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.

Tailoring OAM spectrum of high-order harmonic generation driven by two mixed Laguerre–Gaussian beams with nonzero radial nodes

The extreme ultraviolet(XUV)light beam carrying orbital angular momentum(OAM)can be produced via high-order harmonic generation(HHG)due to the interaction of an intense vortex infrared laser and a gas medium.Here we show that the OAM spectrum of vortex HHG can be readily tailored by varying the radial node(from 0 to 2)in the driving laser consisting of two mixed Laguerre-Gaussian(LG)beams.We find that due to the change in spatial profile of HHG,the distribution range of the OAM spectrum can be broadened and its shape can be modified by increasing the radial node.We also show that the OAM mode range becomes much wider and its distribution shape becomes more symmetric when the harmonic order is increased from the plateau to the cutoff when the driving laser has the nonzero radial nodes.Through the map of coherence length and the evolution of harmonic field in the medium,we reveal that the favorable off-axis phase-matching conditions are greatly modified due to the change of intensity and phase distributions of driving laser with the radial node.We anticipate this work to stimulate some interests in generating the XUV vortex beam with tunable OAM spectrum through the gaseous HHG process achieved by manipulating the mode properties of the driving laser beam.

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.

Effect of Carrier Envelope Phase on High-Order Harmonic Generation from Solid

The dependence of harmonic emission from a solid on the carrier envelope phase (CEP) is discussed by numerically solving the time-dependent Schr?dinger equation. The harmonic spectra periodically exhibit three distinct oscillating structures, which indicate the different dependences of the cutoff energies on the CEP. Furthermore,with time-dependent population imaging and the populations of different energy bands, the underlying physical mechanism is explored.

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.

Modulation of multiphoton resonant high-order harmonic spectra driven by two frequency-comb fields

The frequency-comb structure in the extreme ultraviolet（XUV） and vacuum ultraviolet（VUV） regions can be realized by the high-order harmonic generation（HHG） process driven by frequency-comb fields, providing an alternative approach for the measurement of an unknown frequency in XUV or VUV. We consider the case of two driving frequency-comb fields with the same repetition frequency and the carrier frequencies of fundamental-and third-harmonics, respectively.The many-mode Floquet theorem（MMFT） is employed to provide a nonperturbative and exact treatment of the interaction between a quantum system and the frequency-comb laser fields. Multiphoton transition paths involving both fundamentaland third-harmonic photons are opened due to the coupling of the third-harmonic frequency-comb field. The multiphoton transition paths are superpositioned when the carrier-envelope-phase shifts（CEPs） fulfill the matching condition. And the interference of the multiphoton transition paths can be controlled by tuning the relative envelope delay between the fields.We find that the quasienergy structure, as well as the multiphoton resonant high-order harmonic generation（HHG） spectra,driven by the two frequency-comb fields can be coherently controlled via the interference of multiphoton transition paths.It is also found that the spectral intensities of the generated harmonics can be modulated, and the modulation behavior is harmonic-sensitive.

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.