High-order Harmonic Generation Yield Research Articles

Strain effects on high-harmonic generation in monolayer hexagonal boron nitride

Based on the time-dependent density functional theory, we theoretically investigate the influence of mechanical strains on the high-order harmonic generation (HHG) in the monolayer hexagonal boron nitride (hBN) crystal. We show that mechanical strains can largely modify the band structure and facilitate the harmonic emission. Compared to uniaxial strains, we find that biaxial strains may enhance the HHG yield significantly, and the HHG spectroscopy generated by a linearly polarized laser is closely related to the symmetry of the deformed hBN. Moreover, when driven by a circularly polarized laser, we find that the appearance of the 3n-order harmonics manifests the restoration of the three-fold rotational symmetry. Our results will be useful in controlling the HHG spectroscopy and probing lattice deformations in crystals.

Ellipticity dependence of high-order harmonic generation in disordered semiconductors

We analyze the ellipticity dependence of high order harmonic generation (HHG) in disordered semiconductors. We show that a disordered crystal can radiated HHG spectra containing only odd harmonics of the laser frequency for all values of the ellipticity of the laser. Furthermore, we show that the HHG yield of our disordered models decreases monotonically with increasing laser ellipticity as observed in recent experiments. I particular, our numerical calculations, based on a coarse grained model, reproduce many of the qualitative features of the experimental HHG spectra of ZnO and GaAs.

High harmonic generation in mixed XUV and NIR fields at a free-electron laser

We present the results of an experiment investigating the generation of high-order harmonics by a femtosecond near-infrared (NIR) laser pulse in the presence of an extreme ultraviolet (XUV) field provided by a free-electron laser (FEL), a process referred to as XUV-assisted high-order harmonic generation (HHG). Our experimental findings show that the XUV field can lead to a small enhancement in the harmonic yield when the XUV and NIR pulses overlap in time, while a strong decrease of the HHG yield and a red shift of the HHG spectrum is observed when the XUV precedes the NIR pulse. The latter observations are in qualitative agreement with model calculations that consider the effect of a decreased number of neutral emitters but are at odds with the predicted effect of the correspondingly increased ionization fraction on the phase matching. Our study demonstrates the technical feasibility of XUV-assisted HHG experiments at FELs, which may provide new avenues to investigate correlation-driven electron dynamics as well as novel ways to study and control propagation effects and phase matching in HHG.

Waveform retrieving of an isolated attosecond pulse using high-order harmonics generation of the superimposed infrared field.

An all-optical method is suggested for the metrology of an isolated, pulse-to-pulse stabilized attosecond pulse. It is shown analytically that high-order harmonic generation (HHG) yield for an intense IR pulse and time-delayed attosecond pulse keeps encoded waveform of the attopulse, which can be decoded by the time delay measurements of the HHG yield. The retrieval method is demonstrated by modeling HHG from Ne atom within time-dependent Kohn-Sham equations. The application of the suggested method for monitoring the carrier-envelope phase of the attosecond pulse is discussed.

Control of high-order harmonic generation in solids by orthogonally polarized laser fields

We theoretically investigate the high-order harmonic generation (HHG) from ZnO crystals driven by orthogonally polarized two-color (OTC) laser fields. By solving the semiconductor Bloch equation (SBE) in two dimensions, it is found that the HHG yields show a high sensitivity to the relative phase between the two fields. By changing the laser intensity, the yields of HHG show two maxima in the high-order region. To reveal the physical origin of these phenomena, we analyze the behavior of the electron-hole pair in the real and reciprocal spaces by the recollision model, respectively. It could qualitatively interpret the results by SBE simulations. Our analysis demonstrates that the OTC laser fields could control the electron-hole dynamics and HHG processes efficiently.

Impact of donor and acceptor dopants in high-harmonic generation spectra of solids

High-order harmonic generation (HHG) from solids is one source of coherent extreme ultraviolet radiation and is considered as a promising way to obtain attosecond pulses, where the key issue is to enhance HHG yield and control its temporal characteristic. The role of the dopant on enhancement of HHG yield is investigated via solving the time-dependent Schrödinger equation. We find that the doped solids possessing an impurity band in the middle of the bandgap can achieve time-domain optimization and yield enhancement in the bursts of HHG. The reason for the enhanced HHG yield is that the impurity band can provide a ladder in the step-by-step transition process. The difference in the Bloch–Zener oscillation dynamics between pristine and doped solids is shown, which also influences the variation of HHG yield and generation of even-order harmonics. In addition, the avoided level crossing between conduction bands assists the promotion of electrons and leads to the mergence between primary and secondary plateaus under nondestructive laser intensity. Finally, the generation of shorter and efficient attosecond pulses is obtained theoretically from the doped solids.

High-power sub-15 fs nonlinear pulse compression at 515 nm of an ultrafast Yb-doped fiber amplifier.

We present an efficient and robust scheme to produce energetic sub-15 fs pulses centered at 515 nm with a peak power exceeding 3 GW. Combining efficient second-harmonic generation of a 135 fs, 50 W Yb-doped fiber amplifier with a low-loss capillary-based visible pulse compression stage, we reach an overall efficiency higher than >20%. The system is also designed to take advantage of the repetition rate flexibility of the fiber amplifier, leading sub-15 fs pulse generation from 166 to 500 kHz with an average power exceeding the 10 watt level. The combined reduction of the laser wavelength and pulse duration is expected to highly improve the yield of high-order harmonic generation to provide high photon flux of ultrashort extreme ultraviolet radiation.

Study of high-order harmonic generation in xenon based on time-dependent density-functional theory

The high-order harmonic generation (HHG) in xenon is studied by using the time-dependent density-functional theory. The dynamics of all electrons on the outer 4th and 5th atomic shells is considered with subsequent separation of contributions of different atomic orbitals to the HHG amplitude. It is shown that giant enhancement of HHG yield in a spectral region near 100 eV is caused by perturbation of the electron–electron interaction potential induced by recolliding photoelectron wavepacket originated from the 5p 0 orbital. This perturbation leads to the collective oscillations of all orbitals on the 4th shell closely localized in space and strongly interacting with each other. The resulting HHG yield is enhanced by more than an order of magnitude compared with the response of the single 5p 0 orbital. The high accuracy of the numerical results is confirmed by comparing the calculated HHG spectra and photoionization cross-sections with experimental results and an analytical parameterization of the HHG yield.

Interference effect in high order harmonic generation by aligned O<sub>2</sub>

High order harmonic generation (HHG) is an important phenomenon when atoms or molecules interact with an intense laser field. It can be used to generate ultrashort laser source, and can also be used to investigate the atomic and molecular dynamics and obtain the electric structure information of molecules. All these require to understand in depth the mechanism of HHG. There are complicated interference effects in HHG spectra of molecules due to multiple re-collision atomic centers in the molecule. In this paper, spectra of aligned O<sub>2</sub> molecule in linearly polarized laser field is investigated by using the Lewenstein' s model. The dependence of the spectrum on the angle θ between the nuclear axis of the molecule and the laser polarization direction is obtained. It is shown that the maximum yield of HHG occurs at <i>θ</i> of 45°, which is in consistence with the experimental result. In addition, it is found that there exists a minimum value in the HHG spectrum for any given value of<i> θ</i>. The harmonic order corresponding to the minimum increases with <i>θ</i> increasing. It is found that the minimum comes from the coherent superposition of contributions from two channels. One channel refers to that the ionized electron from one atomic center, subjected to the electric field of the laser, moves back to its parent atomic center and there it combines with the molecule and emits harmonics; while the other channel is that the ionized electron generated from one atomic center move back to the other atomic center to complete the combination and emission of harmonics. The angle <i>θ-</i>dependent phase difference between contributions from these two channels is calculated and the harmonic order corresponding to the minimum value is obtained. Finally, the reason why the yield of HHG is low for the case of the molecular axis parallel to the laser polarization direction is different from that for the case of the molecular axis perpendicular to the polarization direction. For the parallel case, the contributions to HHG from the two channels are both small so that the amplitude of their coherent superposition is small. While for the perpendicular case, the individual contribution from each channel is not small but their destructive interference leads to small yield in harmonicspectrum.

Influence of the polarization of a multielectron atom in a strong laser field on high-order harmonic generation

We study the ionization and high-order harmonic generation (HHG) in argon by short linearly polarized laser pulses. We compare the populations of atomic orbitals and HHG spectra in a wide range of laser-pulse parameters, taking into account the dynamics of all orbitals based on the time-dependent density-functional theory (TDDFT) and only the most active orbital within the single-active electron (SAE) approximation. At high intensities of laser pulses, the atom polarization leads to suppression in the bound-state depletion due to the screening of the external field. The significant increase in the HHG yield is observed for the TDDFT calculations in comparison with the SAE calculations. The contribution of different orbitals in the TDDFT calculations of HHG spectra is discussed.

Aluminum nanoparticle plasma formation for high-order harmonic generation

We demonstrate the efficient high-order harmonic generation (HHG) of 35 fs pulses from the nanoparticle (NP)–containing plasmas produced during laser ablation of aluminum (Al) target using picosecond and nanosecond pulses. The role of NPs in the enhancement of harmonic yield is discussed. To achieve the maximal HHG yield, we use different experimental schemes, including two-color pump, HHG using extended and multi-jet laser-produced plasmas, ablation of rotating target and temporal variation between the heating and driving pulses. A fivefold increase of harmonic yield from Al NP-containing plasmas compared to the plasmas containing only Al atoms and ions is obtained. The harmonics up to the 35th order are generated from the Al NP-containing plasmas. HHG calculations show that this cutoff is attributed to Al neutral atoms rather than Al ions. To interpret the experimental results, we also study the fundamental mechanism of NP formation. The simulations are carried out for different Al NP-containing ablation plumes. Our calculations and plasma debris analysis show the presence of NPs in the plasmas exposed to the driving 35 fs pulses.

Wavelength scaling laws for high-order harmonic yield from atoms driven by mid- and long-wave infrared laser fields

High-order harmonic generation (HHG) in gases is known to benefit from using mid-infrared driving laser fields, since, due to a favorable wavelength scaling of the electron ponderomotive energy, higher-energy photon production becomes feasible with longer-wavelength drivers. On the other hand, recent studies have revealed a number of physical effects whose importance for HHG increases with increasing laser wavelength. These effects, as a rule, result not only in a general decrease of the harmonic yield but also in a reshaping of the emission spectrum. Therefore, detailed study of the dependence of HHG yield on the laser wavelength has become an important issue for producing intense extremely short extreme ultraviolet (XUV) and x-ray pulses using HHG driven by long-wavelength laser fields. Here we address this issue by calculating the HHG spectra for laser wavelengths ranging from 2 to 20 µm. This study has been carried out in a frame of strong-field approximation modified properly to take into account the effect of the magnetic field of a laser pulse on the dynamics of the field-ionized electron and the atomic bound-state depletion. We show that different regions of the HHG spectrum behave differently with the laser wavelength and discuss the origins of this behavior. In particular, we show that in a weak ionization regime, the dipole-approximation scaling law for the harmonic yield, which is calculated as the integral over the spectral interval of fixed width and relative position with respect to the cutoff energy, obeys the power law, where the absolute value of the exponent is an integer equal to $\mu = {7}$μ=7 for the cutoff and $\mu = {8}$μ=8 for the plateau harmonics. Above a certain critical wavelength, due to the nondipole effects, the efficiency of HHG decreases more strongly than according to a power law, and this decrease is different for different regions of the spectrum. The analytical formulas are derived that match well the calculated wavelength scalings.

Intense X-ray isolated attosecond pulse generation by using low-intensity chirped pulse combined with a UV seeding pulse

We theoretically investigate intense isolated attosecond pulse (IAP) generation from high-order harmonic generation (HHG) driven by a low-intensity chirped pulse combined with a UV seeding pulse. The results show that, driven by a two-color chirped pulse, the harmonic cutoff can be remarkably extended and a spectral continuum in X-ray region can be obtained. Moreover, as the pulse duration increases or the delay time of the two pulses changes, a larger harmonic cutoff can be found. Further, with the introduction of a UV seeding pulse, the efficiency of HHG can be enhanced by three orders of magnitudes due to the UV resonance ionization. Moreover, as the UV pulse intensity increases, the enhanced ratio of HHG yield can be further improved. The enhancement of HHG yield is related to the pulse duration and delay time of the UV pulse. For instance, when adding a shorter duration UV pulse, the enhancement of HHG is dependent on the delay time of the UV pulse. However, when adding a longer duration UV pulse, the HHG enhancement is not very sensitive to the delay time of the UV pulse. Finally, the obtained spectral continuum supports the generation of intense IAP with the duration of 36 as.

Analytic description of high-order harmonic generation in the adiabatic limit with application to an initial s state in an intense bicircular laser pulse

An analytic description of high-order harmonic generation (HHG) is proposed in the adiabatic (low-frequency) limit for an initial $s$ state and a laser field having an arbitrary wave form. The approach is based on the two-state time-dependent effective range theory and is extended to the case of neutral atoms and positively charged ions by introducing ad hoc the Coulomb corrections for HHG. The resulting closed analytical form for the HHG amplitude is discussed in terms of real classical trajectories. The accuracy of the results of our analytic model is demonstrated by comparison with numerical solutions of the time-dependent Schr\odinger equation for a strong bicircular field composed of two equally intense components with carrier frequencies $\ensuremath{\omega}$ and $2\ensuremath{\omega}$ and opposite helicities. In particular, we demonstrate the effect of ionization gating on HHG in a bicircular field, both for the case that the two field components are quasimonochromatic and for the case that the field components are time-delayed short pulses. We show how ionization in a strong laser field not only smooths the usual peak structures in HHG spectra but also changes the positions and polarization properties of the generated harmonics, seemingly violating the standard dipole selection rules. These effects appear for both short and long incident laser pulses. In the case of time-delayed short laser pulses, ionization gating provides an effective tool for control of both the HHG yield and the harmonic polarizations [Frolov et al., Phys. Rev. Lett. 120, 263203 (2018)]. For the case of short laser pulses, we introduce a simple two-dipole model that captures the physics underlying the harmonic emission process, describing both the oscillation patterns in HHG spectra and also the dependence of the harmonic polarizations on the harmonic energy.

Suppressed short-trajectory near-threshold harmonics as a sign of tunnel exit

We study high-order harmonic generation (HHG) from atoms with different ionization potentials by solving numerically the time-dependent Schrödinger equation. A numerical scheme is used which allows us to resolve the contributions of only the short electron trajectory to HHG. With increasing laser wavelengths and reducing laser intensities, the calculated short-trajectory HHG spectra show an energy region near the threshold, where the HHG yields are suppressed strikingly. The width of the region depends on the ionization potential of the target. We show that this suppression can be attributed to the effect of tunnel exit, by providing a distinct HHG feature for studying tunneling. It also provides a chance for exploring other HHG mechanisms beyond tunneling.

Significantly enhanced conversion efficiency of high-order harmonic generation by introducing chirped laser pulses into scheme of spatially inhomogeneous field.

An effective scheme to enhance the yield of high-order harmonic generation originated from spatially inhomogeneous field through the interaction between few-cycle chirped laser pulses and a nano-tip structure is demonstrated. The conversion efficiency of harmonics from chirped laser pulses was significantly improved by nearly three more orders of magnitude than that of chirp-free pulses, and the cutoff energy of the corresponding harmonics was dramatically enhanced. By superimposing a series of properly selected orders of harmonics, isolated attosecond pulses of high intensity can be obtained. Furthermore, we compared the effects of different types of chirps on harmonics.

Application of optimized waveforms for enhancing high-harmonic yields in a three-color laser-field synthesizer.

We apply the optimization method suggested by Jin et al. [Nat. Commun.5, 4003 (2014)24873949] to a three-color laser-field synthesizer in a recent experiment by Burger et al. [Opt. Express25(25), 31130 (2017)29245790] for efficient high-order harmonic generation (HHG). With the experimental laser parameters being precisely tuned according to those returned by the genetic optimization, the three-color waveform composed by a 790-nm laser with its second and third harmonic fields, can enhance the macroscopic HHG yields by one to two orders with only 80% pulse energy compared to the fundamental single-color field. We check that this enhancement can be realized for He or Ne gas at both low and high gas pressures. The optimized waveform enables the short-trajectory emissions dominant to facilitate the buildup of the harmonic field, which is revealed by analyzing the behaviors of electron trajectories and the time-frequency pictures of the single-atom and macroscopic HHG. We also optimize the two-color waveform consisting of the fundamental laser and its third harmonic field for the flexible choice in the experiment. This study provides with a practical route to implement the optimization technique in the experiment for the high-flux harmonic generation from the extreme ultraviolet to the X-rays.

Effective high-order harmonic generation from metal sulfide quantum dots.

In the past, common media for high-order harmonic generation (HHG) has been atoms and molecules. More recently, clusters, and nanoparticles have been introduced as HHG emitting media. Multi-particle media can enhance HHG yields but have more stringent requirements in determining the optimal parameters. Here, we demonstrate, for the first time, the effective application of 1-3 nm metal sulfide quantum dots (QDs) for harmonic generation in the 20 - 115 nm extreme ultraviolet range. We report on the syntheses, ablation of Ag2S, CdS, and ZnS QDs, and HHG from laser-produced plasmas by using single- and two-color pumps. We compare HHG efficiency from the ablated QDs to that of bulk metal sulfides and show a seven-fold increase in harmonic yields. Further, the study also allows us to understand the effects of QD-contained plasma spreading dynamics on HHG yield.

Subcycle interference in high-order harmonic generation from solids

Different from the high-order harmonic generation (HHG) from gases, we find that the yield of HHG from solids exhibits unexpected modulations as a function of the driving laser intensity and wavelength. Its mechanism can be unraveled by the interference between currents inside the solids induced by two adjacent Zener tunneling events. Our simulations agree well with the experimental measurements of HHG from ZnSe and solid Ar. We also find that the dephasing time plays a key role in this subcycle interference and can turn it on or off by controlling the overlap between the channels. It provides an avenue to optimize the ultrafast electron dynamics and HHG emission processes in solids, which will be useful for the compact ultrafast EUV light sources. We also propose an experimental scheme by using ultrashort lasers to explore this interference in other solid materials.

High-order harmonic generation from a solid-surface plasma by relativistic-intensity sub-100-fs mid-infrared pulses.

High-order harmonic generation (HHG) in plasmas induced by ultrashort, relativistic-intensity laser pulses on solid surfaces can provide an efficient source of attosecond pulses and opens routes toward new regimes of laser-matter interactions, x-ray generation, laser particle acceleration, and relativistic nonlinear optics. However, field intensities in the range of Irel∼1019 W/cm2 are typically needed to achieve the relativistic regime of HHG in experiments with near-infrared laser pulses. Here, we show that, in the mid-infrared range, due to the λ-2 scaling of Irel with the driver wavelength λ, relativistic HHG can be observed at much lower levels of laser field intensities. High-peak-power 80-fs, 3.9-μm pulses are focused in our experiments on a solid surface to provide field intensities in the range of 1017 W/cm2. Remarkably, this level of field intensities, considered as low by the standards of relativistic optics in the near infrared, is shown to be sufficient for generation of high-order harmonics with signature properties of relativistic HHG-beam directionality, spectra with extended plateaus, and a high HHG yield sustained for both p- and s-polarized driver fields.