Zeptosecond high harmonic keV x-ray waveforms driven by midinfrared laser pulses

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

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

Multiscale dynamical symmetries and selection rules in nonlinear optics

Symmetries and their associated selection rules are extremely useful in many fields of science. For systems of electromagnetic (EM) fields interacting with matter, the symmetries of matter and the EM fields' time-dependent polarization determine the properties of the nonlinear responses, and they can be facilitated for controlling light emission and enabling ultrafast symmetry breaking spectroscopy of various properties. Here, we formulate a general theory that describes the macroscopic and microscopic dynamical symmetries (including quasicrystal-like symmetries) of EM vector fields, revealing many previously unidentified symmetries and selection rules in light-matter interactions. We demonstrate an example of multiscale selection rules experimentally in the framework of high harmonic generation. This work paves the way for novel spectroscopic techniques in multiscale systems and for imprinting complex structures in extreme ultraviolet-x-ray beams, attosecond pulses, or the interacting medium itself.

High-gain broadband laser amplification of mid-IR pulses in Fe:CdSe crystal at 5 μm with millijoule output energy and multigigawatt peak power

We report on a first of its kind, to our knowledge broadband amplification in a Fe:CdSe single crystal in the mid-IR beyond 5 µm. The experimentally measured gain properties demonstrate saturation fluence close to 13 mJ/cm² and support the bandwidth up to 320 nm (full width at half maximum). Such properties allow the energy of the seeding mid-IR laser pulse, generated by an optical parametric amplifier, to be pushed up to more than 1 mJ. Dispersion management with bulk stretcher and prism compressor enables 5-µm laser pulses of 134-fs duration, providing access to multigigawatt peak power. Ultrafast laser amplifiers based on a family of Fe-doped chalcogenides open the route for wavelength tuning together with energy scaling of mid-IR laser pulses that are strongly demanded for the areas of spectroscopy, laser-matter interaction, and attoscience.

Non-classical high harmonic generation in graphene driven by linearly-polarized laser pulses

Recent studies in high-order harmonic generation (HHG) in solid targets reveal new scenarios of extraordinary rich electronic dynamics, in comparison to the atomic and molecular cases. For the later, the main aspects of the process can be described semiclassically in terms of electrons that recombine when the trajectories revisit the parent ion. HHG in solids has been described by an analogous mechanism, in this case involving electron-hole pair recombinations. However, it has been recently reported that a substantial part of the HHG emission corresponds to situations where the electron and hole trajectories do not overlap in space. According to the present knowledge, HHG from this imperfect recollisions reflects the quantum nature of the process, arising in systems with large Berry curvatures or for elliptically polarized driving fields. In this work, we demonstrate that imperfect recollisions are also relevant in the more general case. We show the signature of such recollisions in the HHG spectrum from monolayer graphene -a system with null Berry curvature- irradiated by linearly polarized driving fields. Our calculations also reveal that imperfect multiple-order recollisions contribute to the harmonic emission when electron-hole excursion times exceed one cycle of the driving field. We believe that our work adds a substantial contribution to the full understanding of the sub-femtosecond dynamics of HHG in solid systems.

Effect of multiple rescatterings on continuum harmonics from asymmetric molecules in multicycle lasers

A wide range of harmonics especially continuum harmonics is a prerequisite for attosecond pulse generation. One can use longer-wavelength lasers to push the cutoff to a higher order. However, this does not translate to the same amount of continuum range extension because multiple rescattering phenomena are also enhanced in the process, potentially affecting the lower end of the continuum harmonics. It is then important to understand exactly how multiple rescatterings affect the harmonic structure and their response to various laser parameters, which is the main theme of this paper. Particularly, by applying the synchrosqueezed time-frequency transform and classical electron trajectory analysis to the asymmetric molecule carbon monoxide (CO), we justify that the multiple rescatterings indeed influence the periodicity of the harmonic spectra and the stable periodicity is, in fact, bounded by the first- and third-order returns. Moreover, for the first time, we find that the high-order rescatterings are asymmetric regarding the molecular rotation of 180°, but always correlate with the first-order returns. Our last result is that by breaking the laser symmetry in an appropriate way, the contribution of multiple rescatterings is removed so that the continuum region is entirely defined by the first-order return energies.

Necklace-structured high-harmonic generation for low-divergence, soft x-ray harmonic combs with tunable line spacing

The extreme nonlinear optical process of high-harmonic generation (HHG) makes it possible to map the properties of a laser beam onto a radiating electron wave function and, in turn, onto the emitted x-ray light. Bright HHG beams typically emerge from a longitudinal phased distribution of atomic-scale quantum antennae. Here, we form a transverse necklace-shaped phased array of linearly polarized HHG emitters, where orbital angular momentum conservation allows us to tune the line spacing and divergence properties of extreme ultraviolet and soft x-ray high-harmonic combs. The on-axis HHG emission has extremely low divergence, well below that obtained when using Gaussian driving beams, which further decreases with harmonic order. This work provides a new degree of freedom for the design of harmonic combs-particularly in the soft x-ray regime, where very limited options are available. Such harmonic beams can enable more sensitive probes of the fastest correlated charge and spin dynamics in molecules, nanoparticles, and materials.

Nondipole effects on the double-slit interference in molecular ionization by xuv pulses

The double-slit interference in single-photon ionization of the diatomic molecular ion H₂ ⁺ is theoretically studied beyond the dipole approximation. Via simulating and comparing the interactions of the prealigned H₂ ⁺ and the hydrogen atom with the xuv pulses propagating in different directions, we illustrate two kinds of effects that are encoded in the interference patterns of the photoelectrons from H₂ ⁺: the single-atom nondipole effect and the two-center-interference one, both associated with the finite speed of light. While the two effects could modify the maxima of the interference fringes, we show that the former one hardly affects the interference minima. Our results and analysis show that the interference minima rule out the influences of the photon-momentum transfer and, potentially, the multielectron effect, thus performing a better role in decoding the zeptosecond time delay for the pulse hitting one and the other atomic centers of the molecule.

Laser Wakefield Driven Generation of Isolated Carrier-Envelope-Phase Tunable Intense Subcycle Pulses

Sources of intense, ultrashort electromagnetic pulses enable applications such as attosecond pulse generation, control of electron motion in solids, and the observation of reaction dynamics at the electronic level. For such applications, both high intensity and carrier-envelope-phase (CEP) tunability are beneficial, yet hard to obtain with current methods. In this Letter, we present a new scheme for generation of isolated CEP tunable intense subcycle pulses with central frequencies that range from the midinfrared to the ultraviolet. It utilizes an intense laser pulse that drives a wake in a plasma, copropagating with a long-wavelength seed pulse. The moving electron density spike of the wake amplifies the seed and forms a subcycle pulse. Controlling the CEP of the seed pulse or the delay between driver and seed leads to CEP tunability, while frequency tunability can be achieved by adjusting the laser and plasma parameters. Our 2D and 3D particle-in-cell simulations predict laser-to-subcycle-pulse conversion efficiencies up to 1%, resulting in relativistically intense subcycle pulses.

Efficient generation of relativistic near-single-cycle mid-infrared pulses in plasmas

Ultrashort intense optical pulses in the mid-infrared (mid-IR) region are very important for broad applications ranging from super-resolution spectroscopy to attosecond X-ray pulse generation and particle acceleration. However, currently, it is still difficult to produce few-cycle mid-IR pulses of relativistic intensities using standard optical techniques. Here, we propose and numerically demonstrate a novel scheme to produce these mid-IR pulses based on laser-driven plasma optical modulation. In this scheme, a plasma wake is first excited by an intense drive laser pulse in an underdense plasma, and a signal laser pulse initially at the same wavelength (1 micron) as that of the drive laser is subsequently injected into the plasma wake. The signal pulse is converted to a relativistic multi-millijoule near-single-cycle mid-IR pulse with a central wavelength of ~5 microns via frequency-downshifting, where the energy conversion efficiency is as high as approximately 30% when the drive and signal laser pulses are both at a few tens of millijoules at the beginning. Our scheme can be realized with terawatt-class kHz laser systems, which may bring new opportunities in high-field physics and ultrafast science.

Electron Beam Driven Generation of Frequency-Tunable Isolated Relativistic Subcycle Pulses

We propose a novel scheme for frequency-tunable subcycle electromagnetic pulse generation. To this end a pump electron beam is injected into an electromagnetic seed pulse as the latter is reflected by a mirror. The electron beam is shown to be able to amplify the field of the seed pulse while upshifting its central frequency and reducing its number of cycles. We demonstrate the amplification by means of 1D and 2D particle-in-cell simulations. In order to explain and optimize the process, a model based on fluid theory is proposed. We estimate that using currently available electron beams and terahertz pulse sources, our scheme is able to produce millijoule-strong midinfrared subcycle pulses.

Ultrashort infrared 2.5-11 μm pulses: spatiotemporal profiles and absolute nonlinear response of air constituents

We measure the detailed spatiotemporal profiles of femtosecond laser pulses in the infrared wavelength range of λ=2.5-11  μm and the absolute nonlinear response of major air constituents (N₂, O₂, and Ar) over this range. The spatiotemporal measurements reveal wavelength-dependent pulse front tilt and temporal stretching in the infrared pulses.

Perspective: Towards single shot time-resolved microscopy using short wavelength table-top light sources

Time-resolved imaging allows revealing the interaction mechanisms in the microcosm of both inorganic and biological objects. While X-ray microscopy has proven its advantages for resolving objects beyond what can be achieved using optical microscopes, dynamic studies using full-field imaging at the nanometer scale are still in their infancy. In this perspective, we present the current state of the art techniques for full-field imaging in the extreme-ultraviolet- and soft X-ray-regime which are suitable for single exposure applications as they are paramount for studying dynamics in nanoscale systems. We evaluate the performance of currently available table-top sources, with special emphasis on applications, photon flux, and coherence. Examples for applications of single shot imaging in physics, biology, and industrial applications are discussed.

Attosecond coherent control of free-electron wave functions using semi-infinite light fields

Light–electron interaction is the seminal ingredient in free-electron lasers and dynamical investigation of matter. Pushing the coherent control of electrons by light to the attosecond timescale and below would enable unprecedented applications in quantum circuits and exploration of electronic motions and nuclear phenomena. Here we demonstrate attosecond coherent manipulation of a free-electron wave function, and show that it can be pushed down to the zeptosecond regime. We make a relativistic single-electron wavepacket interact in free-space with a semi-infinite light field generated by two light pulses reflected from a mirror and delayed by fractions of the optical cycle. The amplitude and phase of the resulting electron–state coherent oscillations are mapped in energy-momentum space via momentum-resolved ultrafast electron spectroscopy. The experimental results are in full agreement with our analytical theory, which predicts access to the zeptosecond timescale by adopting semi-infinite X-ray pulses.

Manipulation of the electron–photon coupling is crucial for quantum circuits and exploration of electronic motions and nuclear phenomena. Here the authors discuss a scheme to coherently control the electron wave function from attosecond to zeptosecond timescales by using semi-infinite light fields.

Nonlinear Optics with 2D Layered Materials

2D layered materials (2DLMs) are a subject of intense research for a wide variety of applications (e.g., electronics, photonics, and optoelectronics) due to their unique physical properties. Most recently, increasing research efforts on 2DLMs are projected toward the nonlinear optical properties of 2DLMs, which are not only fascinating from the fundamental science point of view but also intriguing for various potential applications. Here, the current state of the art in the field of nonlinear optics based on 2DLMs and their hybrid structures (e.g., mixed-dimensional heterostructures, plasmonic structures, and silicon/fiber integrated structures) is reviewed. Several potential perspectives and possible future research directions of these promising nanomaterials for nonlinear optics are also presented.

Multiple recollisions in nonsequential double ionization by counter-rotating two-color circularly polarized laser fields

With the three-dimensional (3D) classical ensemble method, we theoretically investigate the recollision dynamics in strong-field nonsequential double ionization (NSDI) of Ar by counter-rotating two-color circularly polarized laser fields. With the analysis of the NSDI trajectories, we find that not only multiple-recollision but also single-recollision processes occur in the double ionization events. Furthermore, the multiple-recollision and single-recollision processes both undergo the recollision-induced excitation with subsequent ionization (RESI) and recollision-induced ionization (RII). The angle between the momentum and the force of the laser field at the recollision moment can affect the times of the recollision.

Multi-terawatt 10 μm pulse atmospheric delivery over multiple Rayleigh ranges

We predict that long wavelength self-trapped multi-terawatt pulses can be sustained over multiple kilometers in the atmosphere. Unlike filaments, these pulses exhibit low loss propagation and retain most of their launch power at range. A novel mechanism involving an aggregation of weakly linear and nonlinear cumulative optical responses is shown to be responsible and is dominated by an ultrafast dynamical lensing resulting from a field intensity driven many-body Coulomb mediated free electron polarization associated with spatially separated species in the gas. An initial few picosecond pulse can compress down to 140 fs over multiple kilometers.

High-energy mid-infrared sub-cycle pulse synthesis from a parametric amplifier

High-energy phase-stable sub-cycle mid-infrared pulses can provide unique opportunities to explore phase-sensitive strong-field light–matter interactions in atoms, molecules and solids. At the mid-infrared wavelength, the Keldysh parameter could be much smaller than unity even at relatively modest laser intensities, enabling the study of the strong-field sub-cycle electron dynamics in solids without damage. Here we report a high-energy sub-cycle pulse synthesiser based on a mid-infrared optical parametric amplifier and its application to high-harmonic generation in solids. The signal and idler combined spectrum spans from 2.5 to 9.0 µm. We coherently synthesise the passively carrier-envelope phase-stable signal and idler pulses to generate 33 μJ, 0.88-cycle, multi-gigawatt pulses centred at ~4.2 μm, which is further energy scalable. The mid-infrared sub-cycle pulse is used for driving high-harmonic generation in thin silicon samples, producing harmonics up to ~19th order with a continuous spectral coverage due to the isolated emission by the sub-cycle driver.

Stable sub-cycle pulses in the mid-infrared region allow damage-free investigation of electron dynamics in solids. Here, the authors develop a suitable source to this end which is based on an optical parametric amplifier.

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.

Isolated broadband attosecond pulse generation with near- and mid-infrared driver pulses via time-gated phase matching

We present a theoretical analysis of the time-gated phase matching (ionization gating) mechanism in high-order harmonic generation for the isolation of attosecond pulses at near-infrared and mid-infrared driver wavelengths, for both few-cycle and multi-cycle driving laser pulses. Results of our high harmonic generation and three-dimensional propagation simulations show that broadband isolated pulses spanning from the extreme-ultraviolet well into the soft X-ray region of the spectrum can be generated for both few-cycle and multi-cycle laser pulses. We demonstrate the key role of absorption and group velocity matching for generating bright, isolated, attosecond pulses using long wavelength multi-cycle pulses. Finally, we show that this technique is robust against carrier-envelope phase and peak intensity variations.

Limits of Strong Field Rescattering in the Relativistic Regime

Recollision for a laser driven atomic system is investigated in the relativistic regime via a strong field quantum description and Monte Carlo semiclassical approach. We find the relativistic recollision energy cutoff is independent of the ponderomotive potential U_{p}, in contrast to the well-known 3.2U_{p} scaling. The relativistic recollision energy cutoff is determined by the ionization potential of the atomic system and achievable with non-negligible recollision flux before entering a "rescattering free" interaction. The ultimate energy cutoff is limited by the available intensities of short wavelength lasers and cannot exceed a few thousand Hartree, setting a boundary for recollision based attosecond physics.

Lorentz drift compensation in high harmonic generation in the soft and hard X-ray regions of the spectrum

We present a semi-classical study of the effects of the Lorentz force on electrons during high harmonic generation in the soft and hard X-ray regions driven by near- and mid-infrared lasers with wavelengths from 0.8 to 20 μm, and at intensities below 10¹⁵ W/cm². The transverse extent of the longitudinal Lorentz drift is compared for both Gaussian focus and waveguide geometries. Both geometries exhibit a longitudinal electric field component that cancels the magnetic Lorentz drift in some regions of the focus, once each full optical cycle. We show that the Lorentz force contributes a super-Gaussian scaling which acts in addition to the dominant high harmonic flux scaling of λ^-(5-6) due to quantum diffusion. We predict that the high harmonic yield will be reduced for driving wavelengths > 6 μm, and that the presence of dynamic spatial mode asymmetries results in the generation of both even and odd harmonic orders. Remarkably, we show that under realistic conditions, the recollision process can be controlled and does not shut off completely even for wavelengths >10 μm and recollision energies greater than 15 keV.

Exploration of laser-driven electron-multirescattering dynamics in high-order harmonic generation

Multiple rescattering processes play an important role in high-order harmonic generation (HHG) in an intense laser field. However, the underlying multi-rescattering dynamics are still largely unexplored. Here we investigate the dynamical origin of multiple rescattering processes in HHG associated with the odd and even number of returning times of the electron to the parent ion. We perform fully ab initio quantum calculations and extend the empirical mode decomposition method to extract the individual multiple scattering contributions in HHG. We find that the tunneling ionization regime is responsible for the odd number times of rescattering and the corresponding short trajectories are dominant. On the other hand, the multiphoton ionization regime is responsible for the even number times of rescattering and the corresponding long trajectories are dominant. Moreover, we discover that the multiphoton- and tunneling-ionization regimes in multiple rescattering processes occur alternatively. Our results uncover the dynamical origin of multiple rescattering processes in HHG for the first time. It also provides new insight regarding the control of the multiple rescattering processes for the optimal generation of ultrabroad band supercontinuum spectra and the production of single ultrashort attosecond laser pulse.

Multiple rescattering processes in high-order harmonic generation from molecular system

The molecular multiple rescattering processes have been theoretically investigated via solving the time-dependent Schrödinger equation. Not only has the physical model been established, but also the related rescatterings originating from recombination with parent nucleus and with neighboring nucleus have been distinguished. Moreover, it has shown that the rescatterings originating from recombination with parent nucleus are similar with those atomic rescatterings, while those rescatterings from recombination with neighboring nucleus both before and after reversing the direction of the laser field are more sensitive to the internuclear distance. With time-frequency distribution and classical electron dynamics, the underlying mechanisms are revealed.

Fast generation of three-atom singlet state by transitionless quantum driving

Motivated by “transitionless quantum driving”, we construct shortcuts to adiabatic passage in a three-atom system to create a singlet state with the help of quantum zeno dynamics and non-resonant lasers. The influence of various decoherence processes is discussed by numerical simulation and the results reveal that the scheme is fast and robust against decoherence and operational imperfection. We also investigate how to select the experimental parameters to control the cavity dissipation and atomic spontaneous emission which will have an application value in experiment.

Bright circularly polarized soft X-ray high harmonics for X-ray magnetic circular dichroism

We demonstrate, to our knowledge, the first bright circularly polarized high-harmonic beams in the soft X-ray region of the electromagnetic spectrum, and use them to implement X-ray magnetic circular dichroism measurements in a tabletop-scale setup. Using counterrotating circularly polarized laser fields at 1.3 and 0.79 µm, we generate circularly polarized harmonics with photon energies exceeding 160 eV. The harmonic spectra emerge as a sequence of closely spaced pairs of left and right circularly polarized peaks, with energies determined by conservation of energy and spin angular momentum. We explain the single-atom and macroscopic physics by identifying the dominant electron quantum trajectories and optimal phase-matching conditions. The first advanced phase-matched propagation simulations for circularly polarized harmonics reveal the influence of the finite phase-matching temporal window on the spectrum, as well as the unique polarization-shaped attosecond pulse train. Finally, we use, to our knowledge, the first tabletop X-ray magnetic circular dichroism measurements at the N4,5 absorption edges of Gd to validate the high degree of circularity, brightness, and stability of this light source. These results demonstrate the feasibility of manipulating the polarization, spectrum, and temporal shape of high harmonics in the soft X-ray region by manipulating the driving laser waveform.

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.

Beyond crystallography: diffractive imaging using coherent x-ray light sources

X-ray crystallography has been central to the development of many fields of science over the past century. It has now matured to a point that as long as good-quality crystals are available, their atomic structure can be routinely determined in three dimensions. However, many samples in physics, chemistry, materials science, nanoscience, geology, and biology are noncrystalline, and thus their three-dimensional structures are not accessible by traditional x-ray crystallography. Overcoming this hurdle has required the development of new coherent imaging methods to harness new coherent x-ray light sources. Here we review the revolutionary advances that are transforming x-ray sources and imaging in the 21st century.

Tailoring the amplification of attosecond pulse through detuned X-ray FEL undulator

We demonstrate that the amplification of attosecond pulse in X-ray free electron laser (FEL) undulator can be tailored. The characteristic of the amplification of an isolated attosecond pulse in the FEL undulator is investigated. An isolated 180 attoseconds full width half maximum (FWHM) pulse at 1.25 nm with a spectral bandwidth of 1% is injected into an undulator. The simulation results show that for a direct seeding of 3MW, the seed is amplified to the peak power of 106 GW (40 μJ, an output pulse-width of 383 attoseconds) in the presence of a detuning at FEL resonance condition in 100-m long undulator. We note that the introduction of detuning leads to the better performance compared to the case without detuning: shorter by 15.5% in a pulse-width and higher by 76.6% in an output power. Tapering yields a higher power (116% increases in the output power compared to the case without detuning) but a longer pulse (15.4% longer in the pulse-width). It was observed that ± Δλ(r)/8 (Δλ(r)/λ(r) ~1%) is the maximum degree of detuning, beyond which the amplification becomes poor: lower in the output power and longer in the pulse duration. The minimum power for a seed pulse needs to be higher than 1 MW for the successful amplification of an attosecond pulse at 1.25 nm. Also, the electron beam energy-spread must be less than 0.1% for a suitable propagation of attosecond pulse along the FEL undulator under this study.

Molecular alignment dependent electron interference in attosecond ultraviolet photoionization

We present molecular photoionization processes by intense attosecond ultraviolet laser pulses from numerical solutions of time-dependent Schrödinger equations. Simulations preformed on a single electron diatomic [Formula: see text] show minima in molecular photoelectron energy spectra resulting from two center interference effects which depend strongly on molecular alignment. We attribute such sensitivity to the spatial orientation asymmetry of the photoionization process from the two nuclei. A similar influence on photoelectron kinetic energies is also presented.

Universality of returning electron wave packet in high-order harmonic generation with midinfrared laser pulses

We show that a returning electron wave packet in high-order harmonic generation (HHG) with midinfrared laser pulses converges to a universal limit for a laser wavelength above about 3 μm. The results are consistent among the different methods: a numerical solution of the time-dependent Schrödinger equation, the strong-field approximation, and the quantum orbits theory. We further analyze how the contribution from different electron "trajectories" survives the macroscopic propagation in the medium. Our result thus provides a new framework for investigating the wavelength scaling law for the HHG yields.

Multielectron contributions in elliptically polarized high-order harmonic emission from nitrogen molecules

We have studied the polarization and ellipticity of high-order harmonics from nitrogen molecules using the time-dependent density functional theory. The results of our numerical calculations are in excellent agreement with the data of recent experiments. The theoretical analysis of our results reveals that at least three contributions, namely those from the HOMO, the HOMO-1, and the HOMO-2 orbitals, contribute to the observed high harmonic spectra. Furthermore, we confirm that a proper account of the distribution of the alignment in the molecular ensemble is necessary to obtain agreement with the experimental data.

Nuclear reaction induced by carrier-envelope-phase controlled proton recollision in a laser-driven molecule

Nuclear reactions induced by proton recollision with a nearby nucleus are studied in a setup where a neutral molecule is exposed to an extremely intense, few-cycle laser pulse. At the rising edge of the laser pulse, all electrons in the molecule are first ejected by field ionization, resulting in a molecule consisting of the bare nuclei only. A proton in the bare molecule is subsequently accelerated by the laser field in such a way that it recollides with a nearby, heavier nucleus, with a kinetic energy high enough to induce a nuclear reaction. As a specific example, the probability of triggering the (15)N(p,α)(12)C reaction by exposing either a (15)NH molecule or a (15)NH3 molecule to an intense laser pulse is calculated using the classical trajectory Monte Carlo method. We show that the proton recollision process can be controlled both by varying the carrier-envelope phase of the laser field and by the degree of molecular orientation. We also find that the magnetic field of the laser pulse plays a crucial role in the recollision dynamics.

High-harmonic generation and parametric amplification in the soft X-rays from extended electron trajectories

We report, for the first time, the generation of high-order harmonics in a spectral range between 200 eV and 1 keV with an unusual spectral property: only every 4(th) (4i + 1, i∈ℵ) harmonic line appears, whereas the usual high-harmonic spectra consist of every odd (2i + 1) harmonic. We attribute this unique property to the quantum path interference of two extended electron trajectories that experience multiple re-scattering. In the well-established theory, electrons emitted via tunnel ionisation are accelerated by a laser field, return to the ion and recombine. The acceleration typically lasts for less than one optical cycle, and the electrons radiate in the extreme ultraviolet range at recombination. In contrast, for extended trajectories, electrons are accelerated over two or more optical cycles. Here, we demonstrate that two sets of trajectories dominate and provide substantial contributions to the generated soft X-ray radiation because they fulfil the resonance condition for X-ray parametric amplification.

Attosecond extreme ultraviolet vortices from high-order harmonic generation

We present a theoretical study of high-order harmonic generation (HHG) and propagation driven by an infrared field carrying orbital angular momentum (OAM). Our calculations unveil the following relevant phenomena: extreme-ultraviolet harmonic vortices are generated and survive to the propagation effects, vortices transport high-OAM multiples of the corresponding OAM of the driving field and, finally, the different harmonic vortices are emitted with similar divergence. We also show the possibility of combining OAM and HHG phase locking to produce attosecond pulses with helical pulse structure.