Harmonic Cutoff Research Articles

Quality control on vibrator ground force in land vibroseis acquisition

Many quality control (QC) methods are used to monitor the output force from seismic vibrators. These QC tools usually provide the vibrator output force in three aspects — fundamental force, phase, and harmonic distortion — to measure the quality of the ground force compared with the predetermined sweep. As the vibrator works on challenging earth surfaces, such as unconsolidated ground surfaces, the peak harmonic distortion, a key vibrator QC parameter, always exceeds its QC threshold. This necessitates a vibrator reshoot and thereby a degradation of productivity. The purpose of this paper is to demonstrate that in unconsolidated ground surface areas a new setting of the harmonic cutoff frequency on a vibrator controller is recommended. This new setting reduces the unnecessary harmonics around 200 Hz so that the peak harmonic distortion is controlled in the required QC range. Therefore, unnecessary vibrator reshoots can be avoided, leading to improved productivity.

Spectral phase pulse shaping reduces ground state depletion in high-order harmonic generation

High-order harmonic generation (HHG) has become an indispensable process for generating attosecond pulse trains and single attosecond pulses used in the observation of nuclear and electronic motion. As such, improved control of the HHG process is desirable, and one such possibility for this control is through the use of structured laser pulses. We present numerical results from solving the one-dimensional time-dependent Schrödinger equation for HHG from hydrogen using Airy and Gaussian pulses that differ only in their spectral phase. Airy pulses have identical power spectra to Gaussian pulses, but different spectral phases and temporal envelopes. We show that the use of Airy pulses results in less ground state depletion compared to the Gaussian pulse, while maintaining harmonic yield and cutoff. Our results demonstrate that Airy pulses with higher intensity can produce similar HHG spectra to lower intensity Gaussian pulses without depleting the ground state. The different temporal envelopes of the Gaussian and Airy pulses lead to changes in the dynamics of the HHG process, altering the time-dependence of the ground state population and the emission times of the high harmonics.Graphical abstractHigh-order harmonic generation (HHG) using an Airy pulse with a third order spectral phase results in less ground state depletion, but similar harmonic yield, compared to a Gaussian pulse. Top – schematic depiction of the 3-step HHG process for different intensity pulses. Bottom left – time-dependent ground state populations for Gaussian pulses showing that a more intense pulse causes more ground state depletion. Bottom middle – final ground state populations for Airy and Gaussian pulses as a function of intensity showing that Airy pulses result in less ground state depletion for a given intensity. Bottom right – HHG spectra for a more intense Airy pulse and a less intense Gaussian pulse exhibit similar shapes, magnitudes, and plateau cutoff values

Temporal control of high-order harmonic cutoffs in periodic crystals

Temporal control of high-order harmonic cutoffs in periodic crystals

High-order harmonic generation of ZnO crystals in chirped and static electric fields

High harmonic generation in ZnO crystals under chirped single-color field and static electric field are investigated by solving the semiconductor Bloch equation (SBE). It is found that when the chirp pulse is introduced, the interference structure becomes obvious while the harmonic cutoff is not extended. Furthermore, the harmonic efficiency is improved when the static electric field is included. These phenomena are demonstrated by the classical recollision model in real space affected by the waveform of laser field and inversion symmetry. Specifically, the electron motion in k-space shows that the change of waveform and the destruction of the symmetry of the laser field lead to the incomplete X-structure of the crystal-momentum-resolved (k-resolved) inter-band harmonic spectrum. Furthermore, a pre-acceleration process in the solid four-step model is confirmed.

Wavelength scaling of high harmonic yields and cutoff energies in solids driven by mid-infrared pulses.

The effect of driving wavelengths on high harmonic generation (HHG) have long been a fundamental research topic. However, despite of abundant efforts, the investigation of wavelength scaling of HHG in solids is still confined within the scope of theoretical predictions. In this work, we for the first time to the best of our knowledge, experimentally reveal wavelength scaling of HHG yields and cutoff energy in three typical solid media (namely pristine crystals GaSe, CdTe and polycrystalline ZnSe), driven in a broad mid-infrared (MIR) range from 4.0 to 8.7 µm. It is revealed that when the driving wavelength is shorter than 6.5-7.0 µm, HHG yields decrease monotonously with the MIR driving wavelengths, while they rise abruptly by 1-3 orders of magnitude driven at longer wavelength and exhibit a crest at 7.5 µm. In addition, the cutoff energies are found independent on driving wavelengths across the broad MIR pump spectral range. We propose that the interband mechanism dominates the HHG process when the driving wavelength is shorter than 6.5-7.0 µm, and as the driving wavelength increases, intraband contribution leads to an abrupt rise of the HHG yields, which is verified by the HHG polarization measurement driven at 3.0 and 7.0 µm. This work not only experimentally demonstrate the wavelength scaling of HHG in solids, but more importantly blazes the trail for optimizing the HHG performance by choosing a driving wavelength and provides experimental method to distinguish the interband and intraband dynamics.

Tunability of Half Cycle Cutoff Harmonics with Inhomogeneously Enhanced Laser Pulse

For homogeneous driving, half cycle harmonics and its corresponding half cycle cutoff (HCO) show prominent spectral features, allowing one to produce an isolated attosecond pulse with suitable filtering, or vice versa the retrieval of the driving pulse itself. The temporal profile and spatial dependence of the inhomogeneously enhanced field are two important factors that determine the high harmonic generation (HHG) near a plasmonic nanostructure. This leads us to the question of how the HHG spectra and, in particular, the corresponding half cycle harmonics modify with different types of inhomogeneously enhanced fields. To elucidate this, we have made a comparative study of the HHG in three different types of inhomogeneously enhanced laser pulses by employing the time-dependent Schrödinger equation in one dimension. Within our chosen parameter range, the HCO in cutoff and mid-plateau regimes shift towards higher order with the increase of strength of the inhomogeneity in isotropic case. In anisotropic inhomogeneity, the cutoff HCO shifts towards the higher order but the mid-plateau HCO shifts towards lower order with the increase of strength of inhomogeneity. With increasing carrier envelope phase (CEP), the enhanced HCO in the lower-order harmonic region shifts towards higher orders. This shift is nearly linear from near the above threshold to mid-plateau region and becomes saturated in the near cutoff region. The harmonic spectra is modulo-π periodic for the isotropic inhomogeneity and it is modulo-2π periodic for the anisotropic inhomogeneity. This extension of periodicity increases the tunability of the enhanced HCO harmonics with CEP in the anisotropic inhomogeneity than the CEP tuning of the HCO harmonics in the isotropic inhomogeneity or vice versa the retrieval of CEP.

Generation of the isolated highly elliptically polarized attosecond pulse using the polarization gating technique: TDDFT approach.

This paper theoretically investigates the generation of isolated elliptically polarized attosecond pulses with a tunable ellipticity from the interaction of Cl2 molecule and a polarization-gating laser pulse. A three-dimensional calculation based on the time-dependent density functional theory is done. Two different methods are proposed for generating elliptically polarized single attosecond pulses. The first method is based on applying a single-color polarization gating laser and controlling the orientation angle of the Cl2 molecule with respect to the polarization direction of the laser at the gate window. An attosecond pulse with an ellipticity of 0.66 and a pulse duration of 275 as is achieved by tuning the molecule orientation angle to 40° in this method and superposing harmonics around the harmonic cutoff. The second method is based on irradiating an aligned Cl2 molecule with a two-color polarization gating laser. The ellipticity of the attosecond pulses obtained by this method can be controlled by adjusting the intensity ratio of the two colors. Employing an optimized intensity ratio and superposing harmonics around the harmonic cutoff would lead to the generation of an isolated, highly elliptically polarized attosecond pulse with an ellipticity of 0.92 and a pulse duration of 648 as.

Extension of high-order harmonic generation cutoff from laser-ablated tin plasma plumes.

The high-order harmonic spectra from laser-ablated tin plasma plumes are investigated experimentally and theoretically at different laser wavelengths. It is found that the harmonic cutoff is extended to ∼84 eV and the harmonic yield is greatly improved by decreasing the driving laser wavelength from 800 nm to 400 nm. Appling the Perelomov-Popov-Terent'ev theory with the semiclassical cutoff law and one-dimensional time-dependent Schrödinger equation, the contribution of the Sn3+ ion to harmonic generation accounts for the cutoff extension at 400 nm. With the qualitative analysis of the phase mismatching effect, we reveal the phase matching caused by the dispersion of free electrons is greatly optimized in the 400 nm driving field relative to the 800 nm driving field. The high-order harmonic generated from laser-ablated tin plasma plumes driven by the short laser wavelength provides a promising way to extend cutoff energy and generate intensely coherent extreme ultraviolet radiation.

Bi-chromatic driver enabled control of high harmonic generation in atomic targets

We investigated the high-order harmonic generation from interacting time-delayed, linearly polarized bi-chromatic laser pulses with the atomic target. The frequency ratio of secondary to primary fields (), along with the carrier-envelope-phase (CEP) and respective time-delay between the two pulses, are very instrumental in controlling the ionization of the electron and so the quantum dynamics in the continuum. We observed an optimum CEP (φ) and time delay () for a given bi-chromatic frequency ratio, giving maximum cutoff energy. We studied the effect of CEP and time delay for a fixed frequency ratio and observed that the harmonic cutoff could be controlled in an experimentally feasible way. Moreover, the harmonic yield in the energy range 140 eV–240 eV was also calculated, and it was observed that the harmonic yield scales as . The attosecond pulses for different CEP were also calculated by superposing the harmonics in the same energy range, and pulses were observed with peak intensity decreasing with CEP, following the variation of respective harmonic yield with CEP.

High-order harmonic generation by sub-cycle laser pulses and associated scaling laws

We studied the high-harmonic generation by the interaction of sub-cycle laser pulses with the He atom. The sub-cycle pulses are modeled using the complex source vector beam model, which is an exact solution to Maxwell's equations and accurately models the sub-cycle field profiles. We observed that the harmonic cutoff could be extended with the variation of the sub-cycle pulse duration, mainly because of the inherent blueshift associated with shorter pulses. The scaling laws for the harmonic yield and harmonic cutoff energy with pulse duration and fundamental driver wavelengths are also deduced. Furthermore, a detailed wavelet analysis of harmonic generation by sub-cycle pulses is carried out. The appropriate filtering and superposition of the harmonics gave rise to a single attosecond pulse of duration ∼100 as.

High harmonic generation near a bow-tie nanostructure: sensitivity to carrier envelope phase and plasmonic inhomogeneity

High harmonic generation (HHG) from atoms near a plasmonic nanostructure interacting with a relatively low intensity driving laser field is a promising candidate for table top attosecond pulse source. The effect of carrier envelope phase (CEP) of the few cycle driving pulse on inhomogeneous high harmonics generation is well studied in literature, for example, the harmonic cut-off can be efficiently controlled by tuning the CEP. Here, we show selective enhancements of harmonic spectra due to half-cycle cutoff (HCO) which is highly sensitive to the CEP, in both spatially homogeneous and inhomogeneous driving laser fields. Essentially the selective enhancement of spectral structures results from contributions of both short and long trajectories in certain HCO regions. Compared to the homogeneous HHG in the presence of inhomogeneity, these enhanced groups eventually merge to the background with the increase of the strength of inhomogeneity. This limits the maximum possible tunability of selective enhancement. Further, near cut-off harmonics can be a good candidate to produce isolated attosecond pulses, with substantial control via CEP of the driving laser pulse along with the strength of inhomogeneity.

High-order harmonic generation of the cyclo[18]carbon molecule irradiated by circularly polarized laser pulse

High-order harmonic generation of the cyclo[18]carbon (C18) molecule under few-cycle circularly polarized laser pulse is studied by time-dependent density functional theory. Compared with the harmonic emission of the ring molecule C6H6 having similar ionization potential, the C18 molecule has higher efficiency and cutoff energy than C6H6 with the same laser field parameters. Further researches indicate that the harmonic efficiency and cutoff energy of the C18 molecule increase gradually with the increase of the laser intensity of the driving laser or decrease of the wavelength, both are larger than those of the C6H6 molecule. Through the analysis of the time-dependent evolution of the electronic wave packets, it is also found that the higher efficiency of harmonic generation can be attributed to the larger spatial scale of the C18 molecule, which leads to a greater chance for the ionized electrons from one atom to recombine with others of the parent molecule. Selecting the suitable driving laser pulse, it is demonstrated that high-order harmonic generation in the C18 molecule has a wide range of applications in producing circularly polarized isolated attosecond pulse.

Investigation of the multielectron dynamics of CO in intense laser fields by the effective potential analysis of natural orbitals

We simulated the multielectron dynamics of CO in multicolor pulses of a near-IR fundamental ω and harmonics up to 4ω by using the multiconfiguration time-dependent Hartree-Fock method. The dynamics were analyzed in terms of effective potentials that govern the time evolution of molecular orbitals. The effective potential for the highest occupied orbital has a hump barrier responsible for anisotropic ionization of CO and the shape of a hump significantly changes at different internuclear distances. The electronic response became nonadiabatic when a 4ω-field was included, resulting in the enhancement in ionization and the extension of the high-order harmonic generation cutoff.

High-order harmonics generation in the laser-induced lead-free perovskites-containing plasmas

High-order harmonics generation in the laser-induced plasmas produced on the surfaces of lead-free perovskites is studied. We analyze the harmonics generation in (CH3NH3)2CuCl4 and (CH3NH3)2CuBr4 plasmas during their ablation by the femtosecond, picosecond, and nanosecond pulses. The modifications of the high-order harmonics spectra are studied using the -color pump scheme (800 nm and 400 nm, 40 fs pulses). The influence of the variations of laser chirp and pulse duration on the dynamics of high-order harmonics generation is examined. The spectral shift, chirp-related harmonic cutoff scaling, and the role of the pulse duration of converting and heating laser radiation are examined at different conditions of plasma formation and harmonic generation. The dependencies of the pulse duration and the fluence of heating pulses on the harmonic’s blue shift are found. The effect of harmonics broadening and splitting on the two red- and blue-shifted components is demonstrated.

High-order harmonics from backscattering of delocalized electrons

It is shown that electron backscattering can enhance high-harmonic generation in periodic systems with broken translational symmetry. Paradigmatically, we derive for a finite chain of atoms the harmonic cutoff due to electrons backscattered from the edges of the chain and demonstrate a maximum in the harmonic yield if twice the quiver amplitude of the driven electrons equals the chain length. For an intuitive understanding of our quantum results we develop a refined semiclassical trajectory model with finite electron-hole separation after tunneling. We demonstrate that the same "tunnel exit" also holds for interband harmonics in conventional periodic solid-state systems.

Ion-based high-order harmonic generation from water window to keV region with a transverse disruptive pulse for quasi-phase-matching.

A scheme for ion-based high-harmonic generation from water window to keV x-ray is investigated. He1+ ions with 54.42-eV ionization potential extend the harmonic cutoff energy to 1 keV. The transverse selective-zoning method of quasi-phase-matching is utilized to overcome the severe plasma dispersion in a highly ionized medium. The calculated conversion efficiency reaches about 15% of the perfect phase-matching condition. Wavelength tunability is achieved by incorporating a programmable spatial-light modulator to control the quasi-phase-matching pattern.

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.

Chirp form selection to produce intense and broad harmonic spectra and attosecond pulses in the presence of single and superposition initial states

The chirp form selection for producing intense and broad high-order harmonic spectra has been investigated when the initial state is chosen to be the single or superposition states. It is found that, for the case of a single ground initial state, the down-chirp is much better for extending the harmonic cutoff with the stronger emission intensity. Moreover, the multi-color combined field is beneficial to produce the larger harmonic cutoff and higher harmonic intensity. After the control of laser waveform, the combination of 3-color down-chirps with a proper UV pulse is the best condition to obtain the intense X-ray spectral continuum and the isolated attosecond pulse. For the case of superposition initial state, both the up-chirp and down-chirp are beneficial to generate the high-intensity spectral regions. However, with the combination of multi-color field, only the harmonic cutoff can be further extended, and the harmonic intensity presents almost no changes for the superposition initial state case. Finally, by properly choosing the 3-color up-chirps or 3-color down-chirps combined pulses, the stronger intensity harmonic spectra covering the X-ray region can be obtained, which can produce the isolated pulses of 37 as.

Nonlinear chirp combination effect on the improvement of high harmonic spectra and attosecond pulses

The effect of nonlinear chirp combination on the enhancement of harmonic cutoff and harmonic intensity has been investigated by using a two-color chirped pulse. It is found that with the combination of 2-order chirp form, the strongest intensity enhancement of harmonic spectrum can be found. While, with the combination of 2-order and 3-order chirp forms, the largest cutoff extension of the harmonic spectrum can be obtained. Finally, by properly using the harmonic spectra driven by the above two kinds of combined pulses, the single attosecond pulses (SAPs) of 43 as and 33 as can be generated.

Initial state effect on waveform control of high-order harmonic spectrum and attosecond pulse generation

In this paper, the waveform control of high-order harmonic generation and attosecond pulse generation from a different initial state of He atom has been investigated. The results show that (i) by properly controlling the carrier-envelope phases, the time delays and the laser intensities of a 3-color laser pulse, the best waveforms for the harmonic cut-off extension can be found. Although the harmonic cut-offs from the ground initial state and the superposition initial state are almost the same, the harmonic intensities from the superposition initial state are 4 to 5 orders of magnitudes higher than those from the ground initial state. (ii) With the introduction of the inhomogeneous effect, the harmonic cut-offs can be further extended. However, the harmonic intensities from the superposition initial state are remarkably decreased compared with those from the homogeneous pulses, which is unbeneficial to generate the intense attosecond pulses. (iii) When the ground state is chosen to be the initial and with the assistance of the 4th UV pulse, not only the larger harmonic cut-offs can be obtained, but also the stronger harmonic plateaus can be found, which is favorable for producing the intense attosecond pulses. Thus, at the end of this paper, by superposing the harmonics from the best harmonic spectra, the single attosecond pulses with the duration of 36 as can be obtained.