Carrier-envelope phase-dependent high harmonic generation in the water window using few-cycle infrared pulses

Development of a portable and cost-effective femtosecond fibre laser synchronizable with synchrotron X-ray pulses

This study introduces a compact, portable femtosecond fibre laser system designed for synchronization with SPring-8 synchrotron X-ray pulses in a uniform filling mode. Unlike traditional titanium-sapphire mode-locked lasers, which are fixed installations, our system utilizes fibre laser technology to provide a practical alternative for time-resolved spectroscopy, striking a balance between usability, portability and cost-efficiency. Comprehensive evaluations, including pulse characterization, timing jitter and frequency stability tests revealed a centre wavelength of 1600 nm, a pulse energy of 4.5 nJ, a pulse duration of 35 fs with a timing jitter of less than 9 ps, confirming the suitability of the system for time-resolved spectroscopic studies. This development enhances the feasibility of experiments that combine synchrotron X-rays and laser pulses, offering significant scientific contributions by enabling more flexible and diverse research applications.

Interference-induced generation of a chirp-free short isolated attosecond pulse in the water window region with multicolor laser fields

Compensating for the intrinsic attosecond chirp (atto-chirp) of wideband high-order harmonics in the water window region is a significant challenge, in order to obtain isolated attosecond pulses (IAPs) with a width of tens of attoseconds (as). Here, we propose to realize the generation of IAP with duration as short as 20 as, central energy of 365 eV, and bandwidth exceeding 150 eV from chirp-free high harmonics generated by a four-color driving laser, without the necessity for atto-chirp compensation with natural materials. Unlike any other gating methods that an IAP arises from only one electron ionization event, we take advantage of the interference between harmonic radiation produced by multiple ionizing events. We further demonstrate that such chirp-free short IAP survives after taking account of macroscopic propagation effects. Given that the synthesized multicolor laser field can also effectively increase the harmonic flux, this work provides a practical way for experiments to generate the broad bandwidth chirp-free IAPs in the water window region.

Propagation effects in polarization-gated attosecond soft-X-ray pulse generation

Accurate estimation of the duration of soft-x-ray pulses from high-harmonic generation (HHG) remains challenging given their higher photon energies and broad spectral bandwidth. The carrier-envelope-phase (CEP) dependence of generated soft-x-ray spectra is indicative of attosecond pulse generation, but advanced simulations are needed to infer the pulse duration from such data. Here, we employ macroscopic propagation simulations to reproduce experimental polarization-gated CEP-dependent soft-x-ray spectra. The simulations indicate chirped pulses, which we theoretically find to be compressible in hydrogen plasmas, suggesting this as a viable compression scheme for broadband soft-x-rays from HHG.

High-order harmonic generation by aligned homonuclear diatomic cations

We introduce the theory of high-order harmonic generation by aligned homonuclear diatomic cations using a strong-field approximation. The target cation is represented as a system which consists of two atomic (ionic) centres and one active electron, while the driving field is either a monochromatic or bichromatic field. For a linearly polarised driving field, we investigate the differences between the harmonic spectra obtained with a neutral molecule and the corresponding molecular cation. Due to the larger ionisation potential, the molecular cations can withstand much higher laser-field intensity than the corresponding neutral molecule before the saturation effects become significant. This allows one to produce high-order harmonics with energy in the water-window interval or beyond. Also, the harmonic spectrum provides information about the structure of the highest-occupied molecular orbital. In order to obtain elliptically polarised harmonics, we suggest that an orthogonally polarised two-colour field is employed as a driving field. In this case, we analyse the harmonic ellipticity as a function of the relative orientation of the cation in the laser field. We show that the regions with large harmonic ellipticity in the harmonic energy-orientation angle plane are the broadest for cations whose molecular orbital does not have a nodal plane. Finally, we show that the molecular cations exposed to an orthogonally polarised two-colour field represent an excellent setup for the production of elliptically polarised attosecond pulses with a duration shorter than 100 as.

Carrier-envelope phase on-chip scanner and control of laser beams

The carrier-envelope phase (CEP) is an important property of few-cycle laser pulses, allowing for light field control of electronic processes during laser-matter interactions. Thus, the measurement and control of CEP is essential for applications of few-cycle lasers. Currently, there is no robust method for measuring the non-trivial spatial CEP distribution of few-cycle laser pulses. Here, we demonstrate a compact on-chip, ambient-air, CEP scanning probe with 0.1 µm3 resolution based on optical driving of CEP-sensitive ultrafast currents in a metal-dielectric heterostructure. We successfully apply the probe to obtain a 3D map of spatial changes of CEP in the vicinity of an oscillator beam focus with pulses as weak as 1 nJ. We also demonstrate CEP control in the focal volume with a spatial light modulator so that arbitrary spatial CEP sculpting could be realized.

Real-time observation of the Woodward-Hoffmann rule for 1,3-cyclohexadiene by femtosecond soft X-ray transient absorption

The stereochemistry of pericyclic reactions is explained by orbital symmetry conservation, referred to as the Woodward-Hoffmann (WH) rule. Although this rule has been verified using the structures of reactants and products, the temporal evolution of the orbital symmetry during the reaction has not been clarified. Herein, we used femtosecond soft X-ray transient absorption spectroscopy to elucidate the thermal pericyclic reaction of 1,3-cyclohexadiene (CHD) molecules, i.e., their isomerization to 1,3,5-hexatriene. In the present experimental scheme, the ring-opening reaction is driven by the thermal vibrational energy induced by photoexcitation to the Rydberg states at 6.2 eV and subsequent femtosecond relaxation to the ground state of CHD molecules. The direction of the ring opening, which can be conrotatory or disrotatory, was the primary focus, and the WH rule predicts the disrotatory pathway in the thermal process. We observed the shifts in K-edge absorption of the carbon atom from the 1s orbital to vacant molecular orbitals around 285 eV at a delay between 340 and 600 fs. Furthermore, a theoretical investigation predicts that the shifts depend on the molecular structures along the reaction pathways and the observed shifts in induced absorption are attributed to the structural change in the disrotatory pathway. This confirms that the orbital symmetry is dynamically conserved in the ring-opening reaction of CHD molecules as predicted using the WH rule.

Carrier-Envelope Phase Controlling of Ion Momentum Distributions in Strong Field Double Ionization of Methyl Iodide

In strong field ionization of methyl iodide initiated by elliptically polarized few-cycle pulses, a significant correlation was observed between the carrier-envelope phases (CEPs) of the laser and the preferred ejection direction of methyl cation arising from dissociative double ionization. This was attributed to the carrier-envelope phase dependent double ionization yields of methyl iodide. This observation provides a new way for monitoring the absolute CEPs of few-cycle pulses by observing the ion momentum distributions.

HHG at the Carbon K-Edge Directly Driven by SRS Red-Shifted Pulses from an Ytterbium Amplifier

In this work, we introduce a simplified approach to efficiently extend the high harmonic generation (HHG) cutoff in gases without the need for laser frequency conversion via parametric processes. Instead, we employ postcompression and red-shifting of a Yb:CaF2 laser via stimulated Raman scattering (SRS) in a nitrogen-filled stretched hollow core fiber. This driving scheme circumvents the low-efficiency window of parametric amplifiers in the 1100-1300 nm range. We demonstrate this approach being suitable for upscaling the power of a driver with an optimal wavelength for HHG in the highly desirable XUV range between 200 and 300 eV, up to the carbon K-edge. Due to the combination of power scalability of a low quantum defect ytterbium-based laser system with the high conversion efficiency of the SRS technique, we expect a significant increase in the generated photon flux in comparison with established platforms for HHG in the water window. We also compare HHG driven by the SRS scheme with the conventional self-phase modulation (SPM) scheme.

Extension of the bright high-harmonic photon energy range via nonadiabatic critical phase matching

The concept of critical ionization fraction has been essential for high-harmonic generation, because it dictates the maximum driving laser intensity while preserving the phase matching of harmonics. In this work, we reveal a second, nonadiabatic critical ionization fraction, which substantially extends the phase-matched harmonic energy, arising because of the strong reshaping of the intense laser field in a gas plasma. We validate this understanding through a systematic comparison between experiment and theory for a wide range of laser conditions. In particular, the properties of the high-harmonic spectrum versus the laser intensity undergoes three distinctive scenarios: (i) coincidence with the single-atom cutoff, (ii) strong spectral extension, and (iii) spectral energy saturation. We present an analytical model that predicts the spectral extension and reveals the increasing importance of the nonadiabatic effects for mid-infrared lasers. These findings are important for the development of high-brightness soft x-ray sources for applications in spectroscopy and imaging.

Efficient generation of femtosecond millijoule pulses at 3.1 µm

3.2-mJ, 92-fs pulses centered at 3.1 µm are generated at a 1-kHz repetition rate through a tabletop optical parametric chirped pulse amplification (OPCPA) system based on ZnGeP₂ crystals. Pumped by a 2-µm chirped pulse amplifier with a flat-top beam profile, the amplifier achieves a 16.5% overall efficiency, which, to the best of our knowledge, is the highest efficiency achieved by OPCPA at this wavelength. Harmonics up to the seventh order are observed after focusing the output in the air.

100-mJ class, sub-two-cycle, carrier-envelope phase-stable dual-chirped optical parametric amplification

Based on dual-chirped optical parametric amplification (DC-OPA) and type-I BiB₃O₆ (BiBO) crystals, the generation of >100 mJ, 10.4 fs, 10 Hz, carrier-envelope phase (CEP)-stable laser pulses, which are centered at 1.7 µm, was demonstrated producing a peak power of 10 TW. CEP-dependent high harmonic generation (HHG) was implemented to confirm the sub-two-cycle pulse duration and CEP stabilization of infrared (IR) laser pulses. As far as we know, the obtained pulse energy and peak power represented the highest values for sub-two-cycle CEP-stable IR optical parametric amplification. Additionally, the prospects of achieving high-energy water window isolated attosecond pulses (IAPs) via our developed laser source were discussed.

Broadband (8.5-13.5 µm) intra-pulse difference frequency generation in a LiGaS2 crystal of a 90 fs 744 nm laser pulse after its continuous redshift in air

Broadband frequency downconversion of a 90 fs 744 nm Ti:sapphire laser pulse into the mid-infrared (IR) was demonstrated via its filamentation-induced self-frequency shift in air and subsequent intra-pulse difference frequency generation in a LiGaS₂ crystal. The filamentation of the laser pulse in air provided its continuous spectral broadening to the Stokes wing with spectral humps separated by ∼1000cm^-1 that was appropriate for the laser pulse difference frequency conversion into the mid-IR. The difference frequency emission spectrum spanned from 8.5 to 13.5 µm at the e^-2 level. The transform limited pulse duration of the mid-IR pulse was 47 fs, which corresponded to a 1.3-cycle laser pulse. Energy conversion efficiency was up to 10^-4 and 5⋅10^-4 without and with chirp compensation, respectively.

Apparatus for generation of nanojoule-class water-window high-order harmonics

In our recent study [Fu et al., Commun. Phys. 3(1), 92 (2020)], we have developed an approach for energy-scaling of high-order harmonic generation in the water-window region under a neutral-medium condition. More specifically, we obtained a nanojoule-class water-window soft x-ray harmonic beam under a phase-matching condition. It has been achieved by combining a newly developed terawatt-class mid-infrared femtosecond laser and a loose-focusing geometry for high-order harmonic generation. The generated beam is more than 100 times intense compared to previously reported results. The experimental setup included two key parts: a terawatt mid-infrared femtosecond driving laser [Fu et al., Sci. Rep. 8(1), 7692 (2018)] and a specially designed gas cell. Despite the dramatic drop in the optimal gas pressure for phase-matching due to loose-focusing geometry, it still reached the 1 bar level for helium. Thus, we have designed a double-structured pulsed-gas cell with a differential pumping system, which enabled providing sufficiently high gas pressure. Moreover, it allowed reducing gas consumption significantly. A robust energy-scalable apparatus for high-order harmonic generation developed in this study will enable the generation of over ten-nanojoule water-window attosecond pulses in the near future.

Controllable multichannel acousto-optic modulator and frequency synthesizer enabled by nonlinear MEMS resonator

Nonlinear physics-based harmonic generators and modulators are critical signal processing technologies for optical and electrical communication. However, most optical modulators lack multi-channel functionality while frequency synthesizers have deficient control of output tones, and they additionally require vacuum, complicated setup, and high-power configurations. Here, we report a piezoelectrically actuated nonlinear Microelectromechanical System (MEMS) based Single-Input-Multiple-Output multi-domain signal processing unit that can simultaneously generate programmable parallel information channels (> 100) in both frequency and spatial domain. This significant number is achieved through the combined electromechanical and material nonlinearity of the Lead Zirconate Titanate thin film while still operating the device in an ambient environment at Complementary-Metal-Oxide-Semiconductor compatible voltages. By electrically detuning the operation point along the nonlinear regime of the resonator, the number of electrical and light-matter interaction signals generated based on higher-order non-Eigen modes can be controlled meticulously. This tunable multichannel generation enabled microdevice is a potential candidate for a wide variety of applications ranging from Radio Frequency communication to quantum photonics with an attractive MEMS-photonics monolithic integration ability.

Generation and compression of an intense infrared white light continuum in YAG irradiated by picosecond pulses

An intense white light (WL) continuum from 1600 to 2400 nm is generated in a 20-mm-long YAG irradiated by 1-ps, 1030-nm pulses. Long filamentation formed in the YAG is proven to be responsible for the enhancement of the longer-wavelength spectral part of the WL. The WL is compressed down to 24.6 fs ( 3.9 cycles at 1900 nm) after optical parametric chirped-pulse amplification in a lithium niobate crystal near degeneracy, confirming that its spectral phase is well behaved. The pulse compression experiment reveals that the group delay introduced in the WL generation process is dominated by the dispersion of YAG.

Wavelength-Dependent Features of Photoelectron Spectra from Nanotip Photoemission

If a metal nanotip is irradiated with the light of a wavelength much larger than the nanotip’s radius of curvature, optical near-fields become excited. These fields are responsible for distinct strong-field electron dynamics, due to both the field enhancement and spatial localization. By classical trajectory, Monte Carlo (CTMC) simulation, and the integration of the time-dependent Schrödinger equation (TDSE), we find that the photoelectron spectra for nanotip strong-field photoemission, irradiated by mid-infrared laser pulses, present distinctive wavelength-dependent features, especially in the mid- to high-electron energy regions, which are different from the well known ones. By extracting the electron trajectories from the CTMC simulation, we investigate these particular wavelength-dependent features. Our theoretical results contribute to understanding the photoemission and electron dynamics at nanostructures, and pave new pathways for designing high-energy nanometer-sized ultrafast electron sources.

Interplay of Open-Shell Spin-Coupling and Jahn-Teller Distortion in Benzene Radical Cation Probed by X-ray Spectroscopy

We report a theoretical investigation and elucidation of the X-ray absorption spectra of neutral benzene and of the benzene cation. The generation of the cation by multiphoton ultraviolet (UV) ionization and the measurement of the carbon K-edge spectra of both species using a table-top high-harmonic generation source are described in the companion experimental paper [Epshtein, M.; et al. J. Phys. Chem. A http://dx.doi.org/10.1021/acs.jpca.0c08736]. We show that the 1s_C → π transition serves as a sensitive signature of the transient cation formation, as it occurs outside of the spectral window of the parent neutral species. Moreover, the presence of the unpaired (spectator) electron in the π-subshell of the cation and the high symmetry of the system result in significant differences relative to neutral benzene in the spectral features associated with the 1s_C → π* transitions. High-level calculations using equation-of-motion coupled-cluster theory provide the interpretation of the experimental spectra and insight into the electronic structure of benzene and its cation. The prominent split structure of the 1s_C → π* band of the cation is attributed to the interplay between the coupling of the core → π* excitation with the unpaired electron in the π-subshell and the Jahn-Teller distortion. The calculations attribute most of the splitting (∼1-1.2 eV) to the spin coupling, which is visible already at the Franck-Condon structure, and we estimate the additional splitting due to structural relaxation to be around ∼0.1-0.2 eV. These results suggest that X-ray absorption with increased resolution might be able to disentangle electronic and structural aspects of the Jahn-Teller effect in the benzene cation.

Characterizing the carrier-envelope phase stability of mid-infrared laser pulses by high harmonic generation in solids

We present a novel approach for measuring the carrier-envelope phase (CEP) stability of a laser source by employing the process of high harmonic generation (HHG) in solids. HHG in solids driven by few-cycle pulses is very sensitive to the waveform of the driving pulse, therefore enabling to track the shot-to-shot CEP fluctuations of a laser source. This strategy is particularly practical for pulses at long central wavelength up to the mid-infrared spectral range where usual techniques used in the visible or near-infrared regions are challenging to transpose. We experimentally demonstrate this novel tool by measuring the CEP fluctuations of a mid-infrared laser source centered at 9.5~μm.

Attosecond science based on high harmonic generation from gases and solids

Recent progress in high power ultrafast short-wave and mid-wave infrared lasers has enabled gas-phase high harmonic generation (HHG) in the water window and beyond, as well as the demonstration of HHG in condensed matter. In this Perspective, we discuss the recent advancements and future trends in generating and characterizing soft X-ray pulses from gas-phase HHG and extreme ultraviolet (XUV) pulses from solid-state HHG. Then, we discuss their current and potential usage in time-resolved study of electron and nuclear dynamics in atomic, molecular and condensed matters.

Different methods are demonstrated in recent years to produce attosecond pulses. Here, the authors discuss recent development and future prospects of the generation of such pulses from gases and solids and their potential applications in spectroscopy and ultrafast dynamics in atoms, molecules and other complex systems.

High-field mid-infrared pulses derived from frequency domain optical parametric amplification

We present a novel, to the best of our knowledge, approach for scaling the peak power of mid-infrared laser pulses with few-cycle duration and carrier-to-envelope phase stabilization. Using frequency domain optical parametric amplification (FOPA), selective amplification is performed on two spectral slices of broadband pulses centered at 1.8 µm wavelength. In addition to amplification, the Fourier plane is used for specific pulse shaping to control both the relative polarization and the phase/delay between the two spectral slices of the input pulses. At the output of the FOPA, intrapulse difference frequency generation provides carrier-envelope phase stabilized two-cycle pulses centered at 9.5 µm wavelength with 25.5 µJ pulse energy. The control of the carrier-envelope phase is demonstrated through the dependence of high-harmonic generation in solids. This architecture is perfectly adapted to be scaled in the future to high average and high peak powers using picosecond ytterbium laser technologies.

Observing the Importance of the Phase-Volume Effect for Few-Cycle Light-Matter Interactions

The spatially dependent phase distribution of focused few-cycle pulses, i.e., the focal phase, is much more complex than the well-known Gouy phase of monochromatic beams. As the focal phase is imprinted on the carrier-envelope phase (CEP), for accurate modeling and interpretation of CEP-dependent few-cycle laser-matter interactions, both the coupled spatially dependent phase and intensity distributions must be taken into account. In this Letter, we demonstrate the significance of the focal phase effect via comparison of measurements and simulations of CEP-dependent photoelectron spectra. Moreover, we demonstrate the impact of this effect on few-cycle light-matter interactions as a function of their nonlinear intensity dependence to answer the general question: if, when, and how much should one be concerned about the focal phase?

Efficient table-top dual-wavelength beamline for ultrafast transient absorption spectroscopy in the soft X-ray region

We present a table-top beamline providing a soft X-ray supercontinuum extending up to 370 eV from high-order harmonic generation with sub-13 fs 1300 nm driving pulses and simultaneous production of sub-5 fs pulses centered at 800 nm. Optimization of high harmonic generation in a long and dense gas medium yields a photon flux of  ~ 1.4 × 106 photons/s/1% bandwidth at 300 eV. The temporal resolution of X-ray transient absorption experiments with this beamline is measured to be 11 fs for 800 nm excitation. This dual-wavelength approach, combined with high flux and high spectral and temporal resolution soft X-ray absorption spectroscopy, is a new route to the study of ultrafast electronic dynamics in carbon-containing molecules and materials at the carbon K-edge.

Attosecond Pulse Amplification in a Plasma-Based X-Ray Laser Dressed by an Infrared Laser Field

High-harmonic generation (HHG) of laser radiation has led to attosecond pulse formation which offers unprecedented temporal resolution in observing and controlling electron and nuclear dynamics. But the energy of attosecond pulses remains quite small, especially for photon energies exceeding 100 eV, which limits their practical applications. We propose a method for amplification of attosecond pulses in the active medium of a plasma-based x-ray laser dressed by a replica of the laser field used for HHG. The experimental implementation is suggested in hydrogenlike C5+ x-ray laser at 3.4 nm wavelength in the "water window" range.

Attosecond soft X-ray high harmonic generation

High harmonic generation (HHG) of an intense laser pulse is a highly nonlinear optical phenomenon that provides the only proven source of tabletop attosecond pulses, and it is the key technology in attosecond science. Recent developments in high-intensity infrared lasers have extended HHG beyond its traditional domain of the XUV spectral range (10-150 eV) into the soft X-ray regime (150 eV to 3 keV), allowing the compactness, stability and sub-femtosecond duration of HHG to be combined with the atomic site specificity and electronic/structural sensitivity of X-ray spectroscopy. HHG in the soft X-ray spectral region has significant differences from HHG in the XUV, which necessitate new approaches to generating and characterizing attosecond pulses. Here, we examine the challenges and opportunities of soft X-ray HHG, and we use simulations to examine the optimal generating conditions for the development of high-flux, attosecond-duration pulses in the soft X-ray spectral range. This article is part of the theme issue 'Measurement of ultrafast electronic and structural dynamics with X-rays'.

Enhancing high harmonic generation by the global optimization of a two-color chirped laser field

Enhanced high harmonics are generated by local and global optimization approaches to achieve a supercontinuum spectrum. Based on time-dependent density functional theory calculations, the optimum convolution of a two-color chirped pulse from an N2O molecule implements a significant enhancement of cutoff frequency and high harmonic yield. The optimization is done by controlling the effective chirp parameters and the carrier-envelope phase of the designed laser field. Indeed, all of the effective parameters are adjusted simultaneously for the global optimization; whereas, just two variables are tuned to obtain the desired cutoff frequency based on the local optimization. The results show that the global optimization approach extends the cutoff frequency by 96% compared to the single-color field, which could produce an isolated 25 as output pulse. This method opens up a valuable route by a pulse shaping mechanism for the control of high harmonic generation and ultrafast measurements for reducing the computational time and repeatability of an experiment with high accuracy.

Identification of tunneling and multiphoton ionization in intermediate Keldysh parameter regime

Quantitative identification of tunneling ionization (TI) and multiphoton ionization (MPI) with Keldysh parameter γ in intermediate regime is of great importance to better understand various ionization-triggered strong-field phenomena. We theoretically demonstrate that the numerical observable ionization delay time is a more reliable indicator for characterizing the transition from TI to MPI under different laser parameters. Using non-linear iterative curve fitting algorithm (NICFA), the detected time-dependent probability current of ionized electrons can be decoupled into weighted TI and MPI portions. This enables us to confirm that the observed plateau-like structure in ionization delay time picture at the intermediate γ originates from the competition between TI and MPI processes. A hybrid quantum and classical approach (HQCA) is developed to evaluate the weights of TI and MPI electrons in good agreement with NICFA result. Moreover, the well separated TI and MPI electrons using HQCA are further propagated classically for mapping their final momentum, which well reproduces the experimental or ab-initio numerical calculated signatures of ionized electron momentum distribution in a rather broad γ regime.

A fast and adaptable method for high accuracy integration of the time-dependent Schrödinger equation

We present an adaptable, fast, and robust method for integrating the time-dependent Schrödinger equation. We apply the method to calculations of High Harmonic (HHG) and Above Threshold Ionisation (ATI) spectra for a single atomic electron in an intense laser field. Our approach implements the stabilized bi-conjugate gradient method (BiCG-STAB) for solving a sparse linear system to evolve the electronic wavefunction in time. The use of this established method makes the propagation scheme less restrictive compared to other schemes which may have particular requirements for the form of the equation, such as use of a three-point finite-difference approximation for spatial derivatives. Our method produces converged solutions significantly faster than existing methods, particularly if high accuracy is required. We demonstrate that this approach is suitable for a range of different parameters and show that in many circumstances significant gains can be made with the use of a fourth-order time propagator as opposed to the more common second-order Crank-Nicolson (CN) method.

Carrier-envelope phase-dependent molecular high-order harmonic generation from H2+ in a multi-cycle regime

Carrier-envelope phase (CEP) dependence of high-order harmonic generation (HHG) from H2+ in a multi-cycle laser pulse is investigated by solving the non-Born-Oppenheimer time-dependent Schrödinger equation (TDSE). It is found that high harmonics in the plateau exhibit counterintuitive frequency modulation (FM) as the CEP of the multi-cycle laser varies. Based on the classical electron trajectories and time-frequency analysis, this multi-cycle CEP-dependent FM is demonstrated to result from the interference of half-cycle HHG radiations, which is modulated by laser-driven nuclear motion. The mechanism of the CEP-dependent FM is further confirmed by simulations based on a simple algorithm in the time domain, which satisfactorily reproduces the TDSE results. The CEP-dependent FM encodes rich information on the correlated electron and nuclear dynamics, which paves the way for probing nuclear motion with attosecond resolution.

Apparatus for soft x-ray table-top high harmonic generation

There has been considerable recent interest in tabletop soft X-ray attosecond sources enabled by the new generation of intense, few-cycle laser sources at operating wavelengths longer than 800 nm. In our recent work [Johnson et al., Sci. Adv. 4(5), eaar3761 (2018)], we have demonstrated a new regime for the generation of X-ray attosecond pulses in the water window (284-540 eV) by high-harmonic generation, which resulted in soft X-ray fluxes of ≈10⁹ photons/s and a maximum photon energy of 600 eV, an order of magnitude and 50 eV higher, respectively, than previously attained with few-cycle drivers. Here we present the key elements of our apparatus for the generation and detection of soft X-ray high harmonic radiation in the water window. Of critical importance is a differentially pumped gas target capable of supporting the multi-atmospheric pressures required to phase-match the high energy emission while strongly constraining the gas density, suppressing the effects of ionization and absorption outside the interaction region.

Generation of 1 kHz, 2.3 mJ, 88 fs, 2.5 μm pulses from a Cr2+:ZnSe chirped pulse amplifier

We demonstrate the generation of 2.3 mJ, 88 fs, 2.5 μm laser pulses at 1 kHz repetition rate from a three-stage chirped pulse amplifier employing Cr²⁺:ZnSe crystals as the active gain media. 5 μJ seed of the amplifier is obtained via intrapulse difference frequency generation in a bismuth triborate (BIBO) crystal from spectrally broadened Ti:Sapphire amplifier output. A multi-pass amplifier followed by two single-pass amplifiers pumped by Q-switched Ho:YAG lasers boost the pulse energy to 6.5 mJ, yielding 2.3 mJ, 88 fs pulses upon pulse compression. Our results show the highest peak power at 2.5 μm with 1 kHz repetition rate. Such a laser will be a powerful source for studying strong-field physics and extending high-harmonic generation towards the keV region.

Element Selectivity in Second-Harmonic Generation of GaFeO_{3} by a Soft-X-Ray Free-Electron Laser

Nonlinear optical frequency conversion has been challenged to move down to the extreme ultraviolet and x-ray region. However, the extremely low signals have allowed researchers to only perform transmission experiments of the gas phase or ultrathin films. Here, we report second harmonic generation (SHG) of the reflected beam of a soft x-ray free-electron laser from a solid, which is enhanced by the resonant effect. The observation revealed that the double resonance condition can be met by absorption edges for transition metal oxides in the soft x-ray range, and this suggests that the resonant SHG technique can be applicable to a wide range of materials. We discuss the possibility of element-selective SHG spectroscopy measurements in the soft x-ray range.

Towards a petawatt-class few-cycle infrared laser system via dual-chirped optical parametric amplification

Expansion of the wavelength range for an ultrafast laser is an important ingredient for extending its range of applications. Conventionally, optical parametric amplification (OPA) has been employed to expand the laser wavelength to the infrared (IR) region. However, the achievable pulse energy and peak power have been limited to the mJ and the GW level, respectively. A major difficulty in the further energy scaling of OPA results from a lack of suitable large nonlinear crystals. Here, we circumvent this difficulty by employing a dual-chirped optical parametric amplification (DC-OPA) scheme. We successfully generate a multi-TW IR femtosecond laser pulse with an energy of 100 mJ order, which is higher than that reported in previous works. We also obtain excellent energy scaling ability, ultrashort pulses, flexiable wavelength tunability, and high-energy stability, which prove that DC-OPA is a superior method for the energy scaling of IR pulses to the 10 J/PW level.

High-flux soft x-ray harmonic generation from ionization-shaped few-cycle laser pulses

Laser-driven high-harmonic generation provides the only demonstrated route to generating stable, tabletop attosecond x-ray pulses but has low flux compared to other x-ray technologies. We show that high-harmonic generation can produce higher photon energies and flux by using higher laser intensities than are typical, strongly ionizing the medium and creating plasma that reshapes the driving laser field. We obtain high harmonics capable of supporting attosecond pulses up to photon energies of 600 eV and a photon flux inside the water window (284 to 540 eV) 10 times higher than previous attosecond sources. We demonstrate that operating in this regime is key for attosecond pulse generation in the x-ray range and will become increasingly important as harmonic generation moves to fields that drive even longer wavelengths.

Application of the complex Kohn variational method to attosecond spectroscopy

The complex Kohn variational method is extended to compute light-driven electronic transitions between continuum wave functions in atomic and molecular systems. This development enables the study of multiphoton processes in the perturbative regime for arbitrary light polarization. As a proof of principle, we apply the method to compute the photoelectron spectrum arising from the pump-probe two-photon ionization of helium induced by a sequence of extreme ultraviolet and infrared light pulses. We compare several two-photon ionization pump-probe spectra, resonant with the (2s2p) 1P 1 o Feshbach resonance, with independent simulations based on the atomic B-spline close-coupling STOCK code, and find good agreement between the two approaches. This finite-pulse perturbative approach is a step towards the ab initio study of weak-field attosecond processes in polyelectronic molecules.

Single-shot, real-time carrier-envelope phase measurement and tagging based on stereographic above-threshold ionization at short-wave infrared wavelengths

A high-precision, single-shot, and real-time carrier-envelope phase (CEP) measurement at 1.8 μm laser wavelength based on stereographic photoelectron spectroscopy is presented. A precision of the CEP measurement of 120 mrad for each and every individual laser shot for a 1 kHz pulse train with randomly varying CEP is demonstrated. Simultaneous to the CEP measurement, the pulse lengths are characterized by evaluating the spatial asymmetry of the measured above-threshold ionization (ATI) spectra of xenon and referenced to a standard pulse-duration measurement based on frequency-resolved optical gating. The validity of the CEP measurement is confirmed by implementing phase tagging for a CEP-dependent measurement of ATI in xenon with high energy resolution.

Generating Carrier-Envelope-Phase Stabilized Few-Cycle Pulses from a Free-Electron Laser Oscillator

We propose a scheme to generate carrier-envelope-phase (CEP) stabilized few-cycle optical pulses from a free-electron laser oscillator. The CEP stabilization is realized by the continuous injection of CEP-stabilized seed pulses from an external laser to the free-electron laser oscillator whose cavity length is perfectly synchronized to the electron bunch repetition. Operated at a midinfrared wavelength, the proposed method is able to drive a photon source based on high harmonic generation (HHG) to explore the generation of isolated attosecond pulses at photon energies above 1 keV with a repetition of >10  MHz. The HHG photon source will open a door to full-scale experiments of attosecond x-ray pulses and push ultrafast laser science to the zeptosecond regime.

Charge migration and charge transfer in molecular systems

The transfer of charge at the molecular level plays a fundamental role in many areas of chemistry, physics, biology and materials science. Today, more than 60 years after the seminal work of R. A. Marcus, charge transfer is still a very active field of research. An important recent impetus comes from the ability to resolve ever faster temporal events, down to the attosecond time scale. Such a high temporal resolution now offers the possibility to unravel the most elementary quantum dynamics of both electrons and nuclei that participate in the complex process of charge transfer. This review covers recent research that addresses the following questions. Can we reconstruct the migration of charge across a molecule on the atomic length and electronic time scales? Can we use strong laser fields to control charge migration? Can we temporally resolve and understand intramolecular charge transfer in dissociative ionization of small molecules, in transition-metal complexes and in conjugated polymers? Can we tailor molecular systems towards specific charge-transfer processes? What are the time scales of the elementary steps of charge transfer in liquids and nanoparticles? Important new insights into each of these topics, obtained from state-of-the-art ultrafast spectroscopy and/or theoretical methods, are summarized in this review.

Streaking of 43-attosecond soft-X-ray pulses generated by a passively CEP-stable mid-infrared driver

Attosecond metrology has so far largely remained limited to titanium:sapphire lasers combined with an active stabilization of the carrier-envelope phase (CEP). These sources limit the achievable photon energy to ∼100 eV which is too low to access X-ray absorption edges of most second- and third-row elements which are central to chemistry, biology and material science. Therefore, intense efforts are underway to extend attosecond metrology to the soft-X-ray (SXR) domain using mid-infrared (mid-IR) drivers. Here, we introduce and experimentally demonstrate a method that solves the long-standing problem of the complete temporal characterization of ultra-broadband (≫10 eV) attosecond pulses. We generalize the recently proposed Volkov-transform generalized projection algorithm (VTGPA) to the case of multiple overlapping photoelectron spectra and demonstrate its application to isolated attosecond pulses. This new approach overcomes all key limitations of previous attosecond-pulse reconstruction methods, in particular the central-momentum approximation (CMA), and it incorporates the physical, complex-valued and energy-dependent photoionization matrix elements. These properties make our approach general and particularly suitable for attosecond supercontinua of arbitrary bandwidth. We apply this method to attosecond SXR pulses generated from a two-cycle mid-IR driver, covering a bandwidth of ∼100 eV and reaching photon energies up to 180 eV. We extract an SXR pulse duration of (43±1) as from our streaking measurements, defining a new world record. Our results prove that the popular and broadly available scheme of post-compressing the output of white-light-seeded optical parametric amplifiers is adequate to produce high-contrast isolated attosecond pulses covering the L-edges of silicon, phosphorous and sulfur. Our new reconstruction method and experimental results open the path to the production and characterization of attosecond pulses lasting less than one atomic unit of time (24 as) and covering X-ray absorption edges of most light elements.

Generation of octave-spanning mid-infrared pulses from cascaded second-order nonlinear processes in a single crystal

We report on experimental generation of a 6.8 μJ laser pulse spanning from 1.8 to 4.2 μm from cascaded second-order nonlinear processes in a 0.4-mm BiB₃O₆ (BIBO) crystal. The nonlinear processes are initiated by intra-pulse difference frequency generation (DFG) using spectrally broadened Ti:Sapphire spectrum, followed by optical parametric amplification (OPA) of the DFG pulse. The highest energy, 12.6 μJ, is achieved in a 0.8-mm BIBO crystal with a spectrum spanning from 1.8 to 3.5 μm. Such cascaded nonlinear processes are enabled by the broadband pump and the coincident phase matching angle of DFG and OPA. The spectrum is initiated from the DFG process and is thus expected to have passive stable carrier-envelope phase, which can be used to seed either a chirped pulse amplifier (CPA) or an optical parametric chirped pulse amplifier (OPCPA) for achieving high-energy few-cycle mid-infrared pulses. Such cascaded second-order nonlinear processes can be found in many other crystals such as KTA, which can extend wavelengths further into mid-infrared. We achieved a 0.8 μJ laser pulse spanning from 2.2 to 5.0 μm in KTA.

Ultrabroadband tunable OPA design using a spectrally broadened pump source

A robust optical parametric amplifier (OPA) scheme is proposed in which we have experimentally achieved broadband bandwidth for a collinear OPA design that exhibits good beam quality and spatial distribution using a type-I β barium borate crystal. The applied pump pulses are simultaneously spectrally broadened and temporally stretched in a multi-plate system before being used to amplify the temporally stretched white light. In this case, the phase matching can be obtained for a broad range of wavelengths, and we have managed to achieve bandwidths three times broader than a conventional narrowband pumped collinear OPA. With a bandwidth as broad as 400 nm centered at 1400 nm, as well as a broadband angular dispersion-free idler, the signal bandwidth supports transform-limited pulses as short as 7.5 fs which correspond to sub-two optical cycles for this center wavelength. Furthermore, the system is easily tunable over a 400 nm range of bandwidths starting from 1100 to 1500 nm. The proposed scheme provides a versatile near-infrared/middle-infrared source with a broad bandwidth and fine tuning capability which paves the way for ultrafast spectroscopy and strong field applications.

53-attosecond X-ray pulses reach the carbon K-edge

The motion of electrons in the microcosm occurs on a time scale set by the atomic unit of time—24 attoseconds. Attosecond pulses at photon energies corresponding to the fundamental absorption edges of matter, which lie in the soft X-ray regime above 200 eV, permit the probing of electronic excitation, chemical state, and atomic structure. Here we demonstrate a soft X-ray pulse duration of 53 as and single pulse streaking reaching the carbon K-absorption edge (284 eV) by utilizing intense two-cycle driving pulses near 1.8-μm center wavelength. Such pulses permit studies of electron dynamics in live biological samples and next-generation electronic materials such as diamond.

Isolated attosecond pulses are produced using high harmonic generation and sources of these pulses often suffer from low photon flux in soft X-ray regime. Here the authors demonstrate efficient generation and characterization of 53 as pulses with photon energy near the water window.

Towards Terawatt Sub-Cycle Long-Wave Infrared Pulses via Chirped Optical Parametric Amplification and Indirect Pulse Shaping

We present an approach for both efficient generation and amplification of 4-12 μm pulses by tailoring the phase matching of the nonlinear crystal Zinc Germanium Phosphide (ZGP) in a narrowband-pumped optical parametric chirped pulse amplifier (OPCPA) and a broadband-pumped dual-chirped optical parametric amplifier (DC-OPA), respectively. Preliminary experimental results are obtained for generating 1.8-4.2 μm super broadband spectra, which can be used to seed both the signal of the OPCPA and the pump of the DC-OPA. The theoretical pump-to-idler conversion efficiency reaches 27% in the DC-OPA pumped by a chirped broadband Cr²⁺:ZnSe/ZnS laser, enabling the generation of  Terawatt-level 4-12 μm pulses with an available large-aperture ZGP. Furthermore, the 4-12 μm idler pulses can be compressed to sub-cycle pulses by compensating the tailored positive chirp of the idler pulses using the bulk compressor NaCl, and by indirectly controlling the higher-order idler phase through tuning the signal (2.4-4.0 μm) phase with a commercially available acousto-optic programmable dispersive filter (AOPDF). A similar approach is also described for generating high-energy 4-12 μm sub-cycle pulses via OPCPA pumped by a 2 μm Ho:YLF laser.

Single-order laser high harmonics in XUV for ultrafast photoelectron spectroscopy of molecular wavepacket dynamics

We present applications of extreme ultraviolet (XUV) single-order laser harmonics to gas-phase ultrafast photoelectron spectroscopy. Ultrashort XUV pulses at 80 nm are obtained as the 5th order harmonics of the fundamental laser at 400 nm by using Xe or Kr as the nonlinear medium and separated from other harmonic orders by using an indium foil. The single-order laser harmonics is applied for real-time probing of vibrational wavepacket dynamics of I₂ molecules in the bound and dissociating low-lying electronic states and electronic-vibrational wavepacket dynamics of highly excited Rydberg N₂ molecules.

High-energy two-cycle pulses at 3.2 μm by a broadband-pumped dual-chirped optical parametric amplification

A design for efficient generation of mid-infrared pulses at 3.2 μm is presented, which is based on numerical simulations of the broadband-pumped dual-chirped optical parametric amplification (DC-OPA) in LiNbO₃ doped with 5 mol.% MgO (MgO:LiNbO₃). The broadband seed can be generated by difference frequency generation in KTA using spectrally-broadened Ti:Sapphire lasers. The broad DC-OPA phase-matching bandwidth-spanning from 2.4 μm to 4.0 μm-is achieved by chirping both the broadband Ti:Sapphire pump pulses and the seed pulses in such a way that the individual temporal slice of pump spectrum is able to phase match that of seed spectrum. This phase matching scheme allows the use of longer crystals without gain narrowing or loss of conversion efficiency. The theoretical conversion efficiency from the pump to the idler reaches 19.1 %, enabling generation of a few hundred mJ of mid-IR energy with an available large-aperture MgO:LiNbO₃ crystal. Furthermore, the commercially available acousto-optic programmable dispersive filter (AOPDF) ensures compression of such a broad bandwidth down to 20 fs (two optical cycles at 3.2 μm).

Attosecond streaking measurement of extreme ultraviolet pulses using a long-wavelength electric field

Long-wavelength lasers have great potential to become a new-generation drive laser for tabletop coherent light sources in the soft X-ray region. Because of the significantly low conversion efficiency from a long-wavelength light field to high-order harmonics, their pulse characterization has been carried out by measuring the carrier-envelope phase and/or spatial dependences of high harmonic spectra. However, these photon detection schemes, in general, have difficulty in obtaining information on the spectral phases, which is crucial to determine the temporal structures of high-order harmonics. Here, we report the first attosecond streaking measurement of high harmonics generated by few-cycle optical pulses at 1.7 μm from a BiB₃O₆-based optical parametric chirped-pulse amplifier. This is also the first demonstration of time-resolved photoelectron spectroscopy using high harmonics from a long-wavelength drive laser other than Ti:sapphire lasers, which paves the way towards ultrafast soft X-ray photoelectron spectroscopy.

Low chromatic Fresnel lens for broadband attosecond XUV pulse applications

Fresnel zone plates show a great potential in achieving high spatial resolution imaging or focusing for XUV and soft/hard X-ray radiation, however they are usually strictly monochromatic due to strong chromatic dispersion and thus do not support broad radiation spectra, preventing their application to attosecond XUV pulses. Here we report on the design and theoretical simulations based on the design of an achromatic hybrid optics combining both, a refractive and diffractive lens in one optical element. We are able to show by calculation that the chromatic dispersion along the optical axis can be greatly reduced compared to a standard Fresnel zone plate while preserving the temporal structure of the attosecond XUV pulses at focus.

Indirect high-bandwidth stabilization of carrier-envelope phase of a high-energy, low-repetition-rate laser

We demonstrate a method of stabilizing the carrier-envelope phase (CEP) of low-repetition-rate, high-energy femtosecond laser systems such as TW-PW class lasers. A relatively weak high-repetition-rate (~1 kHz) reference pulse copropagates with a low-repetition-rate (10 Hz) high-energy pulse, which are s- and p-polarized, respectively. Using a Brewster angle window, the reference pulse is separated after the power amplifier and used for feedback to stabilize its CEP. The single-shot CEP of the high-energy pulse is indirectly stabilized to 550 mrad RMS, which is the highest CEP stability ever reported for a low-repetition-rate (10-Hz) high-energy laser system. In this novel method, the feedback frequency of the reference pulse from the front-end preamplifier can be almost preserved. Thus, higher CEP stability can be realized than for lower frequencies. Of course, a reference pulse with an even higher repetition rate (e.g., 10 kHz) can be easily employed to sample and feed back CEP jitter over a broader frequency bandwidth.