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DOE OSTI2024

Laser pulse induced second- and third-harmonic generation of gold nanorods with real-time time-dependent density functional tight binding (RT-TDDFTB) method

In this paper, we investigate second- and third-harmonic generation processes in Au nanorod systems using the real-time time-dependent density functional tight binding method. Our study focuses on the computation of nonlinear signals based on the time dependent dipole response induced by linearly polarized laser pulses interacting with nanoparticles. We systematically explore the influence of various laser parameters, including pump intensity, duration, frequency, and polarization directions, on harmonic generation. We demonstrate all the results using Au nanorod dimer systems arranged in end-to-end configurations, and disrupting the spatial symmetry of regular single nanorod systems is crucial for second-harmonic generation processes. Furthermore, we study the impact of nanorod lengths, which lead to variable plasmon energies, on harmonic generation, and estimates of polarizabilities and hyper-polarizabilities are provided.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2024

Ultrafast high-harmonic spectroscopy of solids

High-harmonic spectroscopy, an ultrafast all-optical technique initially conceptualized in atomic and molecular systems, has now emerged as a powerful platform for studying the structure and dynamics of condensed matter. Unlike that in the gas phase, solid-state high-harmonic generation relies on the fundamental response from high atomic density and periodicity, leading to interband transitions and coherent driving of electrons and holes in their respective bands. These mechanisms make high-harmonic spectroscopy particularly sensitive to the electronic band structure, topological properties and many-body correlations in condensed media. An advantage of high-harmonic spectroscopy over other spectroscopic methods is its ability to probe ultrafast phenomena, capturing femto- to attosecond dynamics of multi-band and strongly correlated electron interactions in solids. Furthermore, in this Review, we discuss the latest experimental and theoretical advances in ultrafast high-harmonic spectroscopy of solids and provide perspectives for future research in this field.

High-harmonic generation↗

DOE OSTI2026

Efficiency-optimized relativistic plasma harmonics for extreme fields

Bright harmonic radiation from relativistically oscillating laser plasmas offers a direct route for generating extreme electromagnetic fields. Theory predicts that under optimized conditions, the plasma medium can support strong spatiotemporal compression of laser energy in a coherent harmonic focus (CHF), delivering intensity boosts many orders of magnitude greater than the incident driving laser pulse. Although diffraction-limited performance (spatial compression) and attosecond phase locking (temporal compression) have been demonstrated experimentally, efficient coupling of relativistically intense laser pulse energy into the emitted harmonic cone has not been realized so far. Here we demonstrate that this highly nonlinear interaction can be tailored to deliver the maximum conversion efficiencies predicted from simulations. By fine-tuning the temporal profile of the driving laser on sub-picosecond (<10 −12 s) timescales, energies >9 mJ between the 12th and 47th harmonics are observed. These results are in agreement with the theoretically expected efficiency dependence on harmonic order, verifying that optimal conditions have been achieved in the generation process. This is the important final element required to achieve the expected intensity boosts from a CHF in experiments. Although obtaining spatiotemporal compression and optimal efficiency simultaneously remains challenging, the path to realizing extreme optical field strengths approaching the critical field of quantum electrodynamics (the Schwinger limit at >10 16 V cm −1 or >10 29 W cm −2 ) is now open, permitting all-optical studies of the quantum vacuum and new frontiers for intense attosecond science.

High-harmonic generation↗

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 OSTI2024

Wideband Impedance Passivation of MMCs for Suppressing Harmonic Oscillations

Harmonic instability and associated oscillation events have become one of the main concerns in MMC-based HVdc systems. These oscillations can appear in the range from a few hundred hertz to several kilohertz, and the root cause is identified as delay-induced negative damping of MMC impedance appearing at the system resonance frequency. Here, this paper introduces a wideband impedance reshaping method through MMC control to eliminate such negative damping for both grid-following (GFL) and grid-forming (GFM) MMCs, which makes the MMC impedance completely passive from the second harmonic frequency upward, thus preventing all harmonic oscillations. First, simplified impedance models of MMCs are derived for the harmonic stability analysis and the impedance reshaping control design. Next, a passivity-based impedance reshaping method is presented, as well as practical considerations for its implementation. In addition, to maintain the MMC's disturbance ride-through capability, an adaptive activation scheme is developed, which enables the wideband impedance reshaping control only in the presence of harmonic oscillation events. The effectiveness of the proposed method is validated by frequency domain analysis and by electromagnetic transient (EMT) simulations of two typical MMC-based power systems.

17 WIND ENERGY↗

DOE OSTI2024

Lightwave-electronic harmonic frequency mixing

Electronic frequency mixers are fundamental building blocks of electronic systems. Harmonic frequency mixing in particular enables broadband electromagnetic signal analysis across octaves of spectrum using a single local oscillator. However, conventional harmonic frequency mixers do not operate beyond hundreds of gigahertz to a few terahertz. If extended to the petahertz scale in a compact and scalable form, harmonic mixers would enable field-resolved optical signal analysis spanning octaves of spectra in a monolithic device without the need for frequency conversion using nonlinear crystals. Here, we demonstrate lightwave-electronic harmonic frequency mixing beyond 0.350 PHz using plasmonic nanoantennas. We demonstrate that the mixing process enables complete, field-resolved detection of spectral content far outside that of the local oscillator, greatly extending the range of detectable frequencies compared to conventional heterodyning techniques. Our work has important implications for applications where optical signals of interest exhibit coherent femtosecond-scale dynamics spanning multiple harmonics.

Science & Technology - Other Topics↗

NASA NTRS1982

A problem in representing the core magnetic field of the earth using spherical harmonics

Although there are computational advantages to the representation of the earth's magnetic field by spherical harmonic coefficients of the magnetic potential, up to the thirteenth degree and order, the following disadvantages emerge: (1) the use of spherical harmonics of up to a certain degree does not remove wavelengths greater than a certain value from the surface fields, and (2) the total field magnitudes represented by spherical harmonics up to a certain degree have minimum wavelengths equal to the circumference of the earth divided by twice the maximum degree of the harmonic used. The implications of the ways in which surface fields are separated into core and crustal components are discussed, and it is concluded that since field signals are generated in the core, the representation of the core field by spherical harmonics of potential does not adequately represent all core field components.

Carle, H. M.↗

NASA NTRS1984

Fundamental and harmonic emission in interplanetary type 2 radio bursts

Three interplanetary type II radio bursts which show two prominent and long duration bands in their dynamic spectra were analyzed in detail and compared to similar bands in meter wavelength type II events. These bands, which differ by a factor of about two in frequency, were interpreted in terms of fundamental and harmonic emission. The fundamental component has a greater average intensity than the harmonic, due largely to short intense brightenings. The fundamental spectral profile is more narrow than that of the harmonic, with harmonic band typically exhibiting a larger bandwidth to frequency ratio than the fundamental by a factor of two. The fundamental has a larger source size than the harmonic, 160 degrees versus 110 degrees, on average, as viewed from the Sun. Two of the events have source positions which correlate well with the associated flare positions.

Lengyel-Frey, D.↗

NASA NTRS1985

Fundamental and harmonic emission in interplanetary type II radio bursts

Three interplanetary type II radio bursts which show two prominent and long duration bands in their dynamic spectra were analyzed in detail and compared to similar bands in meter wavelength type II events. These bands, which differ by a factor of about two in frequency, were interpreted in terms of fundamental and harmonic emission. The fundamental component has a greater average intensity than the harmonic, due largely to short intense brightenings. The fundamental spectral profile is more narrow than that of the harmonic, with harmonic band typically exhibiting a larger bandwidth to frequency ratio than the fundamental by a factor of two. The fundamental has a larger source size than the harmonic, 160 degrees versus 110 degrees, on average, as viewed from the sun. Two of the events have source positions which correlate well with the associated flare positions.

Lengyel-Frey, D.↗

NASA NTRS2007

The Local Stellar Velocity Field via Vector Spherical Harmonics

We analyze the local field of stellar tangential velocities for a sample of 42,339 nonbinary Hipparcos stars with accurate parallaxes, using a vector spherical harmonic formalism.We derive simple relations between the parameters of the classical linear model (Ogorodnikov-Milne) of the local systemic field and low-degree terms of the general vector harmonic decomposition. Taking advantage of these relationships, we determine the solar velocity with respect to the local stars of (V(sub X), V(sub Y), V(sub Z)) = (10.5, 18.5, 7.3) +/- 0.1 km s(exp -1) not for the asymmetric drift with respect to the local standard of rest. If only stars more distant than 100 pc are considered, the peculiar solar motion is (V(sub X), V(sub Y), V(sub Z)) = (9.9, 15.6, 6.9) +/- 0.2 km s(exp -1). The adverse effects of harmonic leakage, which occurs between the reflex solar motion represented by the three electric vector harmonics in the velocity space and higher degree harmonics in the proper-motion space, are eliminated in our analysis by direct subtraction of the reflex solar velocity in its tangential components for each star...

kinematics↗

NASA NTRS2014

Driving an Active Vibration Balancer to Minimize Vibrations at the Fundamental and Harmonic Frequencies

Vibrations of a principal machine are reduced at the fundamental and harmonic frequencies by driving the drive motor of an active balancer with balancing signals at the fundamental and selected harmonics. Vibrations are sensed to provide a signal representing the mechanical vibrations. A balancing signal generator for the fundamental and for each selected harmonic processes the sensed vibration signal with adaptive filter algorithms of adaptive filters for each frequency to generate a balancing signal for each frequency. Reference inputs for each frequency are applied to the adaptive filter algorithms of each balancing signal generator at the frequency assigned to the generator. The harmonic balancing signals for all of the frequencies are summed and applied to drive the drive motor. The harmonic balancing signals drive the drive motor with a drive voltage component in opposition to the vibration at each frequency.

Holliday, Ezekiel S.↗

NASA NTRS2018

Contributions of Spherical Harmonics to Gravitational Moment

A scalar gravitational potential function expressed as a series of spherical harmonics frequently serves as the basis for a model of an astronomical body's gravitational field. The contribution of a generic spherical harmonic to gravitational gradient is expressed as a dyadic, which is then used to obtain an analytical expression in vector-dyadic form for the contribution to the moment of gravitational forces about the mass center of a small body such as a spacecraft. The expression developed for a harmonic's contribution to gravitational gradient can be applied in areas beyond the scope of the paper; for example, gravitational gradient plays an important role in the state propagation matrix and the state transition matrix that are used in spacecraft trajectory targeting and Kalman filtering. Additionally, it can be employed in numerical simulations of orbit determination based on measurements obtained with a gradiometer in low-Earth orbit. Contributions of spherical harmonics to gravitational moment may be of interest in connection with attitude control of a spacecraft in the vicinity of a body with an irregular shape, such as an asteroid. Normalized spherical harmonic coefficients up to degree and order 10 are obtained for the asteroid 216 Kleopatra and used in numerical evaluations of contributions to gravitational moment.

Roithmayr, Carlos M.↗

NASA NTRS2021

GRACE Fast Mascons from Spherical Harmonics and a Regularization Design Trade Study

Mass concentration (mascon) solutions have become a prominent medium for investigating time-variable gravity recovered by GRACE and GRACE Follow-On. While GRACE Level-2 spherical harmonic products require various post-processing techniques to eliminate correlated noise, mascon formulations employ spatial regularization strategies during the estimation step to improve signal recovery. However, mascon estimation has traditionally required large computing resources and GRACE Level-1B processing capabilities. In this study, we show that a typical mascon estimation system can be reformulated to allow for the estimation of regularized mascons from Level-2 spherical harmonics. Provided that spherical harmonic solution covariances are available, the computed mascons will be mathematically equivalent to similar mascons estimated from Level-1B observations. This method is computationally efficient, better leverages GRACE spherical harmonics than past methods, and matches the performance of typical mascon solutions without locking scientists into pre-determined regularization designs. We develop a proof-of-concept solution using ITSG-Grace2018 and compare results with traditional mascons from JPL and NASA GSFC. We then assess the effects of spherical harmonic truncation and use of regularization correlations on basin signal recovery. We find that spherical expansions to degree and order 60 provide the minimum expansion necessary to study most basins, while larger expansions help further localize signals. We also find that diagonal regularizations (i.e., regularizations that do not contain inter-mascon correlations) are adversely affected by leakage, especially across boundaries such as coastlines where signals are not highly correlated, whereas including inter-mascon correlations and regional boundaries in the regularization greatly improves signal recovery.

M. J. Croteau↗

NASA NTRS1995

Simulation of 100-300 GHz solid-state harmonic sources

Accurate and efficient simulations of the large-signal time-dependent characteristics of second-harmonic Transferred Electron Oscillators (TEO's) and Heterostructure Barrier Varactor (HBV) frequency triplers have been obtained. This is accomplished by using a novel and efficient harmonic-balance circuit analysis technique which facilitates the integration of physics-based hydrodynamic device simulators. The integrated hydrodynamic device/harmonic-balance circuit simulators allow TEO and HBV circuits to be co-designed from both a device and a circuit point of view. Comparisons have been made with published experimental data for both TEO's and HBV's. For TEO's, excellent correlation has been obtained at 140 GHz and 188 GHz in second-harmonic operation. Excellent correlation has also been obtained for HBV frequency triplers operating near 200 GHz. For HBV's, both a lumped quasi-static equivalent circuit model and the hydrodynamic device simulator have been linked to the harmonic-balance circuit simulator. This comparison illustrates the importance of representing active devices with physics-based numerical device models rather than analytical device models.

NONLINEAR CIRCUITS↗

DOE OSTI2024

Harmonic and Subharmonic RF Injection Locking of THz Metasurface Quantum-Cascade VECSEL

Harmonic and subharmonic RF injection locking is demonstrated in a terahertz (THz) quantum-cascade vertical-external-cavity surface-emitting laser (QC-VECSEL). By tuning the RF injection frequency around integer multiples and submultiples of the cavity round-trip frequency, different harmonic and subharmonic orders can be excited in the same device. Modulation-dependent behavior of the device has been studied with recorded lasing spectral broadening and locking bandwidths in each case. In particular, harmonic injection locking results in the observation of harmonic spectra with bandwidths over 200 GHz. A semiclassical Maxwell-density matrix formalism has been applied to interpret QC-VECSEL dynamics, which aligns well with experimental observations.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2024

Reconstruction of magnetic island electron temperature in mixed second and third harmonic electron cyclotron emission conditions

Here we develop a method to use the mixed third and second harmonic electron cyclotron emission (ECE) signal in the DIII-D tokamak to reconstruct the electron temperature profile of a rotating magnetic island. The third harmonic ECE is removed by extracting the rotating-island-associated fluctuations in the mixed signal, and the extracted fluctuation is combined with the equilibrium temperature obtained from other diagnostics after correcting for the third harmonic reabsorption. The accuracy of the reconstruction is studied by considering a DIII-D shot where an unmixed signal from an island is available on the low field side of the plasma and a mixed signal from the same island is available from the high field side. It is found that the reconstruction method successfully reproduces the island shape and temperature perturbation magnitude without the distortion caused by third harmonic ECE mixing. However, the radial location of the reconstructed island is somewhat displaced relative to the location of the q = 2 surface in the axisymmetric equilibrium reconstruction, resulting in a corresponding inaccuracy in the absolute temperature of the island. It is conjectured that this may arise from an inaccuracy of the reconstructed axisymmetric equilibrium in this region.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

First measurement of symmetric cumulants of hexagonal flow harmonics in Pb-Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV

Correlations between event-by-event fluctuations of anisotropic flow harmonics are measured in Pb-Pb collisions at a center-of-mass energy per nucleon pair of 5.02 TeV, as recorded by the ALICE detector at the LHC. This study presents correlations up to the hexagonal flow harmonic 𝑣 6 , which was measured for the first time. The magnitudes of these higher-order correlations are found to vary as a function of collision centrality and harmonic order. These measurements are compared to viscous hydrodynamic model calculations with EKRT initial conditions and to the iEBE-VISHNU model with T R ⁢ENTo initial conditions. The observed discrepancies between the data and the model calculations vary depending on the harmonic combinations. Due to the sensitivity of model parameters estimated with Bayesian analyses to these higher-order observables, the results presented in this work provide new and independent constraints on the initial conditions and transport properties in theoretical models used to describe the system created in heavy-ion collisions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

3D small-gain formula allowing strong focusing and harmonic lasing for a ring-based x-ray free electron laser oscillator

We present a detailed derivation of a formula for the small-gain calculation for an x-ray free electron laser oscillator (XFELO) based on a medium-energy (3–4 GeV) storage ring. We found harmonic lasing and strong focusing are essential for this beam energy range. Taking the small-signal low-gain formula developed by Kim and his colleagues, we modified it in such a way that the gain can be calculated without the “no focusing approximation,” and a strong focusing can be applied, as well as harmonic lasing. In this formula, the gain is represented as a product of two factors with one of them depending only on the harmonic number, undulator period, and gap. Using this factor, we show that it is favorable to use harmonic lasing to achieve hard x-ray FEL working in the small-signal low-gain regime with the medium-energy electron beam. Our formula also allows FEL optimization by varying the vertical gradient of the undulator, the vertical dispersion, and the horizontal and vertical focusing, independently. As an example, we applied this formula to study the feasibility of an XFELO option for the National Synchrotron Light Source II (NSLS-II) upgrade. Since a quite high peak current is required for the FEL, collective effects of beam dynamics in medium-energy synchrotrons significantly affect the electron beam parameters. We carried out a multiparameter optimization taking collective effects into account. Note, even though our example is for a ring-based XFELO at 3 to 4 GeV, the formula and, in particular, the approach developed here may be applied to other types of FELs. Published by the American Physical Society 2024

36 MATERIALS SCIENCE↗