Generating femtosecond coherent X-ray pulses in a diffractionlimited storage ring with the echo-enabled harmonic generation scheme

To study ultrafast processes at the sub-picosecond level, novel methods based on coherent harmonic generation technologies have been proposed to generate ultrashort radiation pulses in existing ring-based light sources. Using the High Energy Photon Source as an example, we numerically test the feasibility of implementing one coherent harmonic generation technology, i.e.,the echo-enabled harmonic generation(EEHG) scheme, in a diffraction-limited storage ring(DLSR). Two different EEHG element layouts are considered, and the effect of the EEHG process on the electron beam quality is also analyzed. Studies suggest that soft X-ray pulses, with pulse lengths of a few femtoseconds and peak powers of up to1 MW, can be generated by using the EEHG scheme, while causing little perturbation to the regular operation of a DLSR.

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.

Optimization of extreme ultraviolet vortex beam based on high harmonic generation

In high harmonic generation(HHG),Laguerre–Gaussian(LG) beams are used to generate extreme ultraviolet(XUV)vortices with well-defined orbital angular momentum(OAM),which have potential applications in fields such as microscopy and spectroscopy.An experimental study on the HHG driven by vortex and Gaussian beams is conducted in this work.It is found that the intensity of vortex harmonics is positively correlated with the laser energy and gas pressure.The structure and intensity distribution of the vortex harmonics exhibit significant dependence on the relative position between the gas jet and the laser focus.The ring-like structures observed in the vortex harmonics,and the interference of quantum paths provide an explanation for the distinct structural characteristics.Moreover,by adjusting the relative position between the jet and laser focus,it is possible to discern the contributions from different quantum paths.The optimization of the HH vortex field is applicable to the XUV,which opens up a new way for exploiting the potential in optical spin or manipulating electrons by using the photon with tunable orbital angular momentum.

Elliptically polarized high-order harmonic generation of Ar atom in an intense laser field

High-order harmonic generation(HHG) of Ar atom in an elliptically polarized intense laser field is experimentally investigated in this work.Interestingly,the anomalous ellipticity dependence on the laser ellipticity(ε) in the lower-order harmonics is observed,specifically in the 13rd-order,which displays a maximal harmonic intensity at ε ≈ 0.1,rather than at ε = 0 as expected.This contradicts the general trend of harmonic yield,which typically decreases with the increase of laser ellipticity.In this study,we attribute this phenomenon to the disruption of the symmetry of the wave function by the Coulomb effect,leading to the generation of a harmonic with high ellipticity.This finding provides valuable insights into the behavior of elliptically polarized harmonics and opens up a potential way for exploring new applications in ultrafast spectroscopy and light–matter interactions.

Wavelength Dependent Nonlinear Spectroscopic Study of Third Harmonic Generation Probed by Rotational Maker Fringes Method

Efficient third-order nonlinearities of the Zinc Oxide and Al-doped Zinc Oxide were studied by Third Harmonic Generation (Third Harmonic Generation) Maker fringes to establish the effect Aluminum of Aluminum doping (Al-doping) on the cubic nonlinearities. Adding the Al-dopant to the Zinc Oxide crystal structure results in changes that affect the optical and nonlinear characteristics. Presented results indicate that the magnitude of X(3) was enhanced at single experimental wavelengths;however, across the broadband experimental spectrum, the effect of Al-doping remained relatively constant. The observed enhancement of third-order nonlinearity was purely from the bound electronic response. The observation is attributed to increased charge carriers and spontaneous polarization in the Zinc Oxide and Al-doped Zinc Oxide crystal structure.

Role of the dressed and bound states on below-threshold harmonic generation of He atom

High-order harmonic generation below ionization threshold of He atom in the laser field is investigated by solving the three-dimensional time-dependent Schrodinger equation. An angular momentum-dependent model potential of He atom was used for getting the accurate energy levels of singlet states. The satellite-peak structures of the below-threshold harmonic generation(BTHG) of He are observed. We analyze the emission properties of the BTHG by employing a synchrosqueezing transform technique. We find that the satellite-peak structures have two types related to two kinds of transitions. One is the transition of the dressed states of the excited states, the other is the transition between the excited states and the ground state in the field-free case. Furthermore, our results show that the maximum Stark shift of the 2 p state is about 0.9 Up(penderomotive energy), and that of the 4 p state is about 1.0 Up. It indicates that the energy difference between some satellite-and main-peaks of the BTHG can be used to measure the maximum Stark shift of the excited states of He atom in the laser field.

Extension of high-order harmonics and generation of an isolated attosecond pulse in the chirped laser field

This paper theoretically investigates the high-order harmonic generation cutoff extension using intense few-cycle linearly chirped laser pulses. It shows that the cutoff of the harmonic can be extended remarkably by optimising the chirping parameters. The time-frequency characteristics of high-order harmonics with different chirping parameters are analysed by means of wavelet transform of the dipole acceleration. It also gives out the classical three-step model pictures of electron. By superposing a properly selected range of the harmonic spectrum, it obtains an isolated 65as pulse.

Effect of laser intensity on quantum trajectories in the macroscopic high-order harmonic generation

We macroscopically investigate the effect of the laser intensity and gas density on quantum trajectories in the highorder harmonic generation of Ne atoms irradiated by few-cycle, 800-nm laser pulses. The time–frequency profile of the harmonics shows that the long quantum trajectory is dominant at both lower and higher gas densities for a low laser intensity. At high laser intensities, the long quantum trajectory plays an important role for lower gas densities, while the short quantum trajectory is dominant at higher gas densities. An analysis of the phase mismatch for high-order harmonic generation shows that the primary emission of the quantum trajectories is determined by dynamic changes in the laser electric field during the propagation process.

Second Harmonic Generation of Lamb Wave in Numerical Perspective

The influences of phase and group velocity matching on cumulative second harmonic generation of Lamb waves are investigated in numerical perspective. Finite element simulations of nonlinear Lamb wave propagation are performed for Lamb wave mode pairs with exact and approximate phase velocity matching, with and without group velocity matching, respectively. The evolution of time-domain second harmonic Lamb waves is analyzed with the propagation distance. The amplitudes of primary and second harmonic waves are calculated to characterize the acoustic nonlinearity. The results verify that phase velocity matching is necessary for generation of the cumulative second harmonic Lamb wave in numerical perspective, while group velocity matching is demonstrated to not be a necessary condition.

Selection of quantum path in high-order harmonics and isolated sub-100 attosecond generation in few-cycle spatially inhomogeneous laser fields

We theoretically study the selection of the quantum path in high-order harmonics（HHG） and isolated attosecond pulse generation from a one-dimensional（1D） model of a H_2~＋ molecule in few-cycle inhomogeneous laser fields.We show that the inhomogeneity of the laser fields play an important role in the HHG process.The cutoff of the harmonics can be extended remarkably,and the harmonic spectrum becomes smooth and has fewer modulations.We investigate the time-frequency profile of the time-dependent dipole,which shows that the short quantum path is enhanced and the long quantum path disappears in spatially inhomogeneous fields.The semi-classical three-step model is also applied to illustrate the physical mechanism of HHG.The influence of driving field carrier-envelop phase（CEP） on HHG is also discussed.By superposing a series of properly selected harmonics,an isolated attosecond pulse（IAP） with duration 53 as can be obtained by a 15-fs,1600-nm laser pulse with the parameter ε = 0.0013（e is the parameter that determines the order of inhomogeneity of the laser field）.

Restraint of spatial distribution in high-order harmonic generation from a model of hydrogen molecular ion

The spatial distribution in high-order harmonic generation（HHG） is theoretically investigated by using a few-cycle laser pulse from a two-dimensional model of a hydrogen molecular ion. The spatial distribution in HHG demonstrates that the harmonic spectra are sensitive to the carrier envelope phase and the duration of the laser pulse. The HHG can be restrained by a pulse with the duration of 5 fs in the region from the 90 th to 320th order. This characteristic is illustrated by the probability density of electron wave packet distribution. The electron is mainly located near the nucleus along the positive-x direction from 3.0 o.c. to 3.2 o.c., which is an important time to generate the HHG in the plateau area. We also demonstrate the time-frequency distribution in the region of the positive-and negative-x direction to explain the physical mechanism.

Tunable second harmonic generation from a Kerr-lens mode-locked Yb:YCa4O(BO3)3 femtosecond laser

We experimentally demonstrated a diode-pumped Kerr-lens mode-locked femtosecond（fs） laser with a self-frequency doubling Yb：YCa_4O（BO_3）_3 crystal.Sub-40 fs laser pulses were directly generated from the oscillator without extracavity compression.The central wavelength was tunable from 1039 nm to 1049 nm with a typical bandwidth of 35 nm and an average output power of 53 mW.For the first time,a self-frequency doubled second harmonic green laser with tunable range from 519 nm to 525 nm was observed.

Helicity of harmonic generation and attosecond polarization with bichromatic circularly polarized laser fields

We theoretically investigate the high-order harmonic generation(HHG) of helium atom driven by bichromatic counterrotating circularly polarized laser fields. By changing the intensity ratio of the two driving laser fields, the spectral chirality of the HHG can be controlled. As the intensity ratio increases, the spectral chirality will change from positive-to negativevalue around a large intensity ratio of the two driving fields when the total laser intensity keeps unchanged. However, the sign of the spectral chirality can be changed from positive to negative around a small intensity ratio of the two driving fields when the total laser intensity changes. At this time, we can effectively control the helicity of the harmonic spectrum and the polarization of the resulting attosecond pulses by adjusting the intensity ratio of the two driving laser fields. As the intensity ratio and the total intensity of the driving laser fields increase, the relative intensity of either the left-circularly or right-circularly polarized harmonic can be enhanced. The attosecond pulses can evolve from being elliptical to near linear correspondingly.

A scaling law of high-order harmonic generation

Using a nonperturbative quantum electrodynamics theory of high-order harmonic generation （HHG）, a scaling law of HHG is established. The scaling law states that when the atomic binding energy Eb, the wavelength ）, and the intensity I of the laser field change simultaneously to kEb, λ/k, and k3I, respectively. The characteristics of the HHG spectrum remain unchanged, while the harmonic yield is enhanced k3 times. That HHG obeys the same scaling law with above-threshold ionization is a solid proof of the fact that the two physical processes have similar physical mechanisms. The variation of integrated harmonic yields is also discussed.

Dual bound states in the continuum enhanced second harmonic generation with transition metal dichalcogenides monolayer

The emergence of two dimensional(2D)materials has opened new possibilities for exhibiting second harmonic genera-tion(SHG)at the nanoscale,due to their remarkable optical response related to stable excitons at room temperature.However,the ultimate atomic-scale interaction length with light makes the SHG of Transition Metal Dichalcogenides(TM-Ds)monolayers naturally weak.Here,we propose coupling a monolayer of TMDs with a photonic grating slab that works with doubly resonant bound states in the continuum(BIC).The BIC slabs are designed to exhibit a pair of BICs,reson-ant with both the fundamental wave(FW)and the second harmonic wave(SHW).Firstly,the spatial mode matching can be fulfilled by tilting FW's incident angle.We theoretically demonstrate that this strategy leads to more than four orders of magnitude enhancement of SHG efficiency than a sole monolayer of TMDs,under a pump light intensity of 0.1 GW/cm^(2).Moreover,we demonstrate that patterning the TMDs monolayer can further enhance the spatial overlap coefficient,which leads to an extra three orders of magnitude enhancement of SHG efficiency.These results demonstrate remarkable pos-sibilities for enhancing SHG with nonlinear 2D materials,opening many opportunities for chip-based light sources,nano-lasers,imaging,and biochemical sensing.

Role of excited states in the elliptically polarized harmonic generation

We theoretically investigate the contribution of the excited state to the ellipticity of the harmonics from H＋ at different orientation angles irradiated by a linearly polarized laser pulse. It is found that the first excited state has a significant influence to the ellipticity of the harmonics, and the contribution of higher excited states to the ellipticity can be neglected. Moreover, the conclusion is not dependent on the laser intensity.

Photoinduced Second Harmonic Generation of Bi_2S_3 Microcrystallite Doped Silica Glass

Silica glasses doped with Bi2S3 microcystallite was prepared by the sol-gel process. Photoinduced second harmonic generation (SHG) was observed in the glass when it was irradiated with intense 1.06 mum and frequency doubled laser beams from a mode-locked Nd: YAG laser. It was found that the signal intensity increased with the irradiating time and approached a saturation gradually. The effect may be explained reasonably by the DC field model.

Carrier envelope phase effect on the spatial distribution of high-order harmonic generation in asymmetric molecule

The spatial distribution in high-order harmonic generation（HHG） from the asymmetric diatomic molecule He H^（2＋） is investigated by numerically solving the non-Born–Oppenheimer time-dependent Schr？dinger equation（TDSE）. The spatial distribution of the HHG spectra shows that there is little contribution in HHG around the geometric center of two nuclei（z = 1.17 a.u.） and the equilibrium internuclear position of the H nucleus（z = 3.11 a.u.）. We demonstrate the carrier envelope phase（CEP） effect on the spatial distribution of HHG in a few-cycle laser pulse. The HHG process is investigated by the time evolution of the electronic density distribution. The time–frequency analysis of HHG from two nuclei in HeH^（2＋） is presented to further explain the underlying physical mechanism.

Role of Bloch oscillation in high-order harmonic generation from periodic structure

The high-order harmonic generation from a model solid structure driven by an intense laser pulse is investigated using the semiconductor Bloch equations(SBEs). The main features of harmonic spectrum from SBEs agree well with the result of the time-dependent Schro¨dinger equation(TDSE), and the cut-off energy can be precisely estimated by the recollision model. With increasing the field strength, the harmonic spectrum shows an extra plateau. Based on the temporal population of electron and the time–frequency analysis, the harmonics in the extra plateau are generated by the Bloch oscillation. Due to the ultrafast time response of the Bloch electron, the generated harmonics provide a potential source of shorter isolated attosecond pulse.

Attosecond pulse generation from two-electron harmonic emission spectrum

In this paper, we theoretically investigate the high-order harmonic generation and attosecond pulse generation when a two-electron He atom is exposed to the intense laser pulse. It shows that due to the two-electron double recombination mechanism, an extended plateau beyond the classical single-electron harmonic has been obtained on the two-electron harmonic spectrum. Further by using this two-electron harmonic extension scheme combined with the two-color field, two supercontinuum bandwidths with 200 e V have been obtained. As a result, a series of sub-60 as extreme ultraviolet（XUV）pulses have been directly generated.