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

Enhancing the efficiency of high-order harmonics with two-color non-collinear wave mixing in silica

The emission of high-order harmonics from solids under intense laser-pulse irradiation is revolutionizing our understanding of strong-field solid-light interactions, while simultaneously opening avenues towards novel, all-solid, coherent, short-wavelength table-top sources with tailored emission profiles and nanoscale light-field control. To date, broadband spectra in solids have been generated well into the extreme-ultraviolet (XUV), but the comparatively low conversion efficiency in the XUV range achieved under optimal conditions still lags behind gas-based high-harmonic generation (HHG) sources. Here, we demonstrate that two-color high-order harmonic wave mixing in a fused silica solid is more efficient than solid HHG driven by a single color. This finding has significant implications for compact XUV sources where gas-based HHG is not feasible, as solid XUV wave mixing surpasses solid-HHG in performance. Moreover, our results enable utilizing solid high-order harmonic wave mixing as a probe of structure or material dynamics of the generating solid, which will enable reducing measurement times compared to the less efficient regular solid HHG. The emission intensity scaling that follows perturbative optical wave mixing, combined with the angular separation of the emitted frequencies, makes our approach a decisive step for all-solid coherent XUV sources and for studying light-engineered materials.

Highly versatile, two-color setup for high-order harmonic generation using spatial light modulators

We present a novel, interferometric, two-color, high-order harmonic generation setup based on a turn-key Ytterbium-doped femtosecond laser source and its second harmonic. Each interferometer arm contains a spatial light modulator with individual capabilities to manipulate the spatial beam profiles and to stabilize the relative delay between the fundamental and the second harmonic. In addition, separate control of the relative power and focusing geometries of the two color beams is implemented to conveniently perform automated scans of multiple parameters. A live diagnostics system gives continuous information during ongoing measurements.

Channel separation of secondary generated radiation induced by orthogonal XUV and IR pulses

The secondary generated radiation induced by orthogonal linearly polarized extreme ultraviolet (XUV) and infrared (IR) pulses is analyzed for the spectral region of the second XUV harmonic. The polarization-filtering-based method is utilized to separate two spectrally overlapping and competing channels, which are the XUV second harmonic generation (SHG) by IR-dressed atom and XUV-assisted recombination channel of high-order harmonic generation in the IR field [Phys. Rev. A98, 063433 (2018)10.1103/PhysRevA.98.063433]. We demonstrate the use of the separated XUV SHG channel for accurately retrieving the IR-pulse waveform and find the range of IR-pulse intensities for which this retrieving is applicable.

In-line ultra-thin attosecond delay line with direct absolute-zero delay reference and high stability

We introduce an ultra-thin attosecond optical delay line based on controlled wavefront division of a femtosecond infrared pulse after transmission through a pair of micrometer-thin glass plates with negligible dispersion effects. The time delay between the two pulses is controlled by rotating one of the glass plates from absolute zero to several optical cycles, with 2.5 as to tens of attosecond resolution with 2 as stability, as determined by interferometric self-calibration. The performance of the delay line is validated by observing attosecond-resolved oscillations in the yield of high harmonics induced by time delayed infrared pulses, in agreement with a numerical simulation for a simple model atom. This approach can be extended in the future for performing XUV-IR attosecond pump-probe experiments.

The Role of Electron Trajectories in XUV-Initiated High-Harmonic Generation

High-harmonic generation spectroscopy is a powerful tool for ultrafast spectroscopy with intrinsic attosecond time resolution. Its major limitation—the fact that a strong infrared driving pulse is governing the entire generation process—is lifted by extreme ultraviolet (XUV)-initiated high-harmonic generation (HHG). Tunneling ionization is replaced by XUV photoionization, which decouples ionization from recollision. Here we probe the intensity dependence of XUV-initiated HHG and observe strong spectral frequency shifts of the high harmonics. We are able to tune the shift by controlling the instantaneous intensity of the infrared field. We directly access the reciprocal intensity parameter associated with the electron trajectories and identify short and long trajectories. Our findings are supported and analyzed by ab initio calculations and a semiclassical trajectory model. The ability to isolate and control long trajectories in XUV-initiated HHG increases the range of the intrinsic attosecond clock for spectroscopic applications.

Enhanced high-harmonic generation up to the soft X-ray region driven by mid-infrared pulses mixed with their third harmonic

We systematically study the efficiency enhancement of high-harmonic generation (HHG) in an Ar gas cell up to the soft X-ray (SXR) range using a two-color laser field composed of 2.1 μm (ω) and 700 nm (3ω) with parallel linear polarization. Our experiment follows the recent theoretical investigations that determined two-color mid-infrared (IR) pulses, mixed with their third harmonic (ω + 3ω), to be close to optimal driving waveforms for enhancing HHG efficiency in the SXR region [Jin et al., Nature Comm. 5, 4003 (2014)]. We observed sub-optical-cycle-dependent efficiency enhancements of up to 8.2 of photon flux integrated between 20 - 70 eV, and up to 2.2 between 85 - 205 eV. Enhancement of HHG efficiency was most pronounced for the lowest tested backing pressure (≈ 140 mbar), and decreased monotonically as the pressure was increased. The single-color (ω)-driven HHG was optimal at the highest backing pressure tested in the experiment (≈ 375 mbar). Our numerical simulations based on single-atom response and 3D pulse propagation show good qualitative agreement with experimental observations. The lower enhancement at high pressure and higher photon energy indicates that phase matching of two-color-driven HHG is more sensitive to ionization rate and pulse propagation effects than the single-color case. We show that with further improvements to the relative phase jitter and the spatio-temporal overlap of the two beams, the efficiency enhancement could be further improved by at least a factor of ≈ 2.

Enhancement of high-order harmonics in a plasma waveguide formed in clustered Ar gas

Generation of high-order harmonics (HHs) is intensified by using a plasma waveguide created by a laser in a clustered gas jet. The formation of a plasma waveguide and the guiding of a laser beam are also demonstrated. Compared to the case without a waveguide, harmonics were strengthened up to nine times, and blue-shifted. Numerical simulation by solving the time-dependent Schrödinger equation in strong field approximation agreed well with experimental results. This result reveals that the strengthening is the result of improved phase matching and that the blue shift is a result of change in fundamental laser frequency due to self-phase modulation (SPM).

Self-probing spectroscopy of XUV photo-ionization dynamics in atoms subjected to a strong-field environment

Single-photon ionization is one of the most fundamental light matter interactions in nature, serving as a universal probe of the quantum state of matter. By probing the emitted electron, one can decode the full dynamics of the interaction. When photo-ionization is evolving in the presence of a strong laser field, the fundamental properties of the mechanism can be signicantly altered. Here we demonstrate how the liberated electron can perform a self-probing measurement of such interaction with attosecond precision. Extreme ultraviolet attosecond pulses initiate an electron wavepacket by photo-ionization, a strong infrared field controls its motion, and finally electron-ion collision maps it into re-emission of attosecond radiation bursts. Our measurements resolve the internal clock provided by the self-probing mechanism, obtaining a direct insight into the build-up of photo-ionization in the presence of the strong laser field.

Attosecond physics at the nanoscale

Recently two emerging areas of research, attosecond and nanoscale physics, have started to come together. Attosecond physics deals with phenomena occurring when ultrashort laser pulses, with duration on the femto- and sub-femtosecond time scales, interact with atoms, molecules or solids. The laser-induced electron dynamics occurs natively on a timescale down to a few hundred or even tens of attoseconds (1 attosecond  =  1 as  =  10^-18 s), which is comparable with the optical field. For comparison, the revolution of an electron on a 1s orbital of a hydrogen atom is  ∼152 as. On the other hand, the second branch involves the manipulation and engineering of mesoscopic systems, such as solids, metals and dielectrics, with nanometric precision. Although nano-engineering is a vast and well-established research field on its own, the merger with intense laser physics is relatively recent. In this report on progress we present a comprehensive experimental and theoretical overview of physics that takes place when short and intense laser pulses interact with nanosystems, such as metallic and dielectric nanostructures. In particular we elucidate how the spatially inhomogeneous laser induced fields at a nanometer scale modify the laser-driven electron dynamics. Consequently, this has important impact on pivotal processes such as above-threshold ionization and high-order harmonic generation. The deep understanding of the coupled dynamics between these spatially inhomogeneous fields and matter configures a promising way to new avenues of research and applications. Thanks to the maturity that attosecond physics has reached, together with the tremendous advance in material engineering and manipulation techniques, the age of atto-nanophysics has begun, but it is in the initial stage. We present thus some of the open questions, challenges and prospects for experimental confirmation of theoretical predictions, as well as experiments aimed at characterizing the induced fields and the unique electron dynamics initiated by them with high temporal and spatial resolution.

Optimal generation of spatially coherent soft X-ray isolated attosecond pulses in a gas-filled waveguide using two-color synthesized laser pulses

We numerically demonstrate the generation of intense, low-divergence soft X-ray isolated attosecond pulses in a gas-filled hollow waveguide using synthesized few-cycle two-color laser waveforms. The waveform is a superposition of a fundamental and its second harmonic optimized such that highest harmonic yields are emitted from each atom. We then optimize the gas pressure and the length and radius of the waveguide such that bright coherent high-order harmonics with angular divergence smaller than 1 mrad are generated, for photon energy from the extreme ultraviolet to soft X-rays. By selecting a proper spectral range enhanced isolated attosecond pulses are generated. We study how dynamic phase matching caused by the interplay among waveguide mode, neutral atomic dispersion, and plasma effect is achieved at the optimal macroscopic conditions, by performing time-frequency analysis and by analyzing the evolution of the driving laser's electric field during the propagation. Our results, when combined with the on-going push of high-repetition-rate lasers (sub- to few MHz's) may eventually lead to the generation of high-flux, low-divergence soft X-ray tabletop isolated attosecond pulses for applications.

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.

In situ frequency gating and beam splitting of vacuum- and extreme-ultraviolet pulses

Monochromatization of high-harmonic sources has opened fascinating perspectives regarding time-resolved photoemission from all phases of matter. Such studies have invariably involved the use of spectral filters or spectrally dispersive optical components that are inherently lossy and technically complex. Here we present a new technique for the spectral selection of near-threshold harmonics and their spatial separation from the driving beams without any optical elements. We discover the existence of a narrow phase-matching gate resulting from the combination of the non-collinear generation geometry in an extended medium, atomic resonances and absorption. Our technique offers a filter contrast of up to 10⁴ for the selected harmonics against the adjacent ones and offers multiple temporally synchronized beamlets in a single unified scheme. We demonstrate the selective generation of 133, 80 or 56 nm femtosecond pulses from a 400-nm driver, which is specific to the target gas. These results open new pathways towards phase-sensitive multi-pulse spectroscopy in the vacuum- and extreme-ultraviolet, and frequency-selective output coupling from enhancement cavities.

Extreme-Ultraviolet-Initated High-Order Harmonic Generation: Driving Inner-Valence Electrons Using Below-Threshold-Energy Extreme-Ultraviolet Light

We propose a novel scheme for resolving the contribution of inner- and outer-valence electrons in extreme-ultraviolet (XUV)-initiated high-harmonic generation in neon. By probing the atom with a low-energy (below the 2s ionization threshold) ultrashort XUV pulse, the 2p electron is steered away from the core, while the 2s electron is enabled to describe recollision trajectories. By selectively suppressing the 2p recollision trajectories, we can resolve the contribution of the 2s electron to the high-harmonic spectrum. We apply the classical trajectory model to account for the contribution of the 2s electron, which allows for an intuitive understanding of the process.

Avalanche of stimulated forward scattering in high harmonic generation

Optical amplifiers in all ranges of the electromagnetic spectrum exhibit an essential characteristic, namely the input signal during the propagation in the amplifier medium is multiplied by the avalanche effect of the stimulated emission to produce exponential growth. We perform a theoretical study motivated and supported by experimental data on a He gas amplifier driven by intense 30-fs-long laser pulses and seeded with attosecond pulse trains generated in a separated Ne gas jet. We demonstrate that the strong-field theory in the frame of high harmonic generation fully supports the appearance of the avalanche effect in the amplification of extreme ultraviolet attosecond pulse trains. We theoretically separate and identify different physical processes taking part in the interaction and we demonstrate that X-ray parametric amplification dominates over others. In particular, we identify strong-field mediated intrapulse X-ray parametric processes as decisive for amplification at the single-atom level. We confirm that the amplification takes place at photon energies where the amplifier is seeded and when the seed pulses are perfectly synchronized with the driving strong field in the amplifier. Furthermore, propagation effects, phase matching and seed synchronization can be exploited to tune the amplified spectral range within the seed bandwidth.

Scalability of components for kW-level average power few-cycle lasers

In this paper, the average power scalability of components that can be used for intense few-cycle lasers based on nonlinear compression of modern femtosecond solid-state lasers is investigated. The key components of such a setup, namely, the gas-filled waveguides, laser windows, chirped mirrors for pulse compression and low dispersion mirrors for beam collimation, focusing, and beam steering are tested under high-average-power operation using a kilowatt cw laser. We demonstrate the long-term stable transmission of kW-level average power through a hollow capillary and a Kagome-type photonic crystal fiber. In addition, we show that sapphire substrates significantly improve the average power capability of metal-coated mirrors. Ultimately, ultrabroadband dielectric mirrors show negligible heating up to 1 kW of average power. In summary, a technology for scaling of few-cycle lasers up to 1 kW of average power and beyond is presented.

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.

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.

Coherent amplification of attosecond light pulses in the water-window spectral region

We present a theoretical study on coherent extreme ultraviolet (XUV) attosecond pulse amplification mediated by nonlinear parametric enhanced forward scattering occurring in the interaction of a strong femtosecond infrared (IR) laser pulse combined with a weak attosecond XUV pulse train with an atom. We predict large amplification of XUV radiation when the IR strong pulse and the XUV weak pulse are optimally phased. We study high-order harmonic processes (HHG) in He, He(+) and Ne(++), and show how although the HHG yield is largely affected by the particular atom used as target, nonlinear parametric XUV amplification is only weakly affected. We conclude that XUV nonlinear parametric attosecond pulse amplification can be most efficiently observed by using atoms with a high ionization potential and that the nonlinear amplification is robust at high photon energies where HHG is not efficient, such as in the water-window spectral region.

Spatial properties of odd and even low order harmonics generated in gas

High harmonic generation in gases is developing rapidly as a soft X-ray femtosecond light-source for applications. This requires control over all the harmonics characteristics and in particular, spatial properties have to be kept very good. In previous literature, measurements have always included several harmonics contrary to applications, especially spectroscopic applications, which usually require a single harmonic. To fill this gap, we present here for the first time a detailed study of completely isolated harmonics. The contribution of the surrounding harmonics has been totally suppressed using interferential filtering which is available for low harmonic orders. In addition, this allows to clearly identify behaviors of standard odd orders from even orders obtained by frequency-mixing of a fundamental laser and of its second harmonic. Comparisons of the spatial intensity profiles, of the spatial coherence and of the wavefront aberration level of 5ω at 160 nm and 6ω at 135 nm have then been performed. We have established that the fundamental laser beam aberrations can cause the appearance of a non-homogenous donut-shape in the 6ω spatial intensity distribution. This undesirable effect can be easily controlled. We finally conclude that the spatial quality of an even harmonic can be as excellent as in standard generation.

Route to optimal generation of soft X-ray high harmonics with synthesized two-color laser pulses

High harmonics extending to X-rays have been generated from gases by intense lasers. To establish these coherent broadband radiations as an all-purpose tabletop light source for general applications in science and technology, new methods are needed to overcome the present low conversion efficiencies. Here we show that the conversion efficiency may be drastically increased with an optimized two-color pulse. By employing an optimally synthesized 2-µm mid-infrared laser and a small amount of its third harmonic, we show that harmonic yields from sub- to few-keV energy can be increased typically by ten-fold over the optimized single-color one. By combining with favorable phase-matching and together with the emerging high-repetition MHz mid-infrared lasers, we anticipate efficiency of harmonic yields can be increased by four to five orders in the near future, thus paving the way for employing high harmonics as useful broadband tabletop light sources from the extreme ultraviolet to the X-rays, as well as providing new tools for interrogating ultrafast dynamics of matter at attosecond timescales.

Enhanced high harmonic generation driven by high-intensity laser in argon gas-filled hollow core waveguide

We show that a significant enhancement of the photon flux produced by high harmonic generation can be obtained through guided configuration at high laser intensity largely above the saturation intensity. We identify two regimes. At low pressure, we observe an intense second plateau in the high harmonic spectrum in argon. At relatively high pressure, complex interplay between strongly time-dependent ionization processes and propagation effects leads to important spectral broadening without loss of spectral brightness. We show that the relevant parameter for this physical process is the product of laser peak power by gas pressure. We compare source performances with high harmonic generation using a gas jet in loose focusing geometry and conclude that the source developed is a good candidate for injection devices such as seeded soft x-ray lasers or free electron lasers in the soft x-ray range.

Macroscopic effects in noncollinear high-order harmonic generation

We study two-color high-order harmonic generation using an intense driving field and its weak second harmonic, crossed under a small angle in the focus. Employing sum- and difference-frequency generation processes, such a noncollinear scheme can be used to measure and control macroscopic phase matching effects by utilizing a geometrical phase mismatch component, which depends on the noncollinear angle. We further show how spatial phase effects in the generation volume are mapped out into the far field allowing a direct analogy with temporal carrier envelope effects in attosecond pulse generation.

Parametric amplification of attosecond pulse trains at 11 nm

We report the first experimental demonstration of the parametric amplification of attosecond pulse trains at around 11 nm. The helium amplifier is driven by intense laser pulses and seeded by high-order harmonics pulses generated in a neon gas jet. Our measurements suggest that amplification takes place only if the seed pulse-trains are perfectly synchronized in time with the driving laser field in the amplifier. Varying the delay, we estimate the durations of the individual extreme ultraviolet pulses within the train to be on the order of 0.2 fs. Our results demonstrate that strong-field parametric amplification can be a suitable tool to amplify weak attosecond pulses from non-destructive pump-probe experiments and it is an important step towards designing amplifiers for realization of energetic XUV pulses with sub-femtosecond duration using compact lasers fitting in university laboratories.

A high-flux high-order harmonic source

We develop and implement an experimental strategy for the generation of high-energy high-order harmonics (HHG) in gases for studies of nonlinear processes in the soft x-ray region. We generate high-order harmonics by focusing a high energy Ti:Sapphire laser into a gas cell filled with argon or neon. The energy per pulse is optimized by an automated control of the multiple parameters that influence the generation process. This optimization procedure allows us to obtain energies per pulse and harmonic order as high as 200 nJ in argon and 20 nJ in neon, with good spatial properties, using a loose focusing geometry (f#≈400) and a 20 mm long medium. We also theoretically examine the macroscopic conditions for absorption-limited conversion efficiency and optimization of the HHG pulse energy for high-energy laser systems.