Harmonic Radiation Research Articles

Power Line Harmonic Radiation Observed by the Van Allen Probes Spacecraft

AbstractWe present a systematic analysis of Power Line Harmonic Radiation (PLHR) electromagnetic wave events observed by the Van Allen Probes spacecraft over the entire duration of the mission (2012–2019). PLHR events are radiated by electric power systems on the ground at harmonics of the base power system frequency (50 or 60 Hz, depending on the region). We analyze wave intensities at frequencies corresponding to the first few harmonics and we demonstrate that they are significantly enhanced at the times when the field‐aligned magnetic footprint of the spacecraft is above industrialized areas. Considering the spacecraft locations close to the equatorial plane, this represents experimental evidence that PLHR emissions may propagate up to radial distances as large as about 4 Earth radii. Average frequency spectra above selected industrialized regions reveal increased wave intensities at the frequencies corresponding to the first and the third harmonics, in particular during the nighttime. Multicomponent wave measurements allow us to perform a detailed wave analysis of polarization and propagation properties of the events. The waves are typically right‐handed elliptically or nearly circularly polarized, propagating with oblique wave normal angles from low latitude sources and more field‐aligned wave vectors from high latitude sources. The sign of the parallel component of the Poynting flux confirms that the events indeed propagate from the anticipated ground regions. Few events observed above the United States region propagate in the opposite direction, which is interpreted as wave bouncing between the hemispheres.

Mode conversion and laser energy absorption by plasma under an inhomogeneous external magnetic field.

The interaction of a high-frequency laser with plasma in the presence of an inhomogeneous external magnetic field has been studied here with the help of particle-in-cell simulations. It has been shown that the laser enters the plasma as an extraordinary wave (X-wave), where the electric field of the wave oscillates perpendicular to both the external magnetic field and propagation direction and as it travels through the plasma, its dispersion property changes due to the inhomogeneity of the externally applied magnetic field. Our study shows that the X-wave's electromagnetic energy is converted to an electrostatic mode as it encounters the upper-hybrid (UH) resonance layer. In the later stage of the evolution, this electrostatic wave breaks and converts its energy to electron kinetic energy. Our study reveals two additional processes involved in decay of the electrostatic mode at the UH resonance layer. We have shown that the energy of the electrostatic mode at the upper-hybrid resonance layer also converts to a low-frequency lower-hybrid mode and high-frequency electromagnetic harmonic radiations. The dependence of energy conversion processes on the gradient of the external magnetic field has also been studied and analyzed.

Uncommon Electromagnetic Radiations Related to Extra-High Voltage/Ultra-High Voltage Power Projects in China

Based on the high-resolution electromagnetic field intensity observed by the DEMETER satellite, the harmonic electromagnetic radiations in the ionosphere closely above the extra-high voltage and ultra-high voltage power projects in the Chinese power grid have been detected. In the time-frequency spectrograms, these radiations are characterized by parallel spectral lines with spacings of 50, 100, 150, or 600 Hz. The highest frequency can reach approximately 8,850 Hz. The radiations are probably attributed to the nonlinear devices such as converters or geomagnetic disturbance. The harmonic radiations over alternating current-to-direct current (AC-to-DC) substations of power system are generally more diverse and stronger than those over AC-to-AC substations. The measurements on the ground demonstrate that the weak magnetic radiations at several kilohertz with an intensity in the order of nT do exist around substations. A simple physical model is established to understand the characteristics of harmonic radiations propagating from the Earth’s surface to the ionosphere.

Efficient high-order harmonics generation from overdense plasma irradiated by a two-color co-rotating circularly polarized laser pulse.

High-order harmonics generated from the interaction between a two-color circularly polarized laser and overdense plasma is proposed analytically and investigated numerically. By mixing two circularly polarized lasers rotating in the same direction with different frequencies (ω0, 2ω0), the laser envelope is modulated to oscillate at the laser fundamental frequency while the peak intensity of each cycle becomes greater than that of the monochromatic light. This feature makes the plasma oscillate more violently and frequently under the striking of the two-color laser than the monochromatic one, thereby generating stronger harmonics and attosecond pulses. In addition, the incorporation of the 2ω0 light greatly expands the spectral width of harmonics, which facilitates the production of shorter attosecond pulses. Particle-in-cell simulations prove that under the same condition, the harmonic radiation efficiency in the two-color laser case can be improved by orders of magnitude, and isolated attosecond pulses can be even generated as a bonus in some cases.

Grid Frequency Measurement through a PLHR Analysis Obtained from an ELF Magnetometer.

The stability of the power grid’s frequency is crucial for industrial, commercial, and domestic applications. The standard frequency in Europe’s grid is 50 Hz and it must be as stable as possible; therefore, reliable measurement is essential to ensure that the frequency is within the limits defined in the standard EN 50160:2010. In this article, a method has been introduced for the measurement of the grid frequency through a power line harmonics radiation analysis. An extremely low-frequency magnetometer was developed with the specific purpose of monitoring, in real time, the electromagnetic field produced by electrical installations in the range from 0 to 2.2 kHz. Zero-crossing and Fast Fourier transform algorithms were applied to the output signal to calculate the grid frequency as a non-invasive method. As a final step, data for a complete month (May 2021) were compared with a commercial power quality analyzer connected to the main line to validate the results. The zero-crossing algorithm gave the best result on 3 May 2021, with a coefficient of determination (R2) of 0.9801. Therefore, the indirect measurement of the grid frequency obtained through this analysis satisfactorily fits the grid frequency.

On Global Dynamics of Schrödinger Map Flows on Hyperbolic Planes Near Harmonic Maps

The results of this paper are twofold. In the first part, we prove that for Schrödinger map flows from hyperbolic planes to Riemannian surfaces with non-positive sectional curvatures, the harmonic maps which are holomorphic or anti-holomorphic of arbitrary size are asymptotically stable. In the second part, we prove that for Schrödinger map flows from hyperbolic planes into Kähler manifolds, the admissible harmonic maps of small size are asymptotically stable. The asymptotic stability results stated here contain two types: one is the convergence in $$L^{\infty }_x$$ as the previous works, the other is convergence to harmonic maps plus radiation terms in the energy space, which is new in literature of Schrödinger map flows without symmetric assumptions.

Formation of the spatial structure of pump radiation in the focal plane of a lens for different types of stimulated light scattering

Experiments of our earlier work on the study of stimulated thermal scattering of the second harmonic of neodymium laser radiation in toluene are reproduced in order to confirm the put forward hypothesis about the nature of the laser beam structure decay in the focal plane of a short-focus lens. Experiments were carried out under similar conditions, but with a liquid (CCl4), in which there is no two-photon absorption of the second harmonic radiation from a neodymium laser. A conclusion is made that the spatial structure decay of the laser beam of the second harmonic of the Nd : YAG laser radiation focused by short-focus lenses with a numerical aperture NA ∼ 0.1 in toluene is associated with two-photon absorption.

Polarization dependence of atomic high-order harmonic generation: Description using a discrete basis

The optical generation of high-order harmonics is known to have a strong polarization dependence: In contrast to linearly polarized excitation, circularly polarized light induces practically no harmonics. In the current paper we focus on atomic targets, the case when a well-established physical picture explains the effect: For circular polarization, the photoionized electrons never return to their parent nuclei, and the energy they gained while being accelerated by the field is not transferred into high-order harmonic radiation. This is essentially a picture that is based on real-space electron trajectories (or the dynamics of the wave functions). Here, we provide an alternative description that uses the discrete Sturmian basis, and points out how quantum mechanical interference effects and selection rules can explain the polarization dependence of the process. This emphasizes the importance of space-time symmetries during the process of high-order harmonic generation.

Manipulation of the high-order harmonic generation in monolayer hexagonal boron nitride by two-color laser field.

We theoretically investigate the high-order harmonic generation (HHG) of the monolayer hexagonal boron nitride by two-color laser pulses, based on the abinitio time-dependent density-functional theory. We find that the waveform of the two-color laser field can dramatically control the harmonic spectrum. The two-color laser field can enhance the harmonic radiation more efficiently than the monochromatic pulse laser with the same incident energy. We investigate the influence of incident laser pulse parameters on the harmonic radiation, such as the relative phase of the two-color field, the amplitude ratio between component electric fields, and the laser orientation. We show that the HHG spectrum is controlled by both the electric field and the vector potential. The electronic band structure and the laser-matter energy transfer play an important role in determining the laser polarization for optimal HHG in the hBN crystal. Our work supplies a scheme to manipulate HHGs in two-dimensional materials and provides a potential methodology for the generation of intense extreme-ultraviolet pulses.

Effect of Ground Plane on Power Losses and Efficiency for Uniform Period Time Modulated Arrays

In this paper, the analysis of the multipath characteristics of time modulated arrays (TMAs) is presented in a theoretical framework. In particular, the simple two-way propagation concept of the TMA on a perfectly conducting ground plane is investigated by evaluating horizontal and vertical polarization situations. Due to the time difference of the electromagnetic fields at the source and observation point, the effect of the propagation delay of TMAs in the far-field is taken into account. Moreover, the effect of the ground plane on critical parameters of TMAs such as radiation pattern, max sideband level (SBL), total power ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${P}_{\textit {SR}}$ </tex-math></inline-formula> ) associated with harmonic radiation that brings power loss and the efficiency ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\eta $ </tex-math></inline-formula> ) of the system consisting of feed network and harmonic efficiency are investigated for linear TMA positioned parallel and perpendicular to the ground plane. As a result, the power loss expression for the infinite ground plane is revised and it is shown that the ground plane changes the total efficiency.

Separating Non-linear Optical Signals of a Sample from High Harmonic Radiation in a Soft X-ray Free Electron Laser

Second harmonic generation (SHG) is a unique non-linear optical effect that can be used to investigate chemical states of molecules at surfaces/interfaces. By the use of soft X-rays, SHG gains element selectivity through the inner-core excitation resonance. However, it is challenging to observe SHG signals separately from the second-order light generated from the undulator. Here, we report a new ellipsometry method for soft X-ray SHG to suppress the contribution of second-harmonic radiation from the light source. Through measurements of a GaAs(100) crystal, we demonstrate that pure SHG signals can be obtained for the horizontally polarized component. The present method is generally applicable regardless of the incident photon energy and hence the absorption edge of the targeted materials. If combined with optical filters blocking the second-harmonic radiation and equipped with soft X-ray phase shifters, the method allows one to obtain further information from SHG signals such as tensor components of second-order non-linear susceptibility.

Enhanced Amplification of Attosecond Pulses in a Hydrogen-like Plasma-Based X-ray Laser Modulated by an Infrared Field at the Second Harmonic of Fundamental Frequency

In a recent work (Antonov et al., Physical Review Letters 123, 243903 (2019)), it was shown that it is possible to amplify a train of attosecond pulses, which are produced from the radiation of high harmonics of the infrared field of the fundamental frequency, in the active medium of a plasma-based X-ray laser modulated by a replica of the infrared field of the same frequency. In this paper, we show that much higher amplification can be achieved using the second harmonic of the fundamental frequency for modulating of a hydrogen-like active medium. The physical reason for such enhanced amplification is the possibility to use all (even and odd) sidebands induced in the gain spectrum in the case of the modulating field of the doubled fundamental frequency, while only one set of sidebands (either even or odd) could participate in amplification in the case of the modulating field of the fundamental frequency due to the fact that the spectral components of the high-harmonic field are separated by twice the fundamental frequency. Using the plasma of hydrogen-like C5+ ions with an inverted transition wavelength of 3.38 nm in the water window as an example, it is shown that the use of a modulating field at a doubled fundamental frequency makes it possible to increase the intensity of amplified attosecond pulses by an order of magnitude in comparison with the previously studied case of a fundamental frequency modulating field.

Terahertz-assisted even harmonics generation in silicon

SummaryWhen a biased electric/light field is applied to centrosymmetric crystals like silicon, the broken symmetry creates even-order harmonics radiation which can reveal key insights into the material. Recently, the second harmonic has been generated by THz-induced symmetry breaking, but the observation of higher-order radiation remains largely unexplored. Here, we demonstrate picosecond-level ultrafast, nondestructive symmetry manipulation of silicon crystal by using a 500 kV/cm intense terahertz (THz) electric field. The THz-induced fourth harmonic of the infrared probe is also observed and characterized for the first time. In addition, we find that the even-order harmonics show no dependence on the THz field direction thus it allows for sub-cycle symmetry manipulations. Our study paves the way toward ultrafast all-optical crystal symmetry control in the future high-speed electronics and photonics.

Giant Third-Order Nonlinear Response of Mixed Perovskite Nanocrystals

Mixed (FAPbI3)0.92(MAPbBr3)0.08 perovskite thin films exhibit strong nonlinear optical responses, rendering them promising candidates for applications in photonics and optical communications. In this work, we present a systematic study on the ultrafast third-order nonlinear optical processes in mixed perovskite nanocrystals (NCs) by exploring the generation of third harmonic radiation and giant two-photon absorption-based photoluminescence (PL) when excited by femtosecond laser pulses of a 1030 nm central wavelength. A comparative analysis of the coherent third harmonic generation in the thin-film-containing perovskite nanocrystals has shown a 40× enhancement of the third harmonic signal compared to the signal generated in the pure quartz substrate. The cubic dependence of the third-nonlinear optical response of the (FAPbI3)0.92(MAPbBr3)0.08 perovskites on the intensity of the driving radiation was identified using broadband 38 femtosecond driving pulses. The positive nonlinear refractive index (γ = +1.4 × 10−12 cm2·W−1) is found to play an important role in improving the phase-matching conditions of the interacting pulses by generating a strong third order harmonic. The giant two-photon absorption (TPA)-assisted PL peak was monitored and a blue shift of the PL was obtained in the higher intensity range of the laser pulses, with the absorption coefficient β estimated to be~+7.0 cm·MW−1 at a 1030 nm laser wavelength.

On the use of ELF/VLF emissions triggered by HAARP to simulate PLHR and to study associated MLR events

A spectrogram of Power Line Harmonic Radiation (PLHR) consists of a set of lines with frequency spacing corresponding exactly to 50 or 60 Hz. It is distinct from a spectrogram of Magnetospheric Line Radiation (MLR) where the lines are not equidistant and drift in frequency. PLHR and MLR propagate in the ionosphere and the magnetosphere and are recorded by ground experiments and satellites. If the source of PLHR is evident, the origin of the MLR is still under debate and the purpose of this paper is to understand how MLR lines are formed. The ELF waves triggered by High-frequency Active Auroral Research Program (HAARP) in the ionosphere are used to simulate lines (pulses of different lengths and different frequencies). Several receivers are utilized to survey the propagation of these pulses. The resulting waves are simultaneously recorded by ground-based experiments close to HAARP in Alaska, and by the low-altitude satellite DEMETER either above HAARP or its magnetically conjugate point. Six cases are presented which show that 2-hop echoes (pulses going back and forth in the magnetosphere) are very often observed. The pulses emitted by HAARP return in the Northern hemisphere with a time delay. A detailed spectral analysis shows that sidebands can be triggered and create elements with superposed frequency lines which drift in frequency during the propagation. These elements acting like quasi-periodic emissions are subjected to equatorial amplification and can trigger hooks and falling tones. At the end all these known physical processes lead to the formation of the observed MLR by HAARP pulses. It is shown that there is a tendency for the MLR frequencies of occurrence to be around 2 kHz although the exciting waves have been emitted at lower and higher frequencies.Graphical

Сравнительный теоретический анализ генерации гармоник в лазерах на свободных электронах с различными параметрами электронных пучков

We theoretically study the generation of odd and even harmonics in particular in free electron lasers (FELs). The comparative analysis is held for the spectral properties of SPARC and LEUTL FEL radiation. We analyze several different theoretical approaches to the harmonic power computation, in particular with regard to even harmonics. We compare the results with available data for SPARC and LEUTL FELs. The influence of such FEL parameters as the finite beam section, emittance and originating from it betatron oscillations on the harmonic generation and radiation is analyzed.

Asymmetry in high-order harmonic generation of polar molecule CO

Compared with nonpolar molecules, owing to the inherent asymmetry, polar molecules exhibit rich and very complex electronic dynamics under the interaction with strong laser fields. In this work, high-order harmonic generation (HHG) of polar molecules CO is investigated by using the three-dimensional time-dependent Hartree-Fock (3D-TDHF) theory, with all electrons active. Through the high harmonic spectra and time-frequency analyses, it is found that when the laser field polarizes along the molecular axis, the ionized electrons from the two sides (C side and O side) contribute differently to the harmonic radiation. On the one hand, the harmonic intensity from the C side is greater than that from the O side, which is caused by the ionization rate. On the other hand, for the lower-order (7&lt;sup&gt;th&lt;/sup&gt;–17&lt;sup&gt;th&lt;/sup&gt; order) harmonics of plateau region, only the electrons from the C side participate in the HHG. However, for its higher part (18&lt;sup&gt;th&lt;/sup&gt;–36&lt;sup&gt;th&lt;/sup&gt; order), the electrons from both C side and O side contribute to high harmonics simultaneously. Moreover, the difference between contributions from two sides is related to the alignment angle &lt;i&gt;θ&lt;/i&gt; between the laser polarization and the molecular axis, and it reaches a maximum value around &lt;i&gt;θ&lt;/i&gt; = 0º and a minimum value around &lt;i&gt;θ&lt;/i&gt; = 90º. There are two strong resonances around harmonic order H12.6 (19.5 eV) and H18 (27.9 eV) in the harmonic spectra when &lt;i&gt;θ&lt;/i&gt; = 0º. The first resonance around H12.6 reveals that part of electrons ionized from the C side recombine to the vicinity of the further O nucleus. Near the second resonance around H18, there appears a shape resonance. Nevertheless, the shape resonances from the C and O sides are disparate. Based on the strong-field approximation theory, the ratio between photoionization cross sections from C and O sides around the shape resonance is calculated. The ratio is about 5.5 from 3D-TDHF, which is greater than the result of 3 simulated by ePloyScat, where only HOMO is considered. This discrepancy reveals that multi-electron effects enhance the asymmetry of polar molecules. This work provides an in-depth insight into the asymmetry in HHG of polar molecules, which benefits the generation of isolated attosecond pulse . It also promotes the application of high harmonic spectra in tracking the ultrafast dynamics of electrons.

Internal Relationship between Symmetrical and Asymmetric Molecular Harmonic Radiation and Its Structure

Internal Relationship between Symmetrical and Asymmetric Molecular Harmonic Radiation and Its Structure

The effect of initial phase on the emission characteristics of forward electron colliding with a tightly focused linearly polarized few-cycle laser pulse

We have studied the high harmonic radiation property from the scattering of an electron with a focused few-cycle laser pulse by analyzing the distribution of the radiation field and the motion state of the electron. In the time domain, temporal width of the compressed radiation can reach 33 zs (zeptosecond), thus an ultrashort x-ray pulse was generated in the interaction process. The radiation in this process is vastly similar to high harmonic generation in the process of atomic strong-field. The latter depends to a large extent on the phase of carrier-envelope (CE) driving laser pulse. The cutoff of radiation spectrum can reach , and whether the high-order harmonic spectrum in the cut-off region can be well resolved depends on the CE phase. We have investigated the relationship between the maximum radiation intensity and the CE phase, and discussed a potential method to characterize the CE phase of an intense few-cycle laser pulse for broader application prospects.

Generation of elliptically polarized high-order harmonic radiation with bi-elliptical two-color laser beams

High-harmonic generation (HHG) from an atomic gas target provides a valuable tool to generate high-energy radiation on the tabletop. The polarization properties of this radiation can be manipulated if the HHG process is driven by a bi-elliptical orthogonal two-color laser beam (BEOTC beam). Here we theoretically consider this setup within the so-called strong-field approximation and a quantum-orbit approach. We demonstrate that this approach allows the complete description of the geometry of the outgoing elliptically polarized harmonic radiation. In particular, we identify and classify the relevant quantum orbits that contribute to the process and analyze the harmonic spectrum, ellipticities, and offset angles in detail for $\ensuremath{\omega}\text{\ensuremath{-}}2\ensuremath{\omega}$ BEOTC beams with a fundamental wavelength of $\ensuremath{\lambda}=800\phantom{\rule{0.16em}{0ex}}\mathrm{nm}$. For these specific beam parameters, we find that the ellipticity as well as the offset angle of the polarization ellipse with respect to the BEOTC driving beam changes rapidly for consecutive harmonic orders. We show that this oscillatory behavior of the harmonic ellipticity can be explained via the superposition of the dipole radiation emitted from the target atom during different time intervals within one optical cycle of the BEOTC beam. This understanding of the HHG process driven by BEOTC beams will facilitate the generation of highly energetic radiation with complex polarization properties on the tabletop.