraviolet pulses 1 have a complex space-time structure 2 . However, at present, there is no method to observe this intricate detail; all measurements of the duration of attosecond pulses are, to some extent, spatially averaged 1,3-5 . A technique for determining the full space-time structure would enable a detailed study of the highly nonlinear processes that generate these pulses as a function of intensity without averaging 6,7 . Here, we introduce and demonstrate an all-optical method to measure the space-time characteristics of an isolated attosecond pulse. Our measurements show that intensity-dependent phase and quantum-path interference both play a key role in determining the pulse structure. In the generating medium, the attosecond pulse is strongly modulated in space and time. Propagation modifies but does not erase this modulation. Quantum-path interference of the single-atom response, previously obscured by spatial and temporal averaging, may enable measuring the laser-field-driven ion dynamics with sub-cycle resolution.Fully defining an attosecond pulse requires knowledge of its phase variation both temporally and spatially. Until now, temporal 1,3-5,8,9 and spatial 10-12 measurements are achieved only separately. As the temporal characterization methods (known as RABBIT; ref. 1 and CRAB;9,13) rely on the photoelectric effect, they average over the spatial profile of a pulse, mixing the contribution from the different emitters of the extremeultraviolet (XUV) source at a secondary target. On the other hand, spatial measurements of XUV emission have been achieved using small apertures 10,11 or two foci 12 . Although temporal information remains available in principle, neither method seems compatible with RABBIT or CRAB. Therefore, space-time measurements of attosecond pulses have never been made.To solve the space-time problem, we turn to an in situ technique. The in situ method is a unique method of measurement that is feasible only for highly nonlinear processes [14][15][16] . It relies on the fact that adding a single photon to an already highly nonlinear process only weakly perturbs the process 17,18 . Yet, it can modify the spatial and spectral pattern of a beam. The in situ method has been considered in attosecond pulse metrology to determine only the temporal profile of the average attosecond pulse within attosecond pulse trains 14 . For that measurement, a weak second-harmonic beam co-propagates with the fundamental beam to break the symmetry between adjacent attosecond pulses, thereby allowing an even-order harmonic signal. Temporal information was encoded in the even-order harmonic signal as a function of the phase delay between the fundamental and second-harmonic laser pulses 14 .For our spatially encoded in situ measurement, we produce XUV radiation using the fundamental laser pulse with a time-dependent