Harmonic Yield Research Articles

Enhanced high harmonic efficiency through phonon-assisted photodoping effect

High-harmonic generation (HHG) has emerged as a central technique in attosecond science and strong-field physics, providing a tool for investigating ultrafast dynamics. However, the microscopic mechanism of HHG in solids is still under debate, and it is unclear how it is modified in the ubiquitous presence of phonons. Here we theoretically investigate the role of collectively coherent vibrations in HHG in a wide range of solids (e.g., hBN, graphite, 2H-MoS2, and diamond). We predict that phonon-assisted high harmonic yields can be significantly enhanced, compared to the phonon-free case – up to a factor of ~20 for a transverse optical phonon in bulk hBN. We also show that the emitted harmonics strongly depend on the character of the pumped vibrational modes. Through state-of-the-art ab initio calculations, we elucidate the physical origin of the HHG yield enhancement – phonon-assisted photoinduced carrier doping, which plays a paramount role in both intraband and interband electron dynamics. Our research illuminates a clear pathway toward comprehending phonon-mediated nonlinear optical processes within materials, offering a powerful tool to deliberately engineer and govern solid-state high harmonics.

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

Non-perturbative nonlinear optical responses in Weyl semimetals

We report a systematic and detailed investigation on strong-field driven non-perturbative high-harmonic generation from Weyl semimetals in various realistic environments, i.e., going beyond the idealistic situation where the Weyl nodes are at Fermi energy and are energy degenerate. Two classes of topological semimetals are considered: time-reversal broken Weyl semimetal and inversion-symmetry broken Weyl semimetal. It has been found that type-II Weyl semimetal leads to significant enhancement in the yield of the higher-order harmonics. In addition, energy splitting between the Weyl nodes also results in a modest boost in the harmonic yield. The underlying mechanism responsible for the enhancement can be traced to a drastic increase in the conduction band electronic population and noticeable changes in the momentum matrix amplitude. A combined effect of the tilt in the Weyl cones and energy separation between the nodes allows the generation of forbidden even-order harmonics in inversion-symmetric Weyl semimetal. Our findings offer exciting avenues for Weyl semimetals in ultrafast photonics and optoelectronic devices.

Harmonic Generation in Molecular Ag2S Plasma.

The molecular laser-induced plasma (LIP) produced during the ablation of silver sulfide (Ag2S) was used as a medium for high-order harmonic generation in the extreme ultraviolet range. The role of LIP formation, the plasma components, and the geometry of plasma in the harmonic conversion efficiency was analyzed. We also analyzed the influence of the driving pulses (chirp, single-color pump, two-color pump, and delay between heating and converting pulses) on the harmonic yield in Ag2S LIP. The application of molecular plasma was compared with the application of atomic plasma, which comprised similar metallic elements (Ag) as well as other metal LIPs. The harmonics from the Ag2S LIP were 4 to 10 times stronger than those from the Ag LIP. The harmonics up to the 59th order were achieved under the optimal conditions for the molecular plasma.

Many-body enhancement of high-harmonic generation in monolayer MoS2

Many-body effects play an important role in enhancing and modifying optical absorption and other excited-state properties of solids in the perturbative regime, but their role in high harmonic generation (HHG) and other nonlinear response beyond the perturbative regime is not well-understood. We develop here an ab initio many-body method to study nonperturbative HHG based on the real-time propagation of the non-equilibrium Green’s function with the GW self energy. We calculate the HHG of monolayer MoS2 and obtain good agreement with experiment, including the reproduction of characteristic patterns of monotonic and nonmonotonic harmonic yield in the parallel and perpendicular responses, respectively. Here, we show that many-body effects are especially important to accurately reproduce the spectral features in the perpendicular response, which reflect a complex interplay of electron-hole interactions (or exciton effects) in tandem with the many-body renormalization and Berry curvature of the independent quasiparticle bandstructure.

Interference of harmonics emitted by different tunneling momentum channels in laser fields

Abstract By numerically solving the semiconductor Bloch equation (SBEs), we theoretically study the high-harmonic generation of ZnO crystals driven by one-color and two-color intense laser pulses. The results show the enhancement of harmonics and the cut-off remains the same in the two-color field, which can be explained by the recollision trajectories and electron excitation from multi-channels. Based on the quantum path analysis, we investigate contribution of different ranges of the crystal momentum k of ZnO to the harmonic yield, and find that in two-color laser fields, the intensity of the harmonic yield of different ranges from the crystal momentum makes a big difference and the harmonic intensity is depressed from all k channels, which is related to the interferences between harmonics from symmetric k channels.

High-order harmonic generation in liquid crystals

Thermotropic liquid crystals are versatile optical materials that exhibit a state of matter intermediate between liquids and solids. Their properties can change significantly with temperature, pressure, or other external factors, leading to different phases. The transport properties within these materials in different phases are still largely unexplored, and their understanding would enable exciting prospects for innovative technological advancements. High-order harmonic spectroscopy proved to be a powerful spectroscopic tool for investigating the electronic and nuclear dynamics in matter. Here, we report the first experimental observation of high-order harmonic generation in thermotropic liquid crystals in two different phase states, nematic and isotropic. We found the harmonic emission in the nematic phase to be strongly dependent on the relative orientation of the driving field polarization with respect to the liquid crystal alignment. Specifically, the harmonic yield has a maximum when the molecules are aligned perpendicularly to the polarization of the incoming radiation. Our results establish the first step for applying high-order harmonic spectroscopy as a tool for resolving ultrafast electron dynamics in liquid crystals with unprecedented temporal and spatial resolution.

UV-induced resonant excitations of electrons near the Brillouin zone boundary in solid high harmonic generation

Abstract We propose a novel mechanism to manipulate the electron dynamics at the boundary of the Brillouin zone (BZ) through resonant excitation induced by ultraviolet (UV) laser pulses in solid high harmonic generation (HHG). When adding weak UV pulses to a stronger mid-infrared (MIR) driving field, we show that UV pulses with specific wavelengths generate a resonant excitation zone around the Γ point in k − space, which facilitates the interband transition of electrons in the BZ boundary region. The scheme is not only significant for achieving higher harmonic yield, but also exhibits strong robustness at a relatively low MIR driving intensity due to the inherent manipulation of UV pulses for interband dynamics of BZ boundary electrons. The semiclassical four-step model is adopted to elucidate underlying physics.

Elliptically polarized high-order harmonic generation of Ar atom in an intense laser field

High-order harmonic generation (HHG) of Ar atom in an elliptically polarized intense laser field is experimentally investigated in this work. Interestingly, the anomalous ellipticity dependence on the laser ellipticity (ε) in the lower-order harmonics is observed, specifically in the 13rd-order, which displays a maximal harmonic intensity at ε ≈ 0.1, rather than at ε = 0 as expected. This contradicts the general trend of harmonic yield, which typically decreases with the increase of laser ellipticity. In this study, we attribute this phenomenon to the disruption of the symmetry of the wave function by the Coulomb effect, leading to the generation of a harmonic with high ellipticity. This finding provides valuable insights into the behavior of elliptically polarized harmonics and opens up a potential way for exploring new applications in ultrafast spectroscopy and light–matter interactions.

Orientation Dependence of High-Order Harmonic Generation from HeH2+ in a Corotating Two-Color Circularly Polarized Laser Field

By numerically solving the time-dependent Schrödinger equation, we study high-order harmonic generation from the asymmetric diatomic molecule HeH2+ in a corotating two-color circularly polarized laser field. Our results reveal a strong correlation between the molecule orientation and the harmonic yield. The harmonics in the plateau region can achieve an intensity modulation of one to two orders of magnitude with the change in the orientation angle. Through the time-dependent evolution of ionized electron wave packets combined with the analysis of the transition dipole moment between the continuum and bound states, the modulation of the harmonic strength may be attributed to the difference in the recollision angle of ionized electron wave packets relative to the molecules. In addition, the harmonic ellipticity is also affected by the molecular orientation. Notably, we found that the harmonic with greater ellipticity and higher intensity can be obtained with an orientation angle of 147°. These findings open up new avenues for achieving enhanced efficiency, the near-circular polarization of harmonics, and precise control over harmonic polarization states.

Two-Electron Scenario of High-Order Harmonics Generation by Atom in an Intense Infrared Field and Attosecond Pulse

The two-electron scenario is proposed for the high-order harmonic generation (HHG) by an atom interacting with an intense infrared field and attosecond pulse. The two-electron dynamics involved in the proposed scenario is realized for the specific attosecond pulse, which can excite the resonance between the valence and deeper shells. Within the numerical solution of the time-dependent Kohn–Sham equations, we analyze the contribution of the single [Phys. Rev. A 98, 063433 (2018)] and two-electron scenarios of HHG by decreasing the duration of attosecond pulse having carrier frequency detuned from the atomic resonance. Favorable conditions are formulated for the realization of a two-electron scenario, which causes the enhancement of the harmonic yield in the spectral range exceeding the cutoff energy of the HHG spectrum in the infrared field.

High harmonic generation in epitaxially grown zinc oxide films

High harmonic generation (HHG) in solids has been identified as a promising mechanism for light source generation and for spectroscopy of materials. HHG from bulk solids, however, often suffers from nonlinear propagation effects, resulting in a loss of spectral coherence and the skewing of spectroscopic measurements. Here, we study HHG in epitaxial ZnO thin films grown on Al2O3 substrates using atomic layer deposition. We find that the HHG emission consists of narrow spectral peaks, in contrast to those seen in bulk, and that the dependence of the harmonic yield on the film thickness differs for above-gap and below-gap harmonics, which can be understood from analytical models based on the linear and nonlinear response of the medium. The measured harmonic spectra depend qualitatively on the preparation of the films, with as-grown films generating even harmonic orders, which are absent in annealed films. The results are interpreted using transmission electron microscopy measurements, which indicate different morphologies for the as-grown and annealed films.

Tracking Charge Migration with Frequency-Matched Strobo-Spectroscopy.

We present frequency-matched strobo-spectroscopy (FMSS) of charge migration (CM) in bromobutadiyne, simulated with time-dependent density functional theory. CM + FMSS is a pump-probe scheme that uses a frequency-matched high harmonic generation (HHG)-driving laser as an independent probe step, following the creation of a localized hole on the bromine atom that induces CM dynamics. We show that the delay-dependent harmonic yield tracks the phase of the CM dynamics through its sensitivity to the amount of electron density on the bromine end of the molecule. FMSS takes advantage of the intrinsic attosecond time resolution of the HHG process in which different harmonics are emitted at different times and thus probe different locations of the electron hole. Finally, we show that the CM-induced modulation of the HHG signal is dominated by the recombination step of the HHG process, with a negligible contribution from the ionization step.

Enhanced XUV harmonics generated in mixed noble gases using three-color laser fields.

High repetition coherent extreme ultraviolet (XUV) harmonics offer a powerful tool for investigating electron dynamics and understanding the underlying physics in a wide range of systems. We demonstrate the utilization of combined three-color (ω+2ω+3ω) laser fields in the generation of coherent extreme ultraviolet radiation in mixed noble gases. The three-color field results from the combination of fundamental, second-, and third-order harmonics of the near-infrared laser pulses in the nonlinear crystals. Different noble gases were selected as gas targets based on their ionization potentials, which are important parameters for generating higher cut-offs and intensities for the XUV harmonics. Enhanced XUV harmonic intensities were observed in the mixture of He + Kr gases when using three-color laser fields, compared to harmonics generated in the He + Kr mixture under a single-color pump. On the other hand, suppression of XUV harmonic intensity was observed in the mixture of He + Xe under the three-color pump due to the highest ionization level for these two mixed gases at similar laser conditions. Strong harmonic yields in the range of 25 to 80 eV of photon energy were observed.

Investigating high harmonic yield from different alignments of WSe2 semiconductor

This paper theoretically investigates high harmonic generation from a monolayer WSe2 driven by a laser pulse with different alignments, in-plane and out-of-plane polarizations. Our simulations are performed in the framework of the time-dependent density functional theory. Analysis of the dependence of the cutoff energy on the laser field strength shows that the cutoff energy increases linearly/quadratically with the increase of the electric field strength for the out-of-plane/in-plane laser field. Also, the wavelength dependence of high harmonic yield exhibits a sharp decrease with a rate of λ−10 for the in-plane laser field, and a more gradual decline with a rate of λ−4.75 for the out-of-plane laser field. These wavelength dependencies are explained by the tunneling rate and the spatial spread of electron wave-packet due to propagation in time and space. Additionally, it is demonstrated that the maximum harmonic yield is obtained when the in-plane laser is aligned along the armchair direction, or when the out-of-plane laser is polarized at a 20° angle relative to the normal axis of the monolayer plane.

Valley-Selective High Harmonic Generation and Polarization Induced by an Orthogonal Two-Color Laser Field

The valley pseudospin properties of electrons in two-dimensional hexagonal materials result in many fascinating physical phenomena, which opens up the new field of valleytronics. The valley-contrasting physics aims at distinguishing the valley degree of freedom based on valley-dependent effects. Here, we theoretically demonstrate that both of the valley-selective high harmonic generation and valley-selective electronic excitation can be achieved by using an orthogonal two-color (OTC) laser field in gapped graphene. It is shown that the asymmetry degrees of harmonic yields in the plateaus, cutoff energies of generated harmonics and electron populations from two different valleys can be precisely controlled by the relative phase of the OTC laser field. Thus, the selectivity of the dominant valley for the harmonic radiation and electronic polarization can be switched by adjusting the relative phase of the OTC laser field. Our work offers an all-optical route to produce the valley-resolved high harmonic emissions and manipulate the ultrafast valley polarization on a femtosecond timescale in condensed matter.

Generation of coherent XUV radiation at different interaction lengths using the ultrashort laser system

Generation of short wavelengths is obtained using the gas cells having different lengths. A Ti:sapphire laser system at 1[Formula: see text]kHz or 10[Formula: see text]Hz repetition rate is used to produce high harmonic generation (HHG). The gas cell producing optimum harmonic spectrum is determined using the 1[Formula: see text]kHz laser system. The optimum harmonic signal is obtained under the phase-matched condition. The total harmonic yield is increased by adjusting argon gas pressure in the different gas cell lengths (length of the interaction mediums). Harmonics up to the 27th order are obtained. The 1D model is used for the calculation of harmonic yield at different interaction lengths. The high-power laser system at the 10[Formula: see text]Hz repetition rate is used to generate high-order harmonics. The harmonic orders are extended to the 35th harmonic in argon gas. A harmonic spectrum in H2 gas is generated using different pump laser power. The power dependence of the harmonic signal from H2 gas is obtained. The variation of the harmonic spectrum for the different cell parameters is explained as a constructive or destructive buildup of generated harmonics while they propagate through the gas cell.

Two phase-matching regimes in high-order harmonic generation.

High-order harmonic generation (HHG) provides scalable sources of coherent extreme ultraviolet radiation with pulse duration down to the attosecond time scale. Efficient HHG requires the constructive interplay between microscopic and macroscopic effects in the generation volume, which can be achieved over a large range of experimental parameters from the driving field properties to those of the generating medium. Here, we present a systematic study of the harmonic yield as a function of gas pressure and medium length. Two regimes for optimum yield are identified, supporting the predictions of a recently proposed analytical model. Our observations are independent on the focusing geometry and, to a large extent, on the pulse duration and laser intensity, providing a versatile approach to HHG optimization.

Wavelength scaling of high harmonic yields and cutoff energies in solids driven by mid-infrared pulses.

The effect of driving wavelengths on high harmonic generation (HHG) have long been a fundamental research topic. However, despite of abundant efforts, the investigation of wavelength scaling of HHG in solids is still confined within the scope of theoretical predictions. In this work, we for the first time to the best of our knowledge, experimentally reveal wavelength scaling of HHG yields and cutoff energy in three typical solid media (namely pristine crystals GaSe, CdTe and polycrystalline ZnSe), driven in a broad mid-infrared (MIR) range from 4.0 to 8.7 µm. It is revealed that when the driving wavelength is shorter than 6.5-7.0 µm, HHG yields decrease monotonously with the MIR driving wavelengths, while they rise abruptly by 1-3 orders of magnitude driven at longer wavelength and exhibit a crest at 7.5 µm. In addition, the cutoff energies are found independent on driving wavelengths across the broad MIR pump spectral range. We propose that the interband mechanism dominates the HHG process when the driving wavelength is shorter than 6.5-7.0 µm, and as the driving wavelength increases, intraband contribution leads to an abrupt rise of the HHG yields, which is verified by the HHG polarization measurement driven at 3.0 and 7.0 µm. This work not only experimentally demonstrate the wavelength scaling of HHG in solids, but more importantly blazes the trail for optimizing the HHG performance by choosing a driving wavelength and provides experimental method to distinguish the interband and intraband dynamics.

High-order harmonics enhancement in laser-induced plasma

The methods of enhancement of the strong high-order harmonics of femtosecond pulses in laser-induced plasma are demonstrated. It comprises the application of the four techniques allowing the enhancement of harmonics in different spectral ranges. Among them are the selection of targets for ablation to create the conditions for resonance enhancement of single harmonic, formation of the quasi-phase-matching of a spectrally tunable group of harmonics, application of the two-color pump of plasma, and the formation of nanoparticles-contained plasmas. The number of generated coherent XUV photons increased in the region of single resonantly enhanced harmonic (62 nm) and the shorter-wavelength region (30–50 nm). The above techniques of harmonics enhancement allowed a significant (up to 50 times) growth in a whole harmonic yield in the case of indium plasma. We discuss the reasons preventing the joint implementation of the four methods of harmonics enhancement in the same spectral region.