Higher Harmonic Response Research Articles

Ultrafast dephasing in solid-state high harmonic generation: macroscopic origin revealed by real-space dynamics [Invited

Using a fully real-space perspective on high harmonic generation (HHG) in solids, we examine the relationship between microscopic response, macroscopic propagation of this response to the far-field, and the extremely short dephasing times routinely used in the theoretical simulations of experimentally measured solid-state HHG spectra. We find that far-field propagation naturally reduces the contribution to the observed HHG emission from electrons that do not return to the lattice site where they have been injected into the conduction band. We then show that extremely short dephasing times routinely used in microscopic simulations suppress many electron trajectories that contribute to the far-field spectra, leading to significant distortions of the true high harmonic response. We show that a real-space based dephasing mechanism, which preferentially suppresses trajectories that veer too far away from their original lattice site, yields HHG spectra that faithfully retain those trajectories that contribute to the far-field spectra while filtering out those that do not, already at the microscopic level. Our findings emphasize the similarities between atomic and solid-state HHG by highlighting the importance of the intensity-dependent phase of HHG emission and address the longstanding issue regarding the origin of extremely short dephasing times in solid-state HHG.

Role of Spin-Orbit Coupling in High-Order Harmonic Generation Revealed by Supercycle Rydberg Trajectories.

High-harmonic generation is typically thought of as a sub-laser-cycle process, with the electron's excursion in the continuum lasting a fraction of the optical cycle. However, it was recently suggested that long-lived Rydberg states can play a particularly important role in high harmonic generation by atoms driven by the combination of the counterrotating circularly polarized fundamental light field and its second harmonic. Here we report direct experimental evidence of very long and stable Rydberg trajectories contributing to high-harmonic generation in such fields. We track their dynamics inside the laser pulse using the spin-orbit evolution in the ionic core, utilizing the spin-orbit Larmor clock. We confirm their effect on harmonic emission both via microscopic simulations and by showing how this radiation can lead to a well-collimated macroscopic far-field signal. Our observations contrast sharply with the general view that long-lived Rydberg orbits should generate negligible contribution to the macroscopic far-field high harmonic response of the medium.

Harmonic Amplitude Summation for Frequency-tagging Analysis.

In the approach of frequency tagging, stimuli that are presented periodically generate periodic responses of the brain. Following a transformation into the frequency domain, the brain's response is often evident at the frequency of stimulation, F, and its higher harmonics (2F, 3F, etc.). This approach is increasingly used in neuroscience, as it affords objective measures to characterize brain function. However, whether these specific harmonic frequency responses should be combined for analysis-and if so, how-remains an outstanding issue. In most studies, higher harmonic responses have not been described or were described only individually; in other studies, harmonics have been combined with various approaches, for example, averaging and root-mean-square summation. A rationale for these approaches in the context of frequency-based analysis principles and an understanding of how they relate to the brain's response amplitudes in the time domain have been missing. Here, with these elements addressed, the summation of (baseline-corrected) harmonic amplitude is recommended.

Role of intraband dynamics in the generation of circularly polarized high harmonics from solids

Recent studies have demonstrated that the polarization states of high harmonics from solids can differ from those of the driving pulses. To gain insights on the microscopic origin of this behavior, we perform one-particle intraband-only calculations and reproduce some of the most striking observations. For instance, our calculations yield circularly polarized harmonics from elliptically polarized pulses that sensitively depend on the driving conditions. Furthermore, we perform experiments on ZnS and find partly similar characteristics as reported from silicon. Comparison to our intraband-only calculations shows reasonable qualitative agreement for a below-band-gap harmonic. We show that intraband dynamics predict depolarization effects for higher field strengths. For harmonics above the band gap, interband dynamics become important and the high-harmonic response to elliptical excitation looks systematically different. Our work proposes a method to distinguish between different high-harmonic generation mechanisms and it could pave the way to compact solid-state high-harmonic sources with controllable polarization states.

Pb6O5(NO3)2: A Nonlinear Optical Oxynitrate Structurally Based on Lead Oxide Framework.

A high second harmonic generation response is demonstrated by a Pb6O5(NO3)2 lead oxynitrate whose identity was verified upon reinvestigation of the PbO-Pb(NO3)2 system. Its crystal structure exhibits a unique cationic [Pb6O5]2+ framework hosting orientationally ordered NO3- triangles in the channels. Easy preparation and high thermal stability (until ∼500 °C in air) suggest it to be a new promising NLO material.

Spectral caustic in two-color high-order harmonic generation: Role of Coulomb effects

The high-order harmonic spectrum generated in two-color intense laser field under certain conditions has a pronounced maximum caused by the so called spectral caustic. Using a numerical solution of the 3D time-dependent Schr\"odinger equation we study the width of the maximum and the degree of the generation enhancement due to the caustic as a function of the fundamental intensity, wavelength, and atomic ionization potential. It is shown that the degree of this enhancement can be well quantitatively characterized by a single parameter: the ratio of the radius of the free electronic oscillation in the laser field to the atomic size. This behavior can be explained by the Coulomb attraction of the photoelectron to the parent ion, whereas the effect of this attraction on the width of the maximum is negligible. Choosing the field parameters providing a pronounced enhancement, we calculate the high harmonic macroscopic response taking into account the transient phase-matching. We show that the caustic feature can be used to provide a quasi-monochromatic XUV source with an almost linear frequency vs. time dependence. Such source can be used, in particular, for the time-resolved single-shot XUV imaging.

Combination algorithm for cracked rotor fault diagnosis based on NOFRFs and HHR

In this paper, a combination algorithm for diagnosing rotor crack fault is presented. Firstly, the nonlinear output frequency response functions (NOFRFs) are used to analyze the severity of crack damage in the rotor system qualitatively. The NOFRFs are obtained by processing the vibration signal through the nonlinear output frequency response functions. Further analysis of the NOFRFs can determine the crack depth qualitatively. Secondly, the position of the crack is then located using the crack position index (CPI) λ based on the higher harmonic response (HHR) and the dynamic compliance matrix. The simulation and experimental results show that the G2(j2wF) in NOFRFs is very sensitive to crack depth, and the crack position index (CPI) λ can determine the shaft segment effectively where the crack is located. The advantage of this combination algorithm is that it can detect the crack faults by measuring the vibration signal of the cracked rotor at two speeds, which makes the measurement process more simplified and reduces the measurement time for real-time monitoring. At each speed only the vibration response of the two nodes need to be measured, which greatly reduces the number of sensor used in the measurement process and reduces the cost of monitoring. The combination algorithm can diagnose cracked rotor faults effectively and has certain application value in the diagnosis of cracked rotor fault.

Multifunctional property exploration: Bi4O5I2 with high visible light photocatalytic performance and a large nonlinear optical effect.

Exploration of the versatility of materials is very important for increasing the utilization of materials. Herein, we successfully prepared Bi4O5I2 powders via a facile solvothermal method. The Bi4O5I2 photocatalyst exhibited significantly higher photocatalytic activity as compared to the common BiOI photocatalyst in the degradation of methyl orange, methylene blue and rhodamine B under visible light irradiation. Especially, for the degradation of methyl orange, the photocatalytic activity of Bi4O5I2 is about 10 times that of BiOI. Moreover, Bi4O5I2 exhibits an extremely high second harmonic generation response of about 20 × KDP (the benchmark) estimated by the unbiased ab initio calculations. The coexisting multifunction of Bi4O5I2 is mainly because of the increased dipole moment due to the stereochemical activity of lone pairs that promotes separation and transfer of photogenerated carriers, then enhances the photocatalytic activity and results in a high second harmonic generation response. This indicates that Bi4O5I2 may have good potential applications in photocatalytic and nonlinear optical fields.

High-harmonic generation from few-layer hexagonal boron nitride: Evolution from monolayer to bulk response

Two-dimensional materials offer a versatile platform to study high-harmonic generation (HHG), encompassing as limiting cases bulk-like and atomic-like harmonic generation [Tancogne-Dejean and Rubio, Science Advance \textbf{4}, eaao5207 (2018)]. Understanding the high-harmonic response of few-layer semiconducting systems is important, and might open up possible technological applications. Using extensive first-principle calculations within a time-dependent density functional theory framework, we show how the in-plane and out-of-plane nonlinear non-perturbative response of two-dimensional materials evolve from the monolayer to the bulk. We illustrate this phenomenon for the case of multilayer hexagonal BN layered systems. Whereas the in-plane HHG is found not to be strongly altered by the stacking of the layers, we found that the out-of-plane response is strongly affected by the number of layers considered. This is explained by the interplay between the induced electric field by electron-electron interactions and the interlayer delocalization of the wave-functions contributing most to the HHG signal. The gliding of a bilayer is also found to affect the high-harmonic emission. Our results will have important ramifications for the experimental study of monolayer and few-layer two-dimensional materials beyond the case of hexagonal BN studied here as the result we found arew generic and applicable to all 2D semiconducting multilayer systems.

Active acoustic metamaterials using sensor-driver architecture

Acoustic metamaterials can, in principle, overcome the fundamental limitations of passive structures and can enable novel applications that are hard or impossible with passive media. However, active acoustic metamaterials remain elusive, and the few implementations going beyond basic material parameter tunability lag significantly behind the true potential of active media. We will present a design method that results in active metamaterials whose acoustic response is electronically programmed to cover a very large range of non-linear acoustic responses. Specifically, metamaterials obtained with this approach can be configured to have almost any second and higher harmonic response, making them very effective and versatile non-linear acoustic media. We demonstrate experimentally this design methodology in an application in which an acoustically thin metamaterial funnel responds to incident sound waves by producing collimated second harmonics. Past demonstrations of this type of active metamaterials will also be briefly reviewed.

Super-resolution visible photoactivated atomic force microscopy

Imaging the intrinsic optical absorption properties of nanomaterials with optical microscopy (OM) is hindered by the optical diffraction limit and intrinsically poor sensitivity. Thus, expensive and destructive electron microscopy (EM) has been commonly used to examine the morphologies of nanostructures. Further, while nanoscale fluorescence OM has become crucial for investigating the morphologies and functions of intracellular specimens, this modality is not suitable for imaging optical absorption and requires the use of possibly undesirable exogenous fluorescent molecules for biological samples. Here we demonstrate super-resolution visible photoactivated atomic force microscopy (pAFM), which can sense intrinsic optical absorption with ~8 nm resolution. Thus, the resolution can be improved down to ~8 nm. This system can detect not only the first harmonic response, but also the higher harmonic response using the nonlinear effect. The thermoelastic effects induced by pulsed laser irradiation allow us to obtain visible pAFM images of single gold nanospheres, various nanowires, and biological cells, all with nanoscale resolution. Unlike expensive EM, the visible pAFM system can be simply implemented by adding an optical excitation sub-system to a commercial atomic force microscope.

Influence of motion compensation on lock-In thermographic investigations of fatigue crack propagation

Lock-in thermography measurements are influenced by rigid body motion of the specimen due to the mechanical loading. These motion affects asymmetries in the measured temperature fields in the vicinity of the crack. This effect can be eliminated by a motion compensation procedure. Unfortunately, the results of the lock-in thermography are affected by this procedure, too. In this work the influence of the motion compensation procedure on fatigue crack propagation experiments, its gains and disadvantages are studied in a qualitative and quantitative manner. A new method for an automatic determination of the crack length in thermographic measurements is introduced and compared with potential drop measurements. Beside the known thermoelastic and dissipative effects, higher harmonic responses in the discrete Fourier transformation are analyzed and discussed.

Review—Nonlinear Electrochemical Impedance Spectroscopy

Nonlinear Electrochemical Impedance Spectroscopy (NLEIS) is a method of characterizing an electrochemical systems by applying a large amplitude sinusoidal perturbation signal. This article presents a comprehensive review of existing literature on NLEIS analysis development and applications. Two types of NLEIS reports available in the literature, viz. one in which only the fundamental impedance is studied and the other in which both the fundamental and higher harmonic responses are analyzed, are reviewed. Early reports on the development of NLEIS methodology are compiled. Recent advances in the application of NLEIS, in particular in the area of fuel cells, are summarized. In addition, applications of related techniques such as total harmonic distortion and Volterra kernel are included in the purview of this article. There is a large scope for applying NLEIS to understand electrochemical processes. The roadblocks that need to be overcome to enable wider application of NLEIS are identified, and directions for further research are suggested.

Multidimensional high harmonic spectroscopy of polyatomic molecules: detecting sub-cycle laser-driven hole dynamics upon ionization in strong mid-IR laser fields.

High harmonic generation (HHG) spectroscopy has opened up a new frontier in ultrafast science, where electronic dynamics can be measured on an attosecond time scale. The strong laser field that triggers the high harmonic response also opens multiple quantum pathways for multielectron dynamics in molecules, resulting in a complex process of multielectron rearrangement during ionization. Using combined experimental and theoretical approaches, we show how multi-dimensional HHG spectroscopy can be used to detect and follow electronic dynamics of core rearrangement on sub-laser cycle time scales. We detect the signatures of laser-driven hole dynamics upon ionization and reconstruct the relative phases and amplitudes for relevant ionization channels in a CO2 molecule on a sub-cycle time scale. Reconstruction of channel-resolved complex ionization amplitudes on attosecond time scales has been a long-standing goal of high harmonic spectroscopy. Our study brings us one step closer to fulfilling this initial promise and developing robust schemes for sub-femtosecond imaging of multielectron rearrangement in complex molecular systems.

Exact formula for the high harmonic response of a strongly driven two-level system

In this paper we investigate the polarization response for a two-level system under the influence of a strong pump field. We use a strong-field perturbation theory to derive a simple formula for the full spectrum. We use the formula to show that the spectrum has a plateau and a cutoff and is in this way analogous to the well-known high harmonic generation (HHG) spectra generated by noble gases in a strong laser field. Using our formula we derive a simple relation describing the cutoff energy for the two-level system and show that it is similar to the noble gas case but is different in an important way in that it does not depend on the pump wavelength. This is in contrast to the noble gas case where the cutoff depends quadratically on the pump wavelength. Our strong-field perturbation theory can with small modifications be applied to the investigation of the HHG-like spectra generated by strongly driven classical nonlinear oscillator systems.

Low ac field response of Bi-based superconductors with addition of Antimony oxide

We report the effects of the addition of Sb2O3 on the superconducting properties of Bi-2223 system. Samples with composition Bi1.7Pb0.3Ca2Sr2Cu3SbxOy (x=0,0-0.8 wt.%) are prepared by the solid-state reaction method. Ac susceptibility and high harmonic response of polycrystalline superconductors are measured in weak ac and dc magnetic fields. Critical state models are used to explain the nonlinear magnetic response and it is found that the low field odd harmonic response is qualitatively explained reasonably well within the Kim-Anderson regime. We observed that, the low level Antimony doping enhances the transport critical current densities Jc.

Comment on "Al-in-Hornblende Thermobarometry and Sr-Nd-O-Pb Isotopic Compositions of the Early Miocene Alaçam Granite in NW Anatolia (Turkey)"

High harmonic response of high-Tc and Chevrel-phase polycrystalline superconductors are measured in the presence of small ac excitation field and dc magnetic field applied on it. The aim of this work is to study the Josephson weak link behavior and compare the two systems in order to understand the granular nature of polycrystalline superconductors. Critical state models are used to explain the nonlinear magnetic response in polycrystalline superconductors.

Low Field ac Susceptibility and High Harmonics Studies in PbMo6S8 Polycrystalline Superconductor

The ac susceptibility and high harmonic response of polycrystalline PbMo6S8 superconductor are measured in the presence of small ac excitation field and dc magnetic field applied on it. Our experimental results could be explained by the classical Bean critical state model, when the current does not depend on the field and even harmonics are not observed.

Single-Phase Grid-Connected PV System Based on Multi-Carrier PWM and Power Feed-Forward

In the traditional single-phase grid-connected photovoltaic(PV) system, the output grid-current has the shortcomings of high harmonic distortion rate and slow dynamic response. In order to solve these problems, an improved method on the inverter is proposed. The inverter consists of full-bridge circuit and auxiliary circuit. With the multi-carrier PWM, the inverter produces output voltages in five levels, which can reduce the THD of the grid current. At the same time , this paper presents the power feed-forward algorithm based on traditional control method. The output power of PV array is added to the reference of current close-loop as power feed-forward, which improves the dynamic response to the input power changes. At last, the simulation results show the effectiveness of the proposed method.

Influence of Electrode Morphology on Electrochemical Response of SOFC Cathodes

Using finite element calculations, we have investigated theoretically the role of electrode microstructure on the rate of O2 reduction in mixed conducting solid oxide fuel cell (SOFC) cathodes. These calculations were used to predict both impedance and nonlinear higher order harmonic response of single-phase electrodes having idealized 3-D microstructures based on cylinders necked spheres. These calculations show that impedance shape and higher harmonic response are generally very sensitive to the exact details of the microstructure near the electrode/electrolyte interface, even when gradients extend far beyond the interface. In contrast, microstructural details further than about one particle diameter from the interface can be accurately modeled using a macrohomogeneous (average property) description.