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We theoretically study high-order harmonics generation (HHG) and isolated attosecond pulse (IAP) generation in a spatially inhomogeneous chirped two-color (5 fs/800 nm and 12 fs/1600 nm) laser field by solving numerically the time-dependent Schrdinger equation(TDSE) for a one-dimensional (1D) model of He+ ion by the splitting-operator fast-Fourier transform technique. Results show that the inhomogeneity of the laser field plays an important role in the HHG process. The harmonic spectra exhibit a two-plateau structure, and the cutoff of high-order harmonics is extremely extended to 851th order and the smooth supercontinuum harmonic spectrum is obtained in a chirped two-color inhomogeneous laser field. To further understand the physical mechanism of HHG, we give a reasonable explanation for the extension of harmonic plateau by using the semi-classical three-step model, the time-frequency profile of the time-dependent dipole, and the classical electron trajectories. Explicitly, the harmonic order as a function of the ionization time and emission time can be given by the semi-classical three-step model. If we define the path with earlier ionization time and later emission time as a ongelectronic trajectory, and the path with later ionization time and earlier emission time as a short electronic trajectory, then, there exist a few electronic trajectories that contribute to the harmonics in cutoff region. Numerical results show that the short quantum path is enhanced, and the long quantum path is suppressed in spatially inhomogeneous fields, and this is advantageous to generate an IAP. We find that the quantum path can be controlled by increasing inhomogeneity parameter of the laser field. Effects of the time delay on HHG is also discussed. We find that the smooth supercontinuum harmonic spectrum is obtained by adjusting the time delay. When the time delay is t0=1.6up/1, the cutoff of the harmonics can be extended remarkably. By synthesizing the 600th to 680th (80th) order harmonics in the continuum region, an isolated 32 attosecond pulse can be generated by a spatially inhomogeneous chirped two-color laser field with parameters =0.25, =0.00105, t0=1.6/1.
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Keywords:
- spatially inhomogeneous chirped two-color laser field /
- high-order harmonic generation /
- isolated attosecond pulse
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[2] Drescher M, Hentschel M, Kienberger R, Tempea G, Spielmann C, Reider G A, CorkumP B, Krausz F 2001 Science 291 1923
[3] Drescher M, Hentschel M, Kienberger R, Uiberacker M, Yakovlev V, Scrinzi A, Westerwalbesloh T, Kleineberg U, Heinzmann U, Krausz F 2002 Nature 419 803
[4] Krausz F, Ivanov M 2009 Rev. Mod. Phys. 81 163
[5] Lan P F, Lu P X, Li Q G, Li F, Hong W Y, Zhang Q B 2009 Phys. Rev. A 79 043413
[6] Corkum P B 1993 Phys. Rev. Lett. 71 1994
[7] Sansone G, Benedetti E, Calegari F, Vozzi C, Avaldi L, Flammini R, Poletto L, Villoresi P, Altucci C, Velotta R, Stagira S, Silvestri S De, Nisoli M 2006 Science 314 443
[8] 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
[9] Zou P, Li R X, Zeng Z N, Xiong H, Liu P, Leng Y X, Fan P Z, Xu Z Z 2010 Chin. Phys. B 19 019501
[10] Xia C L, Liu X S 2012 Acta Phys. Sin. 61 043303(in Chinese) [夏昌龙, 刘学深 2012 61 043303]
[11] Chen G, Yang Y J, Guo F M 2013 Acta Phys. Sin. 62 073203(in Chinese) [陈高, 杨玉军, 郭福明 2013 62 073203]
[12] Wu J, Zhang G T, Xia C L, Liu X S 2010 Phys. Rev. A 82 013411
[13] Li P C, Zhou X X, Wang G L, Zhao Z X 2009 Phys. Rev. A 80 053825
[14] Kim S, Jin J, Kim Y J, Park I Y, Kim Y, Kim S W 2008 Nature 453 757
[15] Ciappina M F, Biegert J, Quidant R, Lewenstein M 2012 Phys. Rev. A 85 033828
[16] Zeng T T, Li P C, Zhou X X 2014 Acta Phys. Sin. 63 203201(in Chinese) [曾婷婷, 李鹏程, 周效信 2014 63 203201]
[17] Ge X L, Du H, Wang Q, Guo J, Liu X S 2015 Chin. Phys. B 24 023201
[18] Feit M D, Fleck J A, Jr, Steiger A 1982 J. Comput. Phys. 47 412
[19] Antoine P, Piraux B, Maquet A 1995 Phys. Rev. A 51 1750
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[1] Hentschel M, Kienberger R, Spielmann Ch, Reider G A, Milosevic N, Brabec T, Corkum P, Heinzmann U, Drescher M, Krausz F 2001 Nature 414 509
[2] Drescher M, Hentschel M, Kienberger R, Tempea G, Spielmann C, Reider G A, CorkumP B, Krausz F 2001 Science 291 1923
[3] Drescher M, Hentschel M, Kienberger R, Uiberacker M, Yakovlev V, Scrinzi A, Westerwalbesloh T, Kleineberg U, Heinzmann U, Krausz F 2002 Nature 419 803
[4] Krausz F, Ivanov M 2009 Rev. Mod. Phys. 81 163
[5] Lan P F, Lu P X, Li Q G, Li F, Hong W Y, Zhang Q B 2009 Phys. Rev. A 79 043413
[6] Corkum P B 1993 Phys. Rev. Lett. 71 1994
[7] Sansone G, Benedetti E, Calegari F, Vozzi C, Avaldi L, Flammini R, Poletto L, Villoresi P, Altucci C, Velotta R, Stagira S, Silvestri S De, Nisoli M 2006 Science 314 443
[8] 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
[9] Zou P, Li R X, Zeng Z N, Xiong H, Liu P, Leng Y X, Fan P Z, Xu Z Z 2010 Chin. Phys. B 19 019501
[10] Xia C L, Liu X S 2012 Acta Phys. Sin. 61 043303(in Chinese) [夏昌龙, 刘学深 2012 61 043303]
[11] Chen G, Yang Y J, Guo F M 2013 Acta Phys. Sin. 62 073203(in Chinese) [陈高, 杨玉军, 郭福明 2013 62 073203]
[12] Wu J, Zhang G T, Xia C L, Liu X S 2010 Phys. Rev. A 82 013411
[13] Li P C, Zhou X X, Wang G L, Zhao Z X 2009 Phys. Rev. A 80 053825
[14] Kim S, Jin J, Kim Y J, Park I Y, Kim Y, Kim S W 2008 Nature 453 757
[15] Ciappina M F, Biegert J, Quidant R, Lewenstein M 2012 Phys. Rev. A 85 033828
[16] Zeng T T, Li P C, Zhou X X 2014 Acta Phys. Sin. 63 203201(in Chinese) [曾婷婷, 李鹏程, 周效信 2014 63 203201]
[17] Ge X L, Du H, Wang Q, Guo J, Liu X S 2015 Chin. Phys. B 24 023201
[18] Feit M D, Fleck J A, Jr, Steiger A 1982 J. Comput. Phys. 47 412
[19] Antoine P, Piraux B, Maquet A 1995 Phys. Rev. A 51 1750
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