High-order Harmonic Generation Process Research Articles

High-order harmonic generation driven by perfect optical vortex beams: Exploring the orbital angular momentum upscaling law

Orbital angular momentum (OAM) light beams for high-order harmonic generation (HHG) provide an additional degree of freedom to study the light-matter interaction at ultrafast timescales. A more sophisticated configuration is a perfect optical vortex (POV) beam, a light beam with a helical wave front characterized by a phase singularity at its center and an azimuthal phase variation. POV beams are characterized by a radial profile which is independent of the OAM. Here, we study the nonperturbative process of gas-phase HHG using a linearly polarized POV beam. We observe that the harmonics are emitted with similar divergence due to the perfectness of the POV-driven harmonic generation. Furthermore, the topological charge upscaling is rigorously followed. We show that a POV beam is more advantageous than that of the Laguerre-Gaussian beam for cases where a large topological charge with a small core size is required. Our research establishes a pathway for producing bright structured extreme ultraviolet coherent radiation sources—a pivotal tool with multifaceted applications across various technological domains. Published by the American Physical Society 2024

Spectral phase pulse shaping reduces ground state depletion in high-order harmonic generation

High-order harmonic generation (HHG) has become an indispensable process for generating attosecond pulse trains and single attosecond pulses used in the observation of nuclear and electronic motion. As such, improved control of the HHG process is desirable, and one such possibility for this control is through the use of structured laser pulses. We present numerical results from solving the one-dimensional time-dependent Schrödinger equation for HHG from hydrogen using Airy and Gaussian pulses that differ only in their spectral phase. Airy pulses have identical power spectra to Gaussian pulses, but different spectral phases and temporal envelopes. We show that the use of Airy pulses results in less ground state depletion compared to the Gaussian pulse, while maintaining harmonic yield and cutoff. Our results demonstrate that Airy pulses with higher intensity can produce similar HHG spectra to lower intensity Gaussian pulses without depleting the ground state. The different temporal envelopes of the Gaussian and Airy pulses lead to changes in the dynamics of the HHG process, altering the time-dependence of the ground state population and the emission times of the high harmonics.Graphical abstractHigh-order harmonic generation (HHG) using an Airy pulse with a third order spectral phase results in less ground state depletion, but similar harmonic yield, compared to a Gaussian pulse. Top – schematic depiction of the 3-step HHG process for different intensity pulses. Bottom left – time-dependent ground state populations for Gaussian pulses showing that a more intense pulse causes more ground state depletion. Bottom middle – final ground state populations for Airy and Gaussian pulses as a function of intensity showing that Airy pulses result in less ground state depletion for a given intensity. Bottom right – HHG spectra for a more intense Airy pulse and a less intense Gaussian pulse exhibit similar shapes, magnitudes, and plateau cutoff values

Efficient Time-Dependent Method for Strong-Field Ionization of Atoms with Smoothly Varying Radial Steps

We present an efficient numerical method to solve the time-dependent Schrödinger equation in the single-active electron picture for atoms interacting with intense optical laser fields. Our approach is based on a non-uniform radial grid with smoothly increasing steps for the electron distance from the residual ion. We study the accuracy and efficiency of the method, as well as its applicability to investigate strong-field ionization phenomena, the process of high-order harmonic generation, and the dynamics of highly excited Rydberg states.

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.

Macroscopic effects in generation of attosecond XUV pulses via high-order frequency mixing in gases and plasma

We theoretically study the generation of attosecond XUV pulses via high-order frequency mixing (HFM) of two intense generating fields, and compare this process with the more common high-order harmonic generation (HHG) process. We calculate the macroscopic XUV signal by numerically integrating the 1D propagation equation coupled with the 3D time-dependent Schrödinger equation. We analytically find the length scales which limit the quadratic growth of the HFM macroscopic signal with propagation length. Compared to HHG these length scales are much longer for a group of HFM components, with orders defined by the frequencies of the generating fields. This results in a higher HFM macroscopic signal despite the microscopic response being lower than for HHG. In our numerical simulations in a gas target, the intensity of the HFM signal is several times higher than that for HHG, while for a plasma target the HFM generation efficiency is up to three orders of magnitude higher than for HHG. The HFM with relatively long generating pulses provides very narrow XUV lines ( δω/ω=4.6×10−4 ) with well-defined frequencies, thus allowing for a simple extension of optical frequency standards to the XUV range. Finally, we show that the group of HFM components effectively generated due to macroscopic effects provides a train of attosecond pulses such that the carrier-envelope phase of an individual attosecond pulse can be easily controlled by tuning the phase of one of the generating fields.

Role of nuclear dynamics in high harmonic generation redshift of H2 +

The detailed spectral and temporal structures of high-order harmonic generation (HHG) have provided us with a wealth of information about the highly nonlinear response of atoms, molecules, and electronic structures to intense low-frequency laser fields. In this study, we aim to investigate the underlying physics behind the molecular high harmonic spectra redshift beyond the Born–Oppenheimer approximation for and its isotopes with numerical simulations of the time-dependent Schrödinger equation. One widely recognized phenomenon is the occurrence of a spectral redshift at the trailing edge of a laser pulse. However, our findings reveal that even when driven by a sinusoidal laser pulse without a falling edge, the HHG redshift appears and highlights that the observed spectral redshift is not solely due to the declining intensity of the laser pulse. We show that it is a direct consequence of the decrease in ionization energy during the transition from recombination time to ionization time within wave packets at short internuclear distances. Interestingly, our results also demonstrate how a sinusoidal laser pulse without a rising part can disrupt the standard picture of redshift in literatures in the past. This finding suggests that there are additional factors influencing the redshift mechanism beyond just the trailing edge of the laser pulse. These phenomena are elucidated through the analysis of the dynamics of the nuclear wave packet. Our study provides valuable insights into the complex dynamics of HHG processes and sheds light on how different laser pulse characteristics can influence spectral redshifts and harmonic generation in molecular systems.

Molecular orbital tomography of HOMO and HOMO-1 of the nonlinear molecule H2O: The study on multi-orbital effects

Molecular orbital tomography (MOT) through high-order harmonic generation (HHG) is a crucial method for probing individual molecular orbitals. Previous studies mainly focused on linear molecules such as N2, and CO, where valence orbitals were imaged by detecting harmonic emission at various alignments. In this study, we investigate the HHG from the water molecules, with the aim of exploring MOT for nonlinear molecules. By employing the time-dependent density functional theory, we obtain HHG spectra for different angles between the laser polarization and molecular symmetry axis. By manipulating the scanning planes (planes perpendicular to the laser propagation direction and contain the field polarization direction), specific orbitals can be selectively imaged. Particularly, a well-reconstructed highest occupied molecular orbital (HOMO) is obtained when the laser scanning plane approximately aligns with the nodal plane of HOMO-1. However, when the laser polarization deviates from the nodal plane, multiple orbitals contribute to the HHG process, and we visualize the orbital distortions resulting from such effects. Furthermore, HOMO-1, can be reconstructed when the laser scanning plane aligns with the nodal plane of HOMO. This research significantly advances the development of MOT and opens up intriguing possibilities for reconstructing orbitals of more complex molecules.

Tailoring OAM spectrum of high-order harmonic generation driven by two mixed Laguerre–Gaussian beams with nonzero radial nodes

The extreme ultraviolet (XUV) light beam carrying orbital angular momentum (OAM) can be produced via high-order harmonic generation (HHG) due to the interaction of an intense vortex infrared laser and a gas medium. Here we show that the OAM spectrum of vortex HHG can be readily tailored by varying the radial node (from 0 to 2) in the driving laser consisting of two mixed Laguerre–Gaussian (LG) beams. We find that due to the change in spatial profile of HHG, the distribution range of the OAM spectrum can be broadened and its shape can be modified by increasing the radial node. We also show that the OAM mode range becomes much wider and its distribution shape becomes more symmetric when the harmonic order is increased from the plateau to the cutoff when the driving laser has the nonzero radial nodes. Through the map of coherence length and the evolution of harmonic field in the medium, we reveal that the favorable off-axis phase-matching conditions are greatly modified due to the change of intensity and phase distributions of driving laser with the radial node. We anticipate this work to stimulate some interests in generating the XUV vortex beam with tunable OAM spectrum through the gaseous HHG process achieved by manipulating the mode properties of the driving laser beam.

Enhanced XUV Harmonics Generation with an Intense Laser Field in the Overdriven Regime

High-order harmonic generation with high photon flux has been a challenging task in strong-field physics. According to the high-order harmonic generation process, the essential requirements for achieving efficient harmonic radiations inside a gas medium are the improvement of the induced atomic dipole moment amplitude of the single-atom response in the microscopic and the phase matching of the high harmonics in the macroscopic medium. In this work, we demonstrated a feasible approach to enhance the extreme-ultraviolet harmonics in the plateau region by increasing the intensity of the driving laser while keeping the laser energy constant. The simulation results showed that by increasing the laser intensity to the overdriven regime, the average extreme-ultraviolet harmonics yield in the plateau region is approximately twice as high as that obtained optimally in the conventional loose focusing geometry scheme by utilizing a relatively low-intensity driving laser with the same laser energy. The quantitative analysis of the harmonics generation process in the macroscopic medium and the phase matching revealed that the observed enhancement in harmonics can be attributed to the amplification of the induced atomic dipole moment amplitude of the single-atom response in the high-intensity driving laser and the favorable transient phase matching in the overdriven regime. Furthermore, the investigation of the driving laser indicated that the favorable transient phase matching is caused by the spatiotemporal reshaping of the driving laser in the overdriven regime.

Argonda Dairesel Polarize Yüksek Harmonikler: Dipol ve Dipol Olmayan Etki

The interaction of the intense laser pulse, which forms the basis of the strong laser field and non-linear optical physics, with atoms, molecules, and solids leads to the High Order Harmonic Generation (HHG). There are many theoretical and experimental research related to this process defined by the Semi-Classic Model which is called the Three Step Model. In this article, the dipole and non-dipole effects specified in the theoretical Lewenstein model to be used in the Argon atom interacting with the strong circular laser field (800nm) and the resulting higher order harmonic spectrum will be investigated. We compared the results obtained using the non-collinear beams with opposite circular polarizations with those obtained using a single circularly polarized beam or a linearly polarized beam. It could be said that the circular polarization can significantly affect the HHG process in an argon atom exposed to a laser field with 800 nm wavelength and 1015 W/cm2 intensity.

Electron transition dynamics in high-order harmonic generation process from H2+

The high-order harmonic generation from [Formula: see text] has been theoretically investigated by numerically solving the two-dimensional time-dependent Schrödinger equation. A sharp minimum can be seen in the harmonic spectrum for larger internuclear distance. Moreover, the electron transition process between the ground state and the first excited state competes with the ionization process at larger internuclear distance, which is the main reason of the spectral minimum. By superposing the static electric field and adjusting the orientation angle [Formula: see text], it is further proved that the electron transition frequency between two lowest electronic states can be decoded by the minimum.

Probability of ionization of the noble gas atoms and ions for high harmonic generation

Radiation produced in high-order harmonic generation (HHG) process can be utilized to generate attosecond pulses. According to the semi-classical theory of HHG, the maximum emitted photon energy is [Formula: see text]. The ionization potential ([Formula: see text] and ponderomotive energy ([Formula: see text], play important roles in the generated photon energy; therefore, choosing the material and field for HHG is important. Here, investigating the probability of ionization of material in laser and plasmonic field for HHG is important. The ionization probability of noble gases atoms and ions was investigated. Using Ammosov–Delone–Krainov (ADK) model formulas, the parameters for ions and atoms were determined. The results show that helium is the most suitable noble gas atom for HHG in both fields. After ionizing the atoms, the ionization potential increases significantly, and the ionization probability also decreases. Then, ions are better than their corresponding atoms for HHG. Among noble gas atoms and ions, the helium ion is the most suitable for HHG. In addition, the plasmonic field increases the ponderomotive energy and decreases the probability of ionization for all atoms, as shown by the simulation. Then, extreme ultraviolet (XUV) high-energy photon can be efficiently generated using noble gas ions.

High-order harmonic generation from aligned HCN molecules under orthogonally and linearly polarized two-color laser fields

Molecular high-order harmonic generation and molecular orbital ionization probabilities are calculated under orthogonally and linearly polarized two-color laser fields. When a second-harmonic field is applied, the high-order harmonics generated under the linearly polarized two-color laser fields in the antiparallel case are stronger than those generated in the orthogonal polarization case and even stronger than those of the parallel polarization case. The results show that ionization probabilities of various orbitals and harmonic orders are dependent on spatial symmetry of molecular orbitals. It is found that the ionization of low-lying Kohn-Sham molecular orbitals contributes significantly to the ionization and molecular high-order harmonic generation processes. The ionization probability maximum occurs when molecular orbital densities are maximum in the direction of laser field polarization. Furthermore, we show that the degeneracy of π orbitals is broken when the laser-molecule alignment angle deviates from the field axis. Accordingly, we indicated one component of the π orbital is effectively contributed to the ionization and high-order harmonic generation processes. Finally, to confirm the recollision model in the high-order harmonic generation, the quantum time-frequency analysis is used to extract electron paths information on subcycle time scales.

Dynamic core-electron-polarization effect on the high-order harmonic generation process from a quantum-trajectory perspective

It is argued that the dynamic core-electron polarization (DCEP) in polar molecules primarily affects harmonic processes at the ionization step only. This manifestation can also be understood in view of the strong-field assumption that the parent ion's potential becomes irrelevant when the electron is accelerated in the continuum-energy region. However, the scenario becomes vastly different, especially in the case of long-wavelength lasers as shown in this paper, where we demonstrate a complete physical picture of the DCEP on the harmonic process from asymmetric carbon monoxide (CO) molecules comprising the propagation step. To do so, we develop a visualization method for the harmonic process with and without DCEP based on Bohmian mechanics. As tracer particles evolving along quantum trajectories, Bohmian trajectories provide an intuitive picture of the ``harmonic process from the CO molecules. Remarkably, when the change of the harmonic intensity with respect to the DCEP inclusion cannot be explained by the instantaneous ionization rate, the Bohmian trajectories can attribute this change to the difference in the number of returning events and returning time of the electron after the propagation stage. By analyzing the dynamics of individual Bohmian trajectories (the acceleration and the time-frequency profile), we show that the DCEP alters nonlocally the innermost trajectories, which encode all the dynamics of the harmonic process. This insight into the DCEP effect necessitates a careful reinvestigation into other strong-field physics theories on the role of the target over the propagation stage.

High-Intensity Harmonic Generation with Energy Tunability Produced by Robust Two-Color Linearly Polarized Laser Fields

By using the numerical solution of the time-dependent Schrödinger equation, we theoretically explored the high-order harmonic generation process under the interaction of high-intensity two-color ultrashort driving laser pulses with atoms. The symmetry of the electric field of the laser pulse will be broken. The producing electric field was controlled at the subcycle level by an IR laser and its second harmonic, which has the unique characteristic that two sequential half-cycles become distinct, rather than merely opposite in sign. Compared with the case of the atom in the fundamental laser pulse, the harmonic efficiency showed an increase of 1∼2 orders of magnitude at specific harmonic order with this combined pulse action. Through the theoretical analysis with the “three-step model”, it was demonstrated that the enhancement of the harmonic intensity is due to the fast ionization of electrons at the ionization moment and the short time from ionization to recombination of ionized electrons. In addition, effects of the peak field amplitude ratio, the full width at half maximum, the phase delay of the two-color pulses, the laser intensity and ionization probability on the harmonic efficiency enhancement were also investigated.

High-harmonic generation from artificially stacked 2D crystals.

We report a coherent layer-by-layer build-up of high-order harmonic generation (HHG) in artificially stacked transition metal dichalcogenides (TMDC) crystals in their various stacking configurations. In the experiments, millimeter-sized single crystalline monolayers are synthesized using the gold foil-exfoliation method, followed by artificially stacking on a transparent substrate. High-order harmonics up to the 19th order are generated by the interaction with a mid-infrared (MIR) driving laser. We find that the generation is sensitive to both the number of layers and their relative orientation. For AAAA stacking configuration, both odd- and even-orders exhibit a quadratic increase in intensity as a function of the number of layers, which is a signature of constructive interference of high-harmonic emission from successive layers. Particularly, we observe some deviations from this scaling at photon energies above the bandgap, which is explained by self-absorption effects. For AB and ABAB stacking, even-order harmonics remain below the detection level, consistent with the presence of inversion symmetry. Our study confirms our capability of producing nonperturbative high-order harmonics from stacked layered materials subjected to intense MIR fields without damaging samples. Our results have implications for optimizing solid-state HHG sources at the nanoscale and developing high-harmonics as an ultrafast probe of artificially stacked layered materials. Because the HHG process is a strong-field driven process, it has the potential to probe high-momentum and energy states in the bandstructure combined with atomic-scale sensitivity in real space, making it an attractive probe of novel material structures such as the Moiré pattern.

Fourier-Limited Attosecond Pulse from High Harmonic Generation Assisted by Ultrafast Magnetic Fields

One of the main constraints for reducing the temporal duration of attosecond pulses is the attochirp inherent to the process of high-order harmonic generation (HHG). Though the attochirp can be compensated in the extreme-ultraviolet using dispersive materials, this is unfeasible toward x-rays, where the shortest attosecond or even sub-attosecond pulses could be obtained. We theoretically demonstrate that HHG driven by a circularly polarized infrared pulse while assisted by an strong oscillating ultrafast intense magnetic field enables the generation of few-cycle Fourier-limited few attosecond pulses. In such a novel scenario, the magnetic field transversally confines the ionized electron during the HHG process, analogously to a nanowire trapping. Once the electron is ionized, the transverse electron dynamics is excited by the magnetic field, acting as a high-energy reservoir to be released in the form of phase-locked spectrally wide high-frequency harmonic radiation during the electron recollision with the parent ion. In addition, the transverse breathing dynamics of the electron wavepacket, introduced by the magnetic trapping, strongly modulates the recollision efficiency of the electronic trajectories, thus the attosecond pulse emissions. The aftermath is the possibility of producing high-frequency (hundreds of eV) attosecond isolated few-cycle pulses, almost Fourier limited. The isolated intense magnetic fields considered in our simulations, of tens of kT, can be produced in finite spatial volumes considering structured beams or stationary configurations of counter-propagating state-of-the-art multi-terawatt/petawatt lasers.

Phase-coherence dynamics of frequency-comb emission via high-order harmonic generation in few-cycle pulse trains

Frequency-comb emission via high-order harmonic generation (HHG) provides an alternative method for the coherent vacuum ultraviolet (VUV) and extreme ultraviolet (XUV) radiation at ultrahigh repetition rates. In particular, the temporal and spectral features of the HHG were shown to carry profound insight into frequency-comb emission dynamics. Here we present an ab initio investigation of the temporal and spectral coherence of the frequency comb emitted in HHG of He atom driven by few-cycle pulse trains. We find that the emission of frequency combs features a destructive and constructive coherences caused by the phase interference of HHG, leading to suppression and enhancement of frequency-comb emission. The results reveal intriguing and substantially different nonlinear optical response behaviors for frequency-comb emission via HHG. The dynamical origin of frequency-comb emission is clarified by analyzing the phase coherence in HHG processes in detail. Our results provide fresh insight into the experimental realization of selective enhancement of frequency comb in the VUV–XUV regimes.

Theory of entanglement and measurement in high-order harmonic generation

Quantum information science and intense laser matter interaction are two apparently unrelated fields. Here, we introduce the notion of quantum information theory to intense laser driven processes by providing the quantum mechanical description of measurement protocols for high harmonic generation in atoms. This allows to conceive new protocols for quantum state engineering of light. We explicitly evaluate conditioning experiments on individual optical field modes, and provide the corresponding quantum operation for coherent states. The associated positive operator-valued measures are obtained, and give rise to the quantum theory of measurement for the generation of high dimensional entangled states, and coherent state superposition with controllable non-classical features on the attosecond timescale. This establish the use of intense laser driven processes as a novel quantum technology platform for quantum information processing.

Generation of ellipticity-tunable isolated attosecond pulses from diatomic molecules in intense laser fields

We theoretically investigate the high-order harmonic generation (HHG) and the isolated attosecond pulse (IAP) with tunable ellipticity from the aligned molecule. It is found that the ellipticity of harmonic depends on the internuclear distance R. Further analysis presents that the nonzero ellipticity of harmonic generated at R=6a.u. is attributed to the 2pσu state of H2+. The 2pσu state with nonvanishing angular momentum originates from a resonant transition from the 1sσg state induced by the fundamental pulse. With specific intensity of the orthogonally polarized two-color (OTC) laser fields, an IAP with high ellipticity can be obtained. To further illustrate the origin of the high ellipticity, we present the electron trajectories and electron currents induced by the electron wavepackets of H2+, which shows a clear picture of the dynamic process of HHG. Moreover, the polarization of the IAP varies from left to right elliptical polarization by synthesizing the harmonic spectrum with different orders. Such an IAP may serve as a potential tool for probing and manipulating the ultrafast magnetic and chiral dynamics.