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DOE OSTI2018

Cascade random-quasi-phase-matched harmonic generation in polycrystalline ZnSe

Here, we experimentally and numerically investigated the cascade random-quasi-phase-matched harmonic generation in polycrystalline zinc selenide with tightly focused mid-infrared nanosecond laser pulses. We observed a sharp transition between two distinct intensity scaling regimes as a function of pump energy from sub I N to super I N , where I is the pump intensity and N is the harmonic order. To gain an understanding of the observations of this complex nonlinear process, we carried out simulations of the coupled three-wave mixing equations with random grain sizes and orientations. We found a grain size dependence of the effective phase-matching condition, suggesting that manipulation of grain size can be an effective pathway to phase-matching optimization. This approach may provide a framework for effectively enhancing high harmonic generation and other wave mixing effects in polycrystalline materials.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2026

A tutorial on high-order harmonic generation in atoms, molecules, and condensed matter

This tutorial introduces strong-field-driven high-order harmonics, their experimental generation and characterization techniques, and their main applications including attosecond pulse generation and ultrafast spectroscopy of the target material. We begin from the use of atomic targets, where the first high-order harmonic generation (HHG) experiments were realized in the late 1980s. Then, we briefly discuss the basics of the microscopic generation mechanism and how various steps of the mechanism were exploited in applications such as generating isolated attosecond pulses and probing molecular orbitals. We introduce and describe the standard experimental approaches for condensed phase HHG, where we discuss unique technical challenges of the use of solid-state materials, such as the mitigation of plasma formation and laser damage. We cover the fundamentals of high-harmonic spectroscopy in condensed matter systems, such as wide bandgap dielectrics, semiconductors, liquid media, and 2D-crystals. We provide some examples of rapidly emerging spectroscopic capabilities, such as for probing crystal symmetries, Berry phases, and associated non-trivial topological properties of the source material. Finally, we provide an overview of the research field, including some of the challenges, opportunities, and open questions.

Attosecond pulses↗

DOE OSTI2015

Use of extended laser plasma for generation of high-order harmonics of picosecond duration

We report the results of experimental investigations on the generation of picosecond radiation harmonics in extended laser plasma produced on the surface of different metal targets. The effect of plasma length, heating pulse duration and delay between the heating and transformable pulses on the efficiency of conversion to higher harmonics is studied. The λ = 1064 nm radiation conversion to a short-wavelength (down to 50 nm, 21st harmonic) range in extended plasma of several metals is demonstrated. (interaction of laser radiation with matter. laser plasma)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

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. (extreme laser radiation: physics and fundamental applications)

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2016

X-ray spectral diagnostics of laser harmonic generation in the interaction of relativistic femtosecond laser pulses with clusters

It is shown that the production of X-ray emission spectra in the interaction of high-intensity laser radiation with cluster targets may be affected by the bichromatic oscillating electric field arising from the generation of the second harmonic of laser radiation. A technique is proposed for diagnosing harmonic generation in laser – cluster interactions using the spectral line profiles of multiply charged helium ions. The efficiency of second harmonic generation at a laser intensity of 3 × 10{sup 18} W cm{sup -2} is shown to amount to about 2%. (extreme laser radiation: physics and fundamental applications)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2018

Passive harmonic mode-locking in an erbium-doped fibre laser

We report an all-fibre erbium laser operating in the regime of passive harmonic mode-locking based on the effect of nonlinear polarisation rotation. The generation of the 67th harmonic with a pulse repetition rate of 5.62 GHz and a duration of 1.8 ps is demonstrated. It is shown that as the harmonic number increases, both the frequency modulation parameters and the pulse duration change. (paper)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Limiting the number of quantisation levels of a harmonic lens as a method for improving the quality of the generated image

The characteristics (modulation transfer functions) of harmonic lenses made by direct laser patterning of resist are experimentally studied. The influence of technological errors in the manufacture of lenses on the formation of the point spread function is modelled for harmonic lenses with 32 and 256 quantisation levels. Direct laser writing is used to produce lenses with these numbers of levels. It is experimentally shown that the modulation transfer function of the harmonic lens with 32 quantisation levels is significantly greater at high spatial frequencies (50 mm{sup −1}). (paper)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2013

Dark-matter harmonics beyond annual modulation

The count rate at dark-matter direct-detection experiments should modulate annually due to the motion of the Earth around the Sun. We show that higher-frequency modulations, including daily modulation, are also present and in some cases are nearly as strong as the annual modulation. These higher-order modes are particularly relevant if (i) the dark matter is light, O(10) GeV, (ii) the scattering is inelastic, or (iii) velocity substructure is present; for these cases, the higher-frequency modes are potentially observable at current and ton-scale detectors. We derive simple expressions for the harmonic modes as functions of the astrophysical and geophysical parameters describing the Earth's orbit, using an updated expression for the Earth's velocity that corrects a common error in the literature. For an isotropic halo velocity distribution, certain ratios of the modes are approximately constant as a function of nuclear recoil energy. Anisotropic distributions can also leave observable features in the harmonic spectrum. Consequently, the higher-order harmonic modes are a powerful tool for identifying a potential signal from interactions with the Galactic dark-matter halo.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Algebraic discrete quantum harmonic oscillator with dynamic resolution scaling

We develop an algebraic formulation for the discrete quantum harmonic oscillator (DQHO) from the Hamiltonian for two, coupled QHOs and provide a physical picture for the Kravchuk function eigenstates of the oscillator. The familiar $\mathfrak{su}(2)$ structure of the coupled QHO Hamiltonian divides its spectrum into sets corresponding to the DQHO at different resolutions. In addition to energy ladder operators, the formulation allows for the introduction of resolution ladder operators connecting all DQHOs with different resolutions, thus enabling the dynamic scaling of the resolution of finite degree-of-freedom quantum simulations. The coherent state of the DQHO is constructed, and its expected position is proven to oscillate as a classical harmonic oscillator. The DQHO coherent state recovers that of the quantum harmonic oscillator at large resolution.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

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

Abstract 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.

47 OTHER INSTRUMENTATION↗

DOE OSTI2025

High harmonic generation in Haldane model quantum dots

We study theoretically the nonlinear electron dynamics of Haldane model quantum dots placed in the field of an ultrashort optical pulse. One of the tuning parameters of the Haldane model is the phase accumulated by an electron during its transfer between the next nearest neighbor sites. We study how this parameter affect the nonlinear electron dynamics and the generation of high optical harmonics. With increasing the phase from its zero value to 90°, the low-energy electron states in the conduction and valence bands become more localized near the edges of the quantum dot resulting in suppression of the band gap, enhancement of the dipole inter-band coupling, and strong suppression of the average low-energy electron density of the states. As a result, the nonlinear response of the electron system of a Haldane model quantum dot is the strongest at intermediate values of the phase, ≈ 30− 40°. At these values of the phase, the electron dynamics is irreversible and a few first high-order harmonics have the largest intensities. Here, when the phase approaches 90° value the generation of high harmonics is strongly suppressed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Time-dependent density-functional theory of high-order harmonic generation from noble-gas atoms driven by orthogonally polarized two-color laser fields

An orthogonally polarized two-color (OTC) field of frequency ratio 1 : 2 is known to generate both odd and even harmonic spectra in the mutually orthogonal directions of the fundamental and the second-harmonic fields, respectively. Recollision angles of an ionized electron driven back to its parent ion by an OTC field are inferred from the intensity ratio of odd and even harmonics, where the relative phase delays between the two-color fields can be used in time-resolved measurements on a subcycle time scale. Here, we present the ab initio, many-electron calculation of time-resolved recollision angles of noble-gas atoms driven by an OTC field, based on the time-dependent density-functional theory. Our results agree well with experimental data by Shafir et al. in Nat. Phys. 5, 412 (2009) of helium atom and New J. Phys. 12, 073032 (2010) of neon atom.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2019

Conditions for perfect circular polarization of high-order harmonics driven by bichromatic counter-rotating laser fields

Recently, studies of high-order harmonic generation (HHG) from atoms driven by bichromatic counter- rotating circularly polarized laser fields have received considerable attention for this process could be a potential source of coherent circularly polarized extreme ultraviolet (XUV) and soft-x-ray beams in a tabletop-scale setup. In this paper, we address the problem with molecular targets and perform a detailed quantum study of the H 2 + molecule in bichromatic (ω 0 , 2ω 0 ) counter-rotating circular polarized laser fields where we adopt wavelengths (790 and 395 nm) and intensities (2×10 14 W/cm2) reported in a recent experiment [K. M. Dorney et al., Phys. Rev. Lett. 119, 063201 (2017)]. Here, we demonstrate appropriate conditions to produce perfectly circular polarized harmonics. The calculated radiation spectrum contains doublets of left and right circularly polarized harmonics which display perfect circular polarization with use of the trapezoidal pulse shape, and substantial deviations from perfect circular polarization with use of the sine-squared pulse shape. We also study in detail short- and long-cycle counter-rotating circularly polarized driving pulses with a time delay between the two driving fields, ω 0 and 2ω 0 . These time delayed circularly polarized driving pulses are applied to H atoms and H 2 + molecules, and in both atomic and molecular cases we conclude a zero time delay corresponds to the highest HHG intensity for short pulses. Finally, for longer pulses there are no distinct differences in HHG intensities between the zero and nonzero time delays if the latter are within a few optical cycles of the fundamental frequency.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2021

Analytical WKB theory for high-harmonic generation and its application to massive Dirac electrons

Here we propose an analytical approach to high-harmonic generation (HHG) for nonperturbative low-frequency and high-intensity fields based on the (Jeffreys-)Wentzel-Kramers-Brillouin (WKB) approximation. By properly taking into account Stokes phenomena of WKB solutions, we obtain wave functions that systematically include the repetitive dynamics of production and acceleration of electron-hole pairs and quantum interference due to phase accumulation between different pair production times (Stückelberg phase). Using the obtained wave functions without relying on any phenomenological assumptions, we explicitly compute electric current (including intra- and interband contributions) as the source of HHG for a massive Dirac system in (1+1) dimensions under an ac electric field. We demonstrate that the WKB approximation agrees well with numerical results obtained by solving the time-dependent Schrödinger equation and point out that the quantum interference is important in HHG. We also predict in the deep nonperturbative regime that (1) harmonic intensities oscillate with respect to electric-field amplitude E 0 and frequency Ω with a period determined by the Stückelberg phase, (2) the cutoff order of HHG is determined by 2eE 0 ℏΩ 2 , with e being the electron charge, and that (3) noninteger harmonics, controlled by the Stückelberg phase, appear as a transient effect. Our WKB theory is particularly suited for a parameter regime, where the Keldysh parameter γ = (Δ/2)Ω/eE 0 ,with Δ being the gap size, is small. This parameter regime corresponds to intense lasers in the terahertz regime for realistic massive Dirac materials. Our analysis implies that the so-called HHG plateau can be observed at the terahertz frequency within the current technology.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Ultrafast electron dynamics of graphene quantum dots: High harmonic generation

We study theoretically nonlinear optical properties of graphene quantum dots placed in a field of a short and strong linearly polarized optical pulse. We address the problem of high harmonic generation in quantum dots and how such nonlinear effect is affected by dephasing processes in a quantum dot. The dephasing makes the ultrafast electron dynamics more irreversible with a large residual population of the excited quantum dot levels. In relation to the high-harmonic spectrum, with increasing the dephasing time, the intensities of the low-frequency harmonics increase while the cutoff energy decreases. The dependence of the cutoff energy on the amplitude of the optical pulse is also sensitive to the frequency of the pulse. When the frequency of the optical pulse is much less than the quantum dot band gap, this dependence is almost linear, but when the frequency of the pulse is comparable to the band gap, the cutoff energy shows saturation behavior at large field amplitude, >0.4 V/Å.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Signatures of Multiband Effects in High-Harmonic Generation in Monolayer MoS 2

High-harmonic generation (HHG) in solids has been touted as a way to probe ultrafast dynamics and crystal symmetries in condensed matter systems. Here, we investigate the polarization properties of high-order harmonics generated in monolayer MoS 2 , as a function of crystal orientation relative to the mid-infrared laser field polarization. At several different laser wavelengths we experimentally observe a prominent angular shift of the parallel-polarized odd harmonics for energies above approximately 3.5 eV, and our calculations indicate that this shift originates in subtle differences in the recombination dipole strengths involving multiple conduction bands. Further, this observation is material specific and is in addition to the angular dependence imposed by the dynamical symmetry properties of the crystal interacting with the laser field, and may pave the way for probing the vectorial character of multiband recombination dipoles.

2-dimensional systems↗

DOE OSTI2020

Discrete spherical harmonic functions for texture representation and analysis

A basis of discrete harmonic functions for efficient representation and analysis of crystallographic texture is presented. Discrete harmonics are a numerical representation of the harmonics on the sphere. A finite element formulation is utilized to calculate these orthonormal basis functions, which provides several advantageous features for quantitative texture analysis. These include high-precision numerical integration, a simple implementation of the non-negativity constraint and computational efficiency. Simple examples of pole figure and texture interpolation and of Fourier filtering using these basis sets are presented.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Modeling and Harmonic Stability of MMC-HVDC With Passive Circulating Current Filters

A modular multilevel converter (MMC) is an emerging converter technology widely used in wind power applications using high-voltage direct current (HVDC) transmission, and it has been largely investigated in medium-voltage solar harvesting as well as electric motor drives. Different from studies dealing with active circulating current control loops, this paper focuses on impedance modeling and harmonic stability studies for MMCs with passive circulating current filters (PCCFs). A power stage circuit including a PCCF is transformed and remodeled to obtain small-signal formulations. This transformation leads to additional high-order matrix computing complexity due to the added impedance subnetwork matrix from the PCCF as well as relevant crossed-frequency impacts. To simplify the computational burden, the proposed model aims to solve one arm equation instead of all six MMC arm equations. To achieve this result, additional challenges occur when the MMC is connected to a renewable energy source instead of the grid voltage, where low-level zero-sequence components might exist in the neutral point of three phases, especially in the case of no integrated advanced modular voltage balancing control, which prevents computational simplification. To overcome this challenge, further impedance matrix adjustments are conducted in this paper to theoretically suppress the impact of zero-sequence harmonics when obtaining small-signal impedance, taking into account the frequency coupling effect. Finally, simulations are carried out to validate the developed impedance model under different operating scenarios. Harmonic stability case studies of MMCs with PCCFs connected to renewable energy current sources are also presented, where frequency-domain stability analyses based on Bode diagrams are compared to time-domain simulation waveforms and FFTs, which validate the effectiveness of the proposed impedance model.

24 POWER TRANSMISSION AND DISTRIBUTION↗