High-order Harmonic Generation Research Articles

Hot electron effect in high-order harmonic generation from graphene driven by elliptically polarized light

We studied high-order harmonic generation (HHG) in graphene driven by either linearly or elliptically polarized mid-infrared (MIR) light, and we additionally applied terahertz (THz) pulses to modulate the electron distribution in graphene. The high-harmonic spectrum obtained using linearly polarized MIR light contains only odd-order harmonics. We found that the intensities of the fifth- and seventh-order harmonics are reduced by the modulation with the THz pulses. In addition, we found that the THz-induced reduction of the seventh-order harmonic driven by elliptically polarized MIR light (at ellipticity ε = 0.3) is larger than that of seventh-order harmonic driven by linearly polarized MIR light (ε = 0). The observed behavior can be reproduced by theoretical calculations that consider different electron temperatures (caused by the THz pulses). Furthermore, the observed stronger suppression of HHG driven by elliptically polarized light reveals the following: in the case of elliptically polarized light, the generation of harmonics via interband transitions to conduction-band states that are closer to the Dirac point is more important than in the case of linearly polarized light. In other words, the quantum pathways via interband transitions to low-energy states are the origin of the enhancement of HHG that can be achieved in graphene by using elliptically polarized light.

Generation of sub-10-fs deep and extreme ultraviolet pulses for time-resolved photoemission spectroscopy.

We present a light source capable of generating sub-10-fs deep UV (DUV) and extreme UV (EUV) pulses for use in time-resolved photoemission spectroscopy. The fundamental output of a Ti:sapphire laser was compressed using the multi-plate method and mixed with the uncompressed second harmonic in a filamentation four-wave mixing process to generate sub-10-fs DUV pulses. Sub-10-fs EUV pulses were generated via high-order harmonic generation driven by the second harmonic pulses that were compressed using Ar gas and chirped mirrors. The minimum cross correlation time between 267 and 57 nm (corresponding to 21.7 eV) was measured to be 10.6 ± 0.4 fs.

Control over the secondary collision of electron in high-order harmonic generation

We investigated the high-order harmonic generation by interacting linearly polarized laser pulses with the atomic target. The temporal evolution of harmonic emission and the underlying mechanisms of rescattering electrons are thoroughly investigated through a combination of quantum analysis and classical trajectory simulations. The manipulation of the carrier-envelope phase (CEP) provides a promising avenue for controlling electron recollisions, revealing a systematic linear relationship between ionization and recombination times across varying CEP values. Moreover, examining phase properties in emitted harmonics during secondary collisions presents intriguing modulations, offering a potential experimental approach to verify the presence of secondary recollisions.

High-Order Harmonics Generation Using Spherical and Non-Spherical Nanoparticles.

The conversion efficiency of 800 nm, 65 fs radiation toward high-order harmonic generation (HHG) in laser-induced plasmas containing spherical and non-spherical nanoparticles (NPs) produced during the laser ablation of different metals in water using 1064 nm, 70 ps pulses was analyzed. Non-spherical NPs of different forms (triangle, cubic, bowtie, rod, rectangular, ellipsoid, etc.) were synthesized during the aging of some spherical NPs (In, Al, and Cu) in water. These NPs were then dried on the glass substrates and ablated to produce plasmas comprising nanostructured species of different morphologies. It was shown that harmonic generation in all synthesized non-spherical NPs was less efficient by a factor of at least five than in the initial spherical NP. Meanwhile, the spherical NPs that maintained the morphology state during aging (Ni, Ag, Mn, and Au) showed almost similar HHG conversion efficiency compared to the fresh spherical NPs. In all cases, the HHG conversion efficiency using spherical and non-spherical nanoparticles was notably larger compared to the atomic and ionic single-particle plasmas of the same elemental composition. NP plasmas demonstrated featureless harmonic distributions, contrary to the indium and manganese atomic/ionic plasmas, when the resonance enhancement of harmonics was observed.

Numerical experiment of phase-matched ion-based high-order harmonic generation in the water-window x-ray spectral region via electromagnetic envelope equation.

We present a phase-matching scheme for efficient high-order harmonic generation in the water-window x-ray spectral region using a 405-nm driving pulse. A high-intensity pulse (∼1016 W/cm2) is used to produce He1+ ions as the target medium, increasing the cutoff photon energy to the water-window x-ray spectral region. By adjusting the driving pulse divergence, the positive dipole phase variation balances the negative plasma dispersion and geometrical phase shift, achieving phase matching. Using the electromagnetic envelope equation coupled with the Keldysh ionization model, numerical experiments identify the optimal conditions. Results show that the relative conversion efficiencies of the 95th harmonic (4.26 nm) and the 169th harmonic (2.4 nm) reach 66% and 79% of the perfect phase-matching conditions, respectively.

Intra- and intercycle analysis of intraband high-order harmonic generation

Intra- and intercycle analysis of intraband high-order harmonic generation

Numerical investigation of high-order harmonic generation by gold nanorod arrays in hybrid nanostructures: effect of number of gold nanorod

Hybrid metal-dielectric nanostructures are highly effective and helpful in generating and enhancing linear and nonlinear optical phenomena due to their unique optical properties. In this study, the linear optical responses and second- and third-order harmonics have been calculated numerically for this structure. Nonlinear optical response efficiency has been studied at the resonance wavelengths of the nanostructure by varying its parameters (radius and length). The desired efficiency can be achieved by adjusting the radius and length of the nanorods and matching the resonance wavelengths with the fundamental and generation frequencies of nonlinear optical phenomena in specific applications. Moreover, the effect of the number of gold nanorods on harmonic generation has been investigated. By increasing the number of nanorods in pairs, it is possible to generate high-order harmonics. The acquired results can be used to improve optical devices such as biomedical equipment, optical integrated circuits, and sensors.

Noninteger high-order harmonic generation from extended correlated systems

Noninteger high-order harmonic generation from extended correlated systems

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.

High-order harmonic generation in a doped semiconductor by inhomogeneous laser field

High-order harmonic generation in a doped semiconductor by inhomogeneous laser field

Generation of near-circularly polarized high-order harmonics in two-color cross-linearly polarized laser fields

We investigate theoretically the ellipticity of the high-order harmonic generation from the molecule by utilizing two-color cross-linearly polarized laser fields. A significant region of the large ellipticity can be achieved by adjusting the crossing angle and the relative phase between the two laser fields. By controlling the short trajectory, we can obtain the smoother harmonic spectrum. The minimum value observed in the plateau region can be attributed to the two-center interference of the molecule. Furthermore, we investigate the contribution of the two-center interference to the ellipticity of HHG. The underlying physical mechanisms of the ellipticity can be demonstrated by the phase difference and amplitude difference of the x and y components of the harmonics. As a result, we synthesized an isolated attosecond pulse with an ellipticity of 0.98.

Parametric model for high-order harmonic generation with quantized fields

Parametric model for high-order harmonic generation with quantized fields

Coulomb-induced emission time shifts in high-order harmonic generation from H2+

Accurate emission times of high-order harmonic generation (HHG) are vital for high-precision ultrafast detection in attosecond science, but a quantitative analysis of Coulomb effects on this time is absent in the molecular HHG. Here, we investigate the Coulomb-induced emission-time shift in HHG of H2+ with two different internuclear distances R, where the times obtained via the Gabor transform of numerical data from solving the time-dependent Schrödinger equation are used as simulation experiment results. Based on the molecular strong-field approximation, we develop a trajectory-resolved classical model that takes into account the molecular two-center structure. By selecting appropriate electron trajectories and including Coulomb interactions, the classical trajectory method can reproduce Gabor emission times well. This consistence reveals that Coulomb tails cause an emission-time shift of ∼35 as at the R = 2.0 a.u. case and of ∼40-60 as at the R = 2.6 a.u. case under the present laser parameters when compared to the Coulomb-free quantum-orbit model. Our results are of significance to probe the attosecond dynamics via two-center interference.

Isolated-attosecond-pulse high-order harmonic generation of keV x rays

Isolated-attosecond-pulse high-order harmonic generation of keV x rays

Orientation-dependent high-order harmonic generation in HCN: Insights from time-dependent density-functional-theory calculations

Orientation-dependent high-order harmonic generation in HCN: Insights from time-dependent density-functional-theory calculations

Effect of molecular alignment and orientation on elliptically polarized high-order harmonic generation

Effect of molecular alignment and orientation on elliptically polarized high-order harmonic generation

Modified saddle-point method applied to high-order above-threshold ionization and high-order harmonic generation: Slater-type versus asymptotic ground-state wave function

Modified saddle-point method applied to high-order above-threshold ionization and high-order harmonic generation: Slater-type versus asymptotic ground-state wave function

Self-healing high-order harmonic generation from curved relativistic plasma mirrors with Bessel-Gaussian beams

Self-healing high-order harmonic generation from curved relativistic plasma mirrors with Bessel-Gaussian beams

Tunable high-order harmonic generation in GeSbTe nano-films

Abstract High-order harmonic generation (HHG) in solids opens new frontiers in ultrafast spectroscopy of carrier and field dynamics in condensed matter, picometer resolution structural lattice characterization and designing compact platforms for attosecond pulse sources. Nanoscale structuring of solid surfaces provides a powerful tool for controlling the spatial characteristics and efficiency of the harmonic emission. Here we study HHG in a prototypical phase-change material Ge2Sb2Te5 (GST). In this material the crystal phase can be reversibly changed between a crystalline and amorphous phase by light or electric current mediated methods. We show that optical phase-switching is fully reversible and allows for dynamic control of harmonic emission. This introduces GST as new addition to materials that enable flexible metasurfaces and photonic structures that can be integrated in devices and allow for ultrafast optical control.

Quantum mechanical modeling of high-intensity laser pulse interaction with hydrogen atom with considering the magnetic field and polarization

In the study of the non-relativistic interaction between high-intensity femtosecond laser pulses and atoms, the influence of the magnetic field is commonly overlooked. This work investigates the effects of the magnetic field in the high-intensity few-cycle laser pulses with non-relativistic intensity of 3.5×1014W/cm2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$3.5 \ imes 10^{14} { }\\;\\;{\ ext{W}}/{\ ext{cm}}^{2}$$\\end{document} at the center wavelength of 800 nm on the high-order harmonic generation (HHG), attosecond pulse train (APT), isolated attosecond pulse (IAP), and the electron trajectory in the hydrogen atom, employing the numerical solution of the time-dependent Schrödinger equation in three dimensions (3D-TDSE). Two polarizations, linear and circular, are considered. A comparison with the scenario where the magnetic field is not considered shows that the magnetic field can apply significant corrections to the results. Particularly, considering the magnetic field for circular polarization can make the cutoff frequency of HHG coincide with the semi-classical relationship of ħωc=Ip+3.17Up\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbar {\\upomega }_{{\ ext{c}}} = {\ ext{I}}_{{\ ext{p}}} + 3.17{\ ext{U}}_{{\ ext{p}}}$$\\end{document}, a case that for circular polarization does not exist without considering the magnetic field. Moreover, accounting for the magnetic field leads to a reduction in the attosecond pulse duration for circular polarization for APT (360as\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$360{\ ext{ as}}$$\\end{document} versus 241as\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$241{\ ext{ as}}$$\\end{document}) and for IAP (834as\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$834{\ ext{ as}}$$\\end{document} versus 602as\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$602{\ ext{ as}}$$\\end{document}). Additionally, the difference in production efficiency of HHG and APT between linear and circular polarization is reduced by two orders of magnitude, when magnetic field is considered. Although considering the magnetic field complicates the electron trajectory, especially for circular polarization, however, our quantum model provides enhanced insight into how the interaction works, especially when and where the electron collides with the parent nucleus. In this case, the quantum mechanical modeling largely covers the huge difference of not considering the magnetic field in the results predicted by other works.