Abstract

By solving a two-dimensional time-dependent Schrödinger equation we investigate high harmonic generation (HHG) and isolated attosecond pulse generation for the H2+ molecular ion in a circularly polarized laser pulse combined with a Terahertz (THz) field. The harmonic intensity can be greatly enhanced and a continuum spectrum can be obtained when a THz field is added. The HHG process is studied by the semi-classical three-step model and the time-frequency analysis. Our studies show that only short trajectories contribute to HHG. Furthermore, we present the temporal evolution of the probability density of electron wave packet, which perfectly shows a clear picture of the electron’s two-time recombination when a THz field is added, and it is the main mechanism of HHG. By superposing the harmonics in the range of 216–249 eV, an isolated attosecond pulse with a duration of about 69 attoseconds can be generated.

© 2015 Optical Society of America

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References

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  1. P. B. Corkum and F. Krausz, “Attosecond science,” Nature Phys. 3, 381–387 (2007).
    [Crossref]
  2. Ch. Spielmann, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnürer, C. Kan, M. Lenzner, P. Wobrauschek, and and F. Krausz, “Generation of coherent X-rays in the water window using 5-femtosecond laser pulses,” Science 278, 661–664 (1997).
    [Crossref]
  3. P. B. Corkum, “Plasma perspective on strong-field multiphoton ionization,” Phys. Rev. Lett. 71, 1994–1997 (1993).
    [Crossref] [PubMed]
  4. K. J. Schafer, B. Yang, L. F. DiMauro, and K. C. Kulander, “Above threshold ionization beyond the high Harmonic cutoff,” Phys. Rev. Lett. 70, 1599–1602 (1993).
    [Crossref] [PubMed]
  5. Z. Chang, “Single attosecond pulse and xuv supercontinuum in the high-order harmonic plateau,” Phys. Rev. A 70, 043802 (2004).
    [Crossref]
  6. T. Pfeifer, L. Gallmann, M. J. Abel, D. M. Neumark, and S. R. Leone, “Single attosecond pulse generation in the multicycle-driver regime by adding a weak second-harmonic field,” Opt. Lett. 31, 975–977 (2006).
    [Crossref] [PubMed]
  7. J. A. Pérez-Hernández, M. F. Ciappina, M. Lewenstein, L. Roso, and A. Zaïr, “Beyond carbon K-Edge harmonic emission using a spatial and temporal synthesized laser field,” Phys. Rev. Lett. 110, 053001 (2013).
    [Crossref] [PubMed]
  8. T. Löffler, T. Bauer, K. Siebert, H. Roskos, A. Fitzgerald, and S. Czasch, “Terahertz dark-field imaging of biomedical tissue,” Opt. Express 9, 616–621 (2001).
    [Crossref] [PubMed]
  9. K. J. Yuan and A. D. Bandrauk, “Single circularly polarized attosecond pulse generation by intense few cycle elliptically polarized laser pulses and terahertz fields from molecular media,” Phys. Rev. Lett. 110, 023003 (2013).
    [Crossref] [PubMed]
  10. W. Hong, P. Lu, W. Cao, P. Lan, and X. Wang, “Control of quantum paths of high-order harmonics and attosecond pulse generation in the presence of a static electric field,” J. Phys. B 40, 2321–2331 (2007).
    [Crossref]
  11. W. Hong, P. Lu, P. Lan, Q. Zhang, and X. Wang, “Few-cycle attosecond pulses with stabilized-carrier-envelope phase in the presence of a strong terahertz field,” Opt. Express 17, 5139–5146 (2009).
    [Crossref] [PubMed]
  12. E. Balogh, K. Kovacs, P. Dombi, J. A. Fulop, G. Farkas, J. Hebling, V. Tosa, and K. Varju, “Single attosecond pulse from terahertz-assisted high-order harmonic generation,” Phys. Rev. A 84, 023806 (2011).
    [Crossref]
  13. C. L. Xia, G. T. Zhang, J. Wu, and X. S. Liu, “Single attosecond pulse generation in an orthogonally polarized two-color laser field combined with a static electric field,” Phys. Rev. A 81, 043420 (2010).
    [Crossref]
  14. K. Y. Kim, J. H. Glownia, A. J. Taylor, and G. Rodriguez, “Terahertz emission from ultrafast ionizing air in symmetry-broken laser fields,” Opt. Express 15, 4577–4584 (2007).
    [Crossref] [PubMed]
  15. T. Zuo and A. D. Bandrauk, “high-order harmonic generation in intense laser and magentic fields,” J. Nonlinear Opt. Phys. Mater. 4, 533–546(1995).
    [Crossref]
  16. A. D. Bandrauk and H. Z. Lu, “Controlling harmonic generation in molecules with intense laser and static magnetic fields: Orientation effects,” Phys. Rev. A 68, 043408 (2003).
    [Crossref]
  17. X. L. Ge, T. Wang, J. Guo, and X. S. Liu, “Quantum-path control and isolated-attosecond-pulse generation using H+ 2 molecules with moving nuclei in few-cycle laser pulses,” Phys. Rev. A 89, 023424 (2014).
    [Crossref]
  18. M. D. Feit, J. A. Fleck, and A. Steiger, “Solution of the Schrödinger equation by a spectral method,” J. Comput. Phys. 47, 412–433 (1982).
    [Crossref]
  19. D. G. Lappas and Marangos, “Orientation dependence of high-order harmonic generation in hydrogen molecular ions,” J. Phys. B 33, 4679–4689 (2000).
    [Crossref]
  20. C. L. Xia and X. S. Liu, “Quantum path control and isolated attosecond pulse generation with the combination of two circularly polarized laser pulses,” Phys. Rev. A 87, 043406 (2013).
    [Crossref]
  21. M. Möller, Y. Cheng, S. D. Khan, B. Zhao, K. Zhao, M. Chini, G. G. Paulus, and Z. Chang, “Dependence of high-order-harmonic-generation yield on driving-laser ellipticity,” Phys. Rev. A 86, 011401 (2012).
    [Crossref]
  22. R. Kopold, D. B. Milošević, and W. Becker, “Rescattering Processes for Elliptical Polarization: A Quantum Trajectory Analysis,” Phys. Rev. Lett. 84, 3831–3834 (2000).
    [Crossref] [PubMed]
  23. P. B. Corkum, N. H. Burnett, and F. Brunel, “Above-threshold ionization in the long-wavelength limit,” Phys. Rev. Lett. 62, 1259–1262 (1989).
    [Crossref] [PubMed]
  24. M. V. Ammesov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETR 64, 1191–1194 (1986).

2014 (1)

X. L. Ge, T. Wang, J. Guo, and X. S. Liu, “Quantum-path control and isolated-attosecond-pulse generation using H+ 2 molecules with moving nuclei in few-cycle laser pulses,” Phys. Rev. A 89, 023424 (2014).
[Crossref]

2013 (3)

C. L. Xia and X. S. Liu, “Quantum path control and isolated attosecond pulse generation with the combination of two circularly polarized laser pulses,” Phys. Rev. A 87, 043406 (2013).
[Crossref]

J. A. Pérez-Hernández, M. F. Ciappina, M. Lewenstein, L. Roso, and A. Zaïr, “Beyond carbon K-Edge harmonic emission using a spatial and temporal synthesized laser field,” Phys. Rev. Lett. 110, 053001 (2013).
[Crossref] [PubMed]

K. J. Yuan and A. D. Bandrauk, “Single circularly polarized attosecond pulse generation by intense few cycle elliptically polarized laser pulses and terahertz fields from molecular media,” Phys. Rev. Lett. 110, 023003 (2013).
[Crossref] [PubMed]

2012 (1)

M. Möller, Y. Cheng, S. D. Khan, B. Zhao, K. Zhao, M. Chini, G. G. Paulus, and Z. Chang, “Dependence of high-order-harmonic-generation yield on driving-laser ellipticity,” Phys. Rev. A 86, 011401 (2012).
[Crossref]

2011 (1)

E. Balogh, K. Kovacs, P. Dombi, J. A. Fulop, G. Farkas, J. Hebling, V. Tosa, and K. Varju, “Single attosecond pulse from terahertz-assisted high-order harmonic generation,” Phys. Rev. A 84, 023806 (2011).
[Crossref]

2010 (1)

C. L. Xia, G. T. Zhang, J. Wu, and X. S. Liu, “Single attosecond pulse generation in an orthogonally polarized two-color laser field combined with a static electric field,” Phys. Rev. A 81, 043420 (2010).
[Crossref]

2009 (1)

2007 (3)

K. Y. Kim, J. H. Glownia, A. J. Taylor, and G. Rodriguez, “Terahertz emission from ultrafast ionizing air in symmetry-broken laser fields,” Opt. Express 15, 4577–4584 (2007).
[Crossref] [PubMed]

W. Hong, P. Lu, W. Cao, P. Lan, and X. Wang, “Control of quantum paths of high-order harmonics and attosecond pulse generation in the presence of a static electric field,” J. Phys. B 40, 2321–2331 (2007).
[Crossref]

P. B. Corkum and F. Krausz, “Attosecond science,” Nature Phys. 3, 381–387 (2007).
[Crossref]

2006 (1)

2004 (1)

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

2003 (1)

A. D. Bandrauk and H. Z. Lu, “Controlling harmonic generation in molecules with intense laser and static magnetic fields: Orientation effects,” Phys. Rev. A 68, 043408 (2003).
[Crossref]

2001 (1)

2000 (2)

D. G. Lappas and Marangos, “Orientation dependence of high-order harmonic generation in hydrogen molecular ions,” J. Phys. B 33, 4679–4689 (2000).
[Crossref]

R. Kopold, D. B. Milošević, and W. Becker, “Rescattering Processes for Elliptical Polarization: A Quantum Trajectory Analysis,” Phys. Rev. Lett. 84, 3831–3834 (2000).
[Crossref] [PubMed]

1997 (1)

Ch. Spielmann, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnürer, C. Kan, M. Lenzner, P. Wobrauschek, and and F. Krausz, “Generation of coherent X-rays in the water window using 5-femtosecond laser pulses,” Science 278, 661–664 (1997).
[Crossref]

1995 (1)

T. Zuo and A. D. Bandrauk, “high-order harmonic generation in intense laser and magentic fields,” J. Nonlinear Opt. Phys. Mater. 4, 533–546(1995).
[Crossref]

1993 (2)

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

K. J. Schafer, B. Yang, L. F. DiMauro, and K. C. Kulander, “Above threshold ionization beyond the high Harmonic cutoff,” Phys. Rev. Lett. 70, 1599–1602 (1993).
[Crossref] [PubMed]

1989 (1)

P. B. Corkum, N. H. Burnett, and F. Brunel, “Above-threshold ionization in the long-wavelength limit,” Phys. Rev. Lett. 62, 1259–1262 (1989).
[Crossref] [PubMed]

1986 (1)

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

1982 (1)

M. D. Feit, J. A. Fleck, and A. Steiger, “Solution of the Schrödinger equation by a spectral method,” J. Comput. Phys. 47, 412–433 (1982).
[Crossref]

Abel, M. J.

Ammesov, M. V.

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

Balogh, E.

E. Balogh, K. Kovacs, P. Dombi, J. A. Fulop, G. Farkas, J. Hebling, V. Tosa, and K. Varju, “Single attosecond pulse from terahertz-assisted high-order harmonic generation,” Phys. Rev. A 84, 023806 (2011).
[Crossref]

Bandrauk, A. D.

K. J. Yuan and A. D. Bandrauk, “Single circularly polarized attosecond pulse generation by intense few cycle elliptically polarized laser pulses and terahertz fields from molecular media,” Phys. Rev. Lett. 110, 023003 (2013).
[Crossref] [PubMed]

A. D. Bandrauk and H. Z. Lu, “Controlling harmonic generation in molecules with intense laser and static magnetic fields: Orientation effects,” Phys. Rev. A 68, 043408 (2003).
[Crossref]

T. Zuo and A. D. Bandrauk, “high-order harmonic generation in intense laser and magentic fields,” J. Nonlinear Opt. Phys. Mater. 4, 533–546(1995).
[Crossref]

Bauer, T.

Becker, W.

R. Kopold, D. B. Milošević, and W. Becker, “Rescattering Processes for Elliptical Polarization: A Quantum Trajectory Analysis,” Phys. Rev. Lett. 84, 3831–3834 (2000).
[Crossref] [PubMed]

Brunel, F.

P. B. Corkum, N. H. Burnett, and F. Brunel, “Above-threshold ionization in the long-wavelength limit,” Phys. Rev. Lett. 62, 1259–1262 (1989).
[Crossref] [PubMed]

Burnett, N. H.

Ch. Spielmann, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnürer, C. Kan, M. Lenzner, P. Wobrauschek, and and F. Krausz, “Generation of coherent X-rays in the water window using 5-femtosecond laser pulses,” Science 278, 661–664 (1997).
[Crossref]

P. B. Corkum, N. H. Burnett, and F. Brunel, “Above-threshold ionization in the long-wavelength limit,” Phys. Rev. Lett. 62, 1259–1262 (1989).
[Crossref] [PubMed]

Cao, W.

W. Hong, P. Lu, W. Cao, P. Lan, and X. Wang, “Control of quantum paths of high-order harmonics and attosecond pulse generation in the presence of a static electric field,” J. Phys. B 40, 2321–2331 (2007).
[Crossref]

Chang, Z.

M. Möller, Y. Cheng, S. D. Khan, B. Zhao, K. Zhao, M. Chini, G. G. Paulus, and Z. Chang, “Dependence of high-order-harmonic-generation yield on driving-laser ellipticity,” Phys. Rev. A 86, 011401 (2012).
[Crossref]

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

Cheng, Y.

M. Möller, Y. Cheng, S. D. Khan, B. Zhao, K. Zhao, M. Chini, G. G. Paulus, and Z. Chang, “Dependence of high-order-harmonic-generation yield on driving-laser ellipticity,” Phys. Rev. A 86, 011401 (2012).
[Crossref]

Chini, M.

M. Möller, Y. Cheng, S. D. Khan, B. Zhao, K. Zhao, M. Chini, G. G. Paulus, and Z. Chang, “Dependence of high-order-harmonic-generation yield on driving-laser ellipticity,” Phys. Rev. A 86, 011401 (2012).
[Crossref]

Ciappina, M. F.

J. A. Pérez-Hernández, M. F. Ciappina, M. Lewenstein, L. Roso, and A. Zaïr, “Beyond carbon K-Edge harmonic emission using a spatial and temporal synthesized laser field,” Phys. Rev. Lett. 110, 053001 (2013).
[Crossref] [PubMed]

Corkum, P. B.

P. B. Corkum and F. Krausz, “Attosecond science,” Nature Phys. 3, 381–387 (2007).
[Crossref]

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

P. B. Corkum, N. H. Burnett, and F. Brunel, “Above-threshold ionization in the long-wavelength limit,” Phys. Rev. Lett. 62, 1259–1262 (1989).
[Crossref] [PubMed]

Czasch, S.

Delone, N. B.

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

DiMauro, L. F.

K. J. Schafer, B. Yang, L. F. DiMauro, and K. C. Kulander, “Above threshold ionization beyond the high Harmonic cutoff,” Phys. Rev. Lett. 70, 1599–1602 (1993).
[Crossref] [PubMed]

Dombi, P.

E. Balogh, K. Kovacs, P. Dombi, J. A. Fulop, G. Farkas, J. Hebling, V. Tosa, and K. Varju, “Single attosecond pulse from terahertz-assisted high-order harmonic generation,” Phys. Rev. A 84, 023806 (2011).
[Crossref]

Farkas, G.

E. Balogh, K. Kovacs, P. Dombi, J. A. Fulop, G. Farkas, J. Hebling, V. Tosa, and K. Varju, “Single attosecond pulse from terahertz-assisted high-order harmonic generation,” Phys. Rev. A 84, 023806 (2011).
[Crossref]

Feit, M. D.

M. D. Feit, J. A. Fleck, and A. Steiger, “Solution of the Schrödinger equation by a spectral method,” J. Comput. Phys. 47, 412–433 (1982).
[Crossref]

Fitzgerald, A.

Fleck, J. A.

M. D. Feit, J. A. Fleck, and A. Steiger, “Solution of the Schrödinger equation by a spectral method,” J. Comput. Phys. 47, 412–433 (1982).
[Crossref]

Fulop, J. A.

E. Balogh, K. Kovacs, P. Dombi, J. A. Fulop, G. Farkas, J. Hebling, V. Tosa, and K. Varju, “Single attosecond pulse from terahertz-assisted high-order harmonic generation,” Phys. Rev. A 84, 023806 (2011).
[Crossref]

Gallmann, L.

Ge, X. L.

X. L. Ge, T. Wang, J. Guo, and X. S. Liu, “Quantum-path control and isolated-attosecond-pulse generation using H+ 2 molecules with moving nuclei in few-cycle laser pulses,” Phys. Rev. A 89, 023424 (2014).
[Crossref]

Glownia, J. H.

Guo, J.

X. L. Ge, T. Wang, J. Guo, and X. S. Liu, “Quantum-path control and isolated-attosecond-pulse generation using H+ 2 molecules with moving nuclei in few-cycle laser pulses,” Phys. Rev. A 89, 023424 (2014).
[Crossref]

Hebling, J.

E. Balogh, K. Kovacs, P. Dombi, J. A. Fulop, G. Farkas, J. Hebling, V. Tosa, and K. Varju, “Single attosecond pulse from terahertz-assisted high-order harmonic generation,” Phys. Rev. A 84, 023806 (2011).
[Crossref]

Hong, W.

W. Hong, P. Lu, P. Lan, Q. Zhang, and X. Wang, “Few-cycle attosecond pulses with stabilized-carrier-envelope phase in the presence of a strong terahertz field,” Opt. Express 17, 5139–5146 (2009).
[Crossref] [PubMed]

W. Hong, P. Lu, W. Cao, P. Lan, and X. Wang, “Control of quantum paths of high-order harmonics and attosecond pulse generation in the presence of a static electric field,” J. Phys. B 40, 2321–2331 (2007).
[Crossref]

Kan, C.

Ch. Spielmann, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnürer, C. Kan, M. Lenzner, P. Wobrauschek, and and F. Krausz, “Generation of coherent X-rays in the water window using 5-femtosecond laser pulses,” Science 278, 661–664 (1997).
[Crossref]

Khan, S. D.

M. Möller, Y. Cheng, S. D. Khan, B. Zhao, K. Zhao, M. Chini, G. G. Paulus, and Z. Chang, “Dependence of high-order-harmonic-generation yield on driving-laser ellipticity,” Phys. Rev. A 86, 011401 (2012).
[Crossref]

Kim, K. Y.

Kopold, R.

R. Kopold, D. B. Milošević, and W. Becker, “Rescattering Processes for Elliptical Polarization: A Quantum Trajectory Analysis,” Phys. Rev. Lett. 84, 3831–3834 (2000).
[Crossref] [PubMed]

Koppitsch, R.

Ch. Spielmann, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnürer, C. Kan, M. Lenzner, P. Wobrauschek, and and F. Krausz, “Generation of coherent X-rays in the water window using 5-femtosecond laser pulses,” Science 278, 661–664 (1997).
[Crossref]

Kovacs, K.

E. Balogh, K. Kovacs, P. Dombi, J. A. Fulop, G. Farkas, J. Hebling, V. Tosa, and K. Varju, “Single attosecond pulse from terahertz-assisted high-order harmonic generation,” Phys. Rev. A 84, 023806 (2011).
[Crossref]

Krainov, V. P.

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

Krausz, and F.

Ch. Spielmann, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnürer, C. Kan, M. Lenzner, P. Wobrauschek, and and F. Krausz, “Generation of coherent X-rays in the water window using 5-femtosecond laser pulses,” Science 278, 661–664 (1997).
[Crossref]

Krausz, F.

P. B. Corkum and F. Krausz, “Attosecond science,” Nature Phys. 3, 381–387 (2007).
[Crossref]

Kulander, K. C.

K. J. Schafer, B. Yang, L. F. DiMauro, and K. C. Kulander, “Above threshold ionization beyond the high Harmonic cutoff,” Phys. Rev. Lett. 70, 1599–1602 (1993).
[Crossref] [PubMed]

Lan, P.

W. Hong, P. Lu, P. Lan, Q. Zhang, and X. Wang, “Few-cycle attosecond pulses with stabilized-carrier-envelope phase in the presence of a strong terahertz field,” Opt. Express 17, 5139–5146 (2009).
[Crossref] [PubMed]

W. Hong, P. Lu, W. Cao, P. Lan, and X. Wang, “Control of quantum paths of high-order harmonics and attosecond pulse generation in the presence of a static electric field,” J. Phys. B 40, 2321–2331 (2007).
[Crossref]

Lappas, D. G.

D. G. Lappas and Marangos, “Orientation dependence of high-order harmonic generation in hydrogen molecular ions,” J. Phys. B 33, 4679–4689 (2000).
[Crossref]

Lenzner, M.

Ch. Spielmann, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnürer, C. Kan, M. Lenzner, P. Wobrauschek, and and F. Krausz, “Generation of coherent X-rays in the water window using 5-femtosecond laser pulses,” Science 278, 661–664 (1997).
[Crossref]

Leone, S. R.

Lewenstein, M.

J. A. Pérez-Hernández, M. F. Ciappina, M. Lewenstein, L. Roso, and A. Zaïr, “Beyond carbon K-Edge harmonic emission using a spatial and temporal synthesized laser field,” Phys. Rev. Lett. 110, 053001 (2013).
[Crossref] [PubMed]

Liu, X. S.

X. L. Ge, T. Wang, J. Guo, and X. S. Liu, “Quantum-path control and isolated-attosecond-pulse generation using H+ 2 molecules with moving nuclei in few-cycle laser pulses,” Phys. Rev. A 89, 023424 (2014).
[Crossref]

C. L. Xia and X. S. Liu, “Quantum path control and isolated attosecond pulse generation with the combination of two circularly polarized laser pulses,” Phys. Rev. A 87, 043406 (2013).
[Crossref]

C. L. Xia, G. T. Zhang, J. Wu, and X. S. Liu, “Single attosecond pulse generation in an orthogonally polarized two-color laser field combined with a static electric field,” Phys. Rev. A 81, 043420 (2010).
[Crossref]

Löffler, T.

Lu, H. Z.

A. D. Bandrauk and H. Z. Lu, “Controlling harmonic generation in molecules with intense laser and static magnetic fields: Orientation effects,” Phys. Rev. A 68, 043408 (2003).
[Crossref]

Lu, P.

W. Hong, P. Lu, P. Lan, Q. Zhang, and X. Wang, “Few-cycle attosecond pulses with stabilized-carrier-envelope phase in the presence of a strong terahertz field,” Opt. Express 17, 5139–5146 (2009).
[Crossref] [PubMed]

W. Hong, P. Lu, W. Cao, P. Lan, and X. Wang, “Control of quantum paths of high-order harmonics and attosecond pulse generation in the presence of a static electric field,” J. Phys. B 40, 2321–2331 (2007).
[Crossref]

Marangos,

D. G. Lappas and Marangos, “Orientation dependence of high-order harmonic generation in hydrogen molecular ions,” J. Phys. B 33, 4679–4689 (2000).
[Crossref]

Miloševic, D. B.

R. Kopold, D. B. Milošević, and W. Becker, “Rescattering Processes for Elliptical Polarization: A Quantum Trajectory Analysis,” Phys. Rev. Lett. 84, 3831–3834 (2000).
[Crossref] [PubMed]

Möller, M.

M. Möller, Y. Cheng, S. D. Khan, B. Zhao, K. Zhao, M. Chini, G. G. Paulus, and Z. Chang, “Dependence of high-order-harmonic-generation yield on driving-laser ellipticity,” Phys. Rev. A 86, 011401 (2012).
[Crossref]

Neumark, D. M.

Paulus, G. G.

M. Möller, Y. Cheng, S. D. Khan, B. Zhao, K. Zhao, M. Chini, G. G. Paulus, and Z. Chang, “Dependence of high-order-harmonic-generation yield on driving-laser ellipticity,” Phys. Rev. A 86, 011401 (2012).
[Crossref]

Pérez-Hernández, J. A.

J. A. Pérez-Hernández, M. F. Ciappina, M. Lewenstein, L. Roso, and A. Zaïr, “Beyond carbon K-Edge harmonic emission using a spatial and temporal synthesized laser field,” Phys. Rev. Lett. 110, 053001 (2013).
[Crossref] [PubMed]

Pfeifer, T.

Rodriguez, G.

Roskos, H.

Roso, L.

J. A. Pérez-Hernández, M. F. Ciappina, M. Lewenstein, L. Roso, and A. Zaïr, “Beyond carbon K-Edge harmonic emission using a spatial and temporal synthesized laser field,” Phys. Rev. Lett. 110, 053001 (2013).
[Crossref] [PubMed]

Sartania, S.

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[Crossref]

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K. J. Schafer, B. Yang, L. F. DiMauro, and K. C. Kulander, “Above threshold ionization beyond the high Harmonic cutoff,” Phys. Rev. Lett. 70, 1599–1602 (1993).
[Crossref] [PubMed]

Schnürer, M.

Ch. Spielmann, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnürer, C. Kan, M. Lenzner, P. Wobrauschek, and and F. Krausz, “Generation of coherent X-rays in the water window using 5-femtosecond laser pulses,” Science 278, 661–664 (1997).
[Crossref]

Siebert, K.

Spielmann, Ch.

Ch. Spielmann, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnürer, C. Kan, M. Lenzner, P. Wobrauschek, and and F. Krausz, “Generation of coherent X-rays in the water window using 5-femtosecond laser pulses,” Science 278, 661–664 (1997).
[Crossref]

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M. D. Feit, J. A. Fleck, and A. Steiger, “Solution of the Schrödinger equation by a spectral method,” J. Comput. Phys. 47, 412–433 (1982).
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Tosa, V.

E. Balogh, K. Kovacs, P. Dombi, J. A. Fulop, G. Farkas, J. Hebling, V. Tosa, and K. Varju, “Single attosecond pulse from terahertz-assisted high-order harmonic generation,” Phys. Rev. A 84, 023806 (2011).
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E. Balogh, K. Kovacs, P. Dombi, J. A. Fulop, G. Farkas, J. Hebling, V. Tosa, and K. Varju, “Single attosecond pulse from terahertz-assisted high-order harmonic generation,” Phys. Rev. A 84, 023806 (2011).
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Ch. Spielmann, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnürer, C. Kan, M. Lenzner, P. Wobrauschek, and and F. Krausz, “Generation of coherent X-rays in the water window using 5-femtosecond laser pulses,” Science 278, 661–664 (1997).
[Crossref]

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C. L. Xia, G. T. Zhang, J. Wu, and X. S. Liu, “Single attosecond pulse generation in an orthogonally polarized two-color laser field combined with a static electric field,” Phys. Rev. A 81, 043420 (2010).
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C. L. Xia and X. S. Liu, “Quantum path control and isolated attosecond pulse generation with the combination of two circularly polarized laser pulses,” Phys. Rev. A 87, 043406 (2013).
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K. J. Yuan and A. D. Bandrauk, “Single circularly polarized attosecond pulse generation by intense few cycle elliptically polarized laser pulses and terahertz fields from molecular media,” Phys. Rev. Lett. 110, 023003 (2013).
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J. A. Pérez-Hernández, M. F. Ciappina, M. Lewenstein, L. Roso, and A. Zaïr, “Beyond carbon K-Edge harmonic emission using a spatial and temporal synthesized laser field,” Phys. Rev. Lett. 110, 053001 (2013).
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C. L. Xia, G. T. Zhang, J. Wu, and X. S. Liu, “Single attosecond pulse generation in an orthogonally polarized two-color laser field combined with a static electric field,” Phys. Rev. A 81, 043420 (2010).
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Zhao, B.

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M. Möller, Y. Cheng, S. D. Khan, B. Zhao, K. Zhao, M. Chini, G. G. Paulus, and Z. Chang, “Dependence of high-order-harmonic-generation yield on driving-laser ellipticity,” Phys. Rev. A 86, 011401 (2012).
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T. Zuo and A. D. Bandrauk, “high-order harmonic generation in intense laser and magentic fields,” J. Nonlinear Opt. Phys. Mater. 4, 533–546(1995).
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J. Phys. B (2)

W. Hong, P. Lu, W. Cao, P. Lan, and X. Wang, “Control of quantum paths of high-order harmonics and attosecond pulse generation in the presence of a static electric field,” J. Phys. B 40, 2321–2331 (2007).
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Z. Chang, “Single attosecond pulse and xuv supercontinuum in the high-order harmonic plateau,” Phys. Rev. A 70, 043802 (2004).
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[Crossref]

E. Balogh, K. Kovacs, P. Dombi, J. A. Fulop, G. Farkas, J. Hebling, V. Tosa, and K. Varju, “Single attosecond pulse from terahertz-assisted high-order harmonic generation,” Phys. Rev. A 84, 023806 (2011).
[Crossref]

C. L. Xia, G. T. Zhang, J. Wu, and X. S. Liu, “Single attosecond pulse generation in an orthogonally polarized two-color laser field combined with a static electric field,” Phys. Rev. A 81, 043420 (2010).
[Crossref]

C. L. Xia and X. S. Liu, “Quantum path control and isolated attosecond pulse generation with the combination of two circularly polarized laser pulses,” Phys. Rev. A 87, 043406 (2013).
[Crossref]

M. Möller, Y. Cheng, S. D. Khan, B. Zhao, K. Zhao, M. Chini, G. G. Paulus, and Z. Chang, “Dependence of high-order-harmonic-generation yield on driving-laser ellipticity,” Phys. Rev. A 86, 011401 (2012).
[Crossref]

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[Crossref] [PubMed]

K. J. Yuan and A. D. Bandrauk, “Single circularly polarized attosecond pulse generation by intense few cycle elliptically polarized laser pulses and terahertz fields from molecular media,” Phys. Rev. Lett. 110, 023003 (2013).
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Science (1)

Ch. Spielmann, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnürer, C. Kan, M. Lenzner, P. Wobrauschek, and and F. Krausz, “Generation of coherent X-rays in the water window using 5-femtosecond laser pulses,” Science 278, 661–664 (1997).
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Figures (6)

Fig. 1
Fig. 1 High-order harmonic spectra of H 2 + in a circularly polarized laser field (solid black line) and a circularly polarized laser field combined with a THz field with the peak intensity ETHz = 0.06 a.u. (dotted red line).
Fig. 2
Fig. 2 Time-frequency distributions of HHG (the y-component) corresponding to (a) the solid black line in Fig. 1 (the circularly polarized laser pulse) and (b) the dotted red line in Fig. 1 (the circularly polarized laser pulse combined with the THz field with the peak intensity ETHz = 0.06 a.u.).
Fig. 3
Fig. 3 Comparison of the temporal evolutions of the probability density of electron wave packet for the circularly polarized case [(a1)–(a10)] and the circularly polarized laser pulse combined with the THz field case [(b1)–(b10)] with the peak intensity ETHz = 0.06 a.u..
Fig. 4
Fig. 4 Electron trajectories for the case in (a) the circularly polarized laser pulse, (b) the circularly polarized laser pulse combined with the THz field with the peak intensity ETHz = 0.06 a.u..
Fig. 5
Fig. 5 Ionization probability and the dependence of the energy on the ionization (blue circles) and emission times (green triangles) for the case in (a) the circularly polarized laser pulse, (b) the circularly polarized laser pulse combined with the THz field with the peak intensity ETHz = 0.06 a.u..
Fig. 6
Fig. 6 Temporal evolution of the attosecond pulse generated by the circularly polarized laser pulse combined with the THz field with the peak intensity ETHz = 0.06 a.u. in the range of 216–249 eV.

Equations (1)

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i ψ ( x , y , t ) t = [ P x 2 + P y 2 2 + V ( x , y ) + x E x ( t ) + y E y ( t ) ] ψ ( x , y , t )

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