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Isolated attosecond pulses make it possible to study and control the ultrafast electron processes in atoms and molecules. High order harmonic generation (HHG) is the most promising way to generate such pulses, which is benefited from the broad plateau structure of the typical HHG spectrum. In previous HHG studies on the polarization gating pulse with longer pulse duration, one needs to dramatically increase the separation in time between the two counter-rotating circularly-polarized pulses to generate the nearly-linear half-cycle " polarization gate”. This leads to a low harmonic conversion efficiency because the field outside the polarization gate is much stronger than inside the polarization gate. In this paper, by using Lewenstein model, we theoretically simulate the high-order harmonic generation from helium atom subjected to the polarization gating pulse with 10 fs pulse duration. It is found that high-order harmonic spectra each with a higher efficiency and regular structure can still be obtained by reasonably adjusting the delay time ratio and the amplitude ratio of electric fields between the two counter-rotating pulses. Further, a single 175 as pulse in the time domain is obtained by Fourier transforming the 80th order harmonics into the 172nd order harmonic without compensating for the harmonic chirp. This scheme has two main advantages. First, the adjustment of the polarization gate width from half optical cycle into nearly one cycle ensures higher intensity of the synthesized electric field inside the polarization gate. Second, the suitable adjustment of the amplitude ratio between two electric fields ensures the low ionization probability before the polarization gate, and thus further fulfills the harmonic phase matching condition in the process of the propagation.
[1] Schultze M, Fiess M, Karpowicz N, Gagnon J, Korbman M, Hofstetter M, Neppl S, Cavalieri A L, Komninos Y, Mercouris T, Nicolaides C A, Pazourek R, Nagele S, Feist J, Burgdörfer J, Azzeer A M, Ernstorfer R, Kienberger R, Kleineberg U, Goulielmakis E, Krausz F, Yakovlev V S 2010 Science 328 1658
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[2] Drescher M, Hentschel M, Kienberger R, Uiberacker M, Yakovlev V, Scrinzi A, Westerwalbesloh T, Kleineberg U, Heinzmann U, Krausz F 2002 Nature 419 803
Google Scholar
[3] Sansone G, Benedetti E, Calegari F, Vozzi C, Avaldi L, Flammini R, Poletto L, Villoresi P, Altucci C, Velotta R, Stagira S, De Silvestri S, Nisoli M 2006 Science 314 443
Google Scholar
[4] Goulielmakis E, Schultze M, Hofstetter M, Yakovlev V S, Gagnon J, Uiberacker M, Aquila A L, Gullikson E M, Attwood D T, Kienberger R, Krausz F, Kleineberg U 2008 Science 320 1614
Google Scholar
[5] Vincenti H, Quéré F 2012 Phys. Rev. Lett. 108 113904
Google Scholar
[6] Chen J G, Yang Y J, Chen J, Wang B B 2015 Phys. Rev. A 91 043403
Google Scholar
[7] Corkum P B 1993 Phys. Rev. Lett. 71 1994
Google Scholar
[8] Agostini P, Dimauro L F 2004 Rep. Prog. Phys. 67 813
Google Scholar
[9] Yuan K J, Bandrauk A D 2013 Phys. Rev. Lett. 110 023003
Google Scholar
[10] Corkum P B, Burnett N H, Ivanov M Y 1994 Opt. Lett. 19 1870
Google Scholar
[11] Li J, Ren X, Yin Y, Zhao K, Chew A, Cheng Y, Cunningham E, Wang Y, Hu S, Wu Y, Chini M, Chang Z 2017 Nat. Commun. 8 794
Google Scholar
[12] Ferrari F, Calegari F, Lucchini M, Vozzi C, Stagira S, Sansone G, Nisoli M 2010 Nat. Photonics 4 875
Google Scholar
[13] Lan P, Lu P, Cao W, Li Y H, Wang X L 2007 Phys. Rev. A 76 21801
Google Scholar
[14] Kormin D, Borot A, Ma G J, Dallari W, Bergues B, Aladi M, Földes I, Veisz L 2018 Nat. Commun. 9 4992
Google Scholar
[15] Gaumnitz T, Jain A, Pertot Y, Huppert M, Jordan I, Ardana-Lamas F, Wörner H J 2017 Opt. Express 25 27506
Google Scholar
[16] Chang Z 2005 Phys. Rev. A 71 023813
Google Scholar
[17] Zhao K, Zhang Q, Chini M, Wu Y, Wang X W, Chang Z H 2012 Opt. Lett. 37 3891
Google Scholar
[18] Keldysh L V 1965 Sov. Phys. JETP 20 1307
[19] Faisal F H M 1973 J. Phys. B 6 L89
Google Scholar
[20] Reiss H R 1980 Phys. Rev. A 22 1786
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[21] Lewenstein M, Salières P, L’Huillier A 1995 Phys. Rev. A 52 4747
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[22] Ammosov M V, Delone N B, Krainov V 1986 Proc. SPIE 664 1191
Google Scholar
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图 1 偏振控制脉冲总电场(红色曲线)、控制场(绿色曲线)及驱动场(蓝色曲线)随时间变化三维图 (a) 5 fs脉宽和5 fs时间延迟; (c) 10 fs脉宽和22.5 fs时间延迟; (e) 10 fs脉宽和15 fs时间延迟; (b), (d), (f)显示了与(a), (c), (e)图相对应的驱动脉冲电场随时间变化曲线图(阴影部分是偏振门)
Figure 1. Three dimensional diagrams for the total electric field (red), gating field (green), and driving field (blue) in polarization gating pulse as a function of time: (a) 5 fs pulse width and 5 fs time delay; (c) 10 fs pulse width and 22.5 fs time delay; (e) 10 fs pulse width and 15 fs time delay. Panels (b), (d), (f) correspond to the driving electric field versus time in panels (a), (c), (e), respectively (shaded portion is polarization gate).
图 2 脉宽为10 fs的偏振控制脉冲与氦原子相互作用得到的高次谐波发射光谱, 其中黑线表示δtG = T0/2的偏振控制脉冲, 红线表示δtG = 0.82T0的偏振控制脉冲
Figure 2. High order harmonic generation from helium atom in a polarization gating pulse with 10 fs pulse width. The black curve is from the polarization gate width
${\text{δ}}{t_{\rm{G}}} = \dfrac{{{T_0}}}{2}$ , the red curve is from the polarization gate width δtG = 0.82T0.
图 3 谐波阶次随电离时刻及复合时刻的变化关系图
Figure 3. Evolution of the harmonics with ionization (black) and recombination (red) time.
图 4 偏振门内原子电离概率(红线)、驱动脉冲电场(黑线)、椭偏率(蓝线)随时间变化曲线 (a)对称偏振控制方案δtG = 0.5T0; (b)对称偏振控制方案δtG = 0.82T0; (c)不对称偏振控制方案δtG = 0.82T0
Figure 4. Atomic ionization probability (red line), electric field of driving pulse (black line), ellipticity (blue line) in the polarization gate as function of time: (a) Symmetric polarization gating scheme δtG = 0.5T0; (b) symmetric polarization gating scheme δtG = 0.82T0; (c) asymmetric polarization gating scheme δtG = 0.82T0.
图 5 (a)不对称偏振控制脉冲总电场(红色曲线)、控制场(绿色曲线)及驱动场(蓝色曲线)随时间变化三维图; (b)高次谐波发射谱
Figure 5. (a) Three-dimensional diagrams for the total electric field (red curve), gating field (green curve) and driving field (blue curve) in the asymmetric polarization gating pulse as a function of time; (b) high harmonic emission spectra.
图 6 不对称偏振控制方案中谐波发射的时频分析图像
Figure 6. Time-frequency analysis of harmonic emission in asymmetric polarization gating scheme.
图 7 阿秒脉冲产生时域图 (a)不对称偏振控制方案; (b)对称偏振控制方案
Figure 7. Attosecond pulse generation from (a) asymmetric polarization gating scheme and (b) symmetric polarization gating scheme.
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[1] Schultze M, Fiess M, Karpowicz N, Gagnon J, Korbman M, Hofstetter M, Neppl S, Cavalieri A L, Komninos Y, Mercouris T, Nicolaides C A, Pazourek R, Nagele S, Feist J, Burgdörfer J, Azzeer A M, Ernstorfer R, Kienberger R, Kleineberg U, Goulielmakis E, Krausz F, Yakovlev V S 2010 Science 328 1658
Google Scholar
[2] Drescher M, Hentschel M, Kienberger R, Uiberacker M, Yakovlev V, Scrinzi A, Westerwalbesloh T, Kleineberg U, Heinzmann U, Krausz F 2002 Nature 419 803
Google Scholar
[3] Sansone G, Benedetti E, Calegari F, Vozzi C, Avaldi L, Flammini R, Poletto L, Villoresi P, Altucci C, Velotta R, Stagira S, De Silvestri S, Nisoli M 2006 Science 314 443
Google Scholar
[4] Goulielmakis E, Schultze M, Hofstetter M, Yakovlev V S, Gagnon J, Uiberacker M, Aquila A L, Gullikson E M, Attwood D T, Kienberger R, Krausz F, Kleineberg U 2008 Science 320 1614
Google Scholar
[5] Vincenti H, Quéré F 2012 Phys. Rev. Lett. 108 113904
Google Scholar
[6] Chen J G, Yang Y J, Chen J, Wang B B 2015 Phys. Rev. A 91 043403
Google Scholar
[7] Corkum P B 1993 Phys. Rev. Lett. 71 1994
Google Scholar
[8] Agostini P, Dimauro L F 2004 Rep. Prog. Phys. 67 813
Google Scholar
[9] Yuan K J, Bandrauk A D 2013 Phys. Rev. Lett. 110 023003
Google Scholar
[10] Corkum P B, Burnett N H, Ivanov M Y 1994 Opt. Lett. 19 1870
Google Scholar
[11] Li J, Ren X, Yin Y, Zhao K, Chew A, Cheng Y, Cunningham E, Wang Y, Hu S, Wu Y, Chini M, Chang Z 2017 Nat. Commun. 8 794
Google Scholar
[12] Ferrari F, Calegari F, Lucchini M, Vozzi C, Stagira S, Sansone G, Nisoli M 2010 Nat. Photonics 4 875
Google Scholar
[13] Lan P, Lu P, Cao W, Li Y H, Wang X L 2007 Phys. Rev. A 76 21801
Google Scholar
[14] Kormin D, Borot A, Ma G J, Dallari W, Bergues B, Aladi M, Földes I, Veisz L 2018 Nat. Commun. 9 4992
Google Scholar
[15] Gaumnitz T, Jain A, Pertot Y, Huppert M, Jordan I, Ardana-Lamas F, Wörner H J 2017 Opt. Express 25 27506
Google Scholar
[16] Chang Z 2005 Phys. Rev. A 71 023813
Google Scholar
[17] Zhao K, Zhang Q, Chini M, Wu Y, Wang X W, Chang Z H 2012 Opt. Lett. 37 3891
Google Scholar
[18] Keldysh L V 1965 Sov. Phys. JETP 20 1307
[19] Faisal F H M 1973 J. Phys. B 6 L89
Google Scholar
[20] Reiss H R 1980 Phys. Rev. A 22 1786
Google Scholar
[21] Lewenstein M, Salières P, L’Huillier A 1995 Phys. Rev. A 52 4747
Google Scholar
[22] Ammosov M V, Delone N B, Krainov V 1986 Proc. SPIE 664 1191
Google Scholar
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