High-order Harmonics Research Articles

Temperature oscillations provide access to high-order physical aging harmonics of a glass forming melt

A high-resolution, temperature oscillation-based probe of physical aging in complex systems is introduced. The Fourier analysis of the measured responses allows one to extract high-order, aging-related nonlinearities that are not accessible via traditional temperature-jump and temperature-ramp procedures. To demonstrate the potential of this oscillatory approach, we analyze the periodic time evolution of glycerol’s structural relaxation using shear rheology as a vehicle. Thereby, we access up to the sixth harmonic and detect aging fingerprints within a resolution range of three orders of magnitude for temperature amplitudes of up to 4 K. The even harmonics are present since aging is not symmetrical with respect to the direction of temperature change. The high-order aging coefficients obtained for glycerol are described reasonably well within the Tool–Narayanaswamy–Moynihan formalism.

Generation of Complex Vector and Vortex Extreme Ultraviolet Beams Using the S-Waveplate and Spiral Phase Plate during High-Order Harmonics Generation in Argon

Generation of Complex Vector and Vortex Extreme Ultraviolet Beams Using the S-Waveplate and Spiral Phase Plate during High-Order Harmonics Generation in Argon

Experimental analysis of the air- and water-based cooling solution for the three-phase line choke

Modern power systems are affected by current harmonics. The high-order harmonics may result in overheating of the power system and lifetime reduction. Hence, the most novel power systems are equipped with three-phase line chokes. However, power losses generated in three-phase chokes result in a temperature increase within the choke. Most of the commercially available three-phase chokes are equipped with a passive air-based cooling solution. Such a solution results in an increase in the overall size of the device as well as an increase in the manufacturing costs. The water-cooling plates were installed in the commercial three-phase and the cooling performance of the air- and water-based cooling systems were experimentally compared. The chokes were analyzed at the RMS currents that corresponded to 100%, 75% and 50% of the nominal losses of the device. The temperature of the chokes was monitored with the thermocouples and precise IR camera. The comparison of the thermal results showed that the water-cooled choke outperformed the air-cooled unit. The core temperature of the device was reduced from approximately 110 °C to approximately 26 °C for the water-cooled solution compared to the air-cooled one. The temperature distribution in the windings was comparable for both solutions. The highest measured temperature exceeded 100 °C for both cooling solutions. The experimental results presented in this study can be used for further modification of the water-cooling system. Especially, in terms of the water panels’ shape, position and water inlet configuration. Such modifications should lead to further reduction of the device temperature, material and manufacturing costs.

A 12bit 1.6 GS/s pipelined ADC with multi-level dither injection achieving 68 dB SFDR over PVT

This paper presents a 12-bit 1.6 GS/s pipelined analog-to-digital converter (ADC) in a 40-nm CMOS process. A novel dual-capacitor dither injection technique was proposed, based on a randomize multi-level uniform logic, aimed at leveraging multi-level signal jitter to disperse higher-order harmonics and spurious signals within the spectrum. The technique proves highly effective in preserving the linearity of high-speed pipeline ADCs under Process, Voltage, and Temperature (PVT) variations. Additionally, a high-speed amplifier with SC net was designed, and its matching bias circuit design can achieve configurable performance adjustment according to circumstances. Measurement results show that the ADC attains an impressive Signal-to-Noise and Distortion Ratio (SNDR) of 55.9 dB and Spurious-Free Dynamic Range (SFDR) of 71.7 dB at the Nyquist frequency. Furthermore, the SFDR variation remains below 4.2 dB over the temperature range of −40 °C–85 °C.

Efficient angular dispersed high-order harmonic generation by dual laser pulses interacting with a solid target

High-order harmonics emitted from relativistic laser–solid interaction can be used as a bright extreme ultraviolet source. However, such a source usually has mixed frequencies along the emission direction. Through theoretical and numerical studies, we propose a scheme to realize monochromatic harmonic emission along individual directions by using dual laser pulses with orthogonal polarizations, where a relativistic P-polarized laser is used as a pump laser in combination with a moderate S-polarized laser as a seed laser. We find that harmonics of the S-polarized laser can be efficiently generated with several orders of magnitude enhancement and spontaneous angular dispersion depending on the harmonic order. Our scheme may be beneficial to future applications requiring monochromatic radiation along a specific direction or multi-chromatic radiations in different directions.

Effects of polarization direction, amplitude, and photon energy of linearly polarized laser on high order harmonic generation of C60

The study of high-order harmonic generation (HHG) in confined quantum systems is essential for developing a comprehensive physical description of harmonic generation from atoms to bulk solids. Using the time-dependent density-functional theory, we demonstrate how the symmetry of the system modulates the generation of high-order harmonic in fullerene C60 molecules along different orthogonal directions, as well as the effects of amplitude and photon energy of a linearly polarized laser on high-order harmonics generation. We found that the generation of high-order harmonics perpendicular to the laser polarization direction (LPD) is related to the symmetry of molecules along the LPD and the symmetry of molecules perpendicular to the LPD. Within a certain parameter range, the cut-off energy is linearly proportional to the laser amplitude and the laser photon energy.

Development of a Novel Radial-Flux Machine With Enhanced Torque Profile Employing Quasi-Cylindrical PM Pattern

This article presents a novel radial-flux surface-mounted PM (SPM) machine with quasi-cylindrical pole pattern (QCPP). With the proposed configuration, the cogging torque and torque ripple of surface-mounted machines could be greatly decreased due to the adoption of large eccentric distance and the reduction of high-order airgap flux density harmonics. Moreover, the increase of fundamental flux component helps to improve torque generation well. Additionally, the magnet poles are semi-embedded into the rotor, and thus the sleeve in conventional SPM machines is no longer necessary, which helps to reduce the airgap size and improve the torque output further. Besides, the quasi-cylindrical magnet could offer lower rotor eddy loss and higher anti-demagnetization capability than conventional radial and eccentric pole patterns. Studies have been conducted on the novel structure to validate its advantages. Firstly, the topological structure and working principle of the QCPP machine are presented. Then, the influence of the QCPP structural parameters on the torque performance is investigated. Next, an electrical machine with quasi-cylindrical pole pattern is designed. Subsequently, the electromagnetic characteristics, such as flux density distribution, back EMF, average torque, cogging torque, torque ripple, eddy loss in sleeve, rotor stress and anti-demagnetization capability, of the proposed machine are analyzed and compared with those of conventional SPM machine with eccentric magnetic poles and skewing slots. Finally, one research prototype is developed, and experiments are carried out to evaluate the design concept and performance of the proposed QCPP machine.

Generation of High-Order Harmonics by Gallium Ions in Intense Laser Pulse

Generation of High-Order Harmonics by Gallium Ions in Intense Laser Pulse

Dynamic Dead-Time Compensation Method Based on Switching Characteristics of the MOSFET for PMSM Drive System

In order to effectively avoid the shoot-through issue of the semiconductor device (such as the power metal-oxide-semiconductor field-effect transistor (MOSFET)) adopted in the phase leg of the motor drives, a dead-time zone should be inserted. However, the nonlinearity caused by the dead-time effect will bring about voltage/current distortion, as well as high-order harmonics, which largely degrades the performance of motor drives, especially in low-speed operations with slight loads. In this paper, a dead-time compensation method is proposed to suppress such side effects caused by dead-time zones and improve the performance of motor drives. Compared with other existing methods, the proposed method is mainly focused on the switching characteristics of the power MOSFET, which is directly relative to the compensation time in each pulse-width modulation (PWM) period. Firstly, a detailed derivation process is elaborated to reveal the relationship between compensation time and the switching performance of the MOSFET. Meanwhile, the switching process of the MOSFET is also well analyzed, which summarizes the variations in the switching time of the MOSFET with a varied load current. Then, the multipulse test (MPT) is carried out to obtain accurate values of the switching time with the varied load current in a wide range (0–80 A) and form a 2D lookup table. As a result, the compensation method can easily be realized by combining the lookup table and linear interpolation based on the phase current of the motor dynamically. Finally, the effectiveness of the proposed method is verified based on a 12 V permanent magnet synchronous machine (PMSM) drive system. According to the relative experiment results, it can be clearly observed that the time-domain waveform distortion, high-order harmonics, and total harmonic distortion (THD) value are reduced significantly with the proposed dynamic compensation method.

A computational aeroacoustic study of a multi-rotor powered urban air mobility vehicle

The multi-rotor propulsion system has become one of the popular configurations for urban air mobility vehicles due to its capability of high-density vertical take-off and landing operations. The noise characteristics, as a critical criterion for urban air mobility, usually differ for a multi-rotor configuration from a single-rotor configuration. In this work, we investigate the noise generated by a hexacopter configuration using delayed detached eddy simulations and the Ffowcs-Williams and Hawkings acoustic-analogy-based solver. The overall length and the rotor diameter of the vehicle are 4 m and 2 m, respectively, and the target maximum take-off mass is 500 kg. The full configuration and three simplified setups that reduce several individual components are numerically studied to isolate the corresponding effect of each component and to identify their flow/acoustic interactions. The results show that the rotor-rotor interaction leads to remarkable thrust fluctuations and further results in a considerable increase in tonal noise over a broad frequency range. The interaction between the rotors and the support arms also leads to significant thrust fluctuations on the surfaces of both rotor blades and arms, which produces additional tonal noise at high-order harmonics of the blade passing frequency. In contrast, for the current configuration, the existence of the fuselage does not have a significant effect on noise generation. The research should benefit low-noise vehicle design and operation.

Experimental study on Richtmyer–Meshkov instability at a light–heavy interface over a wide range of Atwood numbers

Richtmyer–Meshkov instability (RMI) at a light–heavy single-mode interface over a wide range of post-shock Atwood numbers $A_1$ is studied systematically through elaborate experiments. The interface generation and $A_1$ variation are achieved by the soap-film technology and gas-layer scheme, respectively. Qualitatively, the nonlinear interface evolution features, including spike, bubble and roll-up structures, are more significant in RMI with higher $A_1$ . Quantitatively, both the impulsive model and an analytical linear model perform well in predicting the linear growth rate under a wide range of $A_1$ conditions. For the weakly nonlinear stage, the significant spike acceleration occurring when $A_1$ is high, which is observed experimentally for the first time, results in the evolution law of RMI with high $A_1$ being different from the counterpart with low or intermediate $A_1$ . None of the considered nonlinear models is found to be applicable for RMI under all $A_1$ conditions, and the predictive capabilities of these models are analysed and summarized. Based on the present experimental results, an empirical nonlinear model is proposed for RMI over a wide range of $A_1$ . Further, modal analysis shows that in RMI with high (low or intermediate) $A_1$ , high-order harmonics evolve rapidly (slowly) and cannot (can) be ignored. Accordingly, for RMI with high (low or intermediate) $A_1$ , the modal model proposed by Zhang & Sohn (Phys. Fluids, vol. 9, 1997, pp. 1106–1124) is less (more) accurate than the one proposed by Vandenboomgaerde et al. (Phys. Fluids, vol. 14, 2002, pp. 1111–1122), since the former ignores perturbation solutions higher than fourth order (the latter retains only terms with the highest power in time).

Error-diffusion-kernel parameters for binary pattern in 1-bit fringe projection profilometry.

In fringe projection profilometry, 1-bit processing of 8-bit raster patterns is a common method to suppress nonlinear errors in commercial projectors and realize high-speed projection in industrial projectors. In the process of generating 1-bit fringes from sinusoidal fringes, the generation of high-order harmonics is inevitable; choosing to introduce fewer high-order harmonics of the algorithm is conducive to defocus to obtain a better sinusoidal pattern. This paper proposes a method to expand the error-diffusion kernel of the conventional Floyd-Steinberg diffusion dithering algorithm from 2×3 to 3×5, which can reduce the grayscale change of surrounding pixels and generate 1-bit fringes with fewer high-order harmonics. Meanwhile, this paper optimizes the parameters of the 3×5 error-diffusion kernel and proposes the optimal parameters for this kind of diffusion kernel. The simulation results show that the fringes generated by the proposed 3×5 error-diffusion-kernel algorithms are closer to sinusoidal fringes after Gaussian low-pass filtering. The experimental results show that the accuracy of the 3×5 diffusion kernel algorithms is higher.

Anomalous Relativistic Emission from Self-Modulated Plasma Mirrors.

The interaction of intense laser pulses with plasma mirrors has demonstrated the ability to generate high-order harmonics, producing a bright source of extreme ultraviolet (XUV) radiation and attosecond pulses. Here, we report an unexpected transition in this process. We show that the loss of spatiotemporal coherence in the reflected high harmonics can lead to a new regime of highly efficient coherent XUV generation, with an extraordinary property where the radiation is directionally anomalous, propagating parallel to the mirror surface. With analytical calculations and numerical particle-in-cell simulations, we discover that the radiation emission is due to laser-driven oscillations of relativistic electron nanobunches that originate from a plasma surface instability.

Anti-crosstalk absolute phase retrieval method for microscopic fringe projection profilometry using temporal frequency-division multiplexing.

In microscopic fringe projection profilometry (MFPP), the traditional absolute phase retrieval method using composite frequency fringe has the shortcomings of low accuracy and poor robustness due to mutual crosstalk of harmonic from the different channels of frequency-division multiplexing. In this study, an absolute phase retrieval method that avoids the inter-channel crosstalk is proposed. By introducing guard bands to accommodate the frequency channels corresponding to the second harmonic that dominate the high order harmonics, the aliasing between the second harmonic and the fundamental is eliminated. Consequently, phase maps without crosstalk can be demodulated using appropriate phase-shifting algorithms. The proposed method is well-suited for high-precision three-dimensional shape measurement scenarios in many fields such as integrated circuit manufacturing process control and micro-electro-mechanical system quality inspection. The experiment results demonstrate that the anti-crosstalk method is effective and can realize three-dimensional reconstruction for discontinuous planar surface and spherical surface.

A novel parallel multi-harmonic global multi-channel control algorithm for helicopter active vibration control

The vibrations of the helicopter fuselage are mainly induced by the rotor with blade pass frequency and the high order harmonics. The conventional filtered-x least mean square (FxLMS) control algorithm usually used a uniform convergence factor for all the harmonics which leads poor effect in controlling multi-harmonic vibration. In this paper, a novel parallel multi-harmonic global multi-channel (MHGMC) control method is proposed to suppress the multi-harmonic vibration components transmitted from the main rotor to the fuselage. Bandpass filters are used to separate multiple frequency components of the error signals, the control channel models are identified for the corresponding frequency range to independently control each frequency component, and the reconstruction of the reference input signals can be obtained from the separated error signal, effectively improving the performance of tracking interference signals. In addition, the coupling of the control channels is considered, and the global vibration optimization is taken as the control objective to update the weight coefficient of the controller. An active vibration control system of the helicopter main gearbox eight-strut installation configuration has been established. The simulation and experiment results show that the proposed controller has faster control convergence speed and better control effect of multiple harmonics than the conventional filtered-x least mean square algorithm, and the attenuations of the disturbing frequency harmonic components at all measurement points in the experiment are over 38dB. The experimental results of variable excitation also verify that the proposed control algorithm has excellent adaptability and strong robustness.

High repetition rate relativistic laser-solid-plasma interaction platform featuring simultaneous particle and radiation detection.

We report on a uniquely designed high repetition rate relativistic laser-solid-plasma interaction platform, featuring the first simultaneous measurement of emitted high-order harmonics, relativistic electrons, and low divergence proton beams. This versatile setup enables detailed parametric studies of the particle and radiation spatio-spectral beam properties under a wide range of controlled interaction conditions, such as pulse duration and plasma density gradient. Its array of complementary diagnostics unlocks the potential to unravel interdependencies among the observables and should aid in further understanding the complex collective dynamics at play during laser-plasma interactions and in optimizing the secondary beam properties for applications.

Aeroelastic investigation on an all-movable horizontal tail with free-play nonlinearity

Free-play-induced nonlinear dynamic behavior has been one of the most important topics of aeroelastic research in recent decades. In this paper, the describing function (DF) method is developed to investigate the complex dynamic response of a popular all-movable horizontal tail with free-play. Piecewise expressions for the time history and phase portrait of limit cycle oscillation (LCO) are derived by the developed DF method, which is conducive to understand the mechanism of free-play-induced LCO. Another advantage of the developed DF method is the ability to predict the high-order harmonics, which cannot be realized by the classic DF method. A three-dimensional (3D) all-movable horizontal tail model with torsional free-play was designed and manufactured to implement wind tunnel tests via various initial parameters. A good agreement was found between the numerical and experimental results, which can demonstrate the effectiveness of the proposed method. The influence of the initial parameters of the all-movable horizontal tail on the LCO characteristics is analyzed by both numerical calculations and wind tunnel tests. The method and results in this paper can provide a significant reference for the design of all-movable horizontal tail versus the free-play-induced LCO.

Modifying the Electron Dynamics in High-Order Harmonic Generation via a Two-Color Laser Field

We investigate the harmonic emission from bichromatic periodic potential by numerically solving the time-dependent Schrödinger equation in the velocity gauge. The results show that the harmonic minimum is sensitive to the wavelength. Moreover, distinct crystal momentum states contribute differently to harmonic generation. In momentum space, the electron dynamics reveal a close relationship between the spectral minimum and the electron distribution in higher conduction bands. Additionally, by introducing an ultraviolet pulse to the fundamental laser field, the suppression of the harmonic minimum occurs as a result of heightened electron populations in higher conduction bands. This work sheds light on the harmonic emission originating from a solid with a two-atom basis.

Unraveling Spatiotemporal Transient Dynamics at the Nanoscale via Wavelet Transform-Based Kelvin Probe Force Microscopy.

Mechanistic probing of surface potential changes arising from dynamic charge transport is the key to understanding and engineering increasingly complex nanoscale materials and devices. Spatiotemporal averaging in conventional heterodyne detection-based Kelvin probe force microscopy (KPFM) inherently limits its time resolution, causing an irretrievable loss of transient response and higher-order harmonics. Addressing this, we report a wavelet transform (WT)-based methodology capable of quantifying the sub-ms charge dynamics and probing the elusive transient response. The feedback-free, open-loop wavelet transform KPFM (OL-WT-KPFM) technique harnesses the WT's ability to simultaneously extract spatial and temporal information from the photodetector signal to provide a dynamic mapping of surface potential, capacitance gradient, and dielectric constant at a temporal resolution 3 orders of magnitude higher than the lock-in time constant. We further demonstrate the method's applicability to explore the surface-photovoltage-induced sub-ms hole-diffusion transient in bismuth oxyiodide semiconductor. The OL-WT-KPFM concept is readily applicable to commercial systems and can provide the underlying basis for the real-time analysis of transient electronic and electrochemical properties.

Nonlinear high-order harmonics correction for phase measuring profilometry

Gamma nonlinearity severely affects the accuracy of phase measuring profilometry (PMP). Through averaging two phase maps with inverse errors, conventional methods including double phase-shifting (DPS) and Hilbert transform (HT) only compensate the fundamental harmonic while leaving high-order harmonics. To address this issue, this paper presents an efficient high-order harmonics correction (HHC) method. The averaged phase is encoded into factitious fringes on the computer. Then we directly apply HT on these factitious fringes to generate transformed fringes, while the addition of the ideal phase and residual harmonics is converted to multiplication. Finally, the residual high-order harmonics are suppressed, and the corrected phase is calculated using the phase-shifting algorithm. In comparison to conventional DPS and HT methods, the proposed HHC method can efficiently correct the residual high-order harmonics, thereby enhancing the measuring accuracy.