High-order harmonics generation by few-cycle and multi-cycle femtosecond laser pulses

This paper investigates experimentally high-order harmonic generation （HHG） of neon gas with 5-fs and 25-fs driving laser pulses. It has been demonstrated that the cutoff energy of the harmonic extreme ultraviolet photons is extended to 131 eV and the HHC spectrum near the cutoff region becomes continuum as the driving laser pulse duration is 5 fs; whereas much lower cutoff photon energy and discrete harmonic spectrum near the cutoff region are presented as the laser pulse duration is 25 fs. The results can be explained by the fact that neutral atoms can be exposed to more intense laser field before they are depleted by ionization because of the extremely short rising time of the few-cycle pulse. The 5-fs driving laser pulse paves the way of generation of coherent x-ray in the water window and single attosecond pulse.

Efficient high harmonics generation by enhancement cavity driven with a post-compressed FCPA laser at 10 MHz

Efficient high harmonics generation(HHG) was demonstrated at 10 MHz repetition rate with an external femtosecond enhancement cavity, seeded by a ～70 fs post-compressed 10 MHz fiber chirped pulse amplifier(FCPA) laser. Operation lasting over 30 min with 0.1 m W outcoupled power at 149 nm was demonstrated. It was found that shorter pulse was beneficial for alleviating the nonlinear plasma effect and improving the efficiency of HHG. Low finesse cavity can relax the plasma nonlinearity clamped intra-cavity power and improve the cavity-locking stability. The pulse duration is expected to be below 100 fs for both 1040 nm and 149 nm outputs, making it ideal for applications such as time-resolved photoemission spectroscopy.

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.

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）.

Generation of non-integer high-order harmonics and significant enhancement of harmonic intensity

High-order harmonics from helium atom in the orthogonally two-color(OTC) laser field are investigated by solving the two-dimensional time-dependent Schrodinger equation.Non-integer high-order harmonics are obtained in some ratio of frequencies of two components.Pure odd and even harmonics from atoms could be separated in two components by adjusting the ratio of frequencies in OTC scheme,and the resolution of harmonics is improved at the same time.The physical mechanism is explained by the periodicity of dipole.With the same intensity of the incident laser,the intensity of the high-order harmonics from the OTC field scheme is improved by three orders of magnitude compared to the monochromatic laser field scheme.A theoretical scheme is provided for experimentally achieving improving energy resolution and separation of pure odd and even harmonics in atoms.Also,we provide a means for improving harmonic intensity.

Effect of laser focus in two-color synthesized waveform on generation of soft x-ray high harmonics

Synthesis of multi-color laser pulses has been developed as a promising way to improve low conversion efficiency of high-order harmonic generation(HHG). Here we systematically study the effect of laser focus in a two-color waveform on generation of macroscopic HHG in soft x-rays. We find that the dependence of HHG yields on laser focus at low or high gas pressure is sensitive to the characteristics of single-atom harmonic response, in which “short”-or “long”-trajectory emissions can be selectively controlled by changing the waveform of two-color synthesized laser pulse. We uncover the phase-matching mechanism of HHG in the gas medium by examining the propagation of the two-color waveform and the evolution of time-frequency emissions of high-harmonic field. We further reveal that the nonlinear effects, such as geometric phase, atomic dispersion, and plasma defocusing, are responsible for modification of two-color waveform upon propagation. This work can be used to find better macroscopic conditions for generating soft x-ray HHG by employing two-color optimized waveforms.

Generation of Higher Terahertz Harmonics in Nonlinear Paraelectrics under Focusing in a Wide Temperature Range

It is theoretically investigated the generation of higher harmonics of two-dimensional and three-dimensional terahertz electromagnetic beams in nonlinear crystals. The attention is paid to crystalline paraelectrics like SrTiO3 under the temperatures 60 - 200 K, these crystals possess the cubic nonlinearity. The bias electric field is applied to provide the dominating quadratic nonlinearity. The initial focusing of the beams not only increases the efficiency of generation of higher harmonics, but alto makes possible to select maxima of different higher harmonics at some distances from the input. At lower temperatures the nonlinearity behaves at smaller input amplitudes, whereas at higher temperatures the harmonic generation can be observed at higher frequencies up to 1.5 THz. In three-dimensional beams the peak amplitudes of higher harmonics can be bigger than in two-dimensional beams, but the ratios of these peak values to the maximum values of the focused first harmonic are smaller than in two-dimensional beams.

Interference of harmonics emitted by different tunneling momentum channels in laser fields

By numerically solving the semiconductor Bloch equation(SBEs),we theoretically study the high-harmonic generation of ZnO crystals driven by one-color and two-color intense laser pulses.The results show the enhancement of harmonics and the cut-off remains the same in the two-color field,which can be explained by the recollision trajectories and electron excitation from multi-channels.Based on the quantum path analysis,we investigate contribution of different ranges of the crystal momentum k of ZnO to the harmonic yield,and find that in two-color laser fields,the intensity of the harmonic yield of different ranges from the crystal momentum makes a big difference and the harmonic intensity is depressed from all k channels,which is related to the interferences between harmonics from symmetric k channels.

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.

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.

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.

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.

Generation of an isolated sub-100 attosecond pulse in the water-window spectral region

We propose a scheme to generate isolated attosecond pulses in the water-window spectral region. Based on the numerical solutions of the single active electron model, we investigate high-order harmonic generation in helium atoms driven by a multi-cycle two-colour optical field synthesized by an intense 2000 nm, 20 fs pulse and its frequency-doubled pulse. When the latter is slightly detuned and properly phase shifted with respect to the fundamental laser pulse, an ultra-broad extreme ultraviolet supercontinuum with a spectral width of 130 eV can be generated in the 270 400 eV spectral regions. A supercontinuum from 280-340 eV in the water window can be selected to yield an isolated 67 attosecond pulse without employing any phase compensation. This water window coherent x-ray pulse with less than 100 attosecond duration is a potential tool for studying the ultrafast electronic dynamics of biological samples in water.

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.

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.

Generation of an isolated sub-30 attosecond pulse in a two-color laser field and a static electric field

We theoretically investigate high-order harmonic generation（HHG） from a helium ion model in a two-color laser field,which is synthesized by a fundamental pulse and its second harmonic pulse.It is shown that a supercontinuum spectrum can be generated in the two-color field.However,the spectral intensity is very low,limiting the application of the generated attosecond（as） pulse.By adding a static electric field to the synthesized two-color field,not only is the ionization yield of electrons contributing to the harmonic emission remarkably increased,but also the quantum paths of the HHG can be significantly modulated.As a result,the extension and enhancement of the supercontinuum spectrum are achieved,producing an intense isolated 26-as pulse with a bandwidth of about 170.5 eV.In particular,we also analyse the influence of the laser parameters on the ultrabroad supercontinuum spectrum and isolated sub-30-as pulse generation.

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.

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.

Generation of femtosecond laser pulses at 263 nm by K_3B_6O_(10)Cl crystal

The third harmonic generation（THG） of a linear cavity Ti：sapphire regenerative amplifier by use of a K3B6O（10）Cl（KBOC） crystal is studied for the first time. Output power up to 5.9 mW is obtained at a central wavelength of 263 nm,corresponding to a conversion efficiency of 4.5% to the second harmonic power. Our results show a tremendous potential for nonlinear frequency conversion into the deep ultraviolet range with the new crystal and the output laser power can be further improved.