Harmonic Emission Research Articles

Curvature-assisted high harmonic generation in strongly-driven superconductors

The dynamic of the order parameter in superconductors (SCs) under strong driving is inherently nonlinear, but utilization for nonlinear optics and high harmonic generation (HHG) is hindered by the weak coupling of SCs to transverse homogeneous driving fields. When the superconducting coherence length is large enough to allow for curvature modulations without breaking the superconducting phase, the coupling of the order parameter to the driving-field vector potential changes. Here, we show that with the help of full numerical simulations, mesoscopic curvatures or bending of strongly driven type-II SC structures result in highly nonlinear THz superconducting currents, which lead to far-field HHG extending up to the tens harmonics. It is shown that even and odd harmonics can be controllably emitted by a transport current. The driving mechanism is a nonlinear steering of supercurrent by geometric and finite-size effects. At the same time, the SC state remains fully coherent over the whole sample and within the driving time. The phase matching of the emitted harmonics is discussed.

High-order harmonic generation in boron carbide laser-induced plasma: comparison with carbon and boron plasmas, two-color-pumping-induced enhancement, quasi-phase-matching, and tuning of harmonics

The study of the laser-induced molecular plasma produced during the ablation of boron carbide as a medium for high-order harmonic generation is reported. The efficiency of harmonics generation in this laser-induced plasma is compared with the plasma produced on the surfaces of boron and carbon targets at the intensities of heating and driving pulses of 2 × 1010 and 3 × 1014 W/cm2, respectively. The stability of harmonic emission from boron carbide plasma was notably better compared with the boron and carbon plasmas. The influence of laser-induced plasma formation, the role of ablated components, the delay between heating and driving pulses, and the characteristics of converting pulses on the harmonic efficiency and harmonic cut-off in boron carbide plasma are studied.

Evidence of the Quantum Optical Nature of High-Harmonic Generation

High-harmonic generation is a light up-conversion process occurring in a strong laser field, leading to coherent bursts of extreme ultrashort broadband radiation [Lewenstein , Phys. Rev. A , 2117 (1994)]. As a new perspective, we propose that ultrafast strong-field electronic or photonic processes such as high-harmonic generation can potentially generate nonclassical states of light well before the decoherence of the system occurs [Gorlach , Nat. Commun. , 4598 (2020); Stammer ., Phys. Rev. Lett. , 123603 (2022)]. This could address fundamental challenges in quantum technology such as scalability, decoherence, or the generation of massively entangled states [Lewenstein , Luca Argenti Michael Chini, 27 (2024)]. Here, we report experimental evidence of the nonclassical nature of the harmonic emission in several semiconductors excited by a femtosecond infrared laser. By investigating single- and double-beam intensity cross-correlation [Loudon, Rep. Prog. Phys. , 913 (1980)], we measure characteristic nonclassical features in the single-photon statistics. We observe two-mode squeezing in the generated harmonic radiation, which depends on the laser intensity that governs the transition from super-Poissonian to Poissonian photon statistics. The measured violation of the Cauchy-Schwarz inequality realizes a direct test of multipartite entanglement in high-harmonic generation [Wasak, Phys. Rev. A , 033616 (2014)]. This result is supported by the theory of multimodal detection and the Hamiltonian from which the effective squeezing modes of the harmonics can be derived [Gonoskov , Phys. Rev. B , 125110 (2024); Christ New J. Phys. , 033027 (2011)]. With this work, we show experimentally that high-harmonic generation is a new quantum bosonic platform that intrinsically produces nonclassical states of light with unique features such as multipartite broadband entanglement or multimode squeezing. The source operates at room temperature, using standard semiconductors and a standard commercial fiber laser, opening up new routes for the quantum industry, such as optical quantum computing, communication, and imaging. Published by the American Physical Society 2024

Attosecond emission delay from atoms and molecules using multi-dimensional XUV interferometry

Abstract Multi-dimensional interferometry of high harmonic generation is
demonstrated using an inline Gouy interferometer. The rich data sets acquired with this technique, coupled with its inherent stability, enable robust phase analysis to be performed, allowing the delay in harmonic emission from a range of atomic and molecular gases to be measured relative to harmonic emission from argon with single-digit attosecond precision. Delays of −78 ± 6 as, −25 ± 6 as, 30 ± 3 as and 60 ± 3 as relative to emission from argon were measured for Xe, Kr, CO2 and N2, respectively. The scheme can easily be incorporated in other high harmonic experiments, such as tomographic imaging of molecular orbitals, and provides an experimentally simple route towards probing ultrafast dynamics in molecular systems.

Direction Finding Studies of Simultaneous Auroral 2fce and 3fce Roar Cyclotron Harmonic Radio Emissions

AbstractAuroral roar originates in Earth's ionosphere at altitudes of several hundred kilometers where the upper hybrid frequency matches a harmonic of the electron gyrofrequency. These radio emissions are important for remote sensing of ionospheric plasma conditions and processes, and their physics is similar to that of astrophysical radio emissions. In this study, direction finding was used to establish the distribution of direction of arrival (DOA) angles for the third harmonic emissions and to compare the direction angles of second harmonic and events when they occur simultaneously. Data were collected for 42 events from 9 May 2022 to 20 May 2023 by a three antenna array in Toolik Lake, AK (68.6°N, 149.6°W, 68.5° magnetic latitude) with a DOA distribution centered overhead. 30% of the events coming from the south, for which azimuth deviations due to refraction are less significant, were on the same azimuth within 10°, the uncertainty of the measurement. This is a lower bound on the fraction of simultaneous harmonic and emissions that come from the same auroral arc. All events coming from the south that had a and azimuth angle of arrival within 10° had a higher elevation than elevation within experimental uncertainty, supporting the mechanism by which these emissions are excited at the “double resonance” points on the bottomside of the ionosphere.

Proof-of-principle experiment on quasi-phase matching of high-order harmonic generation via the selected-zoning method with a transverse disruptive pulse.

We demonstrate the proof-of-principle experiment on all-optical quasi-phase matching (QPM) of high-order harmonic generation (HHG) via the transverse selective-zoning method. The dephasing length and the out-of-phase region in the interacting medium are identified in advance by applying a tomographic diagnosis of the generation process. Then a transverse disruptive pulse is employed to suppress the harmonic emission in the out-of-phase region to achieve QPM. The final output is enhanced by 35% with just one QPM zone. This proof-of-principle result provides the feasibility of ion-based HHG for higher cut-off energies, where phase matching is difficult to achieve.

Synthesis, nanocrystalline morphology, lattice dynamics and nonlinear optics of mesoporous SiO2&LiNbO3 nanocomposite

We demonstrate a hybrid nanocomposite combining mesoporous silica, pSiO2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {SiO}_2$$\\end{document}, as a host medium and guest lithium niobate LiNbO3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {LiNbO}_3$$\\end{document} nanocrystals embedded into tubular silica nanochannels by calcination of the precursor mixed solution of lithium and niobium salts. High-resolution transmission electron microscopy, X-ray diffraction and Raman scattering techniques reveal trigonal LiNbO3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {LiNbO}_3$$\\end{document} nanocrystals within the pSiO2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {SiO}_2$$\\end{document} nanochannels, indicating their random texture morphology. Annealing at high temperatures ( 950∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{\\circ }$$\\end{document}C) during calcination also leads to partial crystallization of the pSiO2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {SiO}_2$$\\end{document} matrix with the formation of trigonal α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha$$\\end{document}-SiO2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {SiO}_2$$\\end{document} nanocrystals. The Raman microscopy analysis of the pSiO2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {SiO}_2$$\\end{document}:LiNbO3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {LiNbO}_3$$\\end{document} nanocomposite reveals three structural crystalline phases, α-SiO2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha -\\hbox {SiO}_2$$\\end{document}, LiNbO3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {LiNbO}_3$$\\end{document} and a mixed phase which involves the α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha$$\\end{document}-SiO2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {SiO}_2$$\\end{document} phase of host membrane and LiNbO3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {LiNbO}_3$$\\end{document} nanocrystals embedded into the membrane. The finite size of the LiNbO3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {LiNbO}_3$$\\end{document} nanocrystals results in specific features of the LO-TO phonon frequency splitting, which are investigated by Raman microscopy. In the transmission geometry, the second harmonic generation emission exhibits no Maker fringes and is characterized by a broad angular diagram of diffusely scattered light. The second harmonic generation response is independent of the polarization direction of the incident pump light, thus indicating a spatial isotropy of the nonlinear optical conversion in the pSiO2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {SiO}_2$$\\end{document}:LiNbO3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {LiNbO}_3$$\\end{document} composite, consistent with the randomly oriented textural morphology of the deposited LiNbO3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {LiNbO}_3$$\\end{document} nanocrystals. The contribution of the guest LiNbO3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {LiNbO}_3$$\\end{document} nanocrystals to the second harmonic generation effect was found to be strongly dominant compared to the partially crystallized host pSiO2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {SiO}_2$$\\end{document} matrix. The nanocomposite pSiO2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {SiO}_2$$\\end{document}:LiNbO3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {LiNbO}_3$$\\end{document} membrane, set in the 90∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^\\circ$$\\end{document} nonlinear optical geometry, shows unusually high diffusely transmitted second harmonic generation light (back-reflected emission), apparently supported by internal light reflection from the tubular nanochannel network. Despite the fundamental interest, the revealed anomalous back-reflected second harmonic generation emission from pSiO2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {SiO}_2$$\\end{document}:LiNbO3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {LiNbO}_3$$\\end{document} nanocomposite membranes expands the prospects for their photonic and nonlinear optical applications.

Multiorbital effects in high-order harmonic emission from CO2

Multiorbital effects in high-order harmonic emission from CO2

The influence of resonant light pulses on high harmonic generation in solids

Abstract We have theoretically studied the high harmonic generation (HHG) in solids driven simultaneously by a mid-infrared (MIR) laser and a high-order harmonic pulse with energy around the band gap between the valence band and conduction band. By adding this resonant harmonic light pulse with the relative intensity ratio of 4\%, the high-order harmonic emission from the crystal is enhanced by 1-2 orders of magnitude. The yield of HHG in solid increases monotonically with the relative strength of the resonant harmonic pulses. In addition, we also found that HHG dynamics from the $k$ channel around the boundary of the Brillouin zone can be selectively enhanced by adjusting the frequency of the resonant high-order harmonic pulse. The resonance-enhanced HHG and $k$ channel selection effect in solids is also investigated by using the three-band semi-conductor Bloch equation for HHG in ZnO. We also find that the harmonic in the plateau region driven by adding a resonant light field to the strong MIR driving field has less red-shifted compared with the case driven by the MIR driving field alone.

Circularly Polarized High-Harmonic Beams Carrying Self-Torque or Time-Dependent Orbital Angular Momentum.

In the rapidly evolving field of structured light, self-torque has been recently defined as an intrinsic property of light beams carrying time-dependent orbital angular momentum. In particular, extreme-ultraviolet (EUV) beams with self-torque, exhibiting a topological charge that continuously varies on the subfemtosecond time scale, are naturally produced in high-order harmonic generation (HHG) when driven by two time-delayed intense infrared vortex beams with different topological charges. Until now, the polarization state of such EUV beams carrying self-torque has been restricted to linear states due to the drastic reduction in the harmonic up-conversion efficiency with increasing the ellipticity of the driving field. In this work, we theoretically demonstrate how to control the polarization state of EUV beams carrying self-torque, from linear to circular. The extremely high sensitivity of HHG to the properties of the driving beam allows us to propose two different driving schemes to circumvent the current limitations to manipulate the polarization state of EUV beams with self-torque. Our advanced numerical simulations are complemented with the derivation of selection rules of angular momentum conservation, which enable precise tunability over the angular momentum properties of the harmonics with self-torque. The resulting high-order harmonic emission, carrying time-dependent orbital angular momentum with a custom polarization state, can expand the applications of ultrafast light-matter interactions, particularly in areas where dichroic or chiral properties are crucial, such as magnetic materials or chiral molecules.

Enhancing the efficiency of high-order harmonics with two-color non-collinear wave mixing in silica

The emission of high-order harmonics from solids under intense laser-pulse irradiation is revolutionizing our understanding of strong-field solid-light interactions, while simultaneously opening avenues towards novel, all-solid, coherent, short-wavelength table-top sources with tailored emission profiles and nanoscale light-field control. To date, broadband spectra in solids have been generated well into the extreme-ultraviolet (XUV), but the comparatively low conversion efficiency in the XUV range achieved under optimal conditions still lags behind gas-based high-harmonic generation (HHG) sources. Here, we demonstrate that two-color high-order harmonic wave mixing in a fused silica solid is more efficient than solid HHG driven by a single color. This finding has significant implications for compact XUV sources where gas-based HHG is not feasible, as solid XUV wave mixing surpasses solid-HHG in performance. Moreover, our results enable utilizing solid high-order harmonic wave mixing as a probe of structure or material dynamics of the generating solid, which will enable reducing measurement times compared to the less efficient regular solid HHG. The emission intensity scaling that follows perturbative optical wave mixing, combined with the angular separation of the emitted frequencies, makes our approach a decisive step for all-solid coherent XUV sources and for studying light-engineered materials.

Dependence of high-harmonic generation in twisted bilayer graphene on laser pulse ellipticity

The ellipticity of a laser pulse offers a control knob to tune the efficiency and polarization of emitted higher-order harmonics. In this paper, we systematically investigate the ellipticity dependence of high-harmonic generation in various bilayer graphene systems, such as AA-stacked, AB-stacked, and twisted bilayer graphene. We demonstrate how the underlying symmetries and electronic band structures of different bilayer systems distinctly contribute to the characteristics of ellipticity dependence, such as elliptical enhancement and elliptical dichroism. Additionally, we showcase a unique applicability of high-harmonic spectroscopy as a tool for identifying stacking faults in bilayer graphene systems. Our findings offer valuable insights into the nonlinear optical interactions of twisted bilayer graphene with different twist angles. Published by the American Physical Society 2024

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.

Plasmon‐Enhanced Circular Polarization High‐Harmonic Generation from Silicon

AbstractHigh harmonics of circular polarization can be directly generated by monochromatic circularly polarized incident light owing to the high density and stable structure of crystal media. If the arrangement of multiple coplanar atoms in the unit structure of the crystal exhibits rotational symmetry, the polarization state of the high harmonics generated from the crystal follows specific selection rules that have been observed in the 2D crystal medium. In addition, the geometric symmetry of the coplanar atom distribution is related to the orientation of cubic crystals. This implies that only the polarization along a specific crystal orientation can achieve a selection of high‐harmonic polarization states. However, this is a very weak process in cubic crystals owing to the attenuation of crystal anisotropy to circularly polarized light and the dependence of the electron transition rate on the crystal orientation. In this study, plasmonic nanoantennas are designed on silicon crystal films to enhance this process. The harmonic emission is more than ten times brighter than that without nanoantennas and conformed to the selection rules for high harmonics. The research results offer a new approach for deep­ultraviolet space filtering, carrier control, and the development of compact extreme­ultraviolet light sources.

High harmonic Mach–Zehnder interferometer for probing sub-laser-cycle electron dynamics in solids

High harmonic emissions from crystalline solids contain rich information on the dynamics of electrons driven by intense infrared laser fields and have been intensively studied owing to their potential use as a probe of microscopic electronic structures. In particular, the ability to measure the temporal response of high harmonics may allow us to investigate electron dynamics directly. Here, we demonstrate a Mach–Zehnder high harmonic interferometer, where high harmonics are generated in each path of a Mach–Zehnder interferometer and an interferogram of them is captured. The high harmonic interferometer allows us to detect high harmonic signals with higher sensitivity than conventional high harmonic intensity measurements, and achieve a relative time resolution between the target and reference high harmonics of less than 150 attoseconds, which is sufficient to track sub-cycle dynamics of electrons in solids. Using high harmonic interferometry, we succeeded in capturing the real time dynamics of Floquet states in WSe2, whose indirect signature has so far been caught only by time-averaged measurements. Our simple technique could enable to access attosecond electron dynamics in solids.

Inaccuracies and Uncertainties for Harmonic Estimation in Distribution Networks

The proliferation of electronic loads has led to a substantial increase in harmonic emissions within low-voltage distribution networks. The accurate estimation of the expected levels of harmonics in a network is a daunting task for network operators. Stochastic-based harmonic estimation models can offer a comprehensive assessment of the expected levels of harmonics in the presence of existing and future loads, including electric vehicles and smart-grid-enabled devices. Such models offer a valuable tool for network operators to assess the potential impact of harmonics on future networks and to create sustainable design solutions to meet the increasing demand for electricity while achieving net zero targets. However, several variables associated with these estimations models involve a level of uncertainty due to their stochastic nature, leading to inaccuracies in the estimations. This paper aims to provide a more realistic estimate of these uncertainties in order to improve the outcomes of harmonic estimation models for the development of sustainable distribution networks.

An Investigation of the Third Harmonic Power Line Emission in the Topside Ionosphere During the Recent Solar Minimum Period

AbstractPower line harmonic radiation (PLHR) events are radiated by electric power systems on the ground at harmonics of the base power system frequency (50 or 60 Hz, depending on the region). We analyze the global third harmonics PLHR at 150 and 180 Hz using electric field data collected by China Seismo‐Electromagnetic Satellite during the recent solar minimum between January 2019 and December 2022. The average frequency spectrum over industrialized areas shows that the third harmonic has a high occurrence rate in the U.S. region, as well as in western China and northern India, but is very low in the European region. In particular, in the China region and the U.S. region, more than 11,000 and 24,000 dayside and nightside third harmonic PLHR events have been detected from 2019 to 2022, respectively. Compared to the 150 Hz PLHR occurrence rate detected above the China region, the 180 Hz PLHR occurrence rate above the U.S. region is higher, which reveals a significant regional difference. In addition, both at nighttime and daytime, the PLHR electric field intensities at 180 Hz are higher than that at 60 Hz above the U.S. region, which is also different from the result above the China region.

Time‐domain harmonic source location and evaluation methods based on non‐linear and time‐varying properties of devices

AbstractMost of the existing methods for harmonic analysis are from frequency‐domain perspective. In fact, the essential factor for generating harmonics is non‐linear characteristic or time‐varying property. Therefore, the harmonic generation mechanism and the harmonic source location method are investigated from the time domain perspective in this paper. Firstly, a general model of non‐harmonic sources is established. The non‐harmonic sources will match well with the proposed general model while the harmonic source will not. Then correlation coefficient that reflects compliance degree between each device and the general model is defined for distinguishing harmonic sources from non‐harmonic sources. On this basis, a novel time‐domain harmonic source location method is proposed. Numerous simulations and experiments have demonstrated that the proposed method has good performance under fluctuations, saturations, pre‐distortions, transient process, and resonances. The defined correlation coefficient can reflect non‐linearity/time‐varying degree of the harmonic source, which can be used for evaluating harmonic emission level of each harmonic source. On this basis, a simple harmonic responsibility division method is proposed, which is immune to possible fluctuations, pre‐distortions, saturations, resonances, and impedance variation.

Ultrafast Picometer-Resolved Molecular Structure Imaging by Laser-Induced High-Order Harmonics.

Real-time visualization of molecular transformations is a captivating yet challenging frontier of ultrafast optical science and physical chemistry. While ultrafast x-ray and electron diffraction methods can achieve the needed subangstrom spatial resolution, their temporal resolution is still limited to hundreds of femtoseconds, much longer than the few femtoseconds required to probe real-time molecular dynamics. Here, we show that high-order harmonics generated by intense femtosecond lasers can be used to image molecules with few-ten-attosecond temporal resolution and few-picometer spatial resolution. This is achieved by exploiting the sensitive dependence of molecular recombination dipole moment to the geometry of the molecule at the time of harmonic emission. In a proof-of-principle experiment, we have applied this high-harmonic structure imaging (HHSI) method to monitor the structural rearrangement in NH_{3}, ND_{3}, and N_{2} from one to a few femtoseconds after the molecule is ionized by an intense laser. Our findings establish HHSI as an effective approach to resolve molecular dynamics with unprecedented spatiotemporal resolution, which can be extended to trace photochemical reactions in the future.

Femtosecond Laser Ionization Mass Spectrometry for Online Analysis of Human Exhaled Breath.

A variety of organic compounds in human exhaled breath were measured online by mass spectrometry using the fifth (206 nm) and fourth (257 nm) harmonic emissions of a femtosecond ytterbium (Yb) laser as the ionization source. Molecular ions were enhanced significantly by means of resonance-enhanced, two-color, two-photon ionization, which was useful for discrimination of analytes against the background. The limit of detection was 0.15 ppm for acetone in air. The concentration of acetone in exhaled breath was determined for three subjects to average 0.31 ppm, which lies within the range of normal healthy subjects and is appreciably lower than the range for patients with diabetes mellitus. Many other constituents, which could be assigned to acetaldehyde, ethanol, isoprene, phenol, octane, ethyl butanoate, indole, octanol, etc., were observed in the exhaled air. Therefore, the present approach shows potential for use in the online analysis of diabetes mellitus and also for the diagnosis of various diseases, such as COVID-19 and cancers.