High-order harmonic generation with a two-color laser pulse

We theoretically investigate the electron dynamics of the high-order harmonics generation process by combining a near-infrared 800 nm driving pulse with a mid-infrared 2000 nm control field.We also investigate the emission time of harmonics using time-frequency analysis to illustrate the physical mechanisms of high-order harmonic generation.We calculate the ionization rate using the Ammosov-Delone-Krainov model and interpret the variations in harmonic intensity for different control field strengths and delays.We find that the width of the harmonic plateau can be extended when the control electric field is added,and a supercontinuum from 198 to 435 eV is generated,from which an isolated 61-as pulse can be directly obtained.     

High-order harmonic generation of the N2 molecule in two-color circularly polarized laser fields

The generation of high-order harmonics and the attosecond pulse of the N₂ molecule in two-color circularly polarized laser fields are investigated by the strong-field Lewenstein model. We show that the plateau of spectra is dramatically extended and a continuous harmonic spectrum with the bandwidth of 113 eV is obtained. When a static field is added to the x direction, the quantum path control is realized and a supercontinuum spectrum can be obtained, which is beneficial to obtain a shorter attosecond pulse. The underlying physical mechanism is well explained by the time-frequency analysis and the semi-classical three-step model with a finite initial transverse velocity. By superposing several orders of harmonics in the combination of two-color circularly polarized laser fields and a static field, an isolated attosecond pulse with a duration of 30 as can be generated.     

空间非均匀啁啾双色场驱动下氦离子的高次谐波以及孤立阿秒脉冲的产生

本文理论上研究了初态为基态与第一激发态等权叠加的一维氦离子在空间非均匀啁啾双色场驱动下氦离子的高次谐波发射及孤立阿秒脉冲的产生. 研究表明, 一维氦离子在空间非均匀啁啾双色场驱动下发射的高次谐波相对于均匀场情况截止位置得到明显扩展, 得到了光滑的超连续谱,并应用半经典三步模型解释了高次谐波发射的物理机理. 通过小波变换的方法对连续谱进行了时频分析, 并且与电子的经典运动轨迹进行了对比分析, 结果显示在空间非均匀场中长量子轨道消失, 短量子轨道加强. 讨论了空间非均匀啁啾双色场中时间延迟对谐波和孤立阿秒脉冲产生的影响, 发现适当调整时间延迟值可以得到较大延展的光滑的超连续谐波谱, 本方案中时间延迟为t₀=1.6πup/ω₁时得到了最大延展, 通过对谐波中600次到680次(80次)谐波合成得到32 as的孤立脉冲.     

正交偏振双色激光场作用下生成的孤立阿秒脉冲

我们理论研究了正交偏振双色激光场作用下的高次谐波发射和孤立阿秒脉冲的产生.当y方向加一束中红外激光脉冲(12.5 fs/2000 nm),x方向加一束强度较弱的激光脉冲(12 fs/800 nm)时,我们得到从250 eV到350 eV的超连续谐波平台,在平台范围内叠加50 eV的谐波,可以得到一个脉宽约为97as的孤立阿秒脉冲. 通过时频分析,我们解释了高次谐波发射的物理机制.     

Isolated sub-30-attosecond pulse generation using a multicycle two-color chirped laser and a static electric field

We present a theoretical investigation of high-order harmonic generation in a chirped two-color laser field, which is synthesized by a 10-fs/800-nm fundamental chirped pulse and a 10-fs/1760-nm subharmonic pulse. It is shown that a supercontinuum can be produced using the multicycle two-color chirped field. However, the supercontinuum reveals a strong modulation structure, which is not good for the generation of an isolated attosecond pulse. By adding a static electric field to the multicycle two-color chirped field, not only the harmonic cutoff is extended remarkably, but also the quantum paths of the high-order harmonic generation （HHG） are modified significantly. As a result, both the extension of the supercontinuum and the selection of a single quantum path are achieved, producing an isolated 23-as pulse with a bandwidth of about 170.6 eV. Furthermore, the influences of the laser intensities on the supercontinuum and isolated attosecond pulse generation are investigated.     

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 C₆ H₆ having similar ionization potential, the C₁₈ molecule has higher efficiency and cutoff energy than C₆ H₆ 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 C₆ H₆ 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.     

利用双色啁啾激光场产生超短的单个阿秒脉冲

数值研究了氦原子在两束啁啾激光场形成的组合场驱动下所发射高次谐波的特点.计算结果表明,当两束啁啾激光场的形式为δi(t)=-βiωit2/T (i=1,2)并且啁啾参数分别为β1=0.3和β2=0.6时,高次谐波谱的平台区域能得到很大的扩展,随后通过激光场强度以及相位的优化,谐波截至能量延伸到了812eV.最后通过叠加谐波次数从160次到210次,210次到260次,260次到310次,可获得一系列脉宽为33as的单个阿秒脉冲.     

利用相位啁啾单色中红外激光场产生高次谐波

本文通过求解薛定谔方程,理论探索了高次谐波及孤立阿秒脉冲在相位调制的单色中红外激光场中的产生.研究结果表明,通过加入含时相位啁啾小量,能够有效的提高高次谐波的产生效率,获得超宽平台谐波谱及超短孤立阿秒脉冲.特别是在相位为0.3π的基础上,同时加入啁啾小量βt,在β=0.3时,可得到带宽为822 e V的超连续高次谐波平台.最后通过叠加第二平台高次谐波,可得到带宽仅为2.7 as的孤立阿秒脉冲.且脉冲强度比没有加入啁啾小量的情况下显著增强.     

Isolated attosecond pulse generation with few-cycle two-color counter-rotating circularly polarized laser pulses

Most of the schemes for generating isolated attosecond pulses(IAP) are sensitive to the carrier-envelope phase(CEP)of the driving lasers. We propose a scheme for generating IAP using two-color counter-rotating circularly polarized(TCCRCP) laser pulses. The results demonstrate that the dependence of the IAP generation on CEP stability is largely reduced in this scheme. IAP can be generated at most of CEPs. Therefore, the experiment requirements become lower.     

Controlling the contributions to high-order harmonic generation from different nuclei of N_2 with an orthogonally polarized two-color laser field

The generation of high-order harmonic and the attosecond pulse of the N2 molecule with an orthogonally polarized two-color laser field are investigated by the strong-field Lewenstein model.We show that the control of contributions to high-order harmonic generation(HHG) from different nuclei is realized by properly selecting the relative phase.When the relative phase is chosen to be φ= 0.4π,the contribution to HHG from one nucleus is much more than that from another.Interference between two nuclei can be suppressed greatly; a supercontinuum spectrum of HHG appears from 40 e V to125 e V.The underlying physical mechanism is well explained by the time–frequency analysis and the semi-classical threestep model with a finite initial transverse velocity.By superposing several orders of harmonics,an isolated attosecond pulse with a duration of 80 as can be generated.     

任意夹角的双色偏振激光作用下孤立阿秒脉冲的产生

本文选取脉宽为12 fs波长为2000 nm和800 nm的两束线性偏振激光, 适当调节两束激光的偏振方向的夹角θ, 发现当θ=π/2时, 高次谐波谱的第二级平台出现了“漏斗形”凹槽.当θ为π/6时, 得到了290 eV的超宽连续谱的高次谐波发射, 利用小波变换合理的解释了高次谐波形状及截止位置. 在该段连续谱上任意截取70 eV宽度的频率, 都可以得到脉宽约为60 as的孤立阿秒脉冲. 适当减小截取范围可以得到线性偏振的脉宽94 as的孤立阿秒脉冲. 这为实验中产生能灵活调节的孤立阿秒脉冲提供了一种方案.     

High-order harmonic generation of CO_2 with different vibrational modes in an intense laser field

We apply the strong-field Lewenstein model to demonstrate the high-order harmonic generation of CO_2 with three vibrational modes(balance vibration,bending vibration,and stretching vibration) driven by an intense laser field.The results show that the intensity of harmonic spectra is sensitive to molecular vibrational modes,and the high harmonic efficiency with stretching vibrational mode is the strongest.The underlying physical mechanism of the harmonic emission can be well explained by the corresponding ionization yield and the time-frequency analysis.Finally,we demonstrate the attosecond pulse generation with different vibrational modes and an isolated attosecond pulse with a duration of about 112 as is generated.     

Asymmetric molecular harmonic assisted generation of the attosecond X-ray pulse

In this paper, we theoretically investigate the asymmetric molecular high-order harmonic emission and the attosecond X-ray pulse generation when the asymmetric molecular HeH²⁺ ion is exposed to an intense chirped pulse. It is found that the molecular harmonics are strongly dependent on the internuclear distance R as well as the chirp parameter, showing a smooth and intense harmonic plateau at R = 8.0 a.u. and β = 0.4. Further, by adding a subharmonic controlling pulse with the optimised conditions, a supercontinuum with a bandwidth of 602 eV can be obtained. Finally, by properly superposing the selected harmonics in the supercontinuum region, a series of isolated X-ray pulses with durations of sub-80 as are directly generated.     

优化两色组合场参数获得单个阿秒脉冲

基于经典方法优化了组合场中基频场和低频场的强度比,利用优化后的组合场驱动一维氦原子,通过求解含时薛定谔方程研究了氦原子产生的高次谐波,其截止位置得到扩展,再考虑基频场初相位对产生高次谐波的影响,能够得到脉宽为37as的单个阿秒脉冲.     

多周期双色场方案下附加脉冲频率对阿秒脉冲产生的影响

通过数值求解一维含时薛定谔方程,研究了多周期双色场与氢原子相互作用过程中不同波段的附加脉冲波长对体系高次谐波及阿秒脉冲产生的影响.研究发现,当双色场的附加脉冲波长处于红外波段1600 nm时,比起处于可见光波段的533 nm附加脉冲,谐波谱截止位置得到大幅延展,相应地拓宽了超连续带宽,小波变换后获得了78 as的孤立短脉冲.由合成电场的光学振荡频率解释了附加脉冲波段对谐波谱的影响,同时该结论有利于在获得孤立阿秒脉冲的研究中选择合适的附加脉冲频率.     

High-order harmonic generation in sub-one-cycle regime

We theoretically investigate the high-order harmonic generation from the hydrogen atom driven by the laser pulses with the durations less than the optical cycle.It is found that the switching term of the laser field may have an obvious influence on the cutoff,intensity or plateau structure of the high-order harmonic spectrum.Generally speaking,the switching term can shorten the cutoff of the high-order harmonic spectrum for a relatively longer pulse and extend the cutoff for a relatively shorter pulse.     

中红外组合激光场产生低于50阿秒的单个脉冲

研究了氦离子在中红外组合激光场作用下的高次谐波辐射和孤立阿秒脉冲的产生.研究结果表明,当主脉冲强度相对低时,谐波截止在657阶次处,形成一个宽度为287eV的连续谱.当主脉冲强度相对高时,可使谐波截止拓展到1795阶次,连续谱加宽到834eV.在两种情况下,我们实现了长量子路径选取,并且产生转换效率较高的连续谱.特别是对于相对高的激光强度,叠加450～1590阶次内任意87eV的谐波都可以直接得到50as以内的单个脉冲.     

采用双脉冲提高谐波谱的谱线密度

通过计算线偏振双脉冲激光场与一维氢原子模型相互作用产生的高次谐波辐射谱的含时Schrdinger方程. 研究发现,选用适宜的双脉冲激光组合可以增加谐波谱的密度,这样的谐波谱特别适合作为产生孤立阿秒脉冲的光源. 详细地分析了谐波谱线密度增加的物理机理,给出不同脉宽与谐波谱线密度增加的关系,从而可以有针对性地控制谐波谱线的疏密程度. 关键词： 高次谐波 阿秒脉冲 双脉冲     

中红外组合激光场产生低于50阿秒的单个脉冲

研究了氦离子在中红外组合激光场作用下的高次谐波辐射和孤立阿秒脉冲的产生. 研究结果表明,当主脉冲强度相对低时,谐波截止在657阶次处,形成一个宽度为287 eV的连续谱. 当主脉冲强度相对高时,可使谐波截止拓展到1795阶次,连续谱加宽到834 eV. 在两种情况下,我们实现了长量子路径选取,并且产生转换效率较高的连续谱. 特别是对于相对高的激光强度,叠加450—1590阶次内任意87 eV的谐波都可以直接得到50 as以内的单个脉冲.     

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.