High Harmonic Generation 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.

High harmonic generation enhanced by magnetic dipole resonance in an amorphous silicon metasurface.

We report on the enhancement of high harmonic generation (HHG) yield in a metasurface consisting of amorphous silicon disks in a periodic array on an insulator substrate. The structure was designed and optimized using the finite-difference time-domain method for the maximum enhancement, which reaches the factor of 20-times compared to the unstructred surface. The local field is enhanced by a broadband magnetic resonance mode allowing to use ultrashort laser pulses with Fourier transform limit down to 40 fs. Due to the anisotropic structure of the metasurface, both the local-field enhancement and the HHG yield show strong polarization anisotropy.

Probing phonon dynamics with multidimensional high harmonic carrier-envelope-phase spectroscopy

We explore pump-probe high harmonic generation (HHG) from monolayer hexagonal-boron-nitride, where a terahertz pump excites coherent optical phonons that are subsequently probed by an intense infrared pulse that drives HHG. We find, through state-of-the-art ab initio calculations, that the structure of the emission spectrum is attenuated by the presence of coherent phonons and no longer comprises discrete harmonic orders, but rather a continuous emission in the plateau region. The HHG yield strongly oscillates as a function of the pump-probe delay, corresponding to ultrafast changes in the lattice such as specific bond compression or stretching dynamics. We further show that in the regime where the excited phonon period and the pulse duration are of the same order of magnitude, the HHG process becomes sensitive to the carrier-envelope phase (CEP) of the driving field, even though the pulse duration is so long that no such sensitivity is observed in the absence of coherent phonons. The degree of CEP sensitivity versus pump-probe delay is shown to be a highly selective measure for instantaneous structural changes in the lattice, providing an approach for ultrafast multidimensional HHG spectroscopy. Remarkably, the obtained temporal resolution for phonon dynamics is ∼1 femtosecond, which is much shorter than the probe pulse duration because of the inherent subcycle contrast mechanism. Our work paves the way toward routes of probing phonons and ultrafast material structural changes with subcycle temporal resolution and provides a mechanism for controlling the HHG spectrum.

Simulation of High Harmonic Generation in Xenon Based on Time-Dependent Density-Functional Theory

Abstract The high harmonic generation (HHG) in xenon is studied by using the time-dependent density-functional theory for active 4th and 5th atomic shells. The HHG spectra are calculated for different intensities and carrier-envelope phases of a laser pulse. The HHG spectrum shows enhancement at the frequency region near 100 eV, where the HHG yield is by more than an order of magnitude higher than in the single-active electron approximation. The high accuracy of the obtained results is confirmed by comparing the calculated HHG spectra with experimental results.

Control and enhancement of multiband high harmonic generation by synthesized laser fields

High harmonic generation (HHG) spectroscopy has emerged as an invaluable tool for studying electronic dynamics and structure in crystals. The primary challenges are imposed by the multiple degrees of freedom of the underlying dynamics as well as the low efficiency of the HHG process. Here we show that when the HHG process is driven by a synthesized bichromatic field, its efficiency can be significantly enhanced, increasing the photon flux by 1–2 orders of magnitude. The bichromatic field enhances the signal on a microscopic level by manipulating the tunnel ionization and subsequent electron dynamics driven by the synthesized laser waveform. We examine the scaling of the HHG yield on the field parameters, and observe a pronounced dependence on the HHG energy. Importantly, our study reveals that the different spectral regimes are dictated by different generation mechanisms as well as multiple bands in which the dynamics evolve. Our work demonstrates that shaped laser fields serve as a powerful approach to control multiband electron currents in solids, probe their origin, and enhance the efficiency of the HHG process.

High harmonic studies of structural phase transitions in silicon

Investigation of different structural phases and phase transitions of silicon (Si) is important for both fundamental and technological interests. Here, through the first-principles calculations based on the time-dependent density-functional theory, we study high harmonic generation (HHG) driven by linearly polarized laser in four representative phases of Si along the phase transition path from Si-I (cubic diamond structure) to Si-II (body-centered tetragonal β-Sn structure), Si-II to Si-XII (R8) and to Si-III (body-centered cubic structure, BC8). We find that different Si phases exhibit significantly different HHG yield and distinct HHG mechanisms. Combining the advantage of being ultrafast pulse and the capability of retrieving electronic band structures, HHG in the condensed phase can be potentially useful for characterizing crystal structures and phase transition dynamics of Si and other materials.

Time-frequency analysis of high harmonic generation using a probe XUV pulse.

Interpretation of strong-field phenomena is mostly based on the analysis of classical electron trajectories in an intense laser field, whose specific properties determine general features of nonlinear laser-matter interaction. Currently, the visualization of closed electron trajectories contributing to high harmonic generation (HHG) of the laser field is the prerogative of a theoretical analysis based on the time-frequency spectrogram of the induced dipole acceleration. Here, we propose a method for direct reconstruction of the HHG time-frequency spectrogram using a time-delayed probe XUV pulse. Our analytical theory and ab initio numerical simulations demonstrate that the XUV-assisted HHG yield as a function of time delay and harmonic energy mimics the short-time Fourier transform of the dipole acceleration induced by the laser field, thereby providing possible in-situ experimental access for tracing electron dynamics in strong-field phenomena.

Spectral Interference in High Harmonic Generation from Solids

Various interference effects are known to exist in the process of high harmonic generation (HHG) both at the single atom and macroscopic levels. In particular, the quantum path difference between the long and short trajectories of electron excursion causes the HHG yield to experience interference-based temporal and spectral modulations. In solids, due to additional phenomena such as multi-band superposition and crystal symmetry dependency, the HHG mechanism appears to be more complicated than in gaseous atoms in identifying accompanying interference phenomena. Here, we first report experimental data showing intensity-dependent spectral modulation and broadening of high harmonics observed from bulk sapphire. Then, by adopting theoretical simulation, the extraordinary observation is interpreted as a result of the quantum path interference between the long and short electron/hole trajectories. Specifically, the long trajectory undergoes an intensity-dependent redshift, which coherently combines with the short trajectory to exhibit spectral splitting in an anomalous way of inverse proportion to the driving laser intensity. This quantum interference may be extended to higher harmonics with increasing the laser intensity, underpinning the potential for precise control of the phase matching and modulation even in the extreme ultraviolet and soft X-ray regime. Further, this approach may act as a novel tool for probing arbitrary crystals so as to adjust the electron dynamics of higher harmonics for attosecond spectroscopy.

Strain effects on high-order harmonic generation in solids

Laser-induced high harmonic generation (HHG) in solids strongly depends on the band structure of the target. In this work, we studied the band structure of bulk wurtzite ZnO under different strains. The changes of band structure induced by shear, uniaxial, biaxial, and isotropic strains are compared. It is found that the band gap can be narrowed or widen by modulating the external conditions, which offers an efficient way to engineer the wide-gap crystals to produce HHG. The strain effects on HHG are investigated by numerically solving the semiconductor Bloch equations. Our calculations show that the HHG yield depends sensitively on the change of band structure caused by stress- and temperature-induced strains. In addition, we found that the emission times of HHG and the ratio between inter and intraband contributions to the total solid HHG spectra can be controlled by the magnitude of strain imposed on the solid targets.

Pressure dependence of high order harmonic generation in nitrogen molecular gas and atmospheric air

The effect of the variation of the gas pressure on the high harmonic generation (HHG) from nitrogen molecular gas (N2) and atmospheric air with ultrashort intense laser pulses is measured. The optimum pressure in the interaction region of a gas jet for maximizing the HHG yield is determined for both gases. Enhancement of the HHG output and its extension to higher harmonic orders are observed around the optimum pressure value of 0.33 bar. Theoretical calculations based on one-dimensional models explain this effect and provide reasonable agreement with experimental results.

Scaling Law of High Harmonic Generation in the Framework of Photon Channels.

A photon channel perspective on high harmonic generation (HHG) is proposed by quantizing both the driving laser and high harmonics. It is shown that the HHG yield can be expressed as a sum of the contribution of all the photon channels. From this perspective, the contribution of a specific photon channel follows a simple scaling law and the competition between the channels is well interpreted. Our prediction is shown to be in good agreement with the simulations by solving the time-dependent Schrödinger equation. It also can explain well the experimental results of the HHG in the noncollinear two-color field and bicicular laser field.

Optimization and Characterization of High-Harmonic Generation for Probing Solid Density Plasmas

The creation of high energy density plasma states produced during laser–solid interaction on a sub-picosecond timescale opens a way to create astrophysical plasmas in the lab to investigate their properties, such as the frequency-dependent refractive index. Available probes to measure absorption and phase-changes given by the complex refractive index of the plasma state are extreme-UV (EUV) and soft X-ray (XUV) ultra-short pulses from high harmonic generation (HHG). For demanding imaging applications such as single-shot measurements of solid density plasmas, the HHG probe has to be optimized in photon number and characterized in intensity and wavefront stability from shot-to-shot. In an experiment, a coherent EUV source based on HHG driven by a compact diode-pumped laser is optimized in photons per pulse for argon and xenon, and the shot-to-shot intensity stability and wavefront changes are characterized. The experimental results are compared to an analytical model estimating the HHG yield, showing good agreement. The obtained values are compared to available data for solid density plasmas to confirm the feasibility of HHG as a probe.

Classical effect for enhanced high harmonic yield in ultrashort laser pulses with a moderate laser intensity

We study the influence of pulse duration on high harmonic generation (HHG) by exploring a wide laser-parameter region theoretically. Previous studies have shown that for high laser intensities close to saturation ionization intensity, the HHG inversion efficiency is higher for shorter pulses since the ground-state depletion is weaker in short pulses. Our simulations show that this high efficiency also appears for a moderate laser intensity at which the ionization is not very strong. A classical effect relating to shorter travel distances of the rescattering electron in shorter pulses is shown to contribute importantly to this high efficiency. The effect can be amplified significantly if a two-color laser field is used, suggesting a potential approach to increasing the HHG yield and generating short and bright attosecond pulses.

Efficient generation of highly elliptically polarized attosecond pulses

We theoretically demonstrate a scheme to efficiently generate attosecond pulses with high ellipticity by a counter-rotating bicircular field with frequency ratio of 1 : 3 (800 + 267 nm) and 1 : 4 (1600 + 400 nm). It is shown that efficient attosecond pulses with high ellipticity of 0.54 (800 + 267 nm) and 0.79 (1600 + 400nm) can be generated. We also investigate the scaling law of high harmonic generation yield. It is shown that the intensity of the high harmonics can be increased by more than one order of magnitude in the bicircular fields with higher frequency ratios. The high ellipticity and high efficiency of high harmonics are explained by analyzing the symmetry of driving field and the classical electron trajectories.

Ellipticity dependence of high harmonic yield in intense laser field: case of s-valence electron

Having solved numerically the time-dependent Schrödinger equation, we have analysed the dependence of the high harmonic generation yield on the ellipticity of an intense laser field. For the case of a zero angular momentum of an initial state, it has been shown that the ellipticity dependence of the HHG yield is affected by the harmonic number. The numerical results are interpreted in the framework of our recently developed quasi-classical analytical model for HHG. In the quasi-classical approximation, the difference in the ellipticity dependence of the HHG yield for different harmonics is shown to be caused by the interference effects of quantum orbits.

Phase modulation in polarization beating quasi-phase-matching of high-order-harmonic generation

Polarization beating quasi-phase-matching (PB QPM) in high-harmonic generation (HHG) is currently understood as a purely-intensity-modulation quasi-phase-matching (QPM) technique. In PB QPM, the driver ellipticity oscillates during propagation, modulating the HHG conversion efficiency since the single-atom HHG yield decreases rapidly with increasing ellipticity of the driving laser. We show that PB QPM is in fact based on both intensity and phase modulations. Unfortunately, in PB QPM the intensity and phase contributions oppose each other, resulting in significant reduction in the QPM efficiency.

Bright high-repetition-rate source of narrowband extreme-ultraviolet harmonics beyond 22 eV.

Novel table-top sources of extreme-ultraviolet light based on high-harmonic generation yield unique insight into the fundamental properties of molecules, nanomaterials or correlated solids, and enable advanced applications in imaging or metrology. Extending high-harmonic generation to high repetition rates portends great experimental benefits, yet efficient extreme-ultraviolet conversion of correspondingly weak driving pulses is challenging. Here, we demonstrate a highly-efficient source of femtosecond extreme-ultraviolet pulses at 50-kHz repetition rate, utilizing the ultraviolet second-harmonic focused tightly into Kr gas. In this cascaded scheme, a photon flux beyond ≈3 × 1013 s−1 is generated at 22.3 eV, with 5 × 10−5 conversion efficiency that surpasses similar harmonics directly driven by the fundamental by two orders-of-magnitude. The enhancement arises from both wavelength scaling of the atomic dipole and improved spatio-temporal phase matching, confirmed by simulations. Spectral isolation of a single 72-meV-wide harmonic renders this bright, 50-kHz extreme-ultraviolet source a powerful tool for ultrafast photoemission, nanoscale imaging and other applications.

Spin–orbit effects in atomic high-harmonic generation

Spin–orbit interactions lead to small energy gaps between the outermost p1/2 and p3/2 shells of noble gas atoms. Strong-field pulses tunnel-ionize an electron out of either shell resulting in spin–orbit-driven hole motion. These hole dynamics affect the high-harmonic generation (HHG) yield. However, the spectral shape as well as the angular distribution of the HHG emission is not influenced by spin–orbit coupling. We demonstrate the spin–orbit effect on atomic krypton by solving the multi-electron Schrödinger equation with the time-dependent configuration-interaction singles approach. We also provide pulse parameters where this effect can be identified in experiments through an enhancement in the HHG yield as the wavelength of the strong-field pulse increases.

Measuring the angle-dependent photoionization cross section of nitrogen using high-harmonic generation

We exploit the relationship between high harmonic generation (HHG) and the molecular photorecombination dipole to extract the molecular-frame differential photoionization cross section (PICS) in the extreme ultraviolet (XUV) for molecular nitrogen. A shape resonance and a Cooper-type minimum are reflected in the pump-probe time delay measurements of different harmonic orders, where high-order rotational revivals are observed in N${}_{2}$. We observe the energy- and angle-dependent Cooper minimum and shape resonance directly in the laboratory-frame HHG yield by achieving a high degree of alignment, $\ensuremath{\langle}{\mathrm{cos}}^{2}\ensuremath{\theta}\ensuremath{\rangle}\ensuremath{\ge}0.8$. The interplay between PICS and rotational revivals is confirmed by simulations using the quantitative rescattering theory. Our method of extracting molecular-frame structural information points the way to similar measurements in more complex molecules.

High‐harmonic generation with plasmonics: feasible or unphysical?

High-harmonic generation (HHG) provides for efficient and coherent XUV generation for a wide range of spectroscopic applications, enabling attosecond spectroscopy, ultrafast photo-emission spectroscopy, or ultrahigh spatial resolution imaging [1]. Conventionally HHG is based on the use of high power amplified femtosecond laser pulses, special phase matching techniques, or intra-cavity field enhancement. As a compelling alternative, resonant plasmonic field enhancement in metallic nanostructures has been proposed to achieve the necessary peak intensity for HHG. Using nJ pulses from a Ti:S oscillator, XUV generation attributed to plasmon-enhanced HHG was reported in 2008 by the group of Seung-Woo Kim from KAIST in Daejeon, Korea, first in Ar [2] and later