Single Attosecond Pulse Research Articles

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

Crescent-shaped spatial distribution: radiation properties concerning beam waist from the cross collision of a tightly focused laser pulse and a relativistic electron

The radiation properties of the cross collision between a single electron and an intense laser pulse are researched by numerical simulation methods. Under the condition of tightly-focused laser, the electron trajectories, spatiotemporal distribution and spectrum are compared with that under non-tightly focused lasers. The results show that the torsion effect on the electron during the oscillation process is more notable after the tightly focused laser interacts with electron. The radiation it generates is asymmetric in space, and its time distribution is nearly unimodal and can be regarded as a single attosecond pulse. In frequency domain, the spectrum appears to be a supercontinuum. With the increase of beam waist radius, the symmetry of the spatial distribution enhances and time distribution also exhibits a three-peak structure that is symmetrical about the main peak. Furthermore, the spectrum changes from a supercontinuum to a multimodal distribution. The analysis turns out that tightly focused laser is more realistic compared to non-tightly focused laser or even plane wave, which benefits the design of high-quality x-rays in practical application.

Density-dependent carrier-envelope phase shift in attosecond pulse generation from relativistically oscillating mirrors

Density-dependent carrier-envelope phase shift in attosecond pulse generation from relativistically oscillating mirrors

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.

Circularly polarized attosecond pulses generation from laser interaction with magnetized sub-critical plasmas

We propose a method to generate circularly polarized (CP) attosecond pulses by the interactions of a relativistic-intensity right-hand CP laser pulse and magnetized sub-critical plasma. It is theoretically and numerically demonstrated that when an external magnetic field with an appropriate strength is applied to a sub-critical plasma along the laser propagation, the ponderomotive force of a right-hand CP laser at the vacuum-plasma boundary is significantly enhanced. The electrons are then steadily pushed forward until the timely-increasing charge separation field becomes strong enough to pull them back, forming a dense and counter-moving electron sheet. The relativistic-velocity electron sheet works as a flying mirror to compress the tail of the driving laser and efficiently generate a single CP attosecond pulse. The present scheme shows a stable efficiency on different scale lengths of preplasma and thus may provide a robust way to generate bright and CP attosecond pulses.

Effect of stacking configuration on high harmonic generation from bilayer hexagonal boron nitride.

High harmonic generation from bilayer h-BN materials with different stacking configurations is theoretically investigated by solving the extended multiband semiconductor Bloch equations in strong laser fields. We find that the harmonic intensity of AA'-stacking bilayer h-BN is one order of magnitude higher than that of AA-stacking bilayer h-BN in high energy region. The theoretical analysis shows that with broken mirror symmetry in AA'-stacking, electrons have much more opportunities to transit between each layer. The enhancement in harmonic efficiency originates from additional transition channels of the carriers. Moreover, the harmonic emission can be dynamically manipulated by controlling the carrier envelope phase of the driving laser and the enhanced harmonics can be utilized to achieve single intense attosecond pulse.

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.

Development of attosecond pulses and their application to ultrafast dynamics of atoms and molecules

In the past two decades, the development of laser technology has made attosecond science become a cutting-edge research field, providing various novel perspectives for the study of quantum few-body ultrafast evolution. At present, the attosecond pulses prepared in laboratories are widely used in experimental research in the form of isolated pulses or pulse trains. The ultrafast changing light field allows one to control and track the motions of electrons on an atomic scale, and realize the real-time tracking of electron dynamics on a sub-femtosecond time scale. This review focuses on the research progress of ultrafast dynamics of atoms and molecules, which is an important part of attosecond science. Firstly, the generation and development of attosecond pulses are reviewed, mainly including the principle of high-order harmonic and the separation method of single-attosecond pulses. Then the applications of attosecond pulses are systematically introduced, including photo-ionization time delay, attosecond charge migration, and non-adiabatic molecular dynamics. Finally, the summary and outlook of the application of attosecond pulses are presented.

Modification of laser-induced state in atomic attosecond transient absorption by the XUV pulse pair

Attosecond transient absorption (ATA) has been developed as an all-optical technique for probing electron dynamics in matter. Here we present a scheme that can modify the laser-induced state and the corresponding ATA spectrum via excitation by a pair of XUV attosecond pulses and by a time-delayed mid-infrared (MIR) laser probe. Different from the scheme of the electronic excitation by a single XUV attosecond pulse, the application of a pair of XUV pulses provides extra degrees of freedom, such as the time delay and the intensity ratio between two XUV pulses, which make it possible to adjust the pump process, resulting in the modification of the ATA spectrum. We show that by varying the time delay between the two XUV pulses, the population of the dark state and the ATA spectrum of the laser-induced state have periodic modulations. We also demonstrate that the peak of the ATA spectrum of the laser-induced state appears at a fixed time delay between the XUV pair and the MIR laser when the intensity ratio is large, and it changes with the time delay when the intensity ratio is small, which can be related to either one of two peaks in the population of the dark state.

Isolated ultra-bright attosecond pulses via non-collinear gating

When light with relativistic intensity is incident on a solid target, bright attosecond pulses of extreme ultraviolet and x-ray radiation can be generated in the reflected beam. Unfortunately, the use of multi-cycle laser pulses results in trains of these attosecond pulses. Here we investigate a non-collinear gating scheme applied to surface high-harmonic generation to allow for the extraction of a single intense attosecond pulse from this train. Using 3D and 2D particle in cell (PIC) simulations we demonstrate that it is possible to angularly isolate a single attosecond pulse from the main driving laser pulse using this interaction geometry with intensities I > 1020 W cm−2. This result opens the door to generating bright attosecond pulses from relativistic plasmas without the need to spectrally filter the driving laser pulse.

Generation of single circularly polarized attosecond pulses from near-critical density plasma irradiated by a two-color co-rotating circularly polarized laser.

In this paper, a new method is proposed to efficiently generate a single intense attosecond pulse with circular polarization (CP) through the interaction of an intense driving laser with a near-critical density plasma target. The driving laser is composed of two co-rotating CP lasers with similar frequencies but different pulse widths. When the matching condition is satisfied, the combined field is modulated to a short intense pulse followed by a weak tail. The resulting laser falling edge becomes steeper than the initial sub-pulses, which induces a quick one-time oscillation of the target surface. Meanwhile, the tail guarantees the energy to be compressed simultaneously in both polarization directions to the same extent, so that a single CP attosecond pulse can be produced efficiently and robustly via our method, which has been confirmed through extensive numerical simulations. In addition, our method makes it possible to generate a single CP attosecond pulse even for multi-cycle pulses that are already available for existing laser systems. This provides a novel way to advance the investigation of chiral-sensitive light-matter interactions in attosecond scales.

Roles of the transition amplitude phases in photoelectron asymmetry of single strong attosecond pulse

The angular distributions of the photoelectrons in ionization of hydrogen atom by both circularly and linearly polarized intense extreme ultraviolet (XUV) attosecond pulse are investigated by numerically solving the time-dependent Schrödinger equation. We clearly identify nonperturbative features in studying the asymmetrical photoelectron angular distributions in the polarization plane for the XUV photon energy (16.3 eV) close to the ionization threshold, while such nonperturbative features are absent for higher photon energy (36 eV) in the same pulse intensity region. In addition to the carrier-envelope phase (CEP) dependence, the ejection asymmetry of the photoelectron is also sensitive to the relative phases of transition amplitudes in absorbing one photon and two photons. As a consequence, the CEPs corresponding to the maximal (or zero) asymmetry obviously vary as the pulse intensity increases in a moderately large region from 1 × 1015 W cm−2 to 30 × 1015 W cm−2. We attribute the intensity dependence of the transition amplitude phases to a consequence of the depletion of population as well as the Stark energy shift of the initial state. We show that the relative phases of transition amplitudes can be precisely decoded from the pulse intensity dependence of the ejection asymmetry and those phases are insensitive to the ellipticity of the laser pulse.

Comparative study of different optimization methods for single attosecond pulse generation with a two- or three-color gating scheme

The shaping of the waveform of a two- or three-color driving laser pulse is essential for generating an ultrashort isolated attosecond pulse (IAP) from high-order harmonic generation, which can be implemented in two different ways, i.e., direct coherent synthesizing of electric fields with appropriate parameters (wavelength, intensity, carrier envelope phase, time delay), and superposition of fields undergoing a spectral phase shaping in frequency space view, which additionally results in a chirp and pulse-width broadening. In this work, we perform a comparative study on the IAP generation with these two schemes by virtue of a genetic algorithm, and two very meaningful conclusions are clarified. First, weighing the advantages and disadvantages of the two methods, the width and strength of IAPs optimized from two schemes are basically the same. More optimization parameters in the second method of laser shaping do not show an advantage in shortening width or enhancing the intensity of the IAP compared with the first one. Second, in each case, one can get the shortest IAP when the carrier envelope phases for each spectral component are not required to be precisely controlled. This study provides useful theoretical guidance for generating a shorter IAP with multicolor gating in the experiment.

Generation and characterization of isolated attosecond pulses at 100 kHz repetition rate

The generation of coherent light pulses in the extreme ultraviolet (XUV) spectral region with attosecond pulse durations constitutes the foundation of the field of attosecond science. Twenty years after the first demonstration of isolated attosecond pulses, they continue to be a unique tool enabling the observation and control of electron dynamics in atoms, molecules, and solids. It has long been identified that an increase in the repetition rate of attosecond light sources is necessary for many applications in atomic and molecular physics, surface science, and imaging. Although high harmonic generation (HHG) at repetition rates exceeding 100 kHz, showing a continuum in the cutoff region of the XUV spectrum, was already demonstrated in 2013, the number of photons per pulse was insufficient to perform pulse characterization via attosecond streaking, let alone to perform a pump-probe experiment. Here we report on the generation and full characterization of XUV attosecond pulses via HHG driven by near-single-cycle pulses at a repetition rate of 100 kHz. The high number of 10 6 XUV photons per pulse on target enables attosecond electron streaking experiments through which the XUV pulses are determined to consist of a dominant single attosecond pulse. These results open the door for attosecond pump-probe spectroscopy studies at a repetition rate 1 or 2 orders of magnitude above current implementations.

Theoretical study of high-order harmonics and single ultrashort attosecond pulse generated by optimized combination of laser field

High-order harmonic generation, which is a hot topic of strong ultrafast fields, is one of the most important ways for obtaining the ultraviolet attosecond sources, and has a very wide application prospect. This work focuses on the challenges of the generation of either short or high attosecond pulses. We present the research progress of the high-order harmonics and attosecond pulse generation, and propose an effective and feasible method, and show some results. Specifically, combining the time-dependent Schrödinger equation and new unconstrained optimization algorithm, the objective function with the aim of the widest supercontinuum plateau of He atom is designed and the optimized two-color and three-color laser fields are obtained. The supercontinuum spectra extend up to 100 harmonic orders for the case of the optimized two-color laser field. As a result, a single ultrashort attosecond pulse of 25 as is produced. For the three-color case, the supercontinuum spectra reach up to 170 harmonic orders, and the width of single shortest attosecond pulse obtained by superposing pulses from low order (110 order) to high order (280 order) is obtained to be 17 as . Taking the optimized two-color laser field for example, the macroscopic medium propagation is discussed by solving the Maxwell equation. The results show that the selectivity of quantum trajectories from far-field space distribution can obtain the single ultra-short attosecond pulse.

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

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

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.

Nonlinear Thomson scattering of a relativistic elliptically polarized laser with varied incident pulse widths

Within the frame of classical electrodynamics, nonlinear Thomson scattering by a stationary electron of an elliptically polarized tightly focused laser has been investigated. The electron’s trajectory, energy gain, spatial radiation distribution and temporal characteristics are studied. Due to the properties of the elliptically polarized laser pulse, the energy curve is jagged and the trajectory of electrons is in an elliptical spiral shape. It is demonstrated that the net energy gain of the electron is nearly zero in the few-cycle domain, whereas the net energy gain increases as the laser has a larger pulse width. We describe a mechanism of electron energy gain variation during an elliptical polarized laser pulse. Furthermore, with pulse width increases, the spatial radiation distribution has more sets of local maxima and each set has four local maximums. Additionally, the results show that the electron has the potential to generate a single attosecond pulse when the laser has a few-cycle width pulse. The larger the pulse width is, the weaker the maximal radiation power will be.

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.