Abstract

We propose a method to control the harmonic process by a mid-IR modulated polarization gating for the effective generation of an ultra-broadband supercontinuum in the neutral rare-gas media. Using a mid-IR polarization gating pulse modulated by a weaker 800-nm linearly polarized pulse, the ionization, acceleration and recombination steps in the harmonic process are simultaneously controlled, leading to the efficient generation of an ultra-broadband supercontinuum covered by the spectral range from ultraviolet to water window x ray under the low ionization rate. The right phase-matching technique is employed to macroscopically select the short quantum path of the supercontinuum, then isolated sub-100-as pulses with tunable wavelengths are directly obtained. This supercontinuum also supports the pulse duration far below one atomic unit of time.

© 2010 Optical Society of America

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  1. F. Krausz, “Attosecond physics,” Rev. Mod. Phys. 81,163–234 (2009).
    [CrossRef]
  2. E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, U. Kleineberg, “Single-Cycle Nonlinear Optics,” Science,  320,1614–1617 (2008).
    [CrossRef] [PubMed]
  3. P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71,1994–1997 (1993).
    [CrossRef] [PubMed]
  4. Z. Chang, “Single attosecond pulse and xuv supercontinuum in the high-order harmonic plateau,” Phys. Rev. A 70,043802 (2004).
    [CrossRef]
  5. P. Lan, P. Lu,W. Cao, Y. Li, and X. Wang, “Isolated sub-100-as pulse generation via controlling electron dynamics,” Phys. Rev. A 76,011402 (2007).
    [CrossRef]
  6. P. Lan, P. Lu, Q. Li, W. Hong, and Q. Zhang, “Macroscopic effects for quantum control of broadband isolated attosecond pulse generation with a two-color field,” Phys. Rev. A 79,043413 (2009).
    [CrossRef]
  7. Y. Zheng, Z. Zeng, X. Li, X. Chen, P. Liu, H. Xiong, H. Lu, S. Zhao, P. Wei, L. Zhang, X. Wang, J. Liu, Y. Cheng, R. Li, and Z. Xu, “Enhancement and broadening of extreme-ultraviolet supercontinuum in a relative phase controlled two-color laser field,” Opt. Lett. 33,234–236 (2008).
    [CrossRef] [PubMed]
  8. W. Hong, Y. Li, P. Lu, P. Lan, Q. Zhang. and X. Wang, “Control of quantum paths in multi-cycle regime and efficient broadband attosecond pulse generation,” J. Opt. Soc. Am. B 25, 1684–1689 (2008).
    [CrossRef]
  9. H. Mashiko, S. Gilbertson, C. Li, S. D. Khan, M. M. Shakya, E. Moon, and Z. Chang, “Double optical gating of high-order harmonic generation with carrier-envelope phase stabilized laser,” Phys. Rev. Lett. 100,103906 (2008).
    [CrossRef] [PubMed]
  10. J. Tate, T. Auguste, H. Muller, P. Sali` eres, P. Agostini, and L. F. DiMauro, “Scaling ofWave-Packet Dynamics in an Intense Midinfrared Field,” Phys. Rev. Lett. 98,013901 (2007).
    [CrossRef] [PubMed]
  11. E. Takahashi, T. Kanai, K. Ishikawa, Y. Nabekawa, and K. Midorikawa, “Coherent Water Window X Ray by Phase-Matched High-Order Harmonic Generation in Neutral Media,” Phys. Rev. Lett. 101,253901 (2008).
    [CrossRef] [PubMed]
  12. W. Hong, P. Lu, Q. Li, and Q. Zhang, “Broadband water window supercontinuum generation with a tailored mid-IR pulse in neutral media,” Opt. Lett. 34,2102–2104 (2009).
    [CrossRef] [PubMed]
  13. Q. Zhang, P. Lu, P. Lan, W. Hong, and Z. Yang, “Multi-cycle laser-driven broadband supercontinuum with a modulated polarization gating,” Opt. Express 16,9795–9803 (2008).
    [CrossRef] [PubMed]
  14. M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49,2117–2132 (1994).
    [CrossRef] [PubMed]
  15. M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64,1191–1194 (1986).
  16. E. Priori, G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, P. Villoresi, L. Poletto, P. Ceccherini, C. Altucci, R. Bruzzese, and C. de Lisio, “Nonadiabatic three-dimentional model of high-order harmonic generation in the few-optical cycle regime,” Phys. Rev. A 61,063801 (2000).
    [CrossRef]

2009 (3)

F. Krausz, “Attosecond physics,” Rev. Mod. Phys. 81,163–234 (2009).
[CrossRef]

P. Lan, P. Lu, Q. Li, W. Hong, and Q. Zhang, “Macroscopic effects for quantum control of broadband isolated attosecond pulse generation with a two-color field,” Phys. Rev. A 79,043413 (2009).
[CrossRef]

W. Hong, P. Lu, Q. Li, and Q. Zhang, “Broadband water window supercontinuum generation with a tailored mid-IR pulse in neutral media,” Opt. Lett. 34,2102–2104 (2009).
[CrossRef] [PubMed]

2008 (6)

Q. Zhang, P. Lu, P. Lan, W. Hong, and Z. Yang, “Multi-cycle laser-driven broadband supercontinuum with a modulated polarization gating,” Opt. Express 16,9795–9803 (2008).
[CrossRef] [PubMed]

E. Takahashi, T. Kanai, K. Ishikawa, Y. Nabekawa, and K. Midorikawa, “Coherent Water Window X Ray by Phase-Matched High-Order Harmonic Generation in Neutral Media,” Phys. Rev. Lett. 101,253901 (2008).
[CrossRef] [PubMed]

Y. Zheng, Z. Zeng, X. Li, X. Chen, P. Liu, H. Xiong, H. Lu, S. Zhao, P. Wei, L. Zhang, X. Wang, J. Liu, Y. Cheng, R. Li, and Z. Xu, “Enhancement and broadening of extreme-ultraviolet supercontinuum in a relative phase controlled two-color laser field,” Opt. Lett. 33,234–236 (2008).
[CrossRef] [PubMed]

W. Hong, Y. Li, P. Lu, P. Lan, Q. Zhang. and X. Wang, “Control of quantum paths in multi-cycle regime and efficient broadband attosecond pulse generation,” J. Opt. Soc. Am. B 25, 1684–1689 (2008).
[CrossRef]

H. Mashiko, S. Gilbertson, C. Li, S. D. Khan, M. M. Shakya, E. Moon, and Z. Chang, “Double optical gating of high-order harmonic generation with carrier-envelope phase stabilized laser,” Phys. Rev. Lett. 100,103906 (2008).
[CrossRef] [PubMed]

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, U. Kleineberg, “Single-Cycle Nonlinear Optics,” Science,  320,1614–1617 (2008).
[CrossRef] [PubMed]

2007 (2)

P. Lan, P. Lu,W. Cao, Y. Li, and X. Wang, “Isolated sub-100-as pulse generation via controlling electron dynamics,” Phys. Rev. A 76,011402 (2007).
[CrossRef]

J. Tate, T. Auguste, H. Muller, P. Sali` eres, P. Agostini, and L. F. DiMauro, “Scaling ofWave-Packet Dynamics in an Intense Midinfrared Field,” Phys. Rev. Lett. 98,013901 (2007).
[CrossRef] [PubMed]

2004 (1)

Z. Chang, “Single attosecond pulse and xuv supercontinuum in the high-order harmonic plateau,” Phys. Rev. A 70,043802 (2004).
[CrossRef]

2000 (1)

E. Priori, G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, P. Villoresi, L. Poletto, P. Ceccherini, C. Altucci, R. Bruzzese, and C. de Lisio, “Nonadiabatic three-dimentional model of high-order harmonic generation in the few-optical cycle regime,” Phys. Rev. A 61,063801 (2000).
[CrossRef]

1994 (1)

M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49,2117–2132 (1994).
[CrossRef] [PubMed]

1993 (1)

P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71,1994–1997 (1993).
[CrossRef] [PubMed]

1986 (1)

M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64,1191–1194 (1986).

Altucci, C.

E. Priori, G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, P. Villoresi, L. Poletto, P. Ceccherini, C. Altucci, R. Bruzzese, and C. de Lisio, “Nonadiabatic three-dimentional model of high-order harmonic generation in the few-optical cycle regime,” Phys. Rev. A 61,063801 (2000).
[CrossRef]

Ammosov, M. V.

M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64,1191–1194 (1986).

Aquila, A. L.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, U. Kleineberg, “Single-Cycle Nonlinear Optics,” Science,  320,1614–1617 (2008).
[CrossRef] [PubMed]

Attwood, D. T.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, U. Kleineberg, “Single-Cycle Nonlinear Optics,” Science,  320,1614–1617 (2008).
[CrossRef] [PubMed]

Auguste, T.

J. Tate, T. Auguste, H. Muller, P. Sali` eres, P. Agostini, and L. F. DiMauro, “Scaling ofWave-Packet Dynamics in an Intense Midinfrared Field,” Phys. Rev. Lett. 98,013901 (2007).
[CrossRef] [PubMed]

Balcou, Ph.

M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49,2117–2132 (1994).
[CrossRef] [PubMed]

Bruzzese, R.

E. Priori, G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, P. Villoresi, L. Poletto, P. Ceccherini, C. Altucci, R. Bruzzese, and C. de Lisio, “Nonadiabatic three-dimentional model of high-order harmonic generation in the few-optical cycle regime,” Phys. Rev. A 61,063801 (2000).
[CrossRef]

Cao, W.

P. Lan, P. Lu,W. Cao, Y. Li, and X. Wang, “Isolated sub-100-as pulse generation via controlling electron dynamics,” Phys. Rev. A 76,011402 (2007).
[CrossRef]

Ceccherini, P.

E. Priori, G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, P. Villoresi, L. Poletto, P. Ceccherini, C. Altucci, R. Bruzzese, and C. de Lisio, “Nonadiabatic three-dimentional model of high-order harmonic generation in the few-optical cycle regime,” Phys. Rev. A 61,063801 (2000).
[CrossRef]

Cerullo, G.

E. Priori, G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, P. Villoresi, L. Poletto, P. Ceccherini, C. Altucci, R. Bruzzese, and C. de Lisio, “Nonadiabatic three-dimentional model of high-order harmonic generation in the few-optical cycle regime,” Phys. Rev. A 61,063801 (2000).
[CrossRef]

Chang, Z.

H. Mashiko, S. Gilbertson, C. Li, S. D. Khan, M. M. Shakya, E. Moon, and Z. Chang, “Double optical gating of high-order harmonic generation with carrier-envelope phase stabilized laser,” Phys. Rev. Lett. 100,103906 (2008).
[CrossRef] [PubMed]

Z. Chang, “Single attosecond pulse and xuv supercontinuum in the high-order harmonic plateau,” Phys. Rev. A 70,043802 (2004).
[CrossRef]

Chen, X.

Cheng, Y.

Corkum, P.

M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49,2117–2132 (1994).
[CrossRef] [PubMed]

Corkum, P. B.

P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71,1994–1997 (1993).
[CrossRef] [PubMed]

de Lisio, C.

E. Priori, G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, P. Villoresi, L. Poletto, P. Ceccherini, C. Altucci, R. Bruzzese, and C. de Lisio, “Nonadiabatic three-dimentional model of high-order harmonic generation in the few-optical cycle regime,” Phys. Rev. A 61,063801 (2000).
[CrossRef]

De Silvestri, S.

E. Priori, G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, P. Villoresi, L. Poletto, P. Ceccherini, C. Altucci, R. Bruzzese, and C. de Lisio, “Nonadiabatic three-dimentional model of high-order harmonic generation in the few-optical cycle regime,” Phys. Rev. A 61,063801 (2000).
[CrossRef]

Delone, N. B.

M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64,1191–1194 (1986).

Gagnon, J.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, U. Kleineberg, “Single-Cycle Nonlinear Optics,” Science,  320,1614–1617 (2008).
[CrossRef] [PubMed]

Gilbertson, S.

H. Mashiko, S. Gilbertson, C. Li, S. D. Khan, M. M. Shakya, E. Moon, and Z. Chang, “Double optical gating of high-order harmonic generation with carrier-envelope phase stabilized laser,” Phys. Rev. Lett. 100,103906 (2008).
[CrossRef] [PubMed]

Goulielmakis, E.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, U. Kleineberg, “Single-Cycle Nonlinear Optics,” Science,  320,1614–1617 (2008).
[CrossRef] [PubMed]

Gullikson, E. M.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, U. Kleineberg, “Single-Cycle Nonlinear Optics,” Science,  320,1614–1617 (2008).
[CrossRef] [PubMed]

Hofstetter, M.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, U. Kleineberg, “Single-Cycle Nonlinear Optics,” Science,  320,1614–1617 (2008).
[CrossRef] [PubMed]

Hong, W.

Ishikawa, K.

E. Takahashi, T. Kanai, K. Ishikawa, Y. Nabekawa, and K. Midorikawa, “Coherent Water Window X Ray by Phase-Matched High-Order Harmonic Generation in Neutral Media,” Phys. Rev. Lett. 101,253901 (2008).
[CrossRef] [PubMed]

Ivanov, M. Yu.

M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49,2117–2132 (1994).
[CrossRef] [PubMed]

Kanai, T.

E. Takahashi, T. Kanai, K. Ishikawa, Y. Nabekawa, and K. Midorikawa, “Coherent Water Window X Ray by Phase-Matched High-Order Harmonic Generation in Neutral Media,” Phys. Rev. Lett. 101,253901 (2008).
[CrossRef] [PubMed]

Khan, S. D.

H. Mashiko, S. Gilbertson, C. Li, S. D. Khan, M. M. Shakya, E. Moon, and Z. Chang, “Double optical gating of high-order harmonic generation with carrier-envelope phase stabilized laser,” Phys. Rev. Lett. 100,103906 (2008).
[CrossRef] [PubMed]

Kienberger, R.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, U. Kleineberg, “Single-Cycle Nonlinear Optics,” Science,  320,1614–1617 (2008).
[CrossRef] [PubMed]

Kleineberg, U.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, U. Kleineberg, “Single-Cycle Nonlinear Optics,” Science,  320,1614–1617 (2008).
[CrossRef] [PubMed]

Krainov, V. P.

M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64,1191–1194 (1986).

Krausz, F.

F. Krausz, “Attosecond physics,” Rev. Mod. Phys. 81,163–234 (2009).
[CrossRef]

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, U. Kleineberg, “Single-Cycle Nonlinear Optics,” Science,  320,1614–1617 (2008).
[CrossRef] [PubMed]

L’Huillier, A.

M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49,2117–2132 (1994).
[CrossRef] [PubMed]

Lan, P.

P. Lan, P. Lu, Q. Li, W. Hong, and Q. Zhang, “Macroscopic effects for quantum control of broadband isolated attosecond pulse generation with a two-color field,” Phys. Rev. A 79,043413 (2009).
[CrossRef]

W. Hong, Y. Li, P. Lu, P. Lan, Q. Zhang. and X. Wang, “Control of quantum paths in multi-cycle regime and efficient broadband attosecond pulse generation,” J. Opt. Soc. Am. B 25, 1684–1689 (2008).
[CrossRef]

Q. Zhang, P. Lu, P. Lan, W. Hong, and Z. Yang, “Multi-cycle laser-driven broadband supercontinuum with a modulated polarization gating,” Opt. Express 16,9795–9803 (2008).
[CrossRef] [PubMed]

P. Lan, P. Lu,W. Cao, Y. Li, and X. Wang, “Isolated sub-100-as pulse generation via controlling electron dynamics,” Phys. Rev. A 76,011402 (2007).
[CrossRef]

Lewenstein, M.

M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49,2117–2132 (1994).
[CrossRef] [PubMed]

Li, C.

H. Mashiko, S. Gilbertson, C. Li, S. D. Khan, M. M. Shakya, E. Moon, and Z. Chang, “Double optical gating of high-order harmonic generation with carrier-envelope phase stabilized laser,” Phys. Rev. Lett. 100,103906 (2008).
[CrossRef] [PubMed]

Li, Q.

W. Hong, P. Lu, Q. Li, and Q. Zhang, “Broadband water window supercontinuum generation with a tailored mid-IR pulse in neutral media,” Opt. Lett. 34,2102–2104 (2009).
[CrossRef] [PubMed]

P. Lan, P. Lu, Q. Li, W. Hong, and Q. Zhang, “Macroscopic effects for quantum control of broadband isolated attosecond pulse generation with a two-color field,” Phys. Rev. A 79,043413 (2009).
[CrossRef]

Li, R.

Li, X.

Li, Y.

W. Hong, Y. Li, P. Lu, P. Lan, Q. Zhang. and X. Wang, “Control of quantum paths in multi-cycle regime and efficient broadband attosecond pulse generation,” J. Opt. Soc. Am. B 25, 1684–1689 (2008).
[CrossRef]

P. Lan, P. Lu,W. Cao, Y. Li, and X. Wang, “Isolated sub-100-as pulse generation via controlling electron dynamics,” Phys. Rev. A 76,011402 (2007).
[CrossRef]

Liu, J.

Liu, P.

Lu, H.

Lu, P.

Mashiko, H.

H. Mashiko, S. Gilbertson, C. Li, S. D. Khan, M. M. Shakya, E. Moon, and Z. Chang, “Double optical gating of high-order harmonic generation with carrier-envelope phase stabilized laser,” Phys. Rev. Lett. 100,103906 (2008).
[CrossRef] [PubMed]

Midorikawa, K.

E. Takahashi, T. Kanai, K. Ishikawa, Y. Nabekawa, and K. Midorikawa, “Coherent Water Window X Ray by Phase-Matched High-Order Harmonic Generation in Neutral Media,” Phys. Rev. Lett. 101,253901 (2008).
[CrossRef] [PubMed]

Moon, E.

H. Mashiko, S. Gilbertson, C. Li, S. D. Khan, M. M. Shakya, E. Moon, and Z. Chang, “Double optical gating of high-order harmonic generation with carrier-envelope phase stabilized laser,” Phys. Rev. Lett. 100,103906 (2008).
[CrossRef] [PubMed]

Muller, H.

J. Tate, T. Auguste, H. Muller, P. Sali` eres, P. Agostini, and L. F. DiMauro, “Scaling ofWave-Packet Dynamics in an Intense Midinfrared Field,” Phys. Rev. Lett. 98,013901 (2007).
[CrossRef] [PubMed]

Nabekawa, Y.

E. Takahashi, T. Kanai, K. Ishikawa, Y. Nabekawa, and K. Midorikawa, “Coherent Water Window X Ray by Phase-Matched High-Order Harmonic Generation in Neutral Media,” Phys. Rev. Lett. 101,253901 (2008).
[CrossRef] [PubMed]

Nisoli, M.

E. Priori, G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, P. Villoresi, L. Poletto, P. Ceccherini, C. Altucci, R. Bruzzese, and C. de Lisio, “Nonadiabatic three-dimentional model of high-order harmonic generation in the few-optical cycle regime,” Phys. Rev. A 61,063801 (2000).
[CrossRef]

Poletto, L.

E. Priori, G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, P. Villoresi, L. Poletto, P. Ceccherini, C. Altucci, R. Bruzzese, and C. de Lisio, “Nonadiabatic three-dimentional model of high-order harmonic generation in the few-optical cycle regime,” Phys. Rev. A 61,063801 (2000).
[CrossRef]

Priori, E.

E. Priori, G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, P. Villoresi, L. Poletto, P. Ceccherini, C. Altucci, R. Bruzzese, and C. de Lisio, “Nonadiabatic three-dimentional model of high-order harmonic generation in the few-optical cycle regime,” Phys. Rev. A 61,063801 (2000).
[CrossRef]

Sali, P.

J. Tate, T. Auguste, H. Muller, P. Sali` eres, P. Agostini, and L. F. DiMauro, “Scaling ofWave-Packet Dynamics in an Intense Midinfrared Field,” Phys. Rev. Lett. 98,013901 (2007).
[CrossRef] [PubMed]

Schultze, M.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, U. Kleineberg, “Single-Cycle Nonlinear Optics,” Science,  320,1614–1617 (2008).
[CrossRef] [PubMed]

Shakya, M. M.

H. Mashiko, S. Gilbertson, C. Li, S. D. Khan, M. M. Shakya, E. Moon, and Z. Chang, “Double optical gating of high-order harmonic generation with carrier-envelope phase stabilized laser,” Phys. Rev. Lett. 100,103906 (2008).
[CrossRef] [PubMed]

Stagira, S.

E. Priori, G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, P. Villoresi, L. Poletto, P. Ceccherini, C. Altucci, R. Bruzzese, and C. de Lisio, “Nonadiabatic three-dimentional model of high-order harmonic generation in the few-optical cycle regime,” Phys. Rev. A 61,063801 (2000).
[CrossRef]

Takahashi, E.

E. Takahashi, T. Kanai, K. Ishikawa, Y. Nabekawa, and K. Midorikawa, “Coherent Water Window X Ray by Phase-Matched High-Order Harmonic Generation in Neutral Media,” Phys. Rev. Lett. 101,253901 (2008).
[CrossRef] [PubMed]

Tate, J.

J. Tate, T. Auguste, H. Muller, P. Sali` eres, P. Agostini, and L. F. DiMauro, “Scaling ofWave-Packet Dynamics in an Intense Midinfrared Field,” Phys. Rev. Lett. 98,013901 (2007).
[CrossRef] [PubMed]

Uiberacker, M.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, U. Kleineberg, “Single-Cycle Nonlinear Optics,” Science,  320,1614–1617 (2008).
[CrossRef] [PubMed]

Villoresi, P.

E. Priori, G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, P. Villoresi, L. Poletto, P. Ceccherini, C. Altucci, R. Bruzzese, and C. de Lisio, “Nonadiabatic three-dimentional model of high-order harmonic generation in the few-optical cycle regime,” Phys. Rev. A 61,063801 (2000).
[CrossRef]

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Xiong, H.

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E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, U. Kleineberg, “Single-Cycle Nonlinear Optics,” Science,  320,1614–1617 (2008).
[CrossRef] [PubMed]

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Zeng, Z.

Zhang, L.

Zhang, Q.

Zhao, S.

Zheng, Y.

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E. Priori, G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, P. Villoresi, L. Poletto, P. Ceccherini, C. Altucci, R. Bruzzese, and C. de Lisio, “Nonadiabatic three-dimentional model of high-order harmonic generation in the few-optical cycle regime,” Phys. Rev. A 61,063801 (2000).
[CrossRef]

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[CrossRef]

P. Lan, P. Lu, Q. Li, W. Hong, and Q. Zhang, “Macroscopic effects for quantum control of broadband isolated attosecond pulse generation with a two-color field,” Phys. Rev. A 79,043413 (2009).
[CrossRef]

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H. Mashiko, S. Gilbertson, C. Li, S. D. Khan, M. M. Shakya, E. Moon, and Z. Chang, “Double optical gating of high-order harmonic generation with carrier-envelope phase stabilized laser,” Phys. Rev. Lett. 100,103906 (2008).
[CrossRef] [PubMed]

J. Tate, T. Auguste, H. Muller, P. Sali` eres, P. Agostini, and L. F. DiMauro, “Scaling ofWave-Packet Dynamics in an Intense Midinfrared Field,” Phys. Rev. Lett. 98,013901 (2007).
[CrossRef] [PubMed]

E. Takahashi, T. Kanai, K. Ishikawa, Y. Nabekawa, and K. Midorikawa, “Coherent Water Window X Ray by Phase-Matched High-Order Harmonic Generation in Neutral Media,” Phys. Rev. Lett. 101,253901 (2008).
[CrossRef] [PubMed]

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E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, U. Kleineberg, “Single-Cycle Nonlinear Optics,” Science,  320,1614–1617 (2008).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1.
Fig. 1.

The classical sketch of the electron dynamics in the conventional and modulated PG pulse.

Fig. 2.
Fig. 2.

(a)The harmonic spectrum and (b) its time-frequency distribution in the modulated PG pulse.

Fig. 3.
Fig. 3.

The harmonic spectrum after 3D propagation in the modulated PG pulse.

Fig. 4.
Fig. 4.

(Color online) Isolated attosecond pulses centered at different frequencies.

Equations (15)

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d nl ( t ) = i t dt [ π ε + i ( t t ) / 2 ] 3 / 2
× d * [ p st ( t , t ) A ( t ) ] d [ p st ( t , t ) A ( t ) ]
× exp [ i S st ( t , t ) ] E f ( t ) g ( t ) + c . c . .
p st ( t , t ) = 1 t t t t A ( t ) dt ,
S st ( t , t ) = ( t t ) I p 1 2 p st 2 ( t , t ) ( t t ) + 1 2 t t A 2 ( t ) dt ,
d ( p ) = i 2 7 / 2 π ( 2 I p ) 5 / 4 p ( p 2 + 2 I p ) 3 .
g ( t ) = E f ( t ) exp [ t w ( t ) dt ] .
w ( t ) = ω p C n * 2 ( 4 ω p ω t ) 2 n * 1 exp ( 4 ω p 3 ω t ) ,
ω p = I p h ̄ , ω t = e E l ( t ) 2 m e I p , n * = Z ( I ph I p ) 1 / 2 , C n * 2 = 2 2 n * n * Γ ( n * + 1 ) Γ ( n * ) ,
a q = 1 T 0 T a ( t ) exp ( iqωt ) ,
2 E f ( ρ , z , t ) 1 c 2 2 E f ( ρ , z , t ) t 2 = ω p 2 ( ρ , z , t ) c 2 E f ( ρ , z , t )
2 E h ( ρ , z , t ) 1 c 2 2 E h ( ρ , z , t ) t 2 = ω p 2 ( ρ , z , t ) c 2 E h ( ρ , z , t ) + μ 0 2 P nl ( ρ , z , t ) t 2
E x , ω 0 ( t ) = E 0 ( e 2 ln ( 2 ) ( ( t T d / 2 ) / τ p ) 2 + e 2 ln ( 2 ) ( ( t + T d / 2 ) / τ p ) 2 ) cos ( ω 0 t + π / 2 ) x ,
E y , ω 0 ( t ) = E 0 ( e 2 ln ( 2 ) ( ( t T d / 2 ) / τ p ) 2 e 2 ln ( 2 ) ( ( t + T d / 2 ) / τ p ) 2 ) sin ( ω 0 t + π / 2 ) y ,
E x , ω 1 ( t ) = a ω 1 E 0 e 2 ln ( 2 ) ( t / τ 2 ω 1 ) 2 cos ( ω 1 t + π ) x .

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