🔬 optics

Controlled generation of high-harmonic spatiotemporal optical vortices

This paper demonstrates the controlled upconversion of infrared spatiotemporal optical vortex pulses to extreme ultraviolet frequencies via high-harmonic generation in argon, successfully producing XUV vortices with topological charges scaling linearly with the harmonic order and establishing a pathway for studying their elusive angular momentum in ultrafast spectroscopy.

Original authors: Titouan Gadeyne, Vartika Vishnoi, Thierry Ruchon

Published 2026-08-04

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Titouan Gadeyne, Vartika Vishnoi, Thierry Ruchon

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine light not just as a straight beam, but as a swirling, twisting ribbon of energy. For decades, scientists have known that light can spin like a top (spin angular momentum) and that it can carry a "twist" in its shape, like a corkscrew (orbital angular momentum). Usually, these twists happen across the width of the beam. But recently, physicists discovered a stranger kind of twist: a "spatiotemporal optical vortex" (STOV). Think of this not just as a spinning ribbon, but as a wave packet where the twist happens in both space and time simultaneously. It's like a ripple in a pond that doesn't just move outward, but also spins as it moves forward, carrying a secret "topological charge" that makes it behave like a tiny, invisible tornado.

Why does this matter? Because if we can control these twists, we might be able to use them to probe the tiniest, fastest events in the universe, like how electrons jump between energy levels in atoms. However, there's a catch: we've mostly only been able to make these twisting waves with ordinary, visible light. To really see what's happening inside atoms, we need light with much higher energy, in the extreme ultraviolet (XUV) range. The big question was: Can we take these delicate, twisting STOVs and crank them up to these super-high energies without losing their special shape?

This paper says yes. The researchers at Université Paris-Saclay successfully took their "twisting tornado" pulses of infrared light and smashed them into a cloud of argon gas. This process, called high-harmonic generation, acts like a cosmic upconverter, turning the low-energy infrared light into high-energy XUV light. The team found that the special twisting shape didn't just survive the transformation; it got amplified. If the original light had a twist of 1, the new XUV light had a twist of 25 (or whatever the energy multiplier was). They proved this by showing that the new light formed perfect rings in a detector, just like a target, and that the size of these rings changed exactly as predicted by math when they tweaked the original pulse.

To understand how they did it, imagine trying to write a message on a piece of paper that is being stretched and squashed. The team built a special "pulse shaper" using mirrors and lenses to sculpt their laser beam. They took a standard laser pulse and passed it through a device that spread its colors out, like a prism. Then, they placed a special "vortex plate" in the middle of this spread-out rainbow. This plate acted like a stencil, imprinting a spiral pattern onto the light's colors. When the light was recombined, it wasn't just a beam anymore; it was a STOV pulse, a wave where the peak intensity formed a ring in both space and time.

The challenge was that these STOV pulses are tricky. If you try to make them too strong, they can break apart or lose their shape. The team had to be very precise, using a 2 millijoule laser and carefully aligning their equipment to ensure the pulse remained a perfect, circular ring. They fired these shaped pulses into a jet of argon gas. When the intense laser hit the gas, it ripped electrons away and then slammed them back, causing the atoms to spit out new light at much higher frequencies (the harmonics).

The results were a match for the theory. When they looked at the new XUV light, they saw it forming a ring pattern, just like the original infrared pulse, but much smaller and more energetic. The key discovery was the relationship between the "twist" of the original light and the new light. If the original pulse had a topological charge of $\ell$ , the $q$ -th harmonic (the $q$ -th color of the new light) had a charge of $\ell_q = q \times \ell$ . It was as if the twisting power was multiplied by the energy boost. For example, a pulse with a twist of 1 created a new light with a twist of 25 for the 25th harmonic.

They also tested how robust these twisted pulses were by moving the gas jet slightly closer to or further from the focus point. In normal light, moving the gas a tiny bit might just change the brightness. But with STOVs, moving the gas changed the shape of the pulse itself. As the pulse moved away from the perfect focus, the nice circular ring broke apart into distinct lobes, like a flower petal opening up. The XUV light they produced mirrored this change perfectly, proving that the new light was a faithful, high-energy copy of the original twisted pulse.

This work is a significant step forward because it shows that we can now create these exotic, time-twisting vortices in the extreme ultraviolet range. It's not just a theoretical curiosity; it opens the door to using these XUV STOVs as probes. Because they carry a specific type of angular momentum, they could be used to study how electrons move in space and time, potentially revealing new details about how light and matter interact at the fastest speeds imaginable. The team confirmed their findings with both experiments and computer simulations, showing that the physics holds up even when the light gets this wild and energetic.

Problem and Context
Spatiotemporal optical vortices (STOVs) represent a unique class of light wavepackets characterized by a phase vortex embedded in the space-time domain, carrying an intrinsic orbital angular momentum (OAM) vector perpendicular to their propagation axis. While the OAM of spatial vortices is well-established, the transverse OAM of STOVs remains theoretically debated and experimentally elusive. Although STOVs have been successfully generated and characterized at conventional optical wavelengths, their extension to the extreme ultraviolet (XUV) and X-ray domains has remained a challenge. These high-energy regimes are critical for high-resolution, element-specific, and attosecond-time-resolved spectroscopies. While high-harmonic generation (HHG) has previously been used to create spatial XUV vortices, the controlled upconversion of STOVs to XUV frequencies had not been fully demonstrated, with prior experimental attempts yielding imperfect, non-circular modes that failed to exhibit the expected full ring-like vortex structure.

Methodology
The authors conducted experiments on the ATTOLab platform at CEA Saclay using an Yb-based laser source (1033.6 nm, ~267 fs pulses). To generate the driving pulses, they employed a bespoke 4f pulse shaper incorporating a vortex plate (VP) with topological charges (TC) $\ell = \pm 1$ and $\pm 2$ . This setup utilized a grating and cylindrical lenses to create a spatiospectral image of the incident field, where the VP imprinted an azimuthal phase. A subsequent spherical lens performed a spatial Fourier transform to convert this into a STOV pulse in the space-time domain. The authors optimized the system to ensure high circular symmetry by matching the spatial and spectral extents on the VP, quantified by an inhomogeneity parameter $\eta \approx 1.07$ .

These shaped infrared STOV pulses were focused into a thin argon gas jet to drive high-harmonic generation. The resulting XUV harmonics were analyzed using a variable line spacing (VLS) grating spectrometer coupled with microchannel plates (MCP) and a CCD camera, allowing for spatiospectral imaging in the far-field. Theoretical modeling was performed using a simple analytical approach where the harmonic field amplitude scales as a power law of the driving field ( $|\psi|^{q_{eff}}$ ) and the phase scales linearly with the harmonic order ( $q \times \text{arg}[\psi]$ ), assuming a "thin-slab" approximation to neglect longitudinal phase-matching effects.

Key Contributions and Results

Demonstration of XUV STOVs: The paper reports the first controlled upconversion of STOV pulses to XUV frequencies via HHG. The experiment successfully generated high-harmonic orders ( $q$ ) that form distinct ring-like structures in the far-field spatiospectral domain.
Verification of Topological Charge Scaling: Analysis of the harmonic modes confirms that the XUV pulses possess a topological charge $\ell_q = q \times \ell$ . This is evidenced by the dependence of the ring radii on the harmonic order $q$ and the driving charge $\ell$ : the spatial radius remains roughly constant across orders (due to the cancellation of divergence scaling and wavelength reduction), while the spectral radius increases linearly with $q$ .
Control via Propagation Dynamics: The study demonstrates that the production of these modes is sensitive to the position of the nonlinear medium relative to the focus. As the gas jet is moved away from the focal plane, the circular symmetry of the driving STOV breaks into $|\ell| + 1$ lobes. Consequently, the resulting XUV harmonic rings break into corresponding lobes arranged along a diagonal, with the orientation flipping based on the sign of $\ell$ . This confirms that the harmonic modes encode the space-time structure of the driving pulse.
Experimental vs. Theoretical Agreement: The experimental results show excellent agreement with simulations that rely solely on the coherent and non-perturbative nature of HHG. The authors note that macroscopic effects such as phase-matching, reabsorption, and dipole phases played minor roles under their specific experimental conditions, allowing the STOV structure to be preserved during upconversion.

Significance
The authors claim that this work unlocks the investigation of the elusive transverse orbital angular momentum of light in the XUV regime. By successfully generating XUV STOVs, the study provides a new tool for probing light-matter interactions. The paper suggests these pulses could serve as probes with inherent sensitivity to space-time-coupled physics, potentially enabling the excitation of electronic transitions with specific selection rules regarding transverse OAM or the photoionization of electron wavepackets structured over both space and time. The work emphasizes that careful monitoring of space-time wavepackets and their propagation is a vital step for harnessing these complex states in nonlinear optics.

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