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Extreme ultraviolet vortex light tubes by chromatic wavefront shaping of high harmonics

This paper introduces a strategy for generating extended extreme ultraviolet (EUV) light tubes by using chromatic wavefront shaping to merge successive harmonic vortex foci along the propagation axis, thereby creating longitudinally structured ultrafast EUV fields that are fully decoupled from the generation process and adaptable to various broadband sources.

Original authors: Patricia Estrela, Pablo San Miguel Claveria, Ermelinda Maçôas, José Luís Figueiredo, Gareth Oisín Williams, Hamed Merdji, Marco Piccardo, Susana Freitas, Jorge Vieira, Marta Fajardo

Published 2026-10-09

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Patricia Estrela, Pablo San Miguel Claveria, Ermelinda Maçôas, José Luís Figueiredo, Gareth Oisín Williams, Hamed Merdji, Marco Piccardo, Susana Freitas, Jorge Vieira, Marta Fajardo

Original paper licensed under CC BY 4.0 (https://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

Light is more than just a beam that illuminates a room; it is a complex field that can be shaped, twisted, and timed with incredible precision. For decades, scientists have learned to sculpt light into specific forms, giving it properties like a corkscrew shape that carries a unique kind of spin called orbital angular momentum. These twisted beams, known as vortex beams, have become powerful tools for studying magnetic materials and pushing the limits of imaging technology. While researchers have mastered creating these shapes with visible light, pushing the same concept into the extreme ultraviolet range—a spectrum of light so energetic it can reveal the inner workings of atoms and molecules—has proven difficult. The challenge lies in the fact that extreme ultraviolet light behaves differently than the light we see, and the tools used to shape it often struggle with the wide range of colors present in these high-energy pulses.

A team of researchers has now found a way to turn a known limitation of these tools into a powerful new feature. By working with high-energy light pulses generated from a gas, they have created a long, hollow tube of light that maintains its twisted shape over a surprisingly long distance. Instead of trying to force all the different colors of the light to focus at the exact same spot, the scientists deliberately allowed them to focus at slightly different positions along the beam's path. This clever use of the light's natural tendency to separate by color resulted in a continuous, extended structure that behaves like a solid tube of twisted energy, rather than a series of disconnected points.

The experiment began with a standard laser pulse, which was focused into a cell filled with argon gas. This process, known as high harmonic generation, converts the laser light into a burst of extreme ultraviolet pulses containing a spectrum of different colors, or harmonics. The researchers then placed a specialized optical element, a spiral zone plate, directly in the path of this new light. This device is a flat disk with a pattern of concentric rings that twist like a spiral. When the multi-colored light passes through it, the spiral pattern imprints a twist onto the wavefront of every color, turning the beam into a vortex.

Ordinarily, a lens or a zone plate focuses different colors at different distances, a property called chromaticity that usually blurs the image or breaks the structure. In this study, the team embraced this effect. Because the different colors in the beam focused at slightly different points along the beam's path, their individual focal spots overlapped to form a single, continuous tube of light. The researchers measured this tube to be about 10 micrometers in diameter and stretched over a length of 18 millimeters. This is a significant achievement because it creates a stable, structured field that persists over a distance much longer than the focus of a single color would allow.

To understand what this light tube actually looks like and how it behaves, the team used a crystal detector made of lithium fluoride. As the light passed through the crystal, it left behind a permanent record of its shape in the form of microscopic defects. By scanning the crystal along the path of the beam, the researchers could map out the intensity of the light at different points. They found that the hollow center of the vortex, where no light exists, remained consistent throughout the entire length of the tube. They also confirmed that the light carried the intended twist, or topological charge, by analyzing the interference patterns created when the light interacted with itself. The patterns showed clear spiral structures, confirming that the light was indeed a vortex with the specific properties they designed.

Computer simulations provided a deeper look into the nature of this light, revealing that the tube is not just a static shape but a dynamic train of ultrafast pulses. The light travels as a series of femtosecond vortices, each lasting only about one femtosecond, which is one quadrillionth of a second. These pulses move together along the tube, maintaining their structure as they propagate. The simulations showed that even though the different colors focus at different points, the timing of the pulses is preserved, meaning the ultrafast nature of the light is not lost in the process. This suggests that the light tube is composed of a stream of incredibly short, twisted bursts of energy that could be used to probe matter on the smallest scales of time and space.

The researchers demonstrated that this method works with different types of twists, using spiral plates designed to create either a single twist or a double twist in the light. In both cases, the result was a stable, extended tube of light. This approach offers a new way to engineer light fields without needing to change the source of the light itself. By simply swapping out the optical element at the end of the beam, scientists can now create different longitudinal structures, opening up possibilities for advanced imaging, metrology, and lithography. The work shows that by understanding and utilizing the natural properties of light and optics, rather than fighting against them, it is possible to create complex, structured fields that were previously difficult to achieve in the extreme ultraviolet range.

Technical Summary: Extreme Ultraviolet Vortex Light Tubes by Chromatic Wavefront Shaping of High Harmonics

Problem Statement
Structured light fields, particularly those carrying Orbital Angular Momentum (OAM), offer new degrees of freedom for light-matter interactions and ultrafast imaging. While High Harmonic Generation (HHG) provides a platform for generating ultrafast Extreme Ultraviolet (EUV) pulses with high spatial coherence, creating structured EUV fields remains challenging. Existing methods generally fall into two categories: engineering the driving laser field to imprint structure during generation, or shaping the generated EUV radiation using downstream diffractive optics. The latter approach, utilizing elements like Spiral Zone Plates (SZPs), is often limited by the intrinsic chromaticity of diffractive optics. In broadband HHG sources, this chromaticity causes different harmonic orders to focus at different longitudinal positions, typically viewed as a limitation that prevents the formation of a coherent, extended focal volume.

Methodology
The authors propose a post-generation wavefront shaping strategy that deliberately exploits the chromatic response of a Spiral Zone Plate (SZP) rather than compensating for it.

Experimental Setup: A 1 kHz Ti:Sapphire laser (800 nm, ~50 fs) was focused into an Argon gas cell to generate high harmonics. The resulting EUV beam (centered at H23, 34.8 nm) passed through an Aluminum filter and then through a binary SZP fabricated via electron beam lithography on a silicon nitride membrane.
Optical Design: Two SZPs with topological charges (TC) of $\ell=1$ and $\ell=2$ were used. The focal length of an SZP is wavelength-dependent ( $f \propto 1/\lambda$ ). Consequently, different harmonic orders focus at distinct longitudinal positions along the propagation axis.
Characterization: The transverse intensity profiles of the generated vortices were recorded using a Lithium Fluoride (LiF) crystal detector, which stores EUV exposure as stable color centers readable via confocal microscopy. To resolve individual harmonics, a freestanding grating was placed before the detector to spectrally separate the beam. In-line interferometry was employed to verify the topological charge by analyzing the interference between the zeroth and first diffraction orders.
Simulation: Numerical simulations using a binary spatial Fresnel propagator (LightPipes) modeled the spatiotemporal evolution of the polychromatic vortex field to validate experimental observations and analyze pulse duration.

Key Contributions and Results

Chromaticity as a Design Variable: The study demonstrates that the chromatic separation of focal planes in a broadband HHG spectrum can be engineered to create an "EUV light tube." By mapping the harmonic spectrum onto the propagation axis, successive harmonic vortex foci overlap longitudinally.
Design Criterion: The authors establish a heuristic criterion for continuous longitudinal overlap: the focal separation between successive harmonics ( $\Delta f_q$ ) must be less than or equal to four times the depth of focus (DoF) of the individual harmonic ( $\Delta f_q \le 4 \text{DoF}_q$ ). This condition ensures the maximum intensity of the superimposed field does not drop by more than 20%.
Experimental Realization: Using an SZP with $\ell=2$ , the team generated a polychromatic vortex beam with a transverse diameter of approximately 9–10 $\mu$ m and an extended depth of focus of 18 mm. The topological charge was confirmed to be constant ( $\ell=2$ ) across the harmonic spectrum (H21–H27).
Spatiotemporal Structure: Simulations indicate that while the intensity profile is time-integrated, the field consists of a train of femtosecond vortex structures propagating at the speed of light. For a continuous HHG spectrum, the pulse duration of the vortex structure within the tube is reduced to approximately 1 fs. In the case of an isolated harmonic emission, a single isolated femtosecond vortex pulse would propagate diffraction-free.
Phase Retrieval: Iterative phase-retrieval algorithms applied to the experimental data confirmed that the modal spectrum is dominated by the intended topological charge component, with minor contributions from the residual zeroth order.

Significance and Claims
The paper claims to introduce a new strategy for synthesizing longitudinally structured ultrafast EUV fields that is fully decoupled from the generation process. By exploiting the interplay between the chromatic response of diffractive optics and the broadband HHG spectrum, the authors demonstrate a flexible platform for engineering complex EUV wavefronts.

Decoupling: The approach allows for the modification of longitudinal and topological field distributions simply by exchanging the EUV optic, without re-engineering the HHG source.
Scalability: The wavefront-shaping strategy is presented as transferable to other broadband sources spanning from the mid-infrared to the X-ray regime.
Applications: The generated EUV light tubes are proposed as suitable for applications in imaging, metrology, and lithography, as well as for exploring magnetic interactions over unprecedented spatial and temporal scales.
Limitations: The authors acknowledge that the current efficiency is limited (approx. 10% for the first diffraction order) due to the nature of diffractive optics and substrate transmission losses, though they suggest photon-sieve approaches could improve this.

In summary, the work transforms a traditional limitation of diffractive optics (chromaticity) into a functional degree of freedom, enabling the creation of extended, ultrafast EUV vortex light tubes with constant topological charge across the spectrum.

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