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Sep.  2019
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Generation of attosecond pulses from He atom driven by UV-chirped laser beam

  • Received Date: 2018-09-18
    Accepted Date: 2018-09-28
  • In order to obtain attosecond pulses in X-ray range, the method of generating high intensity harmonic spectra and attosecond pulses by combining ultraviolet and chirped laser beams was introduced. The theoretical analysis was carried out. The results show that, when forward chirp parameter is introduced, harmonic cut-off energy has a slight extension and the efficiency of harmonic radiation decreases significantly. When negative chirp parameter is introduced, harmonic cut-off energy is extended and harmonic radiation efficiency is enhanced under the condition of forward chirp. When a 125nm ultraviolet light source is introduced into the chirped laser, the efficiency of harmonic radiation is obviously enhanced because of the effect of resonance-enhanced ionization. Driven by ultraviolet-forward chirp, harmonic radiation intensity is enhanced 25 times and harmonic cut-off energy is extended. A 382eV platform area is formed. Driven by ultraviolet-negative chirp, harmonic cut-off energy does not changed significantly but the efficiency of harmonic radiation is 110 times higher. A 410eV platform area is formed. By superposing the harmonics in the combined field, a series of single attosecond pulses within 70as can be obtained. This study is helpful for the development of attosecond science.
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  • [1]

    WANG Ch, KANG T F, TIAN J Sh, et al. Analysis of phase dependence of the two single-attosecond-pulse generation techniques [J]. Laser Technology, 2012, 36(4): 516-519 (in Chinese).
    [2]

    LIU H, FENG L Q. Mid-infrared field phase measurement and attosecond pulse generation [J]. Laser Technology, 2017, 41(2): 151-158 (in Chinese).
    [3]

    MAIRESSE Y, BOHAN A D, FRASINSKI L J, et al. Attosecond synchronization of high-harmonic soft X-rays [J]. Science, 2003, 302(5650): 1540-1543. doi: 10.1126/science.1090277
    [4]

    GOULIELMAKIS E, SCHULTZE M, HOFSTETTER M, et al. Single-cycle nonlinear optics [J]. Science, 2008, 320(5883): 1614-1617. doi: 10.1126/science.1157846
    [5]

    FENG L Q, CHU T S. Generation of an isolated sub-40as pulse using two-color laser pulses: Combined chirp effects [J]. Physical Review, 2011, A84(5): 053853.
    [6]

    WEI P F, MIAO J, ZENG Z N, et al. Selective enhancement of a single harmonic emission in a driving laser field with subcycle waveform control [J]. Physical Review Letters, 2013, 110(23): 233903. doi: 10.1103/PhysRevLett.110.233903
    [7]

    WEI P F, ZENG Z N, JIANG J M, et al. Selective generation of an intense single harmonic from a long gas cell with loosely focusing optics based on a three-color laser field [J].Applied Physics Letters, 2014, 104(15): 151101. doi: 10.1063/1.4871513
    [8]

    CORKUM P B. Plasma perspective on strong field multiphoton ionization [J]. Physical Review Letters, 1993, 71(13): 1994-1997. doi: 10.1103/PhysRevLett.71.1994
    [9]

    STRELKOV V V, STERJANTOV A F, SHUBIN N Y, et al. XUV generation with several-cycle laser pulse in barrier-suppression regime [J]. Journal of Physics, 2006, B39(3): 577-589.
    [10]

    TATE J, AUGUSTE T, MULLER H G, et al. Scaling of wave-packet dynamics in an intense midinfrared field [J]. Physical Review Letters, 2007, 98(1): 013901. doi: 10.1103/PhysRevLett.98.013901
    [11]

    ZENG Z, CHENG Y, SONG X, et al. Generation of an extreme ultraviolet supercontinuum in a two-color laser field [J]. Physical Review Letters, 2007, 98(20): 203901. doi: 10.1103/PhysRevLett.98.203901
    [12]

    LU R F, HE H X, GUO Y H, et al. Theoretical study of single attosecond pulse generation with a three-colour laser field [J]. Journal of Physics, 2009, B42(22): 225601.
    [13]

    FENG L Q, CHU T S. High-order harmonics extension and isolated attosecond pulse generation in three-color field: Controlling factors [J]. Physical Letters, 2011, A375(41):3641-3648.
    [14]

    SANSONE G, BENEDETTI E, CALEGARI F, et al. Isolated single-cycle attosecond pulses [J]. Science, 2006, 314(5798): 443-446. doi: 10.1126/science.1132838
    [15]

    ZHAO K, ZHANG Q, CHINI M, et al. Tailoring a 67 attosecond pulse through advantageous phase mismatch [J]. Optics Letters, 2012, 37(18): 3891-3893. doi: 10.1364/OL.37.003891
    [16]

    ZHANG Q B, LU P X, LAN P F, et al. Multi-cycle laser-driven broadband supercontinuum with a modulated polarization gating [J]. Optics Express, 2008, 16(13): 9795-9803. doi: 10.1364/OE.16.009795
    [17]

    KIM S, JIN J, KIM Y J, et al. High-harmonic generation by resonant plasmon field enhancement [J]. Nature, 2008, 453(7196): 757-760. doi: 10.1038/nature07012
    [18]

    FENG L Q. Molecular harmonic extension and enhancement from H2+ ions in the presence of spatially inhomogeneous fields [J]. Physical Review, 2015, A92(5): 053832.
    [19]

    CAO X, JIANG S C, YU C, et al. Generation of isolated sub-10-attosecond pulses in spatially inhomogenous two-color fields [J]. Optics Express, 2014, 22(21): 26153-26161. doi: 10.1364/OE.22.026153
    [20]

    LU R F, ZHANG P Y, HAN K L. Attosecond-resolution quantum dynamics calculations for atoms and molecules in strong laser fields [J]. Physical Review, 2008, E77(6): 066701.
    [21]

    HU J, HAN K L, HE G Z. Correlation quantum dynamics between an electron and D2+ molecule with attosecond resolution [J]. Physical Review Letters, 2005, 95(12): 123001. doi: 10.1103/PhysRevLett.95.123001
    [22]

    FENG L Q, DUAN Y B, CHU T S. Harmonic extension and attosecond pulse generation by using the modified three-color chirped pulse [J]. Annalen der Physik, 2013, 525(12): 915-920. doi: 10.1002/andp.201300051
    [23]

    CHU T S, ZHANG Y, HAN K L. The time-dependent quantum wave packet approach to the electronically nonadiabatic processes in chemical reactions [J]. International Reviews in Physical Chemistry, 2006, 25(1/2): 201-235.
    [24]

    LIU H, LI Y, YAO Z, et al. Chirp pulse control on harmonic cutoff and harmonic intensity [J]. Laser Technology, 2017, 41(5): 708-711 (in Chinese).
    [25]

    ANTOINE P, PIRAUX B, MAQUET A. Time profile of harmonics generated by a single atom in a strong electromagnetic field [J]. Physical Review, 1995, A51(3):R1750-R1753.
    [26]

    FENG L Q, CHU T S. Intensity enhancement in attosecond pulse generation [J]. IEEE Journal of Quantum Electronics, 2012, 48(11): 1462-1466. doi: 10.1109/JQE.2012.2207948
    [27]

    FENG L Q, LI Y, LIU H. High intensity attosecond pulse generation by the improved multi-cycle polarization gating technology[J]. Laser Technology, 2018, 42(4): 451-456(in Chinese).
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Generation of attosecond pulses from He atom driven by UV-chirped laser beam

  • College of Science, Liaoning University of Technology, Jinzhou 121001, China

Abstract: In order to obtain attosecond pulses in X-ray range, the method of generating high intensity harmonic spectra and attosecond pulses by combining ultraviolet and chirped laser beams was introduced. The theoretical analysis was carried out. The results show that, when forward chirp parameter is introduced, harmonic cut-off energy has a slight extension and the efficiency of harmonic radiation decreases significantly. When negative chirp parameter is introduced, harmonic cut-off energy is extended and harmonic radiation efficiency is enhanced under the condition of forward chirp. When a 125nm ultraviolet light source is introduced into the chirped laser, the efficiency of harmonic radiation is obviously enhanced because of the effect of resonance-enhanced ionization. Driven by ultraviolet-forward chirp, harmonic radiation intensity is enhanced 25 times and harmonic cut-off energy is extended. A 382eV platform area is formed. Driven by ultraviolet-negative chirp, harmonic cut-off energy does not changed significantly but the efficiency of harmonic radiation is 110 times higher. A 410eV platform area is formed. By superposing the harmonics in the combined field, a series of single attosecond pulses within 70as can be obtained. This study is helpful for the development of attosecond science.

引言
  • 在过去几年中,阿秒量级超短光源的产生获得了飞速发展[1-2]。高次谐波(high-order harmonic generation, HHG)作为最成功的获得单个阿秒光源的方法被广泛关注和研究[3-4]

    目前,高次谐波的产生可以由强激光场驱动原子、分子或者固体来获得。其中,原子和分子辐射高次谐波作为产生单个阿秒脉冲的主要方法被广泛研究[5-7]。其过程可以由半经典三步模型来描述[8],即电离-加速-回碰过程。随后,通过叠加谐波光谱的平台区可获得阿秒脉冲。根据三步模型的描述,谐波光谱的截止能量在Ip+3.17×I/(4ω2)附近。这里,IpIω分别代表体系电离能、激光强度以及激光频率。因此,为了能够获得X射线范围内的阿秒光源,延伸谐波截止能量是势在必行的。由三步模型可知,谐波辐射能量不仅与激光光强成正比,而且与激光频率成反比。因此,利用高强度激光场或者长波长激光场驱动原子、分子理论上都可以延伸谐波截止能量。但是,随着激光光强的持续增大,体系基态占有率逐渐减少,进而导致谐波辐射效率减小[9],这显然不利于高强度阿秒脉冲的输出。同样,利用长波长激光场,虽然可以有效延伸谐波截止能量,但是谐波辐射效率会随着波长增大而呈指数减弱[10]。因此,为了克服上述弱点,人们提出了许多改进的方案来获得强度较高的X射线范围内的阿秒光源。例如:(1)利用双色或三色组合场,许多短于1个原子单位(24as)的阿秒脉冲可以被获得[11-13]; (2)利用极化门方案,人们获得了许多线偏、椭圆偏、圆偏的超短的单个阿秒脉冲[14-16]; (3)利用金属纳米结构下的等离子体增强效应,人们利用阈值以下的激光场获得了超短的阿秒脉冲[17-19]

    基于上述分析可知,要获得X射线能量范围之内的高强度单个阿秒秒冲需要满足2点要求。(1)谐波截止能量要覆盖X射线范围;(2)要有较强的谐波辐射效率。因此,为了满足上述2点要求,本文中提出了一种利用紫外-啁啾激光束驱动He原子获得高强度阿秒X射线光源的方法。结果表明,在紫外-啁啾激光束驱动下,谐波截止能量和谐波辐射效率都有明显提高。并且在正负向啁啾组合场下可以分别获得382eV和410eV的连续平台区。最后,在平台区选择适当的谐波进行叠加可获得脉宽在70as以下的单个阿秒脉冲。若无特别说明,本文中均采用原子单位(atomic units, a.u.)。

1.   计算方法
  • 激光驱动He原子的3维薛定谔方程为[20-22]:

    式中,V(r)=-1.535r-1是He原子的库仑势能,r为电子坐标; E(t)表示激光场; z表示激光偏振方向; t表示时间; H(t)为哈密顿量,$\nabla $为梯度算符; φ(r, t)为体系波函数, 可由球谐函数来展开(具体方法见参考文献[22]),随后其可通过2阶分裂算服方法进行传播并获得最终波函数[23]。激光场可描述为:

    式中,Eiωiτi(i=1, 2)为2束激光场振幅、频率和脉宽, td为2束激光场延迟时间。本文中采用非线性2阶啁啾形式(1t2)来调控激光波形[24],其中,b为啁啾参量。b>0和b < 0分别表示正向和负向啁啾。

    高次谐波表示为:

    式中,a(t)=-〈φ(r, t)|[H(t), [H(t), r]]|φ(r, t)〉为偶极加速度。

    最后,通过叠加傅里叶变换后的平台区谐波可获得阿秒脉冲:

    式中,IAP(t)表示阿秒脉冲强度,q表示叠加平台区的谐波级次。

2.   结果与分析
  • 图 1中给出了20fs、1600nm单色啁啾激光驱动He原子辐射高次谐波光谱的特点。激光强度为I1=3.5×1014W/cm2。为了方便比较,图中也给出了无啁啾调制(b=0)下He原子辐射谐波的谱图。由图可知,当引入正向啁啾时(例如b=0.002),谐波光谱呈现明显的双平台结构。同时,虽然谐波截止能量有微小延伸,但是第二平台区的谐波辐射效率明显下降。当引入负向啁啾时(例如b=-0.002),不仅谐波截止能量得到明显延伸,并且第二平台区的谐波辐射强度相比于正向啁啾条件下有显注提高。因此,在谐波光谱上呈现了一个410eV的连续平台区,这一结果对输出光子能量较高的阿秒脉冲非常有利。

    Figure 1.  High-order harmonic generation spectra from He driven by the chirped puls

    图 2中给出了He原子在上述啁啾激光驱动下谐波辐射的时频分析图[25]。根据三步模型理论可知,He原子在瞬时激光振幅附近具有最大的电离几率;随后,被电离的电子在激光驱动下加速,最后,在激光反向驱动下有几率与He原子核发生碰撞,进而辐射高次谐波。该过程每半个光学周期就会发生一次。因此,在本文中采用的20fs激光脉宽下(见图 2a)会呈现多个谐波辐射过程,例如图 2b中标注的P1~P5。当引入正向啁啾参量时,激光波形呈现4点明显的变化。例如变化1和变化2:在激光上升区间(t<-0.25TT表示1600nm激光场光学周期),激光瞬时振幅和瞬时频率都有明显减小,如图 2c所示。在这种变化下,电子在t=-2.25T附近电离后(A点附近)会有更多的时间在激光场中进行加速,因此导致谐波辐射能量峰P1得到明显展宽,如图 2d所示。但是,由于t=-2.25T的激光瞬时振幅与无啁啾条件下相比明显减小,因此电子电离几率也会减小,这导致谐波辐射能量峰P1的强度很弱,其在谐波光谱中的贡献很小。这是作者未在谐波光谱中观测到其贡献的原因。变化3和变化4:在激光下降区间(t>0.25T),不仅激光瞬时振幅被增强,而且瞬时频率也被增大,如图 2c所示。这导致激光下降区间的电离几率增大,进而增强了谐波辐射能量峰的强度。但是由于激光瞬时频率的增大,谐波辐射能量峰辐射光子的能量被减小,如图 2d所示。同时,由于正向啁啾的影响,t=-0.75T附近的激光振幅与无啁啾调制下相比有所减小,这导致图 2dP3的强度小于图 2bP3的强度。这也是在正向啁啾调制下谐波平台区强度减弱的原因。当引入负向啁啾参量时,激光波形的变化与正向啁啾调制正好相反。例如变化1和变化2:在激光上升区间(t<-0.25T),瞬时激光振幅和频率都被增大,这导致谐波辐射能量峰辐射的光子能量减弱,但是其辐射强度被增强。变化3和变化4:在激光下降区间(t>0.25T),虽然瞬时激光振幅和频率都被减弱,但是由于激光瞬时振幅在t=0附近没有明显变化。因此当电子在t=0附近电离后,其在负向啁啾的调制下会获得更多的加速能,这导致谐波辐射能量峰P4呈现明显延伸状态,并且其强度基本保持与无啁啾调制下一致。这也是在负向啁啾调制下,谐波光谱呈现展宽并且形成超长连续平台区的原因。

    Figure 2.  Laser profiles and time-frequency analyses of the harmonics

  • 图 3中给出了He原子在紫外-啁啾组合场驱动下辐射高次谐波的特点。其中,紫外光源为3fs、125nm激光场,激光强度为I2=2.0×1013W/cm2。具体来说,对于正向啁啾场情况,当2束激光场延迟时间为td=-2.4T时,不仅谐波截止能量得到延伸,并且谐波辐射效率有25倍的增强,进而在谐波光谱上获得了一个382eV的连续平台区,如图 3a所示。对于负向啁啾场情况,当2束激光场延迟时间为td=0时,虽然谐波截止能量没有明显变化,但是谐波辐射效率有110倍的增强,进而在谐波光谱上呈现了一个410eV的连续平台区,如图 3b所示。这里选择125nm紫外光源是因为其光子能量近似满足He原子基态到第一激发态的双光子共振跃迁能[26]。所以,当适当引入这束紫外光源时,He原子在共振增强电离的影响下,电离几率会明显增强,因此导致谐波辐射效率的增强[26-27]

    Figure 3.  Harmonic spectra driven by the different fields

    图 4中给出了He原子在紫外-啁啾组合场驱动下谐波辐射的时频分析图。对于正向啁啾组合场情况,当紫外光源与啁啾激光场延迟时间为td=-2.4T时,紫外光源主体覆盖了t=-3.0T~t=-2.0T区间,如图 4a所示。因此,当电离过程在A点附近发生时,由于共振增强电离的影响,更多的电子会被电离,这导致随后的谐波辐射能量峰P1的辐射效率有明显的增强,如图 4b所示。因此,在谐波光谱上可观测到谐波截止能量的延伸,以及谐波辐射效率的增强。通过观测图 4b可知,在正向啁啾组合场驱动下谐波平台区来自谐波辐射能量峰P1的贡献。对于负向啁啾组合场情况,当紫外光源与啁啾激光场延迟时间为td=0时,紫外光源主体覆盖了t=-0.5T~t=0.5T区间,如图 4c所示。因此,当电子在t=0附近发生电离时,电离几率在共振增强电离的作用下会被增大,因此导致随后的谐波辐射能量峰P4的辐射效率有明显的增强,如图 4d所示。通过分析图 4d可知,在负向啁啾组合场驱动下谐波平台区来自谐波辐射能量峰P4的贡献。

    Figure 4.  Laser profiles and time-frequency analyses of the harmonics

  • 图 5中给出了叠加组合场谐波平台区而获得的阿秒脉冲。例如:在紫外-正向啁啾组合场驱动下,通过叠加谐波平台区的200阶~300阶谐波;300阶~400阶谐波;400阶~500阶谐波;500阶~600阶谐波;600阶~690阶谐波,可以获得4个67as和1个70as的单个阿秒脉冲,如图 5a所示。在紫外-负向啁啾组合场驱动下,通过叠加谐波平台区的400阶~500阶谐波;500阶~600阶谐波;600阶~700阶谐波;700阶~800阶谐波;800阶~900阶谐波,可以获得5个持续时间在67as的单个阿秒脉冲,如图 5b所示。这里,由于负向啁啾组合场下的谐波效率与正向啁啾组合场相比有大约1个数量级的增强。因此,其获得的阿秒脉冲强度也要比正向啁啾组合场下获得的阿秒脉冲强度高1个数量级。

    Figure 5.  Attosecond pulses produced by superposing the harmonics

3.   结论
  • 本文中提出了一种利用紫外-啁啾组合激光束驱动He原子获得单个阿秒脉冲的理论方法。结果表明,当适当采用一束紫外光源与啁啾场组合驱动He原子时,由于共振增强电离以及啁啾调制的影响,不仅谐波截止能量得到延伸,而且谐波辐射效率也有明显增强。因此,在正负向啁啾组合场驱动下可以分别获得382eV和410eV的连续平台区。最后,通过叠加平台区谐波可获得一些能量可调持续时间在70as以下的单个阿秒脉冲。由于所提出的一种获得阿秒脉冲的新方法,其还未进行实验验证。但是本文中采用的理论方法已经被实验证明其正确性和准确性[11]。因此,本文中的理论预言结果正确、可靠,可以对阿秒脉冲的产生提供新的思路。

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