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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Breakdown of the single-collision condition for soft x-ray high harmonic generation in noble gases

High harmonic generation (HHG) in atomic gases is generally assumed to originate from photoelectrons that are not perturbed by neighboring particles. In this paper, we study theoretically and experimentally the regime where this approximation breaks down. At high laser intensities, we experimentally find that producing soft x-rays beyond this single-collision condition leads to a strong reduction of the coherent HHG response and appearance of incoherent radiation. We generalize our results to phase-matched HHG with mid-infrared drivers, and determine that a minimum pulse energy is needed to simultaneously phase match the HHG process and keep photoelectrons unperturbed by surrounding particles. Therefore, while previous research showed that HHG efficiency is independent of the driving pulse energy if other experimental parameters are scaled accordingly, we find that this rule no longer applies for high photon energies. Our study thus provides important guidelines for the laser parameters needed for the generation of high flux soft x-ray high harmonics.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

High Harmonic Generation Seeding Echo-Enabled Harmonic Generation toward a Storage Ring-Based Tender and Hard X-ray-Free Electron Laser

To align with the global trend of integrating synchrotron light source (SLS) and free electron laser (FEL) facilities on one site, in line with examples such as SPring-8 and SACLA in Japan and ELETTRA and FERMI in Italy, we actively explore FEL options leveraging the ultralow-emittance electron beam of the NSLS-II upgrade. These options show promising potential for synergy with storage ring (SR) operations, thereby significantly enhancing our facility’s capabilities. Echo-enabled harmonic generation (EEHG) is well-suited to SR-based FELs, and has already been demonstrated with the capability of generating extremely narrow bandwidth as well as high brightness, realized using diffraction-limited short pulses in transverse planes and Fourier transform-limited bandwidth in the soft X-ray spectrum. However, regarding a conventional EEHG scheme, the combination of the shortest seed laser wavelength (256 nm) and highest harmonic (200) sets the short wavelength limit to λ = 1.28 nm. To further extend the short wavelength limit down to the tender and hard X-ray region, a vital option is to shorten the seed laser wavelength. Thanks to recent advances in high harmonic generation (HHG), packing 10 9 photons at one harmonic within a few-femtosecond pulse could turn such a novel HHG source into an ideal seeding for EEHG. Thus, compared to the cascaded EEHG, the HHG seeding option could not only lower the cost, but also free the SR space for accommodating more user beamlines. Moreover, to mitigate the SASE background noise on the sample and detector, we combine the HHG seeding EEHG with the crab cavity short pulse scheme for maximum benefit.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Open-source simulation program for extreme ultraviolet and soft x-ray sources based on high-harmonic generation

Light sources based on high-harmonic generation (HHG) underpin ultrafast spectroscopy experiments across a large range of photon energies, spanning from the extreme ultraviolet to the soft x-ray. To this day, their design, implementation, and improvement presens unique challenges, but can be aided by numerical tools. Here we present a new simulation program designed for this purpose, which takes both macroscopic and microscopic aspects of high-harmonic generation into account and is therefore applicable across the broad range of parameters which HHG based light sources are today utilized. The program is validated by comparison with published experimental results and by calculating harmonic emission in four common experimental configurations.

Femtosecond lasers↗
DOE OSTI2026

Theoretical Study of High Harmonic Generation in Monolayer NbSe 2

High harmonic generation (HHG) is a powerful probe of electron dynamics on attosecond to femtosecond time scales and has been successfully used to detect electronic and structural changes in solid-state quantum materials, including transition-metal dichalcogenides (TMDs). Among TMDs, bulk NbSe 2 exhibits charge density wave (CDW) order below 33 K and becomes superconducting below 7.3 K. Monolayer NbSe 2 also has superconducting and CDW behavior and is therefore interesting as a material whose different structural and electronic properties could be probed via HHG. Here, we predict the HHG response of the pristine 2H and CDW phases of monolayer NbSe 2 using real-time time-dependent density functional theory under the application of a simulated laser pulse excitation. We find that due to the lack of inversion symmetry in both monolayer phases, it is possible to excite even harmonics and that the even harmonics appear as the transverse components of the current response under excitations polarized along the zigzag direction of the monolayer, while odd harmonics arise from the longitudinal current response in all excitation directions. This suggests that the even and odd harmonic responses can be controlled via the polarization of the probing field, opening an avenue for potentially useful applications in optoelectronic devices.

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 OSTI2024

High harmonic generation in graphene quantum dots

Abstract We study theoretically the generation of high harmonics in disk graphene quantum dots placed in linearly polarized short pulse. The quantum dots (QD) are described within an effective model of the Dirac type and the length gauge was used to describe the interaction of quantum dots with an optical pulse. The generated radiation spectra of graphene quantum dots can be controlled by varying the quantum dot size, i.e. its radius. With increasing the quantum dot radius, the intensities of low harmonics mainly decrease, while the cutoff frequency increases. The sensitivity of the cutoff frequency to the QD size increases with the intensity of the pulse.

Physics↗
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 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 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 OSTI2021

Enhanced extreme ultraviolet high-harmonic generation from chromium-doped magnesium oxide

High-order harmonic generation (HHG) from crystals is emerging as a new ultrashort source of coherent extreme ultraviolet (XUV) light. Doping the crystal structure can offer a new way to control the source properties. Here, we present a study of HHG enhancement in the XUV spectral region from an ionic crystal, using dopant-induced vacancy defects, driven by a laser centered at a wavelength of 1.55 μm. Our numerical simulations based on solutions of the semiconductor Bloch equations and density-functional theory are supported by our experimental observations and demonstrate an increase in the XUV high harmonic yield from doped bulk magnesium oxide (MgO) compared to undoped MgO, even at a low defect concentration. The anisotropy of the harmonic emission as a function of the laser polarization shows that the pristine crystal's symmetry is preserved. Our study paves the way toward the control of HHG in solids with complex defects caused by transition-metal doping.

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 OSTI2023

Enabling elliptically polarized high harmonic generation with short cross polarized laser pulses

Abstract Enabling elliptically polarized high-order harmonics overcomes a historical limitation in the generation of this highly nonlinear process in atomic, molecular and optical physics with applications in other branches. Here, we shed new light on a controversy between experimental observations and theoretical predictions on the possibility to generate harmonics with large ellipticity using two bichromatic laser pulses which are linearly polarized in orthogonal directions. Results of numerical calculations confirm the previous experimental data that in short laser pulses even harmonics with large ellipticity can be obtained for the interaction of such cross-polarized laser pulses with atoms initially in a s - or p -state, while odd harmonics have low ellipticity. The amount of the ellipticity can be controlled via the relative carrier-envelope phase of the pulses, their intensity ratio and the duration of the pulses.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2022

Probing topological phase transitions using high-harmonic generation

We report the prediction and realization of topological insulators have sparked great interest in experimental approaches to the classification of materials. The phase transition between non-trivial and trivial topological states is important, not only for basic materials science but also for next-generation technology, such as dissipation-free electronics. It is therefore crucial to develop advanced probes that are suitable for a wide range of samples and environments. Here we demonstrate that circularly polarized laser-field-driven high-harmonic generation is distinctly sensitive to the non-trivial and trivial topological phases in the prototypical three-dimensional topological insulator bismuth selenide. The phase transition is chemically initiated by reducing the spin–orbit interaction strength through the substitution of bismuth with indium atoms. We find strikingly different high-harmonic responses of trivial and non-trivial topological surface states that manifest themselves as a conversion efficiency and elliptical dichroism that depend both on the driving laser ellipticity and the crystal orientation. The origins of the anomalous high-harmonic response are corroborated by calculations using the semiconductor optical Bloch equations with pairs of surface and bulk bands. As a purely optical approach, this method offers sensitivity to the electronic structure of the material, including its nonlinear response, and is compatible with a wide range of samples and sample environments.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Direct reconstruction of isolated XUV or soft x-ray attosecond pulses from high-harmonic generation streaking spectra

Characterization of an isolated attosecond pulse (IAP) in the extreme ultraviolet (XUV) or soft x-ray (SXR) region is essential for its applications. Here we propose to retrieve an IAP in the time domain directly through the modulation of high-harmonic generation (HHG) spectra in the presence of a time-delayed intense few-cycle infrared or mid-infrared laser. The retrieval algorithm is derived based on the strong-field approximation and an extended quantitative rescattering model. We show that both isolated XUV pulses with a narrow spectral bandwidth and isolated SXR pulses with a broad bandwidth can be well characterized through the HHG streaking spectra. Such an all-optical method for characterizing the IAP differs from the commonly used approach based on the streaked photoelectron spectra that would require electron spectrometers. We check the robustness of the retrieval method by changing the dressing laser or by adjusting the steps of time delay. We also show that the XUV pulse can be accurately retrieved by treating the HHG streaking spectra calculated from solving the time-dependent Schrödinger equation for single atoms as the ‘experimental’ data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Necklace-structured high-harmonic generation for low-divergence, soft x-ray harmonic combs with tunable line spacing

The extreme nonlinear optical process of high-harmonic generation (HHG) makes it possible to map the properties of a laser beam onto a radiating electron wave function and, in turn, onto the emitted x-ray light. Bright HHG beams typically emerge from a longitudinal phased distribution of atomic-scale quantum antennae. Here, we form a transverse necklace-shaped phased array of linearly polarized HHG emitters, where orbital angular momentum conservation allows us to tune the line spacing and divergence properties of extreme ultraviolet and soft x-ray high-harmonic combs. The on-axis HHG emission has extremely low divergence, well below that obtained when using Gaussian driving beams, which further decreases with harmonic order. This work provides a new degree of freedom for the design of harmonic combs—particularly in the soft x-ray regime, where very limited options are available. Such harmonic beams can enable more sensitive probes of the fastest correlated charge and spin dynamics in molecules, nanoparticles, and materials.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

High-harmonic generation from artificially stacked 2D crystals

Here, we report a coherent layer-by-layer build-up of high-order harmonic generation (HHG) in artificially stacked transition metal dichalcogenides (TMDC) crystals in their various stacking configurations. In the experiments, millimeter-sized single crystalline monolayers are synthesized using the gold foil-exfoliation method, followed by artificially stacking on a transparent substrate. High-order harmonics up to the 19th order are generated by the interaction with a mid-infrared (MIR) driving laser. We find that the generation is sensitive to both the number of layers and their relative orientation. For AAAA stacking configuration, both odd- and even-orders exhibit a quadratic increase in intensity as a function of the number of layers, which is a signature of constructive interference of high-harmonic emission from successive layers. Particularly, we observe some deviations from this scaling at photon energies above the bandgap, which is explained by self-absorption effects. For AB and ABAB stacking, even-order harmonics remain below the detection level, consistent with the presence of inversion symmetry. Our study confirms our capability of producing nonperturbative high-order harmonics from stacked layered materials subjected to intense MIR fields without damaging samples. Our results have implications for optimizing solid-state HHG sources at the nanoscale and developing high-harmonics as an ultrafast probe of artificially stacked layered materials. Because the HHG process is a strong-field driven process, it has the potential to probe high-momentum and energy states in the bandstructure combined with atomic-scale sensitivity in real space, making it an attractive probe of novel material structures such as the Moiré pattern.

2D materials↗
DOE OSTI2025

Extreme-ultraviolet spatiotemporal vortices via high harmonic generation

Spatiotemporal optical vortices (STOVs) are space–time structured light pulses with a unique topology that couples spatial and temporal domains and carry transverse orbital angular momentum (OAM). Up to now, their generation has been limited to the visible and infrared regions of the spectrum. During the last decade, it was shown that through the process of high-order harmonic generation, it is possible to upconvert spatial optical vortices that carry longitudinal OAM from the near-infrared into the extreme-ultraviolet (EUV), thereby producing vortices with distinct femtosecond and attosecond structure. In this work, we demonstrate theoretically and experimentally the generation of EUV spatiotemporal and spatiospectral vortices using near-infrared STOV driving laser pulses. Here, we use analytical expressions for focused STOVs to perform macroscopic calculations of high-order harmonic generation that are directly compared to the experimental results. As STOV beams are not eigenmodes of propagation, we characterize the highly charged EUV STOVs in both the near and far fields to show that they represent conjugated spatiotemporal and spatiospectral vortex pairs. Our work provides high-frequency light beams topologically coupled at the nanometre/attosecond scales domains with transverse OAM that could be suitable to explore electronic dynamics in magnetic materials, chiral media and nanostructures.

High-harmonic generation↗
DOE OSTI2026

Isostructural electronic transition in MoS 2 probed by solid-state high-harmonic generation spectroscopy

Studying materials under extreme pressure in diamond anvil cells (DACs) is key to discovering emergent states of matter, yet no method currently allows the direct measurement of the electronic structure in this environment. Solid-state high-harmonic generation (sHHG) offers a unique all-optical window into the electronic structure of materials. We demonstrate sHHG spectroscopy inside a DAC by probing 2H-MoS 2 , up to 30 GPa, revealing a pressure-induced crossover of the lowest direct bandgap from the K-point to the Γ-point. This transition manifests as a sharp minimum in harmonic intensity and a 30° rotation of the sHHG polarization anisotropy, despite the absence of a structural phase change. First-principles simulations attribute these features to interference between competing excitation pathways at distinct points in the Brillouin zone. Our results establish sHHG as a sensitive probe of electronic transitions at high pressure, enabling access to quantum phenomena that evade detection by conventional techniques.

Nebgen, Bailey R. [University of California, Berke↗