Paraxial optical skyrmions can be viewed as the coherent superposition of a vortex beam and a Gaussian beam with the same frequency and opposite spin directions. The optical skyrmions, whose topological structures are mapped onto the plane perpendicular to the propagation axis, are thus termed 'spatial skyrmions'. In recent years, optical pulses carrying transverse orbital angular momentum (T-OAM)—namely, spatiotemporal optical vortices (STOV)—have been realized experimentally. By replacing the vortex beam with an STOV, the skyrmionic topology can be extended into the spatiotemporal domain, with the topological plane parallel to the optical axis, giving rise to 'spatiotemporal skyrmions'.
Extreme-ultraviolet (EUV) spatiotemporal skyrmions hold great promise, owing to their high photon energy, ultra-fine polarization structures in the spatiotemporal domain, and potential as a novel attosecond light source. The development of such EUV spatiotemporal skyrmions offers broad application prospects. However, conventional light manipulation techniques face significant challenges when extended to the EUV band, primarily due to the strong absorption of optical elements and the difficulties in designing EUV-compatible devices.
High-order harmonic generation (HHG) is a dramatically nonlinear frequency up-conversion process in the interaction between intense laser pulses and matter. Governed by the conservation of energy and angular momentum, the angular momentum of the driving laser field is intrinsically and multiplicatively transferred to the harmonic fields in the HHG process. This mechanism makes HHG a promising route for generating structured and topological EUV light fields.
The team of professor Songlin Zhuang and Yi Liu at the University of Shanghai for Science and Technology has theoretically verified a two-color scheme for generating EUV spatiotemporal skyrmions via the HHG process, and systematically investigated its generation mechanism.
Generation and control mechanism of EUV spatiotemporal skyrmions
Simulations based on the strong-field approximation model demonstrate that the topological structure of the driving field can be robustly transferred to the harmonic field, thereby enabling the generation of various types of spatiotemporal skyrmions in the EUV band. By introducing a qualitative analytical method based on photon absorption probability, the researchers identified the dominant nonlinear absorption channels in the harmonic generation process. The study further reveals that each harmonic component is governed by distinct photon absorption channels, with specific OAM states playing a dominant role in the harmonic generation. Theoretical analysis attributes the effective transfer of the topological texture to the combined constraints of energy, spin angular momentum (SAM), and T-OAM conservation.
Importance of Stokes vector direction matching
Further studies show that the direction matching of Stokes vectors between the two-color driving fields plays a critical role in controlling the harmonic mode: properly direction-matched optical field configurations can robustly realize the aforementioned mechanism, whereas direction mismatch will disrupt the ordered spin–orbit coupling dynamics.
Spatiotemporal mode conversion scheme
The STOV components of spatiotemporal skyrmions split into two lobes upon propagation to the far field, due to the Fourier transform relationship between STOV modes and tilted Hermite-lobed (THL) modes. At first sight, this seems to imply that the skyrmionic structure is not directly accessible in the far field and can only be utilized at the focus through refocusing. Therefore, this far-field mode change represents a limitation and challenge commonly encountered in almost all gas-phase HHG processes involving STOV fields. This significantly restricts the application scenarios of spatiotemporal skyrmions.
The team proposed an experimentally feasible spatiotemporal mode conversion (STMC) scheme that enables the recovery of the near-field spatiotemporal topological structure of the harmonics in the far field, thereby laying the foundation for far-field applications of EUV spatiotemporal skyrmions and vector hopfions.
EUV vector hopfions
Finally, this work extends the generation method of two-dimensional (2D) spatiotemporal skyrmions to three-dimensional (3D) structures, thereby obtaining EUV vector hopfions.
In the realm of attosecond science and EUV optics, EUV spatiotemporal skyrmions and vector hopfions, along with their attosecond pulse trains, will open new avenues for advancing multiple fields. At present, vector structured fields are emerging as powerful new tools for revealing physical mechanisms that are difficult to confirm using conventional means. As spatiotemporal skyrmions interact with matters, the polarization-sensitive time-dependent response of the material is expected to be encoded in the spatial spectrum of the spatiotemporal skyrmions. Consequently, EUV spatiotemporal skyrmions and vector hopfions provide a promising platform for precision metrology, attosecond electron dynamics, chiral recognition, and time-varying photonics, owing to their ultra-fine polarization structures in the spatiotemporal dimensions. Furthermore, the enhanced anti-jamming capability of spatiotemporal skyrmions offers a novel tool for the development of quantum information technologies in attosecond science.
