Attoscience

High harmonic generation: from strong field physics to photon pathways (LIDYL, France)

The ability to produce flashes of light of attosecond duration currently relies on gas phase high harmonic generation (HHG), the cornerstone of attosecond science. HHG is generally explained as the interaction of a very intense classical laser field with matter. Modelling this with a fully classical simulation, the strong field approximation, or directly solving the time-dependent Schrödinger equation, three steps are identified (as shown in the figure): partial ionisation of matter, which occurs close to the maximum of the laser beam’s electric field; acceleration of the ionised part of the electronic wave packet by the same laser field; and, if it passes close to the ionic core, recombination with the parent ion.

Top section) Three-step model of HHG. (Bottom section) The identified processes for the generation of the q=9th harmonic.
Scheme A corresponds to the usual description of nonlinear optics, involving q photons from the driving laser to produce the qth harmonic. Schemes B and C involve a second laser beam, non-collinear with the first one, with one and two additional photon pairs, respectively, interfering with the first one. Depending on the intensity of this second beam, these, or even higher order processes, may become the dominant pathways. HHG is thus generally the result of interference from numerous “photon
pathways,” explaining the peculiar behaviour of its yield.

During this final step, the electronic wave packet releases its excess of kinetic energy in the form of extreme ultraviolet radiation. This three-step model is extremely useful for predicting many properties of HHG, such as its efficiency, its spectral extension in relation to the laser parameters, and its response to various polarisations. However, until now, no description of HHG in terms of “photon pathways” has appeared entirely satisfactory, especially in terms of predicting yield.

A new experiment, conducted in LIDYL (CEA-Saclay), addressed this problem. It was shown that the generation of a given harmonic by HHG results from the coherent addition of multiple interfering processes. Beyond the minimum number of photons required to produce a given harmonic, additional photon pairs, associated with the combination of absorption and stimulated emission, come into play. A very simple model counting the different contributing pathways was proposed, and closely agreed with the experimental results. These results may prove a decisive step in the long quest for a “photonic picture” of HHG, offering new insights into the quantum processes at play in the strong-field regime.

Thierry Ruchon, Mekha Vimal, Martin Luttmann, Titouan Gadeyne, Matthieu Guer, Romain Cazali, David Bresteau, Fabien Lepetit, Olivier Tcherbakoff, Jean-François Hergott, Thierry Auguste, Titouan Gadeyne, Céline Chappuis and Jean-François Hergott (LIDYL)

M. Vimal et al., Phys. Rev. Lett. 131: 203402 (2023)
M. Luttmann et al., Phys. Rev. A 108: 053509 (2023)

Field-driven attosecond charge dynamics in germanium (CUSBO, Italy)

In recent years, attosecond science has made it possible to investigate electron dynamics in matter triggered by ultrashort pulses on their native timescale, namely the attosecond regime. Being able to use light pulses to follow and control ultrafast electron dynamics in matter is a long- sought goal, with important implications in many fields of technology and research. In a semiconductor, for example, charge injection by few-femtosecond infrared (IR) pulses could be used to turn the material into a conductive state, realising ultrafast switches in opto-electronics, a milestone that promises to increase the limiting speed of data processing and information encoding. This technological breakthrough can only stem from a comprehensive knowledge of light-induced charge injection, a key challenge of modern solid-state physics and photonics.

A study, recently published in Nature Photonics, tackled this problem by investigating field-driven carrier injection in a prototype semiconductor (monocrystalline germanium) with attosecond transient reflection spectroscopy. By monitoring the reflectivity of the sample around the M4,5 edge (~ 29.5 eV), a new light-matter interaction regime was discovered where charges are excited by diverse coexisting mechanisms, which compete and develop on different timescales, of the order of few femtoseconds. Both ultrafast transient and long-lasting features of the sample reflectivity were observed, which cannot be ascribed to a single physical mechanism. Detailed numerical simulations, based on advanced theoretical models, allowed the ultrafast charge injection to be mapped in momentum and time, and revealed a complex interaction between various processes in the quantum-mechanical response of the material that had never been observed before. This discovery suggests that it is possible to act on the light properties to control the diverse mechanisms on these extreme time-scales, to optimise charge injection while reducing the energy exchange with the material: a fundamental result for the development of next-generation electro-optical devices.

a Schematic representation of the pump–probe measurement where the ultrafast dynamics
induced by a few-fs IR pulse are probed through the reflected attosecond radiation.
b Experimental differential reflectivity trace ΔR/R for the germanium sample (main panel) and
squared modulus of the simultaneously measured pump vector potential (top panel)

Mauro Nisoli, Matteo Lucchini (CUSBO)

G. Inzani et al., Nature Photonics 17: 1059–1065 (2023)

Advancements in ultra-broadband and efficient UV light pulse generation for attochemistry (DESY, Germany)

Attochemistry is gradually shifting its focus from the study of charge migration and charge transfer in ionised molecules, to the study of the role of electron dynamics in the photo-chemistry of molecules activated by ultraviolet (UV) light [1]. In particular, UV light is respo nsible for the excitation of valence electrons, which leads to chemical changes on longer time-scales that are relevant in nature.

The generation of ultra-short UV pulses poses a major challenge, as material dispersion in this spectral range is unfavourable. The development of novel UV light sources has enabled the generation of ever shorter light pulses, down to a duration of a few femtoseconds. In 2019, sub-2 fs pulses were successfully generated in argon and neon using a technique developed by Francesca Calegari’s group at DESY (Hamburg, Germany), based on the third-harmonic frequency conversion of few-cycle near-infrared (NIR) laser pulses in a high-density gas [2]. Although this technique succeeded in setting a world-record for the shortest UV pulses ever generated, it suffered from low conversion efficiency due to the relatively low gas confinement achieved in the generation setup. In parallel to this work, Travers’ group at Heriot-Watt University (Edinburgh, UK) demonstrated the possibility of frequency converting NIR pulses into deep UV pulses in a gas-filled hollow capillary using the resonant dispersive wave approach [3]. This technique allows for a relatively high conversion efficiency and spectral tuneability, but at the expense of a non-compact setup. Using this approach, the generation of sub-3 fs UV pulses has been demonstrated [4].

Graphical representation of the novel microfluidic chip. Gas is injected into the central generation cell
of the chip, where it interacts with the NIR driving field, producing UV pulses through third-harmonic
generation. Simultaneously, the gas is evacuated via four differential-pumping chambers to prevent
reabsorption of the generated UV radiation.

In work recently published in the Journal of Physics: Photonics, Francesca Calegari’s group has now demonstrated the efficient generation of ultra-broadband femtosecond UV pulses (200-325 nm), using a dual-stage differential-pumping scheme integrated into a glass microfluidic chip that provides an exceptional gas confinement up to several bars in a high-vacuum environment [5]. As in [2], the novel microfluidic chip is fabricated using the FLICE (femtosecond laser irradiation and chemical etching) technique [6]. By delivering UV supercontinua supporting sub-2 fs durations, as well as pulse energies comparable to capillary-based techniques, this compact device makes a step towards the production and application of sub-fs UV pulses for the real-time investigation of electron dynamics in neutral molecules. These ultrashort UV pulses are currently available for Laserlab-Europe users in the attosecond science laboratory of Francesca Calegari at DESY.

Francesca Calegari (DESY)

[1] F. Calegari and F. Martin, Commun. Chem. 6: 184 (2023)
[2] M. Galli et al., Opt. Lett. 44: 1308–11 (2019)
[3] J.C. Travers et al., Nat. Photonics 13: 547–54 (2019)
[4] M. Reduzzi et al., Opt. Express 31: 26854–26864 (2023)
[5] V. Wanie et al., J. Phys. Photonics 6: 025005 (2024)
[6] R. Osellame et al., Laser Photon. Rev. 5: 442–63 (2011)

Attosecond core-level soft-x-ray spectroscopy at ICFO (Spain)

Photochemical reactions are complex, involving many different dynamical processes. Very often, the strongly coupled electron and nuclear dynamics procedure via conical intersections leads to induce radiationless relaxation. Such dynamics form the basis of a lot of relevant biological and chemical functions, but are challenging to resolve. Difficulties arise when trying to trace nuclear and electronic motion simultaneously, as their dynamics are complicated and difficult to disentangle, and occur at comparable ultra-fast timescales.

Figure 1: Coherent ultrabroad spectrum of an isolated attosecond SXR pulse [1] measures the complete electronic structure of all components of a material. Examples are shown for hBN and TiS₂ [3].

To address these challenges, the ICFO team has developed attosecond core-level spectroscopy [1-3] to inves- tigate molecular dynamics [4] in real-time. The method was benchmarked by tracing the evolution of gas-phase furan, an organic carbon, hydrogen and oxygen compound arranged in a pentagonal geometry. The choice of compound was not arbitrary: furan is the prototype for studying heterocyclic organic rings, essential constituents of many different day-to-day products, such as fuels, pharmaceuticals, and agrochemicals. The team was able to time-resolve the details of the entire ring-opening dynamics of furan, specifically the excitation and flow of energy leading to the fission of the bond between one carbon and the oxygen that breaks the cyclical structure. This was achieved by tracking several conical intersections – the ultrafast gateways between different energy states that furan undertakes in its evolution towards ring-opening [4]. Results show that attosecond core-level soft-x-ray spectroscopy is able to disentangle the many-body interactions [5] between carriers and nuclei; the technique can identify electronic and nuclear coherences, quantum beats, optically dark states, and symmetry changes, providing a highly detailed picture of the whole relaxation process.

The described methodology promises deeper insight into long-standing problems related to technological issues, such as inefficient energy conversion and storage in light-harvesting or catalysis. Using the quantum coherence of the light-matter interaction will deliver a tool that will be able to address many exciting fundamental and applied questions of significant importance to science and technology.

Figure 2: (a) Picture of a 2-micron, sub-2-cycle laser pulse interaction in high-pressure helium to generate an isolated 23 as pulse [2]. (b) The entire electron-nuclear dynamics are encoded in the time-energy measurement of furan. Lineouts show the absorption of a pump photon (top). It takes circa 60 fs for the bond to break. The four non-identical bonds of the open ring appear as four peaks in the SXR spectrum [4]

Jens Biegert (ICFO)

[1] S.L. Cousin et al., Opt. Lett. 39: 5383 (2014)
[2] S.L. Cousin et al., Phys. Rev. X 7: 041030 (2017)
[3] A.M. Summers et al., Ultraf. Sci. 3: 4 (2023)
[4] S. Severino et al., arxiv:2209.04330, Nature Photonics https://doi.org/10.1038/ s41566-024-01436-9
[5] T.P.H. Sidiropoulos et al., Nature Comm. 14: 7407 (2023)

Attosecond sources for applications (LLC, Sweden)

Coherent radiation in the extreme-ultraviolet (XUV) to soft X-ray spectral range, produced by high-order harmonic generation (HHG), is useful in a number of applications, including attosecond science and nanoscale imaging. The radiation source may be optimised to target different properties, such as overall efficiency, the time structure (single attosecond pulses or trains of pulses), coherence properties or the ability to focus to a small spot size, and high peak intensity, to suit the application.

Today, many different laser technologies drive HHG sources, including chirped pulse amplifiers (CPAs), optical parametric CPAs, and post-compressed CPAs, with driving wavelengths from the ultraviolet to the infrared. Alongside this, a large variety of generation geometries exist, such as short and dense gas jets, long and dilute gas cells, semi-infinite cells, and gas-filled capillaries. Despite thirty years of collective experience in the community, there is still no general consensus on the optimum configuration.

A team from LLC has worked with academic and industrial collaborators to develop models that describe, in simple terms, the essential physics of HHG [1-4]. The influence of macroscopic parameters on the conversion efficiency has been investigated, such as medium length, medium posi- tion, pressure, and intensity of the driving laser [3, 5]. The relation between pressure and length cor- responding to a high conversion efficiency follows a hyperbolic shape (see Figure 1). The model underpins the large variety and versatility in gas target designs used in the community.

Figure 1: Simulated HHG conversion efficiency for the 23 ^rd harmonic in argon for different pressures and medium lengths at a driving laser intensity of
I = 2.5 × 10 ¹⁴ W/cm ² . The medium was centred at the laser focus; both axes are normalised for scalability (z_R is the Rayleigh length). The analytical hyperbola
model (dashed line) predicts configurations of high conversion efficiency with good accuracy. The horizontal branch represents HHG in gas cells, the vertical branch the conditions in gas jets

The small structure size of modern lithography, in connec- tion with the ongoing change of illumination wavelength to 13.5 nm, requires novel, compact, high brightness and high spatial coherence sources in the extreme-ultraviolet for structure metrology. Other aspects of HHG source development, like divergence and focus area, are also important for attosecond-pump/ attosecond-probe experiments, where a high focused inten- sity is essential to achieve nonlinear interaction with the target. A simplified, semi-classical model of HHG [1, 2] has been developed that provides the basic spatial and spatiotemporal properties of the generated radiation, and describes individual harmonics in terms of Gaussian beams. The model shows the divergence and focusing properties of individual harmonics (see Figure 2), as well as the spatiotemporal properties of the attosecond pulse trains [6]. Moreover, it offers insights into how impairments, like ellipticity and astigmatism, in the driving laser impact the attosecond pulses generated, and how to optimise the source properties by manipulating the driving laser [4, 7].

Figure 2: Spatiotemporal couplings of attosecond pulses upon refocusing. In the Gaussian beam model, the placement of the gas target relative to the geometrical focus of the driving laser determines the wavefront and divergence of individually generated harmonics. Depending on the order, the harmonics can originate from real or virtual source points and can have very different divergences; upon re-focusing, this results in complicated spatiotemporal couplings and impairments of the maximum intensity.

Cord L. Arnold, Per Eng-Johnsson, Johan Mauritsson, Anne-Lise Viotti, Anne L’Huillier (LLC)

[1] C. Guo et al., J. Phys. B: At. Mol. Opt. Phys. 51: 034006 (2018)
[2] H. Wikmark et al., Proc. Nat. Am. Sci. (PNAS) 116: 4779 (2019)
[3] R. Weissenbilder et al., Nat. Rev. Phys. 4: 713 (2022)
[4] M. Plach et al., Ultrafast Sci. 4: 0054 (2024)
[5] E. Appi et al., Opt. Express, 31: 31687 (2023)
[6] M. Hoflund et al., Ultrafast Science 9797453 (2021)
[7] K. Veyrinas et al., N. J. Phys. B 25: 023017 (2023)

All-attosecond pump-probe spectroscopy (MBI, Germany)

The development of femtochemistry towards the end of the 20th century made it possible to study the dynamics in a chemical reaction in real time. For the first time, the motion of atoms in the process of forming or breaking bonds could be observed. Ahmed Zewail was awarded the Nobel Prize in Chemistry 1999 for his pioneering work in this field. The first demonstration of attosecond pulses at the begin- ning of the 21 ^st century, which was awarded the Nobel Prize in Physics 2023, allowed access to the observation of electron dynamics in matter, which move on even faster timescales. However, up to now most attosecond experiments performed have been limited by the fact that one attosecond pulse is typically combined with one femto-second pulse, the oscillating field of the latter serving as a clock to obtain attosecond time resolution.

Since attosecond pulses were first demonstrated, many scientists have aspired to perform experiments in which a first attosecond pump pulse initiates dynamics in an atom, a molecule or a solid, and a second attosecond probe pulse interrogates the system at different time delays. Recent work has brought this goal within reach.

An experiment using a synchronized attosecond x-ray pulse pair from an x-ray free-electron laser (the Linac Coherent Light Source (LCLS)) has recently been reported [1]; here, a single snapshot rather than an entire movie was recorded. In other work, the development of table-top attosecond-pump attosecond-probe spectroscopy (APAPS) has recently resulted in a breakthrough at the Max Born Institute (MBI). Following the first demonstration of APAPS at kilohertz repetition rates (see Figure 1) [2], researchers from the MBI have recently conducted the first table-top all-attosecond transient absorption spectroscopy (AATAS) experiment.

Figure 1: Two-colour APAPS. The generation of Ar⁺, as initiated by a broadband attosecond pump pulse with a photon energy around 20 eV, is probed by a second pulse with a central photon energy of 33.5 eV. This is above the second ionisation potential of Ar, thereby producing Ar²⁺. The Ar²⁺ ion yield increases around zero delay due to the more efficient generation of Ar²⁺ when the probe pulse follows the pump pulse. The inset shows a fit of the attosecond pulse structure.

These recent developments not only mark the begin- ning of a new chapter for attochemistry, but also have the potential to enable the study of extremely fast electron dynamics in atoms, molecules and solids from an entirely new perspective.

Bernd Schütte (MBI)

[1] S. Li et al., Science 383: 1118 (2024)
[2] M. Kretschmar et al., Sci. Adv. 10: eadk9605 (2024)

X-Photon 3D Polymerisation (VULRC, Lithuania)

Ultrafast lasers, at both short pulse durations and high repetition rates, enable practical, non-linear light-matter interaction for advanced material processing. One of the most successful implementations is two-photon polymerisation (TPP), a high precision optical three-dimensional printing technique, which is already being used commercially as an additive manufacturing tool. Novel laser sources and new material choices offer additional options for the fabrication of functional 3D micro-/nano-devices, but also present challenges in determining the exposure parameters that should be used to deliver the optimal outcome in terms of resolution, throughput, repeatability, cost efficiency, and ease of use.

Modern, wavelength-tunable femtosecond laser sources enable the systematic study of laser direct writing processes, which will help to uncover fundamental details, and provide practical know-how and recommendations for implementation. A recent study revealed that, once a certain intensity of TW/cm² is reached at any wavelength, X-nm wavelength enabling an X-photon transition can be applied for well controlled 3D structuring. This finding builds on existing knowledge that a specific, quantised number of photons is needed to realise the material excitation that will trigger a polymerisation reaction, with that number directly related to the laser wavelength and absorption of the material. It was assumed that the polymerisation reaction for TPP, with two photons, would follow an I² scaling law for the light-matter interactions, whereas it is defined by I^x . The initial excitation of the first electrons leads to avalanche ionisation, accompanied by thermal accumulation, which together lead to irreversible photo-modifications.

Exploitation of X-photon excitation for lithography will provide access to various laser wavelengths, thereby extending the spectrum of usable materials, and will eliminate the need for photo-initiators. X-photon high intensity material processing can potentially achieve higher resolution, and could provide more controlled and tailored energy deposition.

TPP – from two-photon polymerisation to towards-perfect polymerisation

Mangirdas Malinauskas and Saulius Juodkazis (VULRC)

E. Skliutas et al., Virtual. Phys. Prototyp. 18: e2228324 (2023)

Laser-induced electron diffraction in chiral molecules (CELIA, France)

Laser-induced electron diffraction (LIED) is an imaging technique in which a molecule is probed by its own electron [1]. Within a few femtoseconds, a strong laser field removes an electron wavepacket from the molecule, accelerates it and drives it back to its parent ion. The rescattering of the electron wavepacket onto the molecular potential produces a diffraction pattern that encodes the molecular structure with Angstrom spatial resolution, dictated by the de Broglie wavelength of the electron, and with attosecond temporal resolution, dictated by the duration of the electron wavepacket.

At CELIA, Nirit Dudovich’s team from the Weizmann Institute of Science (Rehovot, Israel), conducted LIED measurements in chiral molecules, within Laserlab-Europe transnational access. While LIED measurements had so far relied on linearly polarised light, the team used an elliptical laser field to be able to distinguish a chiral molecule (fenchone or alpha-pinene) from its mirror image [2]. The strong field selectively ionised molecules of a given orientation, and drove the electrons along well-defined trajectories. The direction from which an electron recollided with its parent molecule could be controlled by tuning the ellipticity of the field. A velocity-map-imaging spectrometer was used to record the 3D momentum distribution of the diffracted electrons through a tomographic imaging technique, benefiting from the high repeti- tion rate (1 MHz) of the femtosecond laser source.

Depending on the handedness of the molecule, the electrons were found to be preferentially diffracted forwards or backwards along the light propagation axis. This asymmetry, reaching several per cent, varied with the scattering angle of the electron, defining a chiro-sensitive electron-molecule differential cross-section. Different sets of electron trajectories, recolliding from different angles, were identified in the measurements. Interestingly, the results revealed that electrons recolliding from the two ends of an a-pinene molecule were scattered in opposite directions along the light propagation axis, due to their distinct encounters with the chiral potential.

Schematic view of the electron trajectories recolliding from the two ends of a molecule in a strong elliptically polarised laser field (top), and measured forward/backward asymmetry in two opposite enantiomers of a-pinene (bottom)

Two decades ago, the collision between electrons and oriented chiral molecules had been predicted to be highly enantio-sensitive [3], but it had not been possible to demonstrate it before now, because of difficulties in controlling the orientation of the chiral molecules with respect to the electron beam. Strong-field ionisation thus offered an unexpected solution to this issue, and now opens up a new path towards resolving ultrafast chiral dynamics with high spatial and temporal resolutions.

Valérie Blanchet, Yann Mairesse and Bernard Pons (CELIA)

[1] K. Amini and J. Biegert, Adv. At. Mol. Opt. Phys. 69: 163 (2020)
[2] D. Rajak et al., Phys. Rev. X 14: 011015 (2024)
[3] A. Busalla et al., Phys. Rev. Lett. 83: 1562 (1999)