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提出了一种利用非对称波形激光脉冲与原子相互作用在隧穿区发射高次谐波谱的大频移方案. 通过数值求解偶极近似下的三维含时薛定谔方程, 研究了该激光驱动氢原子发射的高次谐波特性. 结果表明, 利用上升沿与下降沿不同的非对称激光驱动氢原子所发射的高次谐波在截止位置附近发生了大的频率红移和蓝移, 通过改变激光脉冲的上升沿或下降沿, 能调控谐波的频移量. 产生频移的原因是激光脉冲上升沿或下降沿对谐波贡献的不同所致, 当下降沿发射谐波的贡献大于上升沿的贡献时, 谐波发生红移, 反之则发生蓝移. 通过改变激光脉冲波形, 在隧穿电离区能够调控截止位置附近原子发射的高次谐波频率, 对于给定的某一阶谐波, 调控的范围可从奇次阶到邻近偶次阶之间的任意频率处.A scheme of the large frequency shift for high-order harmonic generation (HHG) produced by atomic gas driven by an asymmetric laser pulse is proposed in the tunneling ionization regime. By numerically solving the three-dimensional time-dependent Schrodinger equation in the dipole approximation, we theoretically investigate the characteristics of HHG emitted from hydrogen atom driven by the laser pulse with different rising and falling times. Our results show that the HHG spectra of atomic H in cutoff region present a strong redshift and blueshift. The shift can be adjusted by varying the rising time or falling time of the laser pulse. The time frequency analysis, reveals that the reason for the frequency shift comes from different contributions from the rising time or falling time in the asymmetric laser pulse. If the contributed harmonics during the falling time is larger than that during the falling time, the red shift of HHG occurs. otherwise the blue shift appears. Therefore, by shaping the laser pulse waveform, the frequency of atomic HHG for a given order in the cutoff region in the tunneling ionization regime is tunable, which can cover the frequency range from the odd order to the adjacent even order.
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Keywords:
- Keywards: asymmetric laser waveform /
- high-order harmonics /
- redshift /
- blushift
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图 1 (a)下降类激光脉冲波形; (b)氢原子发射的高次谐波谱, 箭头表示谐波频移的方向
Fig. 1. (a) Waveform of laser pulse in falling type; (b) HHG spectra of H atom(arrow indicates the direction of frequency shift).
图 2 (a) (b) 下降类第I, III型激光脉冲波形; (c) (d)相应高次谐波的时频分析
Fig. 2. (a) (b) Laser waveform I, III in falling type; (c) (d) time-frequency profile of theHHG spectra.
图 3 (a) 上升类激光脉冲波形; (b)氢原子发射的高次谐波谱, 箭头表示谐波频移的方向
Fig. 3. (a) Waveform of laser pulse in rising type; (b) HHG spectra of H atom(arrow indicates the direction of frequency shift).
图 4 (a) (b)上升类第I, III种激光脉冲; (c) (d)相应高次谐波的时频分析
Fig. 4. (a) (b) Laser waveform I, III in rising type; (c) (d) time-frequency profile of the HHG spectra.
图 5 (a) (b) H65阶谐波在第III种激光场下的红移、蓝移量; (c) H61和H65谐波的红移量 (蓝移量)与激光强度变化率之间的关系
Fig. 5. (a) (b) The redshift, blueshift of H65 in laser waveform III, respectively; (c) the redshift (blueshift) of H61 and H65 with the rate of change of laser intensity.
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[1] Winterfeldt C, Spielmann C, Gerber G 2008 Rev. Mod. Phys. 80 117
Google Scholar
[2] Kohler M C, Pfeifer T, Hatsagortsyan K Z, Keitel C H 2012 Adv. Atom. Mol. Opt. Phys. 61 159
Google Scholar
[3] Ravasio A, Gauthier D, Maia F R N C, Billon M, Caumes J P, Garzella D, Géléoc M, Gobert O, Hergott J F, Pena A M, Perez H, Carré B, Bourhis E, Gierak J, Madouri A, Mailly D, Schiedt B, Fajardo M, Gautier J, Zeitoun P, Bucksbaum P H, Hajdu J, Merdji H 2009 Phys. Rev. Lett. 103 028104
Google Scholar
[4] Corkum P B, Krausz F 2007 Nat. Phys. 3 381
Google Scholar
[5] Calegari F, Sansone G, Stagiraand S, Vozzi C, Nisoli M 2016 J. Phys. B:At. Mol. Opt. Phys. 49 062001
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[6] Villeneuve D M 2018 Contemp. Phys. 59 47
Google Scholar
[7] Jiao Z H, Wang G L, Li P C, Zhou X X 2014 Phys. Rev. A 90 025401
Google Scholar
[8] Morishita T, Le A T, Chen Z, Lin C D 2008 Phys. Rev. Lett. 100 013903
Google Scholar
[9] Itatani J, Levesquel J, Zeidler D, Niikura H, Pépin H, Kieffer J C, Corkum P B, Villeneuve D M 2004 Nature 432 867
Google Scholar
[10] Corkum P B 1993 Phys. Rev. Lett. 71 1994
Google Scholar
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Google Scholar
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Google Scholar
[13] Miyazaki K, Takada H 1995 Phys. Rev. A 52 3007
Google Scholar
[14] Du H, Xue S, Wang H, Zhang Z, Hu B 2015 Phys. Rev. A 91 063844
Google Scholar
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Google Scholar
[16] Shin H J, Lee D G, Cha Y H, Hong K H, Nam C H 1999 Phys. Rev. Lett. 83 2544
Google Scholar
[17] Weiner A M 2011 Opt. Commun. 284 3669
Google Scholar
[18] 姚云华, 卢晨晖, 徐淑武, 丁晶新, 贾天卿, 张诗按, 孙真荣 2014 物理学报 63 184201
Google Scholar
Yao Y H, Lu C H, Xu S W, Ding J X, Jia T Q, Zhang S A, Sun Z R 2014 Acta Phys. Sin. 63 184201
Google Scholar
[19] Stebbings S L, Süßmann F, Yang Y Y, Scrinzi A, Durach M, Rusina A, Stockman M I, Kling M F 2011 New J. Phys. 13 073010
Google Scholar
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Google Scholar
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Google Scholar
[22] Antoine P, Pirauxand B, Maquet A 1995 Phys. Rev. A 51 R1750
Google Scholar
[23] Kan C, Capjack C E, Rankin R, Burnett N H 1995 Phys. Rev. A 52 R4336
Google Scholar
[24] Tong X M, Chu S I 2000 Phys. Rev. A 61 021802(R)
[25] Lewenstein M, Salières P, L’Huillier A 1995 Phys. Rev. A 52 4747
Google Scholar
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