Phase of the atomic polarization in high-order harmonic generation

Gouy phase and quantum interference with cross-Wigner functions for matter-waves

The Gouy phase is essential for accurately describing various wave phenomena, ranging from classical electromagnetic waves to matter waves and quantum optics. In this work, we employ phase-space methods based on the cross-Wigner transformation to analyze spatial and temporal interference in the evolution of matter waves characterized initially by a correlated Gaussian wave packet. First, we consider the cross-Wigner of the initial wave function with its free evolution, and second for the evolution through a double-slit arrangement. Different from the wave function which acquires a global Gouy phase, we find that the cross-Wigner acquires a Gouy phase difference due to different evolution times. The results suggest that temporal like-Gouy phase difference is important for an accurate description of temporal interference. Furthermore, we propose a technique based on the Wigner function to reconstruct the cross-Wigner from the spatial intensity interference term in a double-slit experiment with matter waves.

High-harmonic generation in liquids with few-cycle pulses: effect of laser-pulse duration on the cut-off energy

High-harmonic generation (HHG) in liquids is opening new opportunities for attosecond light sources and attosecond time-resolved studies of dynamics in the liquid phase. In gas-phase HHG, few-cycle pulses are routinely used to create isolated attosecond pulses and to extend the cut-off energy. Here, we study the properties of HHG in liquids, including heavy water, ethanol and isopropanol, by continuously tuning the pulse duration of a mid-infrared driver from the multi- to the two-cycle regime. Similar to the gas phase, we observe the transition from discrete odd-order harmonics to continuous extreme-ultraviolet emission. However, the cut-off energy is shown to be entirely independent of the pulse duration. These observations are confirmed by ab-initio simulations of HHG in large liquid clusters. Our results support the notion that the cut-off energy is a fundamental property of the liquid, independent of the driving-pulse properties. Our work implies that few-cycle mid-infrared laser pulses are suitable drivers for generating isolated attosecond pulses from liquids and confirm the capability of high-harmonic spectroscopy to determine the mean-free paths of slow electrons in liquids.

X-FAST: A versatile, high-throughput, and user-friendly XUV femtosecond absorption spectroscopy tabletop instrument

We present the X-FAST (XUV Femtosecond Absorption Spectroscopy Tabletop) instrument at the University of Wisconsin-Madison. The instrument produces femtosecond extreme ultraviolet photon pulses via high-harmonic generation in the range of 40-72 eV, as well as optical pump pulses for transient-absorption experiments. The system implements a gas-cooled sample cell that enables studying the dynamics of thermally sensitive thin-film samples. This paper provides potential users with specifications of the optical, vacuum, data acquisition, and sample cooling systems of the X-FAST instrument, along with performance metrics and data of an ultrafast laser-induced phase transition in a Ni2MnGa Heusler thin film.

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.

Selective generation of narrow-band harmonics by a relativistic laser pulse interaction with a detuned plasma grating

The spectral characteristics of high-order harmonics generated by the interaction of a linearly polarized relativistic laser pulse with a plasma grating target are investigated. Through particle-in-cell simulations and an analytical model, it is shown that a plasma grating target with periodic structure can select special harmonics with integer multiples of the grating frequency, and that low-order harmonics with frequencies being integer times of the laser frequency are generated nearly parallel to the target surface from a Fresnel zone plate target with an aperiodic structure. Spectral control of the harmonics can be achieved by introducing a correction factor β to the radius formula of the Fresnel zone plate, which can create a slightly detuned plasma grating, and then only the narrow-band harmonics can be selected nearly parallel to the target surface. The center order of the narrow-band harmonics can be tuned by adjusting the correction factor β, while the bandwidth of the harmonics can be selected by adjusting the other parameter λ_{f} of the detuned plasma grating.

Spectral and Divergence Characteristics of Plateau High-Order Harmonics Generated by Femtosecond Chirped Laser Pulses in a Semi-Infinite Gas Cell

The generation of high-order harmonics in a semi-infinite cell by femtosecond laser pulses is a common practice for reliable coherent and low divergence XUV source beams for applications. Despite the relative simplicity of the experimental method, several phenomena coexist that affect the generated spectral and divergence characteristics of the high harmonic XUV frequency comb. The ionisation degree of the medium and the consequent plasma formation length imposes a spatiotemporal evolution of the fundamental EM field and XUV absorption. Varying the laser pulse chirp and the focusing conditions, as well as the gas density, we measured intense harmonic spectral and divergence variations attributed mainly to self-phase modulations of the laser EM field in the partially ionised medium. Additionally, low-divergence high harmonics are observed for certain laser chirp values attributed to the strong phase matching of only the short electron quantum path. Thus, a tunable, low divergent, and coherent XUV source can be realised for spatiotemporal imaging applications in the nanoscale.

Divergence and efficiency optimization in polarization-controlled two-color high-harmonic generation

Improving the brightness of high-harmonic generation (HHG) sources is one of the major goals for next-generation ultrafast, imaging and metrology applications in the extreme-ultraviolet spectrum. Previous research efforts have demonstrated a plethora of techniques to increase the conversion efficiency of HHG. However, few studies so far have addressed how to simultaneously minimize the divergence and improve focusability, which all contribute to an increased brightness of the source. Here, we investigate how to improve both photon yield and divergence, which is directly linked to focusability, when adding the second harmonic to the fundamental driving field. We study the effects of the relative polarization in two-color HHG and compare the results to a one-color configuration. In a perpendicular two-color field, the relative phase between the two colors can be used to suppress or enhance recombination of either the long or the short trajectories. This allows to exert control over the divergence of the harmonics. In a parallel two-color field, the ionization rate is modified through the two-color phase, which selects trajectories during the ionization step. This enhances the total yield. We elaborate on the underlying mechanisms for parallel, perpendicular, and intermediate polarization angles, and confirm our experimental observations with simulations.

Electron quantum path control in high harmonic generation via chirp variation of strong laser pulses

The quantum phases of the electron paths driven by an ultrafast laser in high harmonic generation in an atomic gas depends linearly on the instantaneous cycle-averaged laser intensity. Using high laser intensities, a complete single ionisation of the atomic gas may occur before the laser pulse peak. Therefore, high harmonic generation could be localised only in a temporal window at the leading edge of laser pulse envelope. Varying the laser frequency chirp of an intense ultrafast laser pulse, the centre, and the width of the temporal window, that the high harmonic generation phenomenon occurs, could be controlled with high accuracy. This way, both the duration and the phase of the electron trajectories, that generate efficiently high harmonics, is fully controlled. A method of spectral control and selection of the high harmonic extreme ultraviolet light from distinct quantum paths is experimentally demonstrated. Furthermore, a phenomenological numerical model enlightens the physical processes that take place. This novel approach of the electron quantum path selection via laser chirp is a simple and versatile way of controlling the time-spectral characteristics of the coherent extreme ultraviolet light with applications in the fields of attosecond pulses and soft x-ray nano-imaging.

Phase-matching control of high-order harmonics with circular Airy-Gaussian beams

We investigate the phase-matching of the high harmonics (HHG) driven by the circular Airy-Gaussian beams (CAiGB), which abruptly auto-focus and subsequently propagate without diffraction. The results show that the harmonics corresponding to both short and long quantum paths can be well phase-matched after the focusing point of the CAiGB. Therefore, the effective interaction length of HHG for CAiGB is much longer than that for the conventional Gaussian beams with the same size of the waist. Our numerical simulations reveal that the harmonics continuously gain up to 1 cm of the propagation distance. This work provides a route to enhance the conversion efficiency of HHG by the coherent control of abrupt auto-focusing beams.

Resolving the quantum dynamics of near cut-off high-order harmonic generation in atoms by Bohmian trajectories

We present an ab initio study of the quantum dynamics of high-order harmonic generation (HHG) near the cutoff in intense laser fields. To uncover the subtle dynamical origin of the HHG near the cutoff, we extend the Bohmian mechanics (BM) approach for the treatment of attosecond electronic dynamics of H and Ar atoms in strong laser fields. The time-dependent Schrödinger equation and the self-interaction-free time-dependent density functional theory are numerically solved accurately and efficiently by means of the time-dependent generalized pseudospectral method for nonuniform spatial discretization of the Hamiltonian. We find that the most devoting trajectories calculated by the BM to the plateau harmonics are shorter traveling trajectories, but the contributions of the short trajectories near the cutoff are suppressed in HHG. As a result, the yields of those harmonics in the region near the cutoff are relatively weak. However, for the last few harmonics just above the cutoff, the HHG intensity becomes a little higher. This is because the HHG just above the cutoff arises from those electrons ionized near the peak of the laser pulse, where the ionization rate is the highest. In addition, the longer Bohmian trajectories return to the core with lower energies, these trajectories contribute to the below-threshold harmonics. Our results provide a deeper understanding of the generation of supercontinuum harmonic spectra and attosecond pulses via near cutoff HHG.

Coulomb-induced ionization time lag after electrons tunnel out of a barrier

After electrons tunnel out of a laser-Coulomb-formed barrier, the movement of the tunneling electron can be affected by the Coulomb potential. We show that this Coulomb effect induces a large time difference (longer than a hundred attoseconds) between the tunneling-out time at which the electron exits the barrier and the ionization time at which the electron is free. This large time difference has important influences on strong-field processes such as above-threshold ionization and high-harmonic generation, with remarkably changing time-frequency properties of electron trajectories. Some semi-quantitative evaluations on these influences are addressed, which provide new insight into strong-field processes and give suggestions on attosecond measurements.

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.

Symphony on strong field approximation

This paper has been prepared by the Symphony collaboration (University of Warsaw, Uniwersytet Jagielloński, DESY/CNR and ICFO) on the occasion of the 25th anniversary of the 'simple man's models' which underlie most of the phenomena that occur when intense ultrashort laser pulses interact with matter. The phenomena in question include high-harmonic generation (HHG), above-threshold ionization (ATI), and non-sequential multielectron ionization (NSMI). 'Simple man's models' provide both an intuitive basis for understanding the numerical solutions of the time-dependent Schrödinger equation and the motivation for the powerful analytic approximations generally known as the strong field approximation (SFA). In this paper we first review the SFA in the form developed by us in the last 25 years. In this approach the SFA is a method to solve the TDSE, in which the non-perturbative interactions are described by including continuum-continuum interactions in a systematic perturbation-like theory. In this review we focus on recent applications of the SFA to HHG, ATI and NSMI from multi-electron atoms and from multi-atom molecules. The main novel part of the presented theory concerns generalizations of the SFA to: (i) time-dependent treatment of two-electron atoms, allowing for studies of an interplay between electron impact ionization and resonant excitation with subsequent ionization; (ii) time-dependent treatment in the single active electron approximation of 'large' molecules and targets which are themselves undergoing dynamics during the HHG or ATI processes. In particular, we formulate the general expressions for the case of arbitrary molecules, combining input from quantum chemistry and quantum dynamics. We formulate also theory of time-dependent separable molecular potentials to model analytically the dynamics of realistic electronic wave packets for molecules in strong laser fields. We dedicate this work to the memory of Bertrand Carré, who passed away in March 2018 at the age of 60.

High-harmonic spectroscopy of transient two-center interference calculated with time-dependent density-functional theory

We demonstrate high-harmonic spectroscopy in many-electron molecules using time-dependent density-functional theory. We show that a weak attosecond-pulse-train ionization seed that is properly synchronized with the strong driving mid-infrared laser field can produce experimentally relevant high-harmonic generation (HHG) signals, from which we extract both the spectral amplitude and the target-specific phase (group delay). We also show that further processing of the HHG signal can be used to achieve molecular-frame resolution, i.e., to resolve the contributions from rescattering on different sides of an oriented molecule. In this framework, we investigate transient two-center interference in CO₂ and OCS, and how subcycle polarization effects shape the oriented/aligned angle-resolved spectra.

Conservation of Torus-knot Angular Momentum in High-order Harmonic Generation

High-order harmonic generation stands as a unique nonlinear optical up-conversion process, mediated by a laser-driven electron recollision mechanism, which has been shown to conserve energy, linear momentum, and spin and orbital angular momentum. Here, we present theoretical simulations that demonstrate that this process also conserves a mixture of the latter, the torus-knot angular momentum J_{γ}, by producing high-order harmonics with driving pulses that are invariant under coordinated rotations. We demonstrate that the charge J_{γ} of the emitted harmonics scales linearly with the harmonic order, and that this conservation law is imprinted onto the polarization distribution of the emitted spiral of attosecond pulses. We also demonstrate how the nonperturbative physics of high-order harmonic generation affect the torus-knot angular momentum of the harmonics, and we show that this configuration harnesses the spin selection rules to channel the full yield of each harmonic into a single mode of controllable orbital angular momentum.

Optics-less focusing of XUV high-order harmonics

By experimentally studying high-order harmonic beams generated in gases, we show how the spatial characteristics of these ultrashort extreme-ultraviolet (XUV) beams can be finely controlled when a single fundamental beam generates harmonics in a thin gas medium. We demonstrate that these XUV beams can be emitted as converging beams and thereby get focused after generation. We study this optics-less focusing using a spatially chirped beam that acts as a probe located inside the harmonic generation medium. We analyze the XUV beam evolution with an analytical model and obtain very good agreement with experimental measurements. The XUV foci sizes and positions vary strongly with the harmonic order, and the XUV waist can be located at arbitrarily large distances from the generating medium. We discuss how intense XUV fields can be obtained with optics-less focusing and how the order-dependent XUV beam characteristics are compatible with broadband XUV irradiation and attosecond science.

Imaging the source of high-harmonics generated in atomic gas media

We report the application of the time gated ion microscopy technique in accessing online the position of the source of harmonics generated in atomic gas media. This is achieved by mapping the spatial extreme-ultraviolet (XUV)-intensity distribution of the harmonic source onto a spatial ion distribution, produced in a separate focal volume of the generated XUV beam through single photon ionization of atoms. It is found that the position of the harmonic source depends on the relative position of the harmonic generation gas medium and the focus of the driving infrared (IR) beam. In particular, by translating the gas medium with respect to the IR beam focus different "virtual" source positions are obtained online. Access to such online source positioning allows better control and provides increased possibilities in experiments where selection of electron trajectory is important. The present study gives also access to quantitative information which is connected to the divergence, the coherence properties and the photon flux of the harmonics. Finally, it constitutes a precise direct method for providing complementary experimental info to different attosecond metrology techniques.

Evidence of depolarization and ellipticity of high harmonics driven by ultrashort bichromatic circularly polarized fields

High harmonics generated by counter-rotating laser fields at the fundamental and second harmonic frequencies have raised important interest as a table-top source of circularly polarized ultrashort extreme-ultraviolet light. However, this emission has not yet been fully characterized: in particular it was assumed to be fully polarized, leading to an uncertainty on the effective harmonic ellipticity. Here we show, through simulations, that ultrashort driving fields and ultrafast medium ionization lead to a breaking of the dynamical symmetry of the interaction, and consequently to deviations from perfectly circular and fully polarized harmonics, already at the single-atom level. We perform the complete experimental characterization of the polarization state of high harmonics generated along that scheme, giving direct access to the ellipticity absolute value and sign, as well as the degree of polarization of individual harmonic orders. This study allows defining optimal generation conditions of fully circularly polarized harmonics for advanced studies of ultrafast dichroisms.

Spatiotemporal filtering of high harmonics in solids

We study the macroscopic spatial and temporal properties of harmonic radiation generated by a model solid in the interaction with an intense, focused laser beam. We show that different temporal contributions to the harmonic yield can be separated in the spatial domain because they lead to radiation with different divergences, similar to what is observed in gas-phase harmonic generation. We show that applying a spatial filter in the far field results in a temporal separation of the two contributions upon refocusing, which yields spatially collimated harmonics, a spectrum with well-resolved peaks, and a subcycle time profile of the harmonic radiation with only one burst per half-cycle.

Extension of water-window harmonic cutoff by laser defocusing-assisted phase matching

We extend a recently demonstrated scheme [Optica4, 976 (2017)OPTIC82334-253610.1364/OPTICA.4.000976] to overcome the limit of conventional harmonic cutoff for different pulse durations, laser wavelengths, and gas targets. By tuning the truncation of long wavelength lasers, we show that the defocusing-assisted phase matching (DAPM) can be achieved in a tightly focused beam and highly ionized short gas cell, and can be used to effectively extend the harmonic cutoff energy and optimize its yield. An analysis of phase matching reveals that at longer wavelengths, greater cutoff extension to the water window region is achieved because of the larger harmonic intrinsic phase (proportional to the cube of laser wavelength), and because DAPM works at relatively higher laser intensities using a Ne target. This scheme provides a promising method for efficiently generating intense attosecond light sources in the extreme ultraviolet to x-rays.

Routes of odd-even harmonic emission from oriented polar molecules

We study odd-even high-harmonic generation (HHG) from oriented asymmetric molecules with different symmetries in strong laser fields. A model based on strong-field approximations is used which allows us to resolve the contributions of different emission routes to odd-even HHG. The comparison between the HHG yields of all routes versus one certain route demonstrates that the routes in which the electron ionizes from the gerade component of the asymmetric orbital contribute mainly to odd-even HHG. We show that the potential mechanism is associated with effects of intramolecular interference in tunneling ionization as the bound electron passes through the barrier formed by the laser field and the asymmetric Coulomb potential. The influences of different emission routes on asymmetric orbital imagining with odd-even HHG are also addressed.

A redshift mechanism of high-order harmonics: Change of ionization energy

We theoretically study the high-order harmonic generation of H₂⁺ and its isotopes beyond the Born-Oppenheimer dynamics. It is surprising that the spectral redshift can still be observed in high harmonic spectra of H₂⁺ driven by a sinusoidal laser pulse in which the trailing (leading) edge of the laser pulse is nonexistent. The results confirm that this spectral redshift originates from the reduction in ionization energy between recombination time and ionization time, which is obviously different from the nonadiabatic spectral redshift induced by the falling edge of the laser pulse. Additionally, the improved instantaneous frequency of harmonics by considering the changeable ionization energy can deeply verify our results. Therefore, this new mechanism must be taken into account when one uses the nonadiabatic spectral redshift to retrieve the nuclear motion.

Control of quasi-phase-matching of high-harmonics in a spatially structured plasma

High-harmonic generation is widely used for providing extreme ultraviolet radiation in attosecond science. Such experiments include photoelectron spectroscopy, diffractive imaging, or the investigation of spin dynamics. Many applications are restricted by a low photon flux which originates from the low efficiency of the generation process. In this article an effective method based on the quasi-phase-matched generation of high harmonics in spatially structured, laser ablated plasma is demonstrated. Through a proper dimensioning of the plasma structure, the harmonic yield is optimized for a controllable range of harmonic orders. By using four coherent zones, the intensity of a single harmonic is increased to a maximal possible value of 16 compared to using a single zone. The Gouy phase shift of the fundamental field is identified as the primary effect responsible for constructive interference of the harmonic fields generated in the individual plasma jets of the plasma structure.

On-the-Fly Control of High-Harmonic Generation Using a Structured Pump Beam

We demonstrate experimentally a relatively simple yet powerful all-optical enhancement and control technique for high harmonic generation. This is achieved by using as a pump beam two different spatial optical modes interfering together to realize tunable periodic quasi-phase matching of the interaction. With this technique, we demonstrate on-the-fly quasi-phase matching of harmonic orders 29-41 at ambient gas pressure levels of 50 and 100 Torr, where an up to 100-fold enhancement of the emission is observed. The technique is scalable to different harmonic orders and ambient pressure conditions.

Coherent diffractive imaging of graphite nanoparticles using a tabletop EUV source

Structural information of nanostructures plays a key role in synthesis of novel nano-sized materials for promising applications such as high-performance nanoelectronics and nanophotonics. In this study, we apply for the first time the state-of-the-art coherent diffractive imaging method to characterize the structure of graphite nanoparticles. A sample with nanographites on a Si₃N₄ support was exposed to 30 nm radiation from a tabletop laser-driven high-order harmonic generation extreme ultraviolet (EUV) source. From the measured far-field diffraction pattern, we were able to reconstruct the distribution of the graphite nanoparticles with a spatial resolution of ∼330 nm using the standard iterative phase retrieval algorithms. A closer look at the reconstructed images reveals possible absorption effects of graphite nanoparticles. This experiment demonstrates the first step towards wide-field and high-resolution imaging of nuclear materials using the newly established lab-scale EUV source. Having such a source opens the door to performing investigations of nuclear graphite and other radioactive material in the lab, thus avoiding the need to transport samples to external facilities.

Spatial Properties of High-Order Harmonic Beams from Plasma Mirrors: A Ptychographic Study

Spatial properties of high-order harmonic beams produced by high-intensity laser-matter interactions carry rich information on the physics of the generation process, and their detailed understanding is essential for applications of these light beams. We present a thorough study of these properties in the case of harmonic generation from plasma mirrors, up to the relativistic interaction regime. In situ ptychographic measurements of the amplitude and phase spatial profiles of the different harmonic orders in the target plane are presented, as a function of the key interaction parameters. These measurements are used to validate analytical models of the harmonic spatial phase in different generation regimes, and to benchmark ultrahigh-order Maxwell solvers of particle-in-cell simulation codes.

Nonadiabatic redshifts in high-order harmonic generation from solids

We studied the multi-plateau high-order harmonic generation (HHG) from solids numerically. It is found that the HHG spectra in the second and higher plateaus are redshifted in short laser pulses due to the nonadiabatic effect. The corresponding FWHMs also increase as a function of the harmonic order, suggesting the step-by-step excitation of higher conduction bands in the HHG process. Although the system is symmetric in the coordinate space, even-order harmonics are present. It is due to the fact that the symmetry of electron motions and the population in the higher conduction bands is broken in the k space and time domain based on the indirect step-by-step excitation model. Our numerical results are in good agreement with recent experimental measurements of Ndabashimiye et al. [Nature 534, 520 (2016)].

Quasi-phase-matching of high-order harmonics in plasma plumes: theory and experiment

We theoretically analyze the phase-matching of high-order harmonic generation (HHG) in multi-jet plasmas and find the harmonic orders for which the quasi-phase-matching (QPM) is achieved depending on the parameters of the plasma and the generating beam. HHG by single- and two-color generating fields is analyzed. The QMP is studied experimentally for silver, indium and manganese plasmas using near IR and mid-IR laser fields. The theory is validated by comparison with our experimental observations, as well as published experimental data. In particular, the plasma densities and the harmonic phase coefficients reconstructed from the observed harmonic spectra using our theory agree with the corresponding parameters found using other methods. Our theory allows defining the plasma jet and the generating field properties, which can maximize the HHG efficiency due to QPM.

Attosecond Probing of Nuclear Dynamics with Trajectory-Resolved High-Harmonic Spectroscopy

We report attosecond-scale probing of the laser-induced dynamics in molecules. We apply the method of high-harmonic spectroscopy, where laser-driven recolliding electrons on various trajectories record the motion of their parent ion. Based on the transient phase-matching mechanism of high-order harmonic generation, short and long trajectories contributing to the same harmonic order are distinguishable in both the spatial and frequency domains, giving rise to a one-to-one map between time and photon energy for each trajectory. The short and long trajectories in H_{2} and D_{2} are used simultaneously to retrieve the nuclear dynamics on the attosecond and ångström scale. Compared to using only short trajectories, this extends the temporal range of the measurement to one optical cycle. The experiment is also applied to methane and ammonia molecules.

Phase matching effects in high harmonic generation at the nanometer scale

Plasmon resonances are known to amplify the electromagnetic fields near metallic nanostructures, providing a promising scheme to generate extreme-ultraviolet harmonics using low power drivings. During high-order harmonic generation (HHG), the driving and harmonic fields accumulate a phase difference as they propagate through the target. In a typical set-up -a laser focused into a gas jet- the propagation distances amount to several wavelengths, and the cumulative phase-mismatch affects strongly the efficiency and properties of the harmonic emission. In contrast, HHG in metallic nanostructures is considered to overcome these limitations, as the common sources of phase mismatch -optical density and focusing geometry- are negligible for subwavelength propagation distances. We demonstrate that phase matching still plays a relevant role in HHG from nanostructures due to the non-perturbative character of HHG, that links the harmonic phase to the intensity distribution of the driving field. Our computations show that widely used applications of phase matching control, such as quantum path selection and the increase of contrast in attosecond pulse generation, are also feasible at the nanoscale.

Unravelling the dynamical origin of below- and near-threshold harmonic generation of H2+ in an intense NIR laser field

Recently, the study of near- and below- threshold regime harmonics as a potential source of intense coherent vacuum-ultraviolet radiation has received considerable attention. However, the dynamical origin of these lower harmonics, particularly for the molecular systems, is less understood and largely unexplored. Here we perform the first fully ab initio and high precision 3D quantum study of the below- and near-threshold harmonic generation of molecules in an intense 800-nm near-infrared (NIR) laser field. Combining with a synchrosqueezing transform of the quantum time-frequency spectrum and an extended semiclassical analysis, we explore in-depth the roles of various quantum trajectories, including short- and long trajectories, multiphoton trajectories, resonance-enhanced trajectories, and multiple rescattering trajectories of the below- and near- threshold harmonic generation processes. Our results shed new light on the dynamical origin of the below- and near-threshold harmonic generation and various quantum trajectories for diatomic molecules for the first time.

Nonperturbative Twist in the Generation of Extreme-Ultraviolet Vortex Beams

High-order harmonic generation (HHG) has been recently proven to produce extreme-ultraviolet (XUV) vortices from the nonlinear conversion of infrared twisted beams. Previous works have demonstrated a linear scaling law of the vortex charge with the harmonic order. We demonstrate that this simple law hides an unexpectedly rich scenario for the buildup of orbital angular momentum (OAM) due to the nonperturbative behavior of HHG. The complexity of these twisted XUV beams appears only when HHG is driven by nonpure vortex modes, where the XUV OAM content is dramatically increased. We explore the underlying mechanisms for this diversity and derive a general conservation rule for the nonperturbative OAM buildup. The simple scaling found in previous works corresponds to the collapse of this scenario for the particular case of pure (single-mode) OAM driving fields.

Periodic density modulation for quasi-phase-matching of optical frequency conversion is inefficient under shallow focusing and constant ambient pressure

The two main mechanisms of a periodic density modulation relevant to nonlinear optical conversion in a gas medium are spatial modulations of the index of refraction and of the number of emitters. For a one-dimensional model neglecting focusing and using a constant ambient pressure, it is shown theoretically and demonstrated numerically that the effects of these two mechanisms during frequency conversion cancel each other exactly. Under the considered conditions, this makes density modulation inefficient for quasi-phase-matching an optical frequency conversion process. This result is particularly relevant for high-order harmonic generation.

Probe of Multielectron Dynamics in Xenon by Caustics in High-Order Harmonic Generation

We investigated the giant resonance in xenon by high-order harmonic generation spectroscopy driven by a two-color field. The addition of a nonperturbative second harmonic component parallel to the driving field breaks the symmetry between neighboring subcycles resulting in the appearance of spectral caustics at two distinct cutoff energies. By controlling the phase delay between the two color components it is possible to tailor the harmonic emission in order to amplify and isolate the spectral feature of interest. In this Letter we demonstrate how this control scheme can be used to investigate the role of electron correlations that give birth to the giant resonance in xenon. The collective excitations of the giant dipole resonance in xenon combined with the spectral manipulation associated with the two-color driving field allow us to see features that are normally not accessible and to obtain a good agreement between the experimental results and the theoretical predictions.

A table-top monochromator for tunable femtosecond XUV pulses generated in a semi-infinite gas cell: Experiment and simulations

We present a new design of a time-preserving extreme-ultraviolet (XUV) monochromator using a semi-infinite gas cell as a source. The performance of this beamline in the photon-energy range of 20 eV-42 eV has been characterized. We have measured the order-dependent XUV pulse durations as well as the flux and the spectral contrast. XUV pulse durations of ≤40 fs using 32 fs, 800 nm driving pulses were measured on the target. The spectral contrast was better than 100 over the entire energy range. A simple model based on the strong-field approximation is presented to estimate different contributions to the measured XUV pulse duration. On-axis phase-matching calculations are used to rationalize the variation of the photon flux with pressure and intensity.

Carrier-envelope-phase insensitivity in high-order harmonic generation driven by few-cycle laser pulses

We present evidence for self-stabilization of the relative spectral phase of high-order harmonic emission against intensity variations of the driving field. Our results demonstrate that, near the laser focus, phase matching of the harmonic field from a macroscopic target can compensate for the intensity dependence of the intrinsic phase of the harmonics emitted by a single radiator. As a consequence, we show experimentally and theoretically the insensitivity of the harmonic spectra produced at the laser focus against variations of the carrier-envelope phase (CEP) of a sub-two-cycle driving field. In addition, the associated attosecond pulse trains exhibit phase locking against CEP changes of the few-cycle driver.

Generation of Bright, Spatially Coherent Soft X-Ray High Harmonics in a Hollow Waveguide Using Two-Color Synthesized Laser Pulses

We investigate the efficient generation of low-divergence high-order harmonics driven by waveform-optimized laser pulses in a gas-filled hollow waveguide. The drive waveform is obtained by synthesizing two-color laser pulses, optimized such that highest harmonic yields are emitted from each atom. Optimization of the gas pressure and waveguide configuration has enabled us to produce bright and spatially coherent harmonics extending from the extreme ultraviolet to soft x rays. Our study on the interplay among waveguide mode, atomic dispersion, and plasma effect uncovers how dynamic phase matching is accomplished and how an optimized waveform is maintained when optimal waveguide parameters (radius and length) and gas pressure are identified. Our analysis should help laboratory development in the generation of high-flux bright coherent soft x rays as tabletop light sources for applications.

Enhanced high-order harmonic generation from spatially prepared filamentation in argon

We experimentally demonstrate enhanced high-order harmonic generation (HHG) from spatially prepared filamentation in Argon. Upon shifting the focus position of an elliptically polarized laser pulse over the filament induced by a linearly polarized laser pulse, an obvious enhancement of harmonic yield by nearly one order of magnitude is observed. The result could be interpreted in terms of the double contributions from both the excited states of target atom and the phase-matching effect of harmonic beam. In contrast to the enhancement phenomena, an obvious suppression of harmonic yield is also presented, which could be attributed to both the ground-state depletion and the plasma effect.

Dynamical origin of near- and below-threshold harmonic generation of Cs in an intense mid-infrared laser field

Near- and below-threshold harmonic generation provides a potential approach to generate vacuum-ultraviolet frequency comb. However, the dynamical origin of in these lower harmonics is less understood and largely unexplored. Here we perform an ab initio quantum study of the near- and below-threshold harmonic generation of caesium (Cs) atoms in an intense 3,600-nm mid-infrared laser field. Combining with a synchrosqueezing transform of the quantum time-frequency spectrum and an extended semiclassical analysis, the roles of multiphoton and multiple rescattering trajectories on the near- and below-threshold harmonic generation processes are clarified. We find that the multiphoton-dominated trajectories only involve the electrons scattered off the higher part of the combined atom-field potential followed by the absorption of many photons in near- and below-threshold regime. Furthermore, only the near-resonant below-threshold harmonic is exclusive to exhibit phase locked features. Our results shed light on the dynamic origin of the near- and below-threshold harmonic generation.

High harmonic generation (HHG) above the HHG threshold is understood using the three-step model, but the near- and below-threshold regimes are largely unexplored. Here, Li et al. shed light on the dynamic origin of the near- and below-threshold harmonic generation of caesium atoms in an intense mid-infrared laser field.

Revealing backward rescattering photoelectron interference of molecules in strong infrared laser fields

Photoelectrons ionized from atoms and molecules in a strong laser field are either emitted directly or rescattered by the nucleus, both of which can serve as efficiently useful tools for molecular orbital imaging. We measure the photoelectron angular distributions of molecules (N2, O2 and CO2) ionized by infrared laser pulses (1320 nm, 0.2 ~ 1 × 10(14) W/cm(2)) from multiphoton to tunneling regime and observe an enhancement of interference stripes in the tunneling regime. Using a semiclassical rescattering model with implementing the interference effect, we show that the enhancement arises from the sub-laser-cycle holographic interference of the contributions of the back-rescattering and the non-rescattering electron trajectory. It is shown that the low-energy backscattering photoelectron interference patterns have encoded the structural information of the molecular initial orbitals and attosecond time-resolved dynamics of photoelectron, opening new paths in high-resolution imaging of sub-Ångström and sub-femtosecond structural dynamics in molecules.

Full quantum trajectories resolved high-order harmonic generation

We use a carrier-envelope-phase stabilized sub-2-cycle laser pulse to generate high-order harmonics and study how the two-dimensional spectrum of harmonics, with the resolutions in temporal frequency and spatial frequency, is shaped by the laser phase. An arrowlike spectrum obtained experimentally when the gas cell is located in front of the laser focus point shows a resolution of full quantum trajectories; i.e., harmonics from different trajectories stand on different positions in this spectrum. In particular, due to the laser phase combined with the classical-like action, the harmonics from short and long trajectories differ maximally in their curvatures of wave fronts in the generation area, and so occupy very different ranges of spatial frequency at the far field. The result directly gives a full map of quantum trajectories in high-order harmonic generation. The conclusion is supported by an analytical model and quantum mechanics simulations.

Spatially and spectrally resolved quantum-path tracing in high-order harmonic generation

We experimentally demonstrate the macroscopic evolution of quantum-path distributions in harmonic emission with spatial and spectral resolution from an argon gas jet, and obviously observe that the spatial profiles of harmonics are gradually split into two components (the red and blue shifts) when the driving laser intensity is increased. Moreover, the red and blue shifts in quantum-path distributions are experimentally traced and clarified in the spatial and spectral domain by choosing the focal position. These results give a more comprehensive understanding and therefore a better control of harmonic emission.

Enhancing the macroscopic yield of narrow-band high-order harmonic generation by Fano resonances

Resonances in the photoabsorption spectrum of the generating medium can modify the spectrum of high-order harmonics. In particular, window-type Fano resonances can reduce photoabsorption within a narrow spectral region and, consequently, lead to an enhanced emission of high-order harmonics in absorption-limited generation conditions. For high harmonic generation in argon it is shown that the 3s3p(6)np(1)P(1) window resonances (n = 4, 5, 6) give rise to enhanced photon yield. In particular, the 3s3p(6)4p(1)P(1) resonance at 26.6 eV allows a relative enhancement up to a factor of 30 in a 100 meV bandwidth compared to the characteristic photon emission of the neighboring harmonic order. This enhanced, spectrally isolated, and coherent photon emission line has a relative energy bandwidth of only ΔE/E = 3 × 10(-3). Therefore, it might be very useful for applications such as precision spectroscopy or coherent diffractive imaging. The presented mechanism can be employed for tailoring and controlling the high harmonic emission of manifold target materials.

Generation of high-photon flux-coherent soft x-ray radiation with few-cycle pulses

We present a tabletop source of coherent soft x-ray radiation with high-photon flux. Two-cycle pulses delivered by a fiber-laser-pumped optical parametric chirped-pulse amplifier operating at 180 kHz repetition rate are upconverted via high harmonic generation in neon to photon energies beyond 200 eV. A maximum photon flux of 1.3·10(8) photons/s is achieved within a 1% bandwidth at 125 eV photon energy. This corresponds to a conversion efficiency of ~10(-9), which can be reached due to a gas jet simultaneously providing a high target density and phase matching. Further scaling potential toward higher photon flux as well as higher photon energies are discussed.

Electron trajectory selection for high harmonic generation inside a short hollow fiber

The 19th harmonic beam divergences from a Ti:sapphire laser generated using a gas jet and 10-mm-long hollow fibers with bore diameters of 300 and 200 μm were investigated. The beam quality factor M(2) of the harmonic beam generated in a 300-μm hollow fiber was found to be better than the gas jet using the phase match including the atomic dipole phase induced by the short trajectory. On the other hand, a 200-μm hollow fiber was found to generate a more divergent beam with a larger M(2) because of the long trajectory. The electron trajectory contributing to high harmonic generation was selected using the phase-matching process inside a short hollow fiber.

Efficient high-order harmonic generation boosted by below-threshold harmonics

High-order harmonic generation (HHG) in gases has been established as an important technique for the generation of coherent extreme ultraviolet (XUV) pulses at ultrashort time scales. Its main drawback, however, is the low conversion efficiency, setting limits for many applications, such as ultrafast coherent imaging, nonlinear processes in the XUV range, or seeded free electron lasers. Here we introduce a novel scheme based on using below-threshold harmonics, generated in a “seeding cell”, to boost the HHG process in a “generation cell”, placed further downstream in the focused laser beam. By modifying the fundamental driving field, these low-order harmonics alter the ionization step of the nonlinear HHG process. Our dual-cell scheme enhances the conversion efficiency of HHG, opening the path for the realization of robust intense attosecond XUV sources.

Effects of driving laser jitter on the attosecond streaking measurement

Driving laser jitter is one of the main factors affecting the attosecond streaking measurement. The effect of carrier-envelope phase (CEP) jitter and the pulse energy jitter on the attosecond pulse characterization is studied in this paper. We have theoretically calculated and experimentally confirmed that CEP jitter could result in a symmetry trace in the streaking spectrogram, while the intensity jitter could result in a slight shift and broadening of the trace. Both of them can lead to an underestimate of the retrieved attosecond pulse duration.