Double optical gating of high-order harmonic generation with carrier-envelope phase stabilized lasers

Robust Isolated Attosecond Pulse Generation with Self-Compressed Subcycle Drivers from Hollow Capillary Fibers

High-order harmonic generation (HHG) arising from the nonperturbative interaction of intense light fields with matter constitutes a well-established tabletop source of coherent extreme-ultraviolet and soft X-ray radiation, which is typically emitted as attosecond pulse trains. However, ultrafast applications increasingly demand isolated attosecond pulses (IAPs), which offer great promise for advancing precision control of electron dynamics. Yet, the direct generation of IAPs typically requires the synthesis of near-single-cycle intense driving fields, which is technologically challenging. In this work, we theoretically demonstrate a novel scheme for the straightforward and compact generation of IAPs from multicycle infrared drivers using hollow capillary fibers (HCFs). Starting from a standard, intense multicycle infrared pulse, a light transient is generated by extreme soliton self-compression in a HCF with decreasing pressure and is subsequently used to drive HHG in a gas target. Owing to the subcycle confinement of the HHG process, high-contrast IAPs are continuously emitted almost independently of the carrier-envelope phase (CEP) of the optimally self-compressed drivers. This results in a CEP-robust scheme which is also stable under macroscopic propagation of the high harmonics in a gas target. Our results open the way to a new generation of integrated all-fiber IAP sources, overcoming the efficiency limitations of usual gating techniques for multicycle drivers.

Wave-Packet Surface Propagation for Light-Induced Molecular Dynamics

Recent advances in laser technology have enabled tremendous progress in light-induced molecular reactions, at the heart of which the breaking and formation of chemical bonds are located. Such progress has been greatly facilitated by the development of an accurate quantum-mechanical simulation method, which, however, does not necessarily accompany clear dynamical scenarios and is rather computationally heavy. Here, we develop a wave-packet surface propagation (WASP) approach to describe the molecular bond-breaking dynamics from a hybrid quantum-classical perspective. Via the introduction of quantum elements including state transitions and phase accumulations to the Newtonian propagation of the nuclear wave packet, the WASP approach naturally comes with intuitive physical scenarios and accuracies. It is carefully benchmarked with the H_{2}^{+} molecule and is shown to be capable of precisely reproducing experimental observations. The WASP method is promising for the intuitive visualization of light-induced molecular dynamics and is straightforward extensible towards complex molecules.

Two-color attosecond chronoscope

We study ionization of atoms in strong orthogonal two-color (OTC) laser fields numerically and analytically. The calculated photoelectron momentum distribution shows two typical structures: a rectangular-like one and a shoulder-like one, the positions of which depend on the laser parameters. Using a strong-field model which allows us to quantitatively evaluate the Coulomb effect, we show that these two structures arise from attosecond response of electron inside an atom to light in OTC-induced photoemission. Some simple mappings between the locations of these structures and response time are derived. Through these mappings, we are able to establish a two-color attosecond chronoscope for timing electron emission, which is essential for OTC-based precise manipulation.

Control of the electron dynamics in solid-state high harmonic generation on ultrafast time scales by a polarization-skewed laser pulse

Since high-order harmonic generation (HHG) from atoms depends sensitively on the polarization of the driving laser field, the polarization gating (PG) technique was developed and applied successfully to generate isolated attosecond pulses from atomic gases. The situation is, however, different in solid-state systems as it has been demonstrated that due to collisions with neighboring atomic cores of the crystal lattice strong HHG can be generated even by elliptically- and circularly-polarized laser fields. Here we apply PG to solid-state systems and find that the conventional PG technique is inefficient for the generation of isolated ultrashort harmonic pulse bursts. In contrast, we demonstrate that a polarization-skewed laser pulse is able to confine the harmonic emission to a time window of less than one-tenth of the laser cycle. This method provides a novel way to control HHG and to generate isolated attosecond pulses in solids.

Generation of the isolated highly elliptically polarized attosecond pulse using the polarization gating technique: TDDFT approach

This paper theoretically investigates the generation of isolated elliptically polarized attosecond pulses with a tunable ellipticity from the interaction of Cl₂ molecule and a polarization-gating laser pulse. A three-dimensional calculation based on the time-dependent density functional theory is done. Two different methods are proposed for generating elliptically polarized single attosecond pulses. The first method is based on applying a single-color polarization gating laser and controlling the orientation angle of the Cl₂ molecule with respect to the polarization direction of the laser at the gate window. An attosecond pulse with an ellipticity of 0.66 and a pulse duration of 275 as is achieved by tuning the molecule orientation angle to 40° in this method and superposing harmonics around the harmonic cutoff. The second method is based on irradiating an aligned Cl₂ molecule with a two-color polarization gating laser. The ellipticity of the attosecond pulses obtained by this method can be controlled by adjusting the intensity ratio of the two colors. Employing an optimized intensity ratio and superposing harmonics around the harmonic cutoff would lead to the generation of an isolated, highly elliptically polarized attosecond pulse with an ellipticity of 0.92 and a pulse duration of 648 as.

Attosecond spectroscopy for the investigation of ultrafast dynamics in atomic, molecular and solid-state physics

Since the first demonstration of the generation of attosecond pulses (1 as = 10^-18s) in the extreme-ultraviolet spectral region, several measurement techniques have been introduced, at the beginning for the temporal characterization of the pulses, and immediately after for the investigation of electronic and nuclear ultrafast dynamics in atoms, molecules and solids with unprecedented temporal resolution. The attosecond spectroscopic tools established in the last two decades, together with the development of sophisticated theoretical methods for the interpretation of the experimental outcomes, allowed to unravel and investigate physical processes never observed before, such as the delay in photoemission from atoms and solids, the motion of electrons in molecules after prompt ionization which precede any notable nuclear motion, the temporal evolution of the tunneling process in dielectrics, and many others. This review focused on applications of attosecond techniques to the investigation of ultrafast processes in atoms, molecules and solids. Thanks to the introduction and ongoing developments of new spectroscopic techniques, the attosecond science is rapidly moving towards the investigation, understanding and control of coupled electron-nuclear dynamics in increasingly complex systems, with ever more accurate and complete investigation techniques. Here we will review the most common techniques presenting the latest results in atoms, molecules and solids.

Space-time coupling of the carrier-envelope phase in ultrafast optical pulses

The carrier-envelope phase (CEP) plays an increasingly important role in precise frequency comb spectroscopy, all-optical atomic clocks, quantum science and technology, astronomy, space-borne-metrology, and strong-field science. Here we introduce an approach for space-time calculation of the CEP in the spatially defined region of interest. We find a significant variation of CEP in the focal volume of refracting focusing elements and accurately calculate its value. We discuss the implications and importance of this finding. Our method is particularly suitable for application to complex, real-world, optical systems thereby making it especially useful to applications in research labs as well as in the engineering of innovative designs that rely on the CEP.

Optimal generation and isolation of attosecond pulses in an overdriven ionized medium

We identify optimal conditions for the generation and isolation of attosecond pulses in an overdriven ionized medium. In a high-pressure and highly ionized gas, the spatiotemporal wavefront rotation of a driving laser can be optimized, leading to complete spatial separation of successive attosecond bursts in the far field. The resulting isolated attosecond pulses (IAPs) are much more divergent such that they are spatially separated from the driving laser in the far field. We show that the time delay of near-field harmonic emission along the radial distance determines the divergence of the attosecond burst in the far field. The generated IAPs are phase matched upon propagation in the second half of the gas medium. Validity of the generation scheme is tested at different carrier-envelope phases for a few-cycle laser pulse and by synthesizing the fundamental and its second harmonic field for a long-duration pulse.

High-Order Phase-Dependent Asymmetry in the Above-Threshold Ionization Plateau

Above-threshold ionization spectra from cesium are measured as a function of the carrier-envelope phase (CEP) using laser pulses centered at 3.1  μm wavelength. The directional asymmetry in the energy spectra of backscattered electrons oscillates three times, rather than once, as the CEP is changed from 0 to 2π. Using the improved strong-field approximation, we show that the unusual behavior arises from the interference of few quantum orbits. We discuss the conditions for observing the high-order CEP dependence, and draw an analogy with time-domain holography with electron wave packets.

Pump-Probe Delay Controlled by Laser-dressed Ionization with Isolated Attosecond Pulses

In a recent work [1], we demonstrated how laser-dressed ionization can be harnessed to control with attosecond accuracy the time delay between an extreme-ultraviolet (XUV) attosecond pulse train and an infrared (IR) femtosecond pulse. In this case, the comb-like photoelectron spectrum obtained by ionizing a gas target with the two superimposed beams exhibits peaks oscillating with the delay. Two of them can be found to oscillate in phase quadrature, allowing an optimal measurement and stabilization of the delay over a large range. Here we expand this technique to isolated attosecond pulses, by taking advantage of the delay-modulation of attosecond streaking traces. Although the photoelectron spectrum contains no peaks in that case, it is possible to reconstruct the pump-probe delay by simply monitoring the mean energy of the spectrum and the amplitude at this energy. In general, we find that active delay stabilization based on laser-dressed ionization is possible as long as the XUV pulses are chirped.

Aurore: A platform for ultrafast sciences

We present the Aurore platform for ultrafast sciences. This platform is based on a unique 20 W, 1 kHz, 26 fs Ti:sapphire laser system designed for reliable operation and high intensity temporal contrast. The specific design ensures the high stability in terms of pulse duration, energy, and beam pointing necessary for extended experimental campaigns. The laser supplies 5 different beamlines, all dedicated to a specific field: attosecond science (Aurore 1), ultrafast phase transitions in solids (Aurore 2 and 3), ultrafast luminescence in solids (Aurore 4), and femtochemistry (Aurore 5). The technical specifications of these five beamlines are described in detail, and examples of the recent results are given.

Generation and measurement of isolated attosecond pulses with enhanced flux using a two colour synthesized laser field

We have generated isolated attosecond pulses and performed attosecond streaking measurements using a two-colour synthesized laser field consisting of a strong near-infrared few-cycle pulse and a weaker multi-cycle pulse centred at 400 nm. An actively stabilized interferometer was used to coherently combine the two pulses. Using attosecond streaking we characterised the electric fields of the two pulses and accurately retrieved the spectrum of the multi-cycle pulse. We demonstrated a two-fold increase in the flux of isolated attosecond pulses produced and show that their duration was minimally affected by the presence of the weaker field due to spectral filtering by a multilayer mirror.

Time-resolved recombination by attosecond-controlled high harmonic generation

We theoretically investigate the coherent control of strong-field high-harmonic generation in the presence of an isolated attosecond pulse. It is found that the rapid modulation of the controlled signal exhibits interference fringe structures in the delay-dependent spectra. By comparing the classical trajectory model with quantum mechanical calculation, it is demonstrated that the fringes are resulted from the interference between the photon- and the tunnelling-initiated recombination pathways. The relative recombination times for the two paths are reconstructed from the interference fringes, which provides a novel scheme for optical observation of the interplay of the photionization and tunneling ionization electron dynamics in attosecond resolution.

Spatially resolved spectral phase interferometry with an isolated attosecond pulse

We demonstrate spatially resolved supercontinuum spectral phase interferometry with an isolated attosecond pulse (IAP). The measured spatial-spectral interferogram over the broadband region indicates a high degree of IAP coherence in both spatial and spectral domains. In addition, the spectral-delay interferogram shows periodic temporal oscillations over the full IAP continuous spectrum, which indicates high temporal coherence. The supercontinuum spectral phase interferometry with broadband IAP will contribute to exploring spatiotemporal dispersive electronic dynamics through phase-based spectroscopy in the future.

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.

Generation of isolated circularly polarized attosecond pulses by three-color laser field mixing

We propose and theoretically demonstrate a method to generate the circularly polarized supercontinuum with three-color electric fields. The three-color field is synthesized from an orthogonally polarized two-color (OTC) laser field and an infrared gating field. All driving pulse durations are extended to 40 fs. We demonstrate that the three-color field imposes curved trajectories for ionized electrons and extends the time interval between each harmonic emitting. Through adjusting intensity ratios among three components of the driving field, a nearly circular isolated attosecond pulse can be generated.

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.

Double optical gating for generating high flux isolated attosecond pulses in the soft X-ray regime

Double optical gating (DOG) technique was implemented with a two-cycle, 1.7 µm driving field to generate isolated attosecond pulses in the 100-250 eV spectrum range. The strong ellipticity dependency of the high harmonics from the 1.7 µm driving field makes polarization based gating method very efficient. When a second harmonic (SH) field is introduced, complete gating can be achieved with less ionization from the leading edge of the driving field, which yields supercontinua with a pulse energy of 0.3 nJ. We perform an attosecond streaking measurement to confirm the generation of isolated attosecond pulses.

Broadband extreme ultraviolet dispersion measurements using a high-harmonic source

We demonstrate direct dispersion measurements of various thin films at extreme ultraviolet (EUV) wavelengths, using a table-top laser-driven high-harmonic generation (HHG) source. In this method, spatially separated identical EUV pulses are generated through HHG with a pair of phase-locked infrared pulses. The EUV pulses are re-imaged to a sample plane using a single toroidal mirror, such that one pulse illuminates the target thin film, while the other pulse passes through a reference aperture. By comparing the EUV interference with and without a sample, we are able to extract the dispersion properties of the sample, integrated over the full film thickness. We have measured thin films of titanium, nickel, copper, and silicon nitride, demonstrating that this technique can be applied to a wide range of materials, only requiring a film thin, enough for sufficient EUV transmission.

CEP-stabilized, sub-18 fs, 10 kHz and TW-class 1 kHz dual output Ti:Sa laser with wavelength tunability option

Generating energetic, few-cycle laser pulses with stabilized carrier-envelope phase at a high-repetition rate constitutes a first step to access the ultra-fast dynamics underlying the interaction of matter with intense, ultrashort pulses in attosecond science or high-field physics. We present here a Ti:Sa-based 1 kHz TW-class laser delivering 17.8 fs pulses with 350 mrad shot-to-shot CEP noise based on an original 10 kHz front-end design. In parallel to this short pulse duration operation mode, it is possible to tune the output wavelength of the front end within a 90 nm range around 800 nm.

Accurate in situ Measurement of Ellipticity Based on Subcycle Ionization Dynamics

Elliptically polarized laser pulses (EPLPs) are widely applied in many fields of ultrafast sciences, but the ellipticity (ϵ) has never been in situ measured in the interaction zone of the laser focus. In this Letter, we propose and realize a robust scheme to retrieve the ϵ by temporally overlapping two identical counterrotating EPLPs. The combined linearly electric field is coherently controlled to ionize Xe atoms by varying the phase delay between the two EPLPs. The electron spectra of the above-threshold ionization and the ion yield are sensitively modulated by the phase delay. We demonstrate that these modulations can be used to accurately determine ϵ of the EPLP. We show that the present method is highly reliable and is applicable in a wide range of laser parameters. The accurate retrieval of ϵ offers a better characterization of a laser pulse, promising a more delicate and quantitative control of the subcycle dynamics in many strong field processes.

Significant Enhancement of N_{2}^{+} Lasing by Polarization-Modulated Ultrashort Laser Pulses

We show that the intensity of self-seeded N_{2}^{+} lasing at 391 nm, assigned to the B^{2}Σ_{u}^{+}(v^{'}=0)→X^{2}Σ_{g}^{+}(v^{''}=0) emission, is enhanced by 2 orders of magnitude by modulating in time the polarization of an intense ultrashort near-IR (40 fs, 800 nm) laser pulse with which N_{2} is irradiated. We find that this dramatic enhancement of the 391 nm lasing is sensitive to the temporal variation of the polarization state within the laser pulse while the intensity of the spontaneous fluorescence emission at 391 nm is kept constant when the polarization state varies. We conclude that a postionization multiple-state coupling, through which the population can be transferred from the X^{2}Σ_{g}^{+} state of N_{2}^{+} to the first electronically excited A^{2}Π_{u} state, leads to the depletion of the population in the X^{2}Σ_{g}^{+} state, and consequently, to the population inversion between the X^{2}Σ_{g}^{+} state and the B^{2}Σ_{u}^{+} state.

Multi-petahertz electron interference in Cr:Al2O3 solid-state material

Lightwave-field-induced ultrafast electric dipole oscillation is promising for realizing petahertz (10¹⁵ Hz: PHz) signal processing in the future. In building the ultrahigh-clock-rate logic operation system, one of the major challenges will be petahertz electron manipulation accompanied with multiple frequencies. Here we study multi-petahertz interference with electronic dipole oscillations in alumina with chromium dopant (Cr:Al₂O₃). An intense near-infrared lightwave-field induces multiple electric inter-band polarizations, which are characterized by Fourier transform extreme ultraviolet attosecond spectroscopy. The interference results from the superposition state of periodic dipole oscillations of 667 to 383 attosecond (frequency of 1.5 to 2.6 PHz) measured by direct time-dependent spectroscopy and consists of various modulations on attosecond time scale through individual electron dephasing times of the Cr donor-like and Al₂O₃ conduction band states. The results indicate the possible manipulation of petahertz interference signal with multiple dipole oscillations using material band engineering and such a control will contribute to the study of ultrahigh-speed signal operation.

Signal processing in electronic devices is in the THz regime. Here the authors measure NIR lightwave-field-induced multiple dipole oscillations in Cr:Al₂O₃ in the time domain reaching PHz scale by using an isolated attosecond pulse and this method shows potential for higher speed signal processing.

Multiple pulse coherent dynamics and wave packet control of the N2 a′′ 1Σ+g dark state by attosecond four-wave mixing

Dark states of molecular nitrogen in the XUV region are spectroscopically investigated using few-femtosecond dynamic wave packet control.

Ellipticity dependence of high-harmonic generation in solids originating from coupled intraband and interband dynamics

The strong ellipticity dependence of high-harmonic generation (HHG) in gases enables numerous experimental techniques that are nowadays routinely used, for instance, to create isolated attosecond pulses. Extending such techniques to solids requires a fundamental understanding of the microscopic mechanism of HHG. Here we use first-principles simulations within a time-dependent density-functional framework and show how intraband and interband mechanisms are strongly and differently affected by the ellipticity of the driving laser field. The complex interplay between intraband and interband effects can be used to tune and improve harmonic emission in solids. In particular, we show that the high-harmonic plateau can be extended by as much as 30% using a finite ellipticity of the driving field. We furthermore demonstrate the possibility to generate, from single circularly polarized drivers, circularly polarized harmonics. Our work shows that ellipticity provides an additional knob to experimentally optimize HHG in solids.The mechanisms of high-order harmonic generation in bulk system and dilute gas are different. Here the authors use first-principle methods to explore the ellipticity dependence and control of the HHG in periodic solids by involving the interband and intraband dynamics in Si and MgO.

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.

Original Ti:Sa 10 kHz front-end design delivering 17 fs, 170 mrad CEP stabilized pulses up to 5 W

We present a compact 10 kHz Ti:Sa front end relying on an original double-crystal regenerative amplifier design. This new configuration optimizes the thermal heat load management, allowing the production of a 110 nm large spectrum and maintaining a good beam profile quality. The front end delivers up to 5 W after compression, 17 fs pulses with a 170 mrad shot-to-shot residual carrier-envelope phase noise.

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.

Carrier-Envelope-Phase Characterization for an Isolated Attosecond Pulse by Angular Streaking

The carrier envelope phase (CEP) is a crucial parameter for a few-cycle laser pulse since it substantially determines the laser waveform. Stepping forward from infrared to extreme ultraviolet (EUV) pulses, we propose a strategy to directly characterize the CEP of an isolated attosecond pulse (IAP) by numerically simulating the tunneling ionization of a hydrogen atom in a combined IAP and phase-stabilized circularly polarized IR laser pulse. The fine modulations of the combined laser fields, due to the variation of the CEP of the IAP, are exponentially enlarged onto the distinct time-dependent tunneling ionization rate. Electrons released at different time with distinct tunneling ionization rates are angularly streaked to different directions. By measuring the resulting photoelectron momentum distribution, the CEP of the IAP can be retrieved. The characterization of the CEP of an IAP will open the possibility of capturing sub-EUV-cycle dynamics.

0.5-keV Soft X-ray attosecond continua

Attosecond light pulses in the extreme ultraviolet have drawn a great deal of attention due to their ability to interrogate electronic dynamics in real time. Nevertheless, to follow charge dynamics and excitations in materials, element selectivity is a prerequisite, which demands such pulses in the soft X-ray region, above 200 eV, to simultaneously cover several fundamental absorption edges of the constituents of the materials. Here, we experimentally demonstrate the exploitation of a transient phase matching regime to generate carrier envelope controlled soft X-ray supercontinua with pulse energies up to 2.9±0.1 pJ and a flux of (7.3±0.1) × 10⁷ photons per second across the entire water window and attosecond pulses with 13 as transform limit. Our results herald attosecond science at the fundamental absorption edges of matter by bridging the gap between ultrafast temporal resolution and element specific probing.

Attosecond soft X-ray pulses hold promise for probing electronic dynamics in real time, but it is challenging to achieve element sensitivity while maintaining temporal resolution. Teichmann et al. report the cover of carbon, nitrogen and oxygen absorption edges with an isolated pulse supporting 13 as duration.

Attosecond science in atomic, molecular, and condensed matter physics

Attosecond science represents a new frontier in atomic, molecular, and condensed matter physics, enabling one to probe the exceedingly fast dynamics associated with purely electronic dynamics in a wide range of systems. This paper presents a brief discussion of the technology required to generate attosecond light pulses and gives representative examples of attosecond science carried out in several laboratories. Attosecond transient absorption, a very powerful method in attosecond science, is then reviewed and several examples of gas phase and condensed phase experiments that have been carried out in the Leone/Neumark laboratories are described.

Circularly polarized carrier-envelope-phase stable attosecond pulse generation based on coherent undulator radiation

In this Letter, we present a new method for generation of circularly polarized attosecond pulses. According to our calculations, shape-controlled, carrier-envelope-phase stable pulses of several hundred nanojoule energy could be produced by exploitation of the coherent undulator radiation of an electron bunch. Our calculations are based on an existing particle accelerator system (FLASH II in DESY, Germany). We investigated the energy dependence of the attosecond pulses on the energy of electrons and the parameters of the radiator undulator, which generate the electromagnetic radiation.

Controlling attosecond angular streaking with second harmonic radiation

High harmonic generation, which produces a coherent burst of radiation every half cycle of the driving field, has been combined with ultrafast wavefront rotation to create a series of spatially separated attosecond pulses, called the attosecond lighthouse. By adding a coherent second harmonic beam with polarization parallel to the fundamental, we decrease the generating frequency from twice per optical cycle to once. The increased temporal separation increases the pulse contrast. By scanning the carrier envelope phase, we see that the signal is 2π periodic.

Spatiotemporal isolation of attosecond soft X-ray pulses in the water window

Attosecond pulses at photon energies that cover the principal absorption edges of the building blocks of materials are a prerequisite for time-resolved probing of the triggering events leading to electronic dynamics such as exciton formation and annihilation. We demonstrate experimentally the isolation of individual attosecond pulses at the carbon K-shell edge (284 eV) in the soft X-ray water window with pulse duration below 400 as and with a bandwidth supporting a 30-as pulse duration. Our approach is based on spatiotemporal isolation of long-wavelength-driven harmonics and validates a straightforward and scalable approach for robust and reproducible attosecond pulse isolation.

Characterizing inner-shell with spectral phase interferometry for direct electric-field reconstruction

In many atomic, molecular and solid systems, Lorentzian and Fano profiles are commonly observed in a broad research fields throughout a variety of spectroscopies. As the profile structure is related to the phase of the time-dependent dipole moment, it plays an important role in the study of quantum properties. Here we determine the dipole phase in the inner-shell transition using spectral phase interferometry for direct electric-field reconstruction (SPIDER) with isolated attosecond pulses (IAPs). In addition, we propose a scheme for pulse generation and compression by manipulating the inner-shell transition. The electromagnetic radiation generated by the transition is temporally compressed to a few femtoseconds in the extreme ultraviolet (XUV) region. The proposed pulse-compression scheme may provide an alternative route to producing attosecond pulses of light.

Characterizing and understanding the profile of atomic spectral lines tells us a great deal about an atom’s properties. Here, the authors combine attosecond transient spectroscopy and the SPIDER technique to reconstruct the dipole oscillation phase of the auto-ionisation inner-shell transition in neon.

Attosecond nonlinear optics using gigawatt-scale isolated attosecond pulses

High-energy isolated attosecond pulses required for the most intriguing nonlinear attosecond experiments as well as for attosecond-pump/attosecond-probe spectroscopy are still lacking at present. Here we propose and demonstrate a robust generation method of intense isolated attosecond pulses, which enable us to perform a nonlinear attosecond optics experiment. By combining a two-colour field synthesis and an energy-scaling method of high-order harmonic generation, the maximum pulse energy of the isolated attosecond pulse reaches as high as 1.3 μJ. The generated pulse with a duration of 500 as, as characterized by a nonlinear autocorrelation measurement, is the shortest and highest-energy pulse ever with the ability to induce nonlinear phenomena. The peak power of our tabletop light source reaches 2.6 GW, which even surpasses that of an extreme-ultraviolet free-electron laser.

The short duration of attosecond pulses makes them interesting for ultrafast experiments, although it has so far been difficult to generate isolated attosecond pulses with sufficiently high power. Here the authors achieve high-intensity isolated attosecond pulses with a tabletop setup, based on a scaled-up high-order harmonic generation process.

Generation of bright isolated attosecond soft X-ray pulses driven by multicycle midinfrared lasers

High harmonic generation driven by femtosecond lasers makes it possible to capture the fastest dynamics in molecules and materials. However, to date the shortest subfemtosecond (attosecond, 10(-18) s) pulses have been produced only in the extreme UV region of the spectrum below 100 eV, which limits the range of materials and molecular systems that can be explored. Here we experimentally demonstrate a remarkable convergence of physics: when midinfrared lasers are used to drive high harmonic generation, the conditions for optimal bright, soft X-ray generation naturally coincide with the generation of isolated attosecond pulses. The temporal window over which phase matching occurs shrinks rapidly with increasing driving laser wavelength, to the extent that bright isolated attosecond pulses are the norm for 2-µm driving lasers. Harnessing this realization, we experimentally demonstrate the generation of isolated soft X-ray attosecond pulses at photon energies up to 180 eV for the first time, to our knowledge, with a transform limit of 35 attoseconds (as), and a predicted linear chirp of 300 as. Most surprisingly, advanced theory shows that in contrast with as pulse generation in the extreme UV, long-duration, 10-cycle, driving laser pulses are required to generate isolated soft X-ray bursts efficiently, to mitigate group velocity walk-off between the laser and the X-ray fields that otherwise limit the conversion efficiency. Our work demonstrates a clear and straightforward approach for robustly generating bright isolated attosecond pulses of electromagnetic radiation throughout the soft X-ray region of the spectrum.

Quantum path selection in high-order harmonic generation from aligned molecules

We theoretically investigate high-order harmonic generation (HHG) from aligned N(2) molecules with a driving field composed of two-color circularly polarized laser pulses. It is shown that the combination of N(2) molecules and the waveform-controlled laser field allows us to select either long or short quantum path, depending on molecular alignment angles, while in atom Ar, two paths show comparable contribution to HHG. The selection of single quantum path in aligned N(2) molecules leads to an ultrabroad and smooth XUV supercontinuum, giving rise to isolated attosecond pulses generation. Moreover, we can control the intensity ratio of two attosecond pulses by adjusting the molecular alignment angles, providing an opportunity for attosecond pump-probe technique.