Attosecond Science Research Articles

Editorial: Strong field physics and attosecond science

emission from Rydberg atoms. Substantial neutral atoms can be excited after tunneling in a strong laser 14 field, in the process known as frustrated tunneling ionization. The generation of coherent emission from 15 the excited-state atoms produced by the frustrated tunneling ionization is demonstrated to be dependent on 16 the chirp of the laser pulse. This chirp dependence also provides a new way to investigate the dynamics 17 of Rydberg states. Kong et al. (Kong et al., 2022) explored the influence of mechanical strains on the 18 high-order harmonic generation in the monolayer hexagonal boron nitride crystal by using time-dependent 19 density functional theory. They found the band structure is sensitive to the structural deformation modulated 20 by strains. This result may be useful in probing lattice deformations in crystals and heuristic to enhance the 21 optoelectronic efficiency of solid-state nano-devices. In conclusion, the Research Topic is created to present the latest advances and trends concerning the 62 strong field physics and attosecond science. Our special thanks to the Frontiers in Physics team for the 63 technical assistance with publishing. Much more efforts are still ongoing in this fascinating area. We expect 64 that this field will attract more and more attentions and benefit potential applications.

Yb:CaYAlO<sub>4</sub> regenerative amplifier

Attosecond science is one of the driving forces for developing the femtosecond amplifiers of high average power and ultrashort pulse duration. In this work, the regenerative amplification is studied experimentally and theoretically based on Yb:CaYAlO<sub>4</sub> crystal for the practical needs of high-repetition-rate attosecond light sources. In the theoretical study, a mode-tunable regenerative cavity with good thermal stability is designed based on the thermal lens calculations of Yb:CaYAlO<sub>4</sub> crystal; the amplified output energy and spectra of <i>π</i> and <i>σ</i> polarization of the crystal are calculated. In the experiment, the <i>π</i>-axis of Yb:CaYAlO<sub>4</sub> crystal is parallel to the laser polarization, and the laser amplifier emits 1.61 mJ pulses with average power 16.1 W. Notably, the dip of the <i>π</i>-polarization emission spectrum near 1025.1 nm compensates for the gain narrowing of the seed laser during amplification. Thus, the center wavelength and the spectral full width at a half maximum of the amplified laser are 1030 nm and 16 nm respectively. Using a grating-pair for compression, 149 fs pulses with peak power 9.5 GW are obtained. In comparison, the σ-polarization emission spectrum of Yb:CaYAlO<sub>4</sub> crystal is relatively flat in a range from 1000 to 1050 nm, but with a larger gain cross-section. When the laser polarization is parallel to the <i>σ</i>-axis of Yb:CaYAlO<sub>4</sub> crystal, 2.87 mJ pulses at 10 kHz repetition rate are achieved, with an average power of 28.7 W. In this case, the center wavelength and the spectral full width at half maximum of the amplified laser are 1037 nm and 11 nm respectively. Using a grating-pair for compression, 178 fs pulses with peak power of 14.2 GW are obtained. The beam quality factor measured is 1.09 along the <i>x</i>-axis of the amplified laser and 1.17 along the <i>y</i>-axis. To the best of our knowledge, this is the highest average power and the maximum pulse energy obtained from the Yb:CaYAlO<sub>4</sub> amplifier. For applications in high-repetition-rate attosecond light sources, terahertz generation and optical parametric amplification, subsequent laser outputs with average power 200 W, pulse energy 20 mJ and pulse duration less than 200 fs are expected to be achieved by adding two stages of traveling-wave amplification.

Development of attosecond pulses and their application to ultrafast dynamics of atoms and molecules

In the past two decades, the development of laser technology has made attosecond science become a cutting-edge research field, providing various novel perspectives for the study of quantum few-body ultrafast evolution. At present, the attosecond pulses prepared in laboratories are widely used in experimental research in the form of isolated pulses or pulse trains. The ultrafast changing light field allows one to control and track the motions of electrons on an atomic scale, and realize the real-time tracking of electron dynamics on a sub-femtosecond time scale. This review focuses on the research progress of ultrafast dynamics of atoms and molecules, which is an important part of attosecond science. Firstly, the generation and development of attosecond pulses are reviewed, mainly including the principle of high-order harmonic and the separation method of single-attosecond pulses. Then the applications of attosecond pulses are systematically introduced, including photo-ionization time delay, attosecond charge migration, and non-adiabatic molecular dynamics. Finally, the summary and outlook of the application of attosecond pulses are presented.

Attosecond Science: an emerging field brought to light by the Physics Nobel Prize

The 2023 Nobel Prize in Physics has been awarded to Anne L’Huillier, Pierre Agostini and Ferenc Krausz “for experimental methods that generate attosecond pulses of light for the study of electron dynamics in matter”. In this article, we contextualize their seminal works and their central roles that led to the emergence of a global ultrafast community exploring the frontiers of electron dynamics in dilute and condensed matter.

Ultrafast thin-disk laser oscillators as driving sources for high harmonic generation

Thin-disk laser oscillators can nowadays reach few tens of femtosecond pulses at gigawatt-level intracavity powers and megahertz-repetition rates becoming increasingly more powerful sources for intra-oscillator high harmonic generation (HHG). Currently, we can generate high harmonics in neon reaching photon energies of 70 eV, which we expect to increase toward 100 eV in the near future. In parallel, the achievable average and peak output powers of these oscillators in the range of 100 W and 100 MW, respectively, make these sources very promising to drive HHG in single-pass configuration after nonlinear pulse compression. Starting from transform-limited 30 to 50-fs soliton output soliton pulses of TDL oscillators, we will likely see these lasers approaching a single-cycle regime becoming highly attractive sources for attosecond science.

Petahertz-scale spectral broadening and few-cycle compression of Yb:KGW laser pulses in a pressurized, gas-filled hollow-core fiber.

We demonstrate efficient generation of coherent super-octave pulses via a single-stage spectral broadening of a Yb:KGW laser in a single, pressurized, Ne-filled, hollow-core fiber capillary. Emerging pulses spectrally spanning over more than 1 PHz (250-1600 nm) at a dynamic range of ∼60 dB, and an excellent beam quality open the door to combining Yb:KGW lasers with modern light-field synthesis techniques. Compression of a fraction of the generated supercontinuum to intense (8 fs, ∼2.4 cycle, ∼650 µJ) pulses allows convenient use of these novel laser sources in strong-field physics and attosecond science.

Quantum Interference Paves the Way for Long-Lived Electronic Coherences.

The creation and dynamical fate of a coherent superposition of electronic states generated in a polyatomic molecule by broadband ionization with extreme ultraviolet pulses is studied using the multiconfiguration time-dependent Hartree method together with an ionization continuum model Hamiltonian. The electronic coherence between the hole states usually lasts until the nuclear dynamics leads to decoherence. A key goal of attosecond science is to control the electronic motion and design laser control schemes to retain this coherence for longer timescales. Here, we investigate this possibility using time-delayed pulses and show how this opens up the prospect of coherent control of charge migration phenomenon.

Multiband Dynamics of Extended Harmonic Generation in Solids under Ultraviolet Injection

Using one-dimensional semiconductor Bloch equations, we investigate the multiband dynamics of electrons in a cutoff extension scheme employing an infrared pulse with additional UV injection. An extended three-step model is firstly validated to play a dominant role in emitting harmonics in the second plateau. Surprisingly, further analysis employing the acceleration theorem shows that, though harmonics in both the primary and secondary present positive and negative chirps, the positive (negative) chirp in the first region is related to the so-called short (long) trajectory, while that in the second region is emitted through ‘general’ trajectory, where electrons tunneling earlier and recombining earlier contribute significantly. The novel characteristics deepen the understanding of high harmonic generation in solids and may have great significance in attosecond science and reconstruction of band dispersion beyond the band edge.

Optimization of surface high-order harmonic generation by tailoring nanostructures

Many applications in attosecond science, lensless imaging, and industrial metrology need coherent extreme-ultraviolet pulses from high-order harmonic generation (HHG) in solids. However, the efficiency of the HHG plateau and the higher cutoff energy are nontrivial due to the limitation of the lower damage threshold of solids irradiated by laser fields. Here, we propose nanoengineered solid bowtie samples to overcome this limitation, which enables one to tailor the characteristic spacing between two nanotips. The near-field effect combined with recombined emissions with multiple scatterings can robustly increase conversion efficiencies and extend the cutoff energies of the HHG plateau. Our result paves the way to the manipulation of harmonic emissions in nanostructures and introduces imaging of the sub-cycle resolution of ultrafast electronic dynamics.

Absolute EUV reflectivity measurements using a broadband high-harmonic source and an in situ single exposure reference scheme.

We present a tabletop setup for extreme ultraviolet (EUV) reflection spectroscopy in the spectral range from 40 to 100 eV by using high-harmonic radiation. The simultaneous measurements of reference and sample spectra with high energy resolution provide precise and robust absolute reflectivity measurements, even when operating with spectrally fluctuating EUV sources. The stability and sensitivity of EUV reflectivity measurements are crucial factors for many applications in attosecond science, EUV spectroscopy, and nano-scale tomography. We show that the accuracy and stability of our in situ referencing scheme are almost one order of magnitude better in comparison to subsequent reference measurements. We demonstrate the performance of the setup by reflective near-edge x-ray absorption fine structure measurements of the aluminum L2/3 absorption edge in α-Al2O3 and compare the results to synchrotron measurements.

Ionization and recombination times of the long trajectory in high-order harmonic generation

Measuring the ionization and recombination times in high-order harmonic generation driven by strong laser fields is of fundamental importance in attosecond science and vital for assessing the temporal accuracy of trajectory-resolved high-harmonic spectroscopy. We investigate the effect of the electron-core interaction on the ionization and recombination times of the long trajectory in high-order harmonic generation. Using a classical model and the analytical $R$-matrix theory for helium, it is found that the attractive interaction leads to a 30-as shift of the ionization times for the long trajectory. By numerically solving the time-dependent Schr\"odinger equation for a helium atom model, we demonstrate that this small time shift can be probed by using orthogonally polarized two-color fields with high probe frequencies.

Controlling the polarization and phase of high-order harmonics with a plasmonic metasurface

Nanostructured surfaces, or metasurfaces, allow exquisite control of linear and nonlinear optical processes by reshaping the amplitude, phase, and polarization of electric and magnetic fields near wavelength-scale heterogeneities. Recently, metasurfaces have broken new ground in high-field attosecond science where they have been utilized to amplify the emission of high-order harmonics of femtosecond infrared laser pulses, a notoriously inefficient process, by enhancing the incident field, and to shape the emitted high harmonics in space. Here we show control of the polarization and phase of high harmonics with a plasmonic metasurface. We design and fabricate perpendicularly aligned rectangular gold antennas on a silicon crystal that generate circularly polarized deep-ultraviolet high harmonics, from a circularly polarized infrared driver, providing a simple path for achieving circular emission from patterned crystals. Our metasurface enhances the circularly polarized harmonics up to ∼ 43 times when compared to the unpatterned surface, where harmonics are quenched. Looking forward, circularly polarized high harmonics will be useful tools for sensing chiral laser–matter interactions and magnetic materials. Our approach paves the way for polarization control at even shorter, extreme ultraviolet, wavelengths.

Relativistic Two-Photon Matrix Elements for Attosecond Delays

The theory of one-photon ionization and two-photon above-threshold ionization is formulated for applications to heavy atoms in attosecond science by using Dirac–Fock formalism. A direct comparison of Wigner–Smith–Eisenbud delays for photoionization is made with delays from the Reconstruction of Attosecond Beating By Interference of Two-photon Transitions (RABBIT) method. Photoionization by an attosecond pulse train, consisting of monochromatic fields in the extreme ultraviolet range, is computed with many-body effects at the level of the relativistic random phase approximation (RRPA). Subsequent absorption and emission processes of infrared laser photons in RABBIT are evaluated by using static ionic potentials as well as asymptotic properties of relativistic Coulomb functions. As expected, light elements, such as argon, show negligible relativistic effects, whereas heavier elements, such a krypton and xenon, exhibit delays that depend on the fine-structure of the ionic target. The relativistic effects are notably close to ionization thresholds and Cooper minima with differences in fine-structure delays predicted to be as large as tens of attoseconds. The separability of relativistic RABBIT delays into a Wigner–Smith–Eisenbud delay and a universal continuum–continuum delay is studied with reasonable separability found for photoelectrons emitted along the laser polarization axis in agreement with prior non-relativistic results.

PHz Electronic Device Design and Simulation for Waveguide-Integrated Carrier-Envelope Phase Detection

Carrier-envelope phase (CEP) detection of ultrashort optical pulses and low-energy waveform field sampling have recently been demonstrated using direct time-domain methods that exploit optical-field photoemission from plasmonic nanoantennas. These devices are compact and integratable solid-state detectors operating at optical frequencies under ambient conditions using low pulse energies (picojoule-level). Potential applications include frequency-comb stabilization, optical time-domain spectroscopy, compact tools for attosecond science and metrology, and petahertz-scale information processing. However, to date these devices have been driven by free-space optical waveforms and their implementation within integrated photonic platforms has yet to be demonstrated. In this work, we design and simulate fully-integrated plasmonic nanoantennas coupled to a SiN-core waveguide for CEP detection. We find that when coupled to realistic on-chip, few-cycle supercontinuum sources, these devices are suitable for direct time-domain CEP detection within integrated photonic platforms. We estimate a signal-to-noise ratio of 30 dB at 50 kHz resolution bandwidth, and address technical details, such as the tuning of the nanoantennas plasmonic resonance, CEP slippage in the waveguide, optical losses, and sensitivity to driving pulse characteristics such as energy and duration. Our results provide the basis for future design and fabrication of time-domain CEP detectors and allow for the development of fully-integrated attosecond science applications, frequency-comb stabilization and light-wave-based PHz electronics.

Extreme-Ultraviolet Shaping and Imaging by High-Harmonic Generation from Nanostructured Silica.

Coherent extreme-ultraviolet pulses from high-harmonic generation have ample applications in attosecond science, lensless imaging, and industrial metrology. However, tailoring complex spatial amplitude, phase, and polarization properties of extreme-ultraviolet pulses is made nontrivial by the lack of efficient optical elements. Here, we have overcome this limitation through nanoengineered solid samples, which enable direct control over amplitude and phase patterns of nonlinearly generated extreme-ultraviolet pulses. We demonstrate experimental configurations and emitting structures that yield spatially patterned beam profiles, increased conversion efficiencies, and tailored polarization states. Furthermore, we use the emitted patterns to reconstruct height profiles, probe the near-field confinement in nanostructures below the diffraction limit of the fundamental radiation, and to image complex structures through coherent diffractive emission from these structures. Our results pave the way for introducing sub-fundamental-wavelength resolution imaging, direct manipulation of beams through nanoengineered samples, and metrology of nanostructures into the extreme-ultraviolet spectral range.

Generation of 8–20 μm Mid-Infrared Ultrashort Femtosecond Laser Pulses via Difference Frequency Generation

Mid-infrared (MIR) ultrashort laser pulses have a wide range of applications in the fields of environmental monitoring, laser medicine, food quality control, strong-field physics, attosecond science, and some other aspects. Recent years have seen great developments in MIR laser technologies. Traditional solid-state and fiber lasers focus on the research of the short-wavelength MIR region. However, due to the limitation of the gain medium, they still cannot cover the long-wavelength region from 8 to 20 µm. This paper summarizes the developments of 8–20 μm MIR ultrafast laser generation via difference frequency generation (DFG) and reviews related theoretical models. Finally, the feasibility of MIR power scaling by nonlinear-amplification DFG and methods for measuring the power of DFG-based MIR are analyzed from the author’s perspective.

Simultaneously Wavelength- and Temperature-Insensitive Mid-Infrared Optical Parametric Amplification with LiGaS2 Crystal

Ultrafast mid-infrared (mid-IR) lasers with a high pulse repetition rate are in great demand in various fields, including attosecond science and strong-field physics. Due to the lack of suitable mid-IR laser gain medium, optical parametric amplifiers (OPAs) are used to generate an ultrafast mid-IR laser. However, the efficiency of OPA is sensitive to phase mismatches induced by wavelength and temperature deviations from the preset points, which thus limits the pulse duration and the average power of the mid-IR laser. Here, we exploited a noncollinear phase-matching configuration to achieve simultaneously wavelength- and temperature-insensitive mid-IR OPA with a LiGaS2 crystal. The noncollinearity can cancel the first-order dependence of phase matching on both wavelength and temperature. Benefitting from the thermal property of the LiGaS2 crystal, some collinear phase-matching solutions derived from the first-order and even third-order wavelength insensitivity have comparatively large temperature bandwidths and can be regarded as approximate solutions with simultaneous wavelength and temperature insensitivity. These simultaneously wavelength- and temperature-insensitive phase-matching designs are verified through numerical simulations in order to generate few-cycle, high-power mid-IR pulses.

Scattering effects from neighboring atoms in core-level WSe2 photoemission

Methods of attosecond science originally developed to investigate systems in the gas phase are currently being adapted to obtain temporal information on the electron dynamics that takes place in condensed-matter systems. In particular, streaking measurements have recently been performed to determine photoemission time delays from the ${\mathrm{WSe}}_{2}$ dichalcogenide. In this work we present a fully atomistic description of the photoemission process in ${\mathrm{WSe}}_{2}$ and provide angularly resolved photoemission cross sections and time delays from the W $4f$, Se $3d$ and Se $4s$ core states of the system. Since these states are spatially localized, we propose a cluster approach in which we build up from smaller to larger clusters, so that we can assess the importance of scattering effects by each new layer of neighboring atoms. We use a static-exchange density functional theory method with $B$-spline functions, where a one-center angular-momentum expansion is supplemented by off-center expansions with fewer partial waves. This enhances convergence in comparison with a one-center expansion, which would require very high angular momenta to characterize the localized fast oscillations near each off-center atomic core. We find that the photoemission delays and fully differential cross sections are strongly affected by scattering events that take place off the neighboring atoms, implying the need to consider their effects for quantitative descriptions of the photoemission process.

Isolating Attosecond Electron Dynamics in Molecules where Nuclei Move Fast.

Capturing electronic dynamics in real time has been the ultimate goal of attosecond science since its beginning. While for atomic targets the existing measurement techniques have been thoroughly validated, in molecules there are open questions due to the inevitable copresence of moving nuclei, which are not always mere spectators of the phototriggered electron dynamics. Previous work has shown that not only can nuclear motion affect the way electrons move in a molecule, but it can also lead to contradictory interpretations depending on the chosen experimental approach. In this Letter we investigate how nuclear motion affects and eventually distorts the electronic dynamics measured by using two of the most popular attosecond techniques, reconstruction of attosecond beating by interference of two-photon transitions and attosecond streaking. Both methods are employed, in combination with abinitio theoretical calculations, to retrieve photoionization delays in the dissociative ionization of H_{2}, H_{2}→H^{+}+H+e^{-}, in the region of the Q_{1} series of autoionizing states, where nuclear motion plays a prominent role. We find that the experimental reconstruction of attosecond beating by interference of two-photon transitions results are very sensitive to bond softening around the Q_{1} threshold (27.8eV), even at relatively low infrared (IR) intensity (I_{0}∼1.4×10^{11} W/cm^{2}), due to the long duration of the probe pulse that is inherent to this technique. Streaking, on the other hand, seems to be a better choice to isolate attosecond electron dynamics, since shorter pulses can be used, thus reducing the role of bond softening. This conclusion is supported by very good agreement between our streaking measurements and the results of accurate theoretical calculations. Additionally, the streaking technique offers the necessary energy resolution to accurately retrieve the fast-oscillating phase of the photoionization matrix elements, an essential requirement for extending this technique to even more complicated molecular targets.

Sub-50 fs pulses at 2050 nm from a picosecond Ho:YLF laser using a two-stage Kagome-fiber-based compressor

The high-energy few-cycle mid-infrared laser pulse beyond 2 μm is of immense importance for attosecond science and strong-field physics. However, the limited gain bandwidth of laser crystals such as Ho:YLF and Ho:YAG allows the generation of picosecond (ps) long pulses and, hence, makes it challenging to generate few-cycle pulse at 2 μm without utilizing an optical parametric chirped-pulse amplifier (OPCPA). Moreover, the exclusive use of the near-infrared wavelength has limited the generation of wavelengths beyond 4 μm (OPCPA). Furthermore, high harmonic generation (HHG) conversion efficiency reduces dramatically when driven by a long-wavelength laser. Novel schemes such as multi-color HHG have been proposed to enhance the harmonic flux. Therefore, it is highly desirable to generate few-cycle to femtosecond pulses from a 2 μm laser for driving these experiments. Here, we utilize two-stage nonlinear spectral broadening and pulse compression based on the Kagome-type hollow-core photonic crystal fiber (HC-PCF) to compress few-ps pulses to sub-50 fs from a Ho:YLF amplifier at 2 μm at 1 kHz repetition rate. We demonstrate both experimentally and numerically the compression of 3.3 ps at 140 μJ pulses to 48 fs at 11 μJ with focal intensity reaching 10 13 W / cm 2 . Thereby, this system can be used for driving HHG in solids at 2 μm. In the first stage, the pulses are spectrally broadened in Kagome fiber and compressed in a silicon-based prism compressor to 285 fs at a pulse energy of 90 μJ. In the second stage, the 285 fs pulse is self-compressed in air-filled HC-PCF. With fine-tuning of the group delay dispersion (GDD) externally in a 3 mm window, a compressed pulse of 48 fs is achieved. This leads to a 70-fold compression of the ps pulses at 2050 nm. We further used the sub-50 fs laser pulses to generate white light by focusing the pulse into a thin medium of YAG.