Harmonic Emission Research Articles

Current Harmonic Aggregation Cases for Contemporary Loads

Power electronic circuits in modern power supplies have improved the conversion efficiency on the one hand but have also increased harmonic emissions. Harmonic currents from the operation of these units affect the voltage waveforms of the network and could compromise the reliability of the network. Load and source non-linearity can, therefore, limit the renewable source’s hosting capacity in the grid, as a large number of inverter units may increase the harmonic distortions. As a result, voltage and current distortions could reach unbearable levels in devices connected to the network. Harmonic estimation modelling often relies on measurement data, and differences may appear in mathematical simulations as the harmonic aggregation or cancellation may generate different results due to the inaccuracies and limitations of the measurement device. In this paper, the effect of harmonic currents cancellation on the aggregation of different load currents is evaluated to show its impact in the network by presenting a comparison between the measurement and mathematical aggregation of harmonics. Furthermore, the harmonic cancellation phenomenon is also qualified for multiple loads connected to the power supply.

Effect of Interlayer Coupling and Symmetry on High-Order Harmonic Generation from Monolayer and Bilayer Hexagonal Boron Nitride

High-order harmonic generation (HHG) is a fundamental process which can be simplified as the production of high energetic photons from a material subjected to a strong driving laser field. This highly nonlinear optical process contains rich information concerning the electron structure and dynamics of matter, for instance, gases, solids and liquids. Moreover, the HHG from solids has recently attracted the attention of both attosecond science and condensed matter physicists, since the HHG spectra can carry information of electron-hole dynamics in bands and inter- and intra-band current dynamics. In this paper, we study the effect of interlayer coupling and symmetry in two-dimensional (2D) material by analyzing high-order harmonic generation from monolayer and two differently stacked bilayer hexagonal boron nitrides (hBNs). These simulations reveal that high-order harmonic emission patterns strongly depend on crystal inversion symmetry (IS), rotation symmetry and interlayer coupling.

Characterization of Laser-Induced Ionization Dynamics in Solid Dielectrics

The formation of an electron-hole plasma during the interaction of intense femtosecond laser pulses with transparent solids lies at the heart of femtosecond laser processing. Advanced micro- and nanomachining applications require improved control over the excitation characteristics. Here, we relate the emission of low-order harmonics to the strong laser-field-induced plasma formation. Together with a measurement of the total plasma density we identify the contribution of two competing ionization mechanisms - strong-field and electron-impact ionization.

Fundamental Electromagnetic Emissions by a Weak Electron Beam in Solar Wind Plasmas with Density Fluctuations

Abstract The generation of Langmuir wave turbulence by a weak electron beam in a randomly inhomogeneous plasma and its subsequent electromagnetic radiation are studied owing to two-dimensional particle-in-cell simulations in conditions relevant to type III solar radio bursts. The essential impact of random density fluctuations of average levels of a few percents of the background plasma on the characteristics of the electromagnetic radiation at the fundamental plasma frequency ω p is shown. Not only wave nonlinear interactions but also processes of Langmuir waves’ transformations on the density fluctuations contribute to the generation of such emissions. During the beam relaxation, the amount of electromagnetic energy radiated at ω p in a plasma with density fluctuations strongly exceeds that observed when the plasma is homogeneous. The fraction of Langmuir wave energy involved in the generation of electromagnetic emissions at ω p saturates around 10−4, i.e., one order of magnitude above that reached when the plasma is uniform. Moreover, whereas harmonic emission at 2ω p dominates over fundamental emission during the time evolution in a homogeneous plasma, fundamental emission is strongly dominant when the plasma contains density fluctuations, at least during several thousands of plasma periods before being overcome by harmonic emission when the total electromagnetic energy begins to saturate.

Influence of driving-laser wavelength on emission of high-order harmonic wave generated by atoms irradiated by ultrashort laser pulse

With the numerical solution of the time-dependent Schrodinger equation, we theoretically investigate the high-order harmonic emissions generated by the atoms irradiated by the ultrashort lasers with different wavelengths but the same pondermotive energy. As the driving-laser wavelength increases, the intensity of the high-harmonic emission decreases. Comparing with the harmonic spectra of atoms driven by a 1000-nm-wavelength laser pulse, a new peak structure appears in the spectra of atoms driven by a 5000-nm-wavelength laser wavelength. It is shown by the time-frequency analysis of the harmonic emission, the time-dependent evolution of the electron density, and the time-dependent population analysis of the eigenstate, that the physical mechanism behind the new peak appearing in the harmonic spectra is the interference between the harmonic emission generated by the electrons ionized out of the excited atoms returning to the parent ions and the harmonic emissions resulting from the ground state ionization.

Origins of complex interference structures in harmonic emission from stretched molecular ion with large internuclear distances

We study high-order harmonic generation (HHG) from stretched molecular ions with large internuclear distances numerically and analytically. We focus on the fine structure of the HHG spectrum related to the contributions of short electron trajectory. In our simulations through numerical solution of time-dependent Schrodinger equation (TDSE), we use a trajectory-dependent filtering procedure to separate the short-trajectory contributions from other contributions of long trajectory and multiple returns. Our TDSE results show that the short-trajectory HHG spectra of molecular ion with larger internuclear distances show some complex interference structures characterized by some remarkable dips and the positions of the dips are sensitive to the laser parameters. With a developed model arising from strong-field approximation (SFA), we are able to identify the physical origins of the complex interference structures. This model considers the charge-resonance effect which induces the strong coupling between the ground state and the first excited state of the molecular ion at large internuclear distance. In this model, the well-known effect of two-center interference occurs in terms of the canonical momentum instead of the momentum related to the instantaneous velocity of the electron in the general SFA. We show that some dips in TDSE results arise from two-center interference of the electronic wave between these two atomic cores of the molecule in the ionization process, while others come from that in the recombination process. These ionization and recombination dips alternately appear in the HHG spectra, with forming the complex interference structures. The main differences between the interference effects in the ionization and the recombination processes are twofold. Firstly, in the ionization process, the destructive two-center interference strongly suppresses the forming of the continuum wavepacket, while in the recombination process, the recombination of the rescattering electron to other bound eigenstates with small weights can also contribute to HHG bedsides the recombination to the ground state and the first excited state with large weights. As a result, in TDSE results, the ionization dips are deeper and more remarkable than the recombination ones. Secondly, in the recombination process, the Coulomb acceleration remarkably changes the de Broglie wavelength of the rescattering electron and therefore changes the position of the interference-induced dip, while in the ionization process, the Coulomb potential plays a small role in the interference effect. As a result, the interference dips in the ionization and the recombination processes differ from each other.

Bright High-Harmonic Generation through Coherent Synchrotron Emission Based on the Polarization Gating Scheme

Relativistic surface high harmonics, combined with the use of polarization gating, present a promising route towards intense single attosecond pulses. However, they impose stringent requirements on ultra-high laser contrast and are restricted by large intensity losses in real experiments. Here, we numerically demonstrate that by setting an optimal time delay in the polarization gating scheme, the intensity of the generated single attosecond pulses can become approximately 100 times stronger than that with nonoptimal time delay in the coherent synchrotron emission process. When a petawatt-class driving laser irradiates a solid target, an ultra-dense electron nanobunch and a strong space-charge sheath develop, and the accumulated electrostatic energy is only released in half of the laser cycle when this electron nanobunch moves backward. This process results in the emission of intense high harmonics. Our study provides a reliable method for developing bright attosecond extreme ultraviolet pulses.

Generation of isolated attosecond pulses from atoms driven by optimized two near-infrared pulses and their second harmonic fields

With the rapid development of laser technology, it is possible to control optical waveforms by coherent superposition of electric fields with multiple color components, which creates conditions for generating the ultra-short isolated attosecond pulses (IAP). Based on the strong-field approximation theory, this work focuses on the IAP generated by the optimized multicolor field synthesized by two fundamental near-infrared lasers and their second harmonic fields. The results show that by applying frequency-doubled pulses to the near-infrared laser fields and optimizing the laser parameters, the emission properties of high order harmonics from single atom can be greatly improved, and the nearly attochirp-free harmonic emission can be realized within a certain energy range. As a result, shorter IAPs are obtained. With the consideration of the macroscopic propagation effect of gas, the IAP with a pulse width up to 40 as is generated under appropriate experimental conditions. Finally, the effects of gas pressure on the properties of the high-order harmonic and attosecond pulses are also investigated. This study provides useful theoretical guidance for generating ultra-short IAPs with near-infrared laser pulses in experiment.

Simulation of Plasma Emission in Magnetized Plasmas

Abstract The recent Parker Solar Probe observations of type III radio bursts show that the effects of the finite background magnetic field can be an important factor in the interpretation of data. In the present paper, the effects of the background magnetic field on the plasma-emission process, which is believed to be the main emission mechanism for solar coronal and interplanetary type III radio bursts, are investigated by means of the particle-in-cell simulation method. The effects of the ambient magnetic field are systematically surveyed by varying the ratio of plasma frequency to electron gyrofrequency. The present study shows that for a sufficiently strong ambient magnetic field, the wave–particle interaction processes lead to a highly field-aligned longitudinal mode excitation and anisotropic electron velocity distribution function, accompanied by a significantly enhanced plasma emission at the second-harmonic plasma frequency. For such a case, the polarization of the harmonic emission is almost entirely in the sense of extraordinary mode. On the other hand, for moderate strengths of the ambient magnetic field, the interpretation of the simulation result is less clear. The underlying nonlinear-mode coupling processes indicate that to properly understand and interpret the simulation results requires sophisticated analyses involving interactions among magnetized plasma normal modes, including the two transverse modes of the magneto-active plasma, namely, the extraordinary and ordinary modes, as well as electron-cyclotron-whistler, plasma oscillation, and upper-hybrid modes. At present, a nonlinear theory suitable for quantitatively analyzing such complex-mode coupling processes in magnetized plasmas is incomplete, which calls for further theoretical research, but the present simulation results could provide a guide for future theoretical efforts.

Simultaneous Frequency and Amplitude Estimation for Grid Quality Monitoring: New Partitioning with Memory Based Newton-Schulz Corrections

High penetration level of renewable energy sources and introduction of controllable loads will result in significant harmonic emissions and sag and swell events in the future electricity networks. Development of the methods for high performance simultaneous estimation of the frequency and amplitude events is required for stable operation of the future electricity networks since zero crossing frequency detection method (which is widely used nowadays in industry) is not accurate enough and does not allow estimation of the amplitude events. The multiple model method which is suitable for simultaneous estimation of the frequency and amplitude is extended in this paper with introduction of a new decomposition technique based on stepwise partitioning, which allows simultaneous construction and accurate and computationally efficient inversion of the information matrix. Recursive calculations of the inverse introduce error accumulation and a new general high order memory based Newton-Schulz iteration is proposed in this paper for correction and reduction of the accumulated error. Moreover, parallel Richardson iterations which are based on partitioning method are proposed in this paper for reduction of the computational complexity. The methods are especially efficient for approximation of the signals with large number of harmonics. The approaches were tested for simultaneous estimation of the frequency and sag and swell signatures in the one-phase synchronized voltage waveform measured at the wall outlet. Simulation results show that the multiple model method provides more accurate frequency estimation in comparison to zero crossing method.In addition, the cascade multiple model method which is based on the multi-windowing technique (where the components of the signals are separated via a proper choice of the window sizes) is introduced in this paper for estimation of the significantly separated frequencies of the electrical signals. The approach was tested in the problem of frequency estimation using the measurement record from the electric vehicle with on-board charger connected to the supply voltage in the laboratory.

Multi-beam vortex generation induced by the non-linear optical anisotropy of graphene

We analyse the high harmonic emission from single-layer graphene driven by infrared vector beams. We demonstrate that graphene’s anisotropy offers a privileged scenario to explore non-trivial light spin-orbit couplings, which substantially extends the possibilities for the generation of high-harmonic structured beams currently studied in atomic and molecular targets. In our case, graphene’s crystal symmetry introduces a spin-dependent diffraction pattern that, coupled with the fundamental conservation of the driver’s topological phase, leads to the splitting of the harmonic field in a multi-beam structure, composed of spatially diverging vortices. Our work demonstrates that anisotropic targets are extraordinary tools to sculpt complex structured short-wavelength beams.

Attosecond Delays of High-Harmonic Emissions from Hydrogen Isotopes Measured by XUV Interferometer

High-harmonic spectroscopy can access structural and dynamical information on molecular systems encoded in the amplitude and phase of high-harmonic generation (HHG) signals. However, measurement of the harmonic phase is a daunting task. Here, we present a precise measurement of HHG phase difference between two isotopes of molecular hydrogen using the advanced extreme-ultraviolet (XUV) Gouy phase interferometer. The measured phase difference is about 200 mrad, corresponding to ~3 attoseconds ( 1 as = 10 − 18 s ) time delay which is nearly independent of harmonic order. The measurements agree very well with numerical calculations of a four-dimensional time-dependent Schödinger equation. Numerical simulations also reveal the effects of molecular orientation and intramolecular two-center interference on the measured phase difference. This technique opens a new avenue for measuring the phase of harmonic emission for different atoms and molecules. Together with isomeric or isotopic comparisons, it also enables the observation of subtle effects of molecular structures and nuclear motion on electron dynamics in strong laser fields.

An Analysis of Electromagnetic Disturbances from an Electric Vehicle Charging Station

The electric vehicles (EVs) could potentially have a significant impact on power quality parameters and distribution networks as they are non-linear loads and their charging might result in tremendous power demand. When connected to the utility grid, a large number of EV charging stations from different manufacturers might create significant harmonic current emissions, impact the voltage profile, and eventually affect the power quality. Nevertheless, practical examples of disturbances from charging stations have not been made public. This paper aims to clarify the characteristics of conductive disturbances and levels of current harmonics generated by charging station and their severity on the quality of electric energy. The analysis was based on tests of a prototype station of an EV charging station integrated with a LED street light. The tests concern the determination of current harmonics and the values of conductive electromagnetic disturbances in the 150 kHz–30 MHz range. The test results of the prototype charger with observed exceedances of current harmonics (25th–39th range) and conducted interference exceedances are comprehensively described. After applying filtering circuits to the final version of the station, retesting in an accredited laboratory showed qualitative compliance.

Time and space waveform optimization to extend the harmonic cutoff and to produce the water window single attosecond pulse

Abstract Based on the three-step theory of high-order harmonic generation, the harmonic cutoff is very sensitive to the few-cycle laser waveform in both time and space regions. Therefore, in this paper, we propose the method to control the harmonic cutoff and to produce the water window attosecond pulse through the optimization of time and space waveform. It is found that, in the time region, by properly choosing the delay and phase of the few-cycle two-color pulse, not only the harmonic intensity is enhanced, but also the quantum path of the harmonic emission can be controlled. Further, with the introduction of the 3rd pulse (i.e., the infrared pulse or the unipolar pulse), the harmonic cutoff from the single harmonic emission peak can be extended, showing a water window harmonic plateau. In the space region, by using the positive spatial inhomogeneous effect, the harmonic cutoff from the basic two-color waveform can also be extended, which leads to a water window spectral continuum. Finally, by Fourier transformation of harmonics during the water window region, the ultrashort single 29 as pulses can be obtained.

Analysis of exact and approximating dependences of active resistance of a conductor on the current frequency based on the influence of skin effect

The operation of semiconductor power converters, which are part of tractionsubstations, frequency-controlled electric drives and other powerful nonlinear loads, cause asignificant emission of higher harmonics of currents to electrical networks. Higher harmonics ofcurrents in electrical networks cause a complex negative effect on the energy efficiency of thenetwork. The increase in power losses in the active resistance under the action of higher harmonicsis due to the increase in the root mean square value of the current and the action of the skin effect.Analytical expressions describing the dependence of the active and impedance of the electricnetwork on the current frequency are determined. Based on them, analytical expressions are obtainedfor the calculation of additional power losses under the action of higher harmonics of currents, whichare due to the skin effect. The dependences of the active resistance of the electric network on thefrequency of higher harmonics are determined on the basis of Bessel equations. The analysis of convergence of the received equations with the data of the international standard IEC 60287-1-1 iscarried out. For the high-frequency zone, simplified approximating dependences are given, whichdetermine the parabolic dependence of the active resistance on the frequency. Simplifiedapproximating dependences of active resistance on the frequency of higher harmonics are obtainedfor engineering calculations. The obtained equations can be used to determine additional powerlosses in the active supports of electrical networks, windings of electric machines, high-frequencytransformers from higher harmonics of currents at different nonlinear loads. In addition, the obtainedexpressions can be used to justify the use of filter-compensating devices.

Method for Evaluation of the Utility’s and Consumers’ Contribution to the Current and Voltage Distortions at the PCC

In this article, a method that allows sharing responsibilities for the generation of harmonic currents between the utility and consumers powered by one point of common coupling (PCC) is addressed. For these purposes, mathematical modeling of the power supply system (PSS) with two consumers is carried out in order to introduce new indices using the simplest PSS structure as an example. Two indices are introduced that quantify the consumers’ contribution to the distortion of current and voltage at the PCC and that evaluate harmonic emission from the utility side. Experimental tests are carried out where both linear and nonlinear loads are considered, capacitive loads are taken into account, and harmonic distortions from the utility side are modeled to show the applicability of the indices in a wide range of load types. The experiments confirmed the theoretical results and illustrated that the quantitative assessment of the contributions is unambiguous. It suggests that the proposed criterion could be a reasonable basis for further tax policy on harmonic pollution for each consumer at the PCC and for the utility.

Control of high-order harmonic emission in solids via the tailored intraband current

Delocalized Bloch electrons in solids are usually regarded as a kind of representative quantum Fermi gas. To unravel the real-space dynamics of Bloch electrons under a tailoring intraband current, we introduced a quasiparticle picture of a wave packet via superposing the multiple Bloch states within a given crystal-momentum region. We find that temporal characteristics and yield modulation in solid-state high-harmonic generation (HHG) depend sensitively on the crystal-momentum region of generating electron-hole pair. Its mechanism could be clarified by the gradual symmetrization of the time-dependent carrier distribution with the growing tunneling-momentum range. Manipulation of tunneling-momentum range is experimentally feasible via photon-carrier doping of appropriate preexcitation pulse. Finally, we elucidate the role of dephasing in the process of HHG. The scheme of customizing intraband current provides an alternative way to regulate the high-harmonic generation of solids.

Python supervised co-simulation for a day-long harmonic evaluation of EV charging

To accurately simulate electric vehicle DC fast chargers' (DCFCs') harmonic emission, a small time step, i.e., typically smaller than 10 μs, is required owing to switching dynamics. However, in practice, harmonics should be continuously assessed with a long duration, e.g., a day. A trade-off between accuracy and time efficiency thus exists. To address this issue, a multi-time scale modeling framework of fast-charging stations (FCSs) is proposed. In the presented framework, the DCFCs' input impedance and harmonic current emission in the ideal grid condition, that is, zero grid impedance and no background harmonic voltage, are obtained based on a converter switching model with a small timescale simulation. Since a DCFC's input impedance and harmonic current source are functions of the DCFC's load, the input impedance and harmonic emission at different loads are obtained. Thereafter, they are used in the fast-charging charging station modeling, where the DCFCs are simplified as Norton equivalent circuits. In the station level simulation, a large time step, i.e., one minute, is used because the DCFCs' operating power can be assumed as a constant over a minute. With this co-simulation, the FCSs' long-term power quality performance can be assessed time-efficiently, without losing much accuracy.

Генерация третьей гармоники при фокусировке фемтосекундного излучения с длиной волны 1032 нм в воздухе

In open publications the results of research on the third harmonic generation in the air by femtosecond laser radiation are presented. Most of the studies have been carried out using a titanium-sapphire laser with a central emission wavelength of 800 nm. This work presents for the first time the results of studies of the third harmonic generation in the air from laser radiation with a wavelength of 1032 nm. The source of the laser radiation was an ytterbium femtosecond laser which generated pulses with duration of ~ 250 fs and a repetition rate of 1 kHz. The average output power of the laser reached 1750 mW. Maximum peak intensity of excitation laser radiation was up to 10 TW/cm2. When focusing the laser radiation its filamentation took place and was accompanied by generation of the third harmonic radiation at wavelength of 344 nm. Spectral, energy and spatial characteristics of the generated third harmonic radiation were investigated. Energy measurements were carried out up to the threshold power of pump radiation at which the competing nonlinear processes in the circuit optical elements of the experimental setup began to occur. The maximum average third harmonic emission power was 1.52 mW with a third harmonic conversion efficiency of about 0.085 %. The far-field beam pattern had a symmetric Gaussian profile with a radiation divergence of 0.11 mrad which corresponds to the diffraction quality of the beam (M2 ≈ 1)

Terahertz-field-induced second harmonic generation for nonlinear optical detection of interfaces buried in transparent materials

We propose and demonstrate experimentally a nonlinear optical technique that allows for detection and characterization of invisible (or low-contrast) microscale objects buried in the bulk of materials transparent in the optical and terahertz frequency ranges. The technique is based on the effect of terahertz-field-induced second harmonic generation and uses collinearly propagating femtosecond optical and picosecond terahertz pulses to probe a sample. Due to a difference between the optical and terahertz velocities, the pulses can be overlapped in different regions of the sample by varying the time delay between them. Overlapping in the bulk of the material does not produce optical second harmonic emission, whereas overlapping at the microobject does produce the emission. The technique was verified experimentally for two plates of fused quartz glued by a thin (15–35 μm thick) layer of optical adhesive. The presence of the adhesive was detected, and its third-order nonlinear susceptibility was measured.