Structured light in the short-wavelength regime opens exciting avenues for the study of ultrafast spin and electronic dynamics. Here, we demonstrate theoretically and experimentally the generation of vector-vortex beams (VVB) in the extreme ultraviolet through high-order harmonic generation (HHG). The up-conversion of VVB, which are spatially tailored in their spin and orbital angular momentum, is ruled by the conservation of the topological Pancharatnam charge in HHG. Despite the complex propagation of the driving beam, high-harmonic VVB are robustly generated with smooth propagation properties. Remarkably, we find out that the conversion efficiency of high-harmonic VVB increases with the driving topological charge. Our work opens the possibility to synthesize attosecond helical structures with spatially varying polarization, a unique tool to probe spatiotemporal dynamics in inhomogeneous media or polarization-dependent systems.

The landscape of ultrafast structured light pulses has significantly advanced thanks to the ability of high-order harmonic generation (HHG) to translate the spatial properties of infrared laser beams to the extreme-ultraviolet (EUV) spectral range. In particular, the up-conversion of orbital angular momentum (OAM) has enabled the generation of high-order harmonics whose OAM scales linearly with the harmonic order and the topological charge of the driving field. Having a well-defined OAM, each harmonic is emitted as an EUV femtosecond vortex pulse. However, the order-dependent OAM across the harmonic comb precludes the synthesis of attosecond vortex pulses. Here we demonstrate a method for generating attosecond vortex pulse trains, i.e., a succession of attosecond pulses with a helical wavefront, resulting from the coherent superposition of a comb of EUV high-order harmonics with the same OAM. By driving HHG with a polarization tilt-angle fork grating, two spatially separated circularly polarized high-order harmonic beams with order-independent OAM are created. Our work opens the route towards attosecond-resolved light-matter interactions with two extra degrees of freedom, spin and OAM, which are particularly interesting for probing chiral systems and magnetic materials.

Isolated attosecond pulse (IAP) generation usually involves the use of short-medium gas cells operated at high pressures. In contrast, long-medium schemes at low pressures are commonly perceived as inherently unsuitable for IAP generation due to the nonlinear phenomena that challenge favourable phase-matching conditions. Here we provide clear experimental evidence on the generation of isolated extreme-ultraviolet attosecond pulses in a semi-infinite gas cell, demonstrating the use of extended-medium geometries for effective production of IAPs. To gain a deeper understanding we develop a simulation method for high-order harmonic generation (HHG), which combines nonlinear propagation with macroscopic HHG solving the 3D time-dependent Schrödinger equation at the single-atom level. Our simulations reveal that the nonlinear spatio-temporal reshaping of the driving field, observed in the experiment as a bright plasma channel, acts as a self-regulating mechanism boosting the phase-matching conditions for the generation of IAPs.

Linearly polarized vector beams are structured lasers whose topology is characterized by a well-defined Poincaré index, which is a topological invariant during high-order harmonic generation. As such, harmonics are produced as extreme-ultraviolet vector beams that inherit the topology of the driver. This holds for isotropic targets such as noble gases, but analogous behaviour in crystalline solids is still open to discussion. Here, we demonstrate that this conservation rule breaks in crystalline solids, in virtue of their anisotropic non-linear susceptibility. We identify the topological properties of the harmonic field as unique probes, sensitive to both the microscopic and macroscopic features of the target’s complex non-linear response. Our simulations, performed in single-layer graphene, show that the harmonic field is split into a multi-beam structure whose topology encodes information about laser-driven electronic dynamics. Our work promotes the topological analysis of the high-order harmonic field as a spectroscopic tool to reveal the nonlinearities in the coupling of light and target symmetries.