Abstract

The phase matching of quantum paths in high-order harmonic generation is investigated in a two-color laser field. Our results show that the phase-matching properties of the short and long trajectories can be modulated effectively by adding a weak second harmonic field. This scheme can not only achieve the quantum path selection, but more importantly it can achieve on-axis phase matching for both of the two trajectories simultaneously. A bright interference pattern induced by the simultaneously phase-matched two trajectories can be observed by placing a near-field on-axis filter, which has great potential for experimentally characterizing the full single-atom dipole moment.

© 2011 OSA

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  1. A. Rundquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Phase-Matched Generation of Coherent Soft X-rays,” Science 280, 1412–1415 (1998).
    [CrossRef] [PubMed]
  2. R. A. Bartels, A. Paul, H. Green, H. C. Kapteyn, M. M. Murnane, S. Backus, I. P. Christov, Y. Liu, D. Attwood, and C. Jacobsen, “Generation of Spatially Coherent Light at Extreme Ultraviolet Wavelengths,” Science 297, 376–378 (2002).
    [PubMed]
  3. M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414, 509–513 (2001).
    [CrossRef] [PubMed]
  4. T. Pfeifer, L. Gallmann, M. J. Abel, P. M. Nagel, D. M. Neumark, and S. R. Leone, “Heterodyne Mixing of Laser Fields for Temporal Gating of High-order Harmonic Generation,” Phys. Rev. Lett. 97, 163901 (2006).
    [CrossRef] [PubMed]
  5. P. Lan, P. Lu, W. Cao, Y. Li, and X. Wang, “Attosecond ionization gating for isolated attosecond electron wave packet and broadband attosecond xuv pulses,” Phys. Rev. A 76, 051801 (2007).
    [CrossRef]
  6. P. B. Corkum, “Plasma Perspective on Strong-Field Multiphoton Ionization,” Phys. Rev. Lett. 71,1994 (1993).
    [CrossRef] [PubMed]
  7. W. Cao, P. Lu, P. Lan, W. Hong, and X. Wang, “Control of quntum pahts in high-order harmonic generation via a ω + 3ω bichromatic laser field,” J. Phys. B 40, 869–875 (2007).
    [CrossRef]
  8. Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L C. Dinu, P. Monchicourt, P. Breger, M. Kovac̆ev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft X-rays,” Science 302, 1540 (2003).
    [CrossRef] [PubMed]
  9. W. Hong, P. Lu, P. Lan, Q. Li, Q. Zhang, Z. Yang, and X. Wang, “Method to generate directly a broadband isolated attosecond pulse with stable pulse duration and high signal-to-noise ratio,” Phys. Rev. A 78, 063407 (2008).
    [CrossRef]
  10. P. Antoine, A. L’Huillier, and M. Lewenstein, “Attosecond Pulse Trains Using High-Order Harmonics,” Phys. Rev. Lett. 77, 1234–1237 (1996).
    [CrossRef] [PubMed]
  11. W. Hong, Q. Zhang, Z. Yang, and P. Lu, “Electron dynamic control for the quantum path in the midinfrared regime using a weak near-infrared pulse,” Phys. Rev. A 80, 053407 (2009).
    [CrossRef]
  12. A. Zaïr, M. Holler, A. Guandalini, F. Schapper, J. Biegert, L. Gallmann, U. Keller, A. S. Wyatt, A. Monmayrant, I. A. Walmsley, E. Cormier, T. Auguste, J. P. Caumes, and P. Salières, “Quantum Path Interferences in High-Order Harmonic Generation,” Phys. Rev. Lett. 100, 143902 (2008).
    [CrossRef] [PubMed]
  13. T. Auguste, P. Salières, A. S. Wyatt, A. Monmayrant, I. A. Walmsley, E. Cormier, A. Zaïr, M. Holler, A. Guandalini, F. Schapper, J. Biegert, L. Gallmann, and U. Keller, “Theoretical and experimental analysis of quantum path interferences in high-order harmonic generation,” Phys. Rev. A 80, 033817 (2009).
    [CrossRef]
  14. M. Holler, A. Zaïr, F. Schapper, T. Auguste, E. Cormier, A. Wyatt, A. Monmayrant, I. A. Walmsley, L. Gallmann, P. Salières, and U. Keller, “Ionization effects on spectral signatures of quantum-path interference in high-harmonic generation,” Opt. Express 17, 5716–5722 (2009).
    [CrossRef] [PubMed]
  15. F. Schapper, M. Holler, T. Auguste, A. Zaïr, M. Weger, P. Salières, L. Gallmann, and U. Keller, “Spatial finger-print of quantum path interferences in high order harmonic generation,” Opt. Express 18, 2987–2994 (2010).
    [CrossRef] [PubMed]
  16. M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49, 2117 (1994).
    [CrossRef] [PubMed]
  17. W. Cao, P. Lu, X. Wang, and G. Yang, “Single-attosecond pulse generation with an intense multicycle driving pulse,” Phys. Rev. A 74, 063821 (2006).
    [CrossRef]
  18. 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 (1986).
  19. 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-dimensional model of high-order harmonic generation in the few-optical-cycle regime,” Phys. Rev. A 61, 063801 (2000).
    [CrossRef]
  20. 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]
  21. A. L’Huillier, P. Balcou, S. Candel, k. J. Schafer, and K. C. Kulander, “Calculations of high-order harmonic-generation processes in xenon at 1064 nm,” Phys. Rev. A 46, 2778 (1992).
    [CrossRef]
  22. P. Balcou, P. Salières, A. L’Huillier, and M. Lewenstein, “Generalized phase-matching conditions for high harmonics: The role of field-gradient forces,” Phys. Rev. A 55, 3204–3210 (1997).
    [CrossRef]
  23. P. Lan, P. Lu, W. Cao, X. Wang, and G. Yang, “Phase-locked high-order-harmonic and sub-100-as pulse generation grom stretched molecules,” Phys. Rev. A 74, 063411 (2006).
    [CrossRef]
  24. M. B. Gaarde and K. J. Schafer, “Space-Time Considerations in the Phase Locking of High Harmonics,” Phys. Rev. Lett. 89, 213901 (2002).
    [CrossRef] [PubMed]

2010 (1)

2009 (4)

T. Auguste, P. Salières, A. S. Wyatt, A. Monmayrant, I. A. Walmsley, E. Cormier, A. Zaïr, M. Holler, A. Guandalini, F. Schapper, J. Biegert, L. Gallmann, and U. Keller, “Theoretical and experimental analysis of quantum path interferences in high-order harmonic generation,” Phys. Rev. A 80, 033817 (2009).
[CrossRef]

M. Holler, A. Zaïr, F. Schapper, T. Auguste, E. Cormier, A. Wyatt, A. Monmayrant, I. A. Walmsley, L. Gallmann, P. Salières, and U. Keller, “Ionization effects on spectral signatures of quantum-path interference in high-harmonic generation,” Opt. Express 17, 5716–5722 (2009).
[CrossRef] [PubMed]

W. Hong, Q. Zhang, Z. Yang, and P. Lu, “Electron dynamic control for the quantum path in the midinfrared regime using a weak near-infrared pulse,” Phys. Rev. A 80, 053407 (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]

2008 (2)

A. Zaïr, M. Holler, A. Guandalini, F. Schapper, J. Biegert, L. Gallmann, U. Keller, A. S. Wyatt, A. Monmayrant, I. A. Walmsley, E. Cormier, T. Auguste, J. P. Caumes, and P. Salières, “Quantum Path Interferences in High-Order Harmonic Generation,” Phys. Rev. Lett. 100, 143902 (2008).
[CrossRef] [PubMed]

W. Hong, P. Lu, P. Lan, Q. Li, Q. Zhang, Z. Yang, and X. Wang, “Method to generate directly a broadband isolated attosecond pulse with stable pulse duration and high signal-to-noise ratio,” Phys. Rev. A 78, 063407 (2008).
[CrossRef]

2007 (2)

P. Lan, P. Lu, W. Cao, Y. Li, and X. Wang, “Attosecond ionization gating for isolated attosecond electron wave packet and broadband attosecond xuv pulses,” Phys. Rev. A 76, 051801 (2007).
[CrossRef]

W. Cao, P. Lu, P. Lan, W. Hong, and X. Wang, “Control of quntum pahts in high-order harmonic generation via a ω + 3ω bichromatic laser field,” J. Phys. B 40, 869–875 (2007).
[CrossRef]

2006 (3)

T. Pfeifer, L. Gallmann, M. J. Abel, P. M. Nagel, D. M. Neumark, and S. R. Leone, “Heterodyne Mixing of Laser Fields for Temporal Gating of High-order Harmonic Generation,” Phys. Rev. Lett. 97, 163901 (2006).
[CrossRef] [PubMed]

W. Cao, P. Lu, X. Wang, and G. Yang, “Single-attosecond pulse generation with an intense multicycle driving pulse,” Phys. Rev. A 74, 063821 (2006).
[CrossRef]

P. Lan, P. Lu, W. Cao, X. Wang, and G. Yang, “Phase-locked high-order-harmonic and sub-100-as pulse generation grom stretched molecules,” Phys. Rev. A 74, 063411 (2006).
[CrossRef]

2003 (1)

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L C. Dinu, P. Monchicourt, P. Breger, M. Kovac̆ev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft X-rays,” Science 302, 1540 (2003).
[CrossRef] [PubMed]

2002 (2)

R. A. Bartels, A. Paul, H. Green, H. C. Kapteyn, M. M. Murnane, S. Backus, I. P. Christov, Y. Liu, D. Attwood, and C. Jacobsen, “Generation of Spatially Coherent Light at Extreme Ultraviolet Wavelengths,” Science 297, 376–378 (2002).
[PubMed]

M. B. Gaarde and K. J. Schafer, “Space-Time Considerations in the Phase Locking of High Harmonics,” Phys. Rev. Lett. 89, 213901 (2002).
[CrossRef] [PubMed]

2001 (1)

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414, 509–513 (2001).
[CrossRef] [PubMed]

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-dimensional model of high-order harmonic generation in the few-optical-cycle regime,” Phys. Rev. A 61, 063801 (2000).
[CrossRef]

1998 (1)

A. Rundquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Phase-Matched Generation of Coherent Soft X-rays,” Science 280, 1412–1415 (1998).
[CrossRef] [PubMed]

1997 (1)

P. Balcou, P. Salières, A. L’Huillier, and M. Lewenstein, “Generalized phase-matching conditions for high harmonics: The role of field-gradient forces,” Phys. Rev. A 55, 3204–3210 (1997).
[CrossRef]

1996 (1)

P. Antoine, A. L’Huillier, and M. Lewenstein, “Attosecond Pulse Trains Using High-Order Harmonics,” Phys. Rev. Lett. 77, 1234–1237 (1996).
[CrossRef] [PubMed]

1994 (1)

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

1993 (1)

P. B. Corkum, “Plasma Perspective on Strong-Field Multiphoton Ionization,” Phys. Rev. Lett. 71,1994 (1993).
[CrossRef] [PubMed]

1992 (1)

A. L’Huillier, P. Balcou, S. Candel, k. J. Schafer, and K. C. Kulander, “Calculations of high-order harmonic-generation processes in xenon at 1064 nm,” Phys. Rev. A 46, 2778 (1992).
[CrossRef]

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 (1986).

Abel, M. J.

T. Pfeifer, L. Gallmann, M. J. Abel, P. M. Nagel, D. M. Neumark, and S. R. Leone, “Heterodyne Mixing of Laser Fields for Temporal Gating of High-order Harmonic Generation,” Phys. Rev. Lett. 97, 163901 (2006).
[CrossRef] [PubMed]

Agostini, P.

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L C. Dinu, P. Monchicourt, P. Breger, M. Kovac̆ev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft X-rays,” Science 302, 1540 (2003).
[CrossRef] [PubMed]

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-dimensional 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 (1986).

Antoine, P.

P. Antoine, A. L’Huillier, and M. Lewenstein, “Attosecond Pulse Trains Using High-Order Harmonics,” Phys. Rev. Lett. 77, 1234–1237 (1996).
[CrossRef] [PubMed]

Attwood, D.

R. A. Bartels, A. Paul, H. Green, H. C. Kapteyn, M. M. Murnane, S. Backus, I. P. Christov, Y. Liu, D. Attwood, and C. Jacobsen, “Generation of Spatially Coherent Light at Extreme Ultraviolet Wavelengths,” Science 297, 376–378 (2002).
[PubMed]

Auguste, T.

F. Schapper, M. Holler, T. Auguste, A. Zaïr, M. Weger, P. Salières, L. Gallmann, and U. Keller, “Spatial finger-print of quantum path interferences in high order harmonic generation,” Opt. Express 18, 2987–2994 (2010).
[CrossRef] [PubMed]

T. Auguste, P. Salières, A. S. Wyatt, A. Monmayrant, I. A. Walmsley, E. Cormier, A. Zaïr, M. Holler, A. Guandalini, F. Schapper, J. Biegert, L. Gallmann, and U. Keller, “Theoretical and experimental analysis of quantum path interferences in high-order harmonic generation,” Phys. Rev. A 80, 033817 (2009).
[CrossRef]

M. Holler, A. Zaïr, F. Schapper, T. Auguste, E. Cormier, A. Wyatt, A. Monmayrant, I. A. Walmsley, L. Gallmann, P. Salières, and U. Keller, “Ionization effects on spectral signatures of quantum-path interference in high-harmonic generation,” Opt. Express 17, 5716–5722 (2009).
[CrossRef] [PubMed]

A. Zaïr, M. Holler, A. Guandalini, F. Schapper, J. Biegert, L. Gallmann, U. Keller, A. S. Wyatt, A. Monmayrant, I. A. Walmsley, E. Cormier, T. Auguste, J. P. Caumes, and P. Salières, “Quantum Path Interferences in High-Order Harmonic Generation,” Phys. Rev. Lett. 100, 143902 (2008).
[CrossRef] [PubMed]

Backus, S.

R. A. Bartels, A. Paul, H. Green, H. C. Kapteyn, M. M. Murnane, S. Backus, I. P. Christov, Y. Liu, D. Attwood, and C. Jacobsen, “Generation of Spatially Coherent Light at Extreme Ultraviolet Wavelengths,” Science 297, 376–378 (2002).
[PubMed]

A. Rundquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Phase-Matched Generation of Coherent Soft X-rays,” Science 280, 1412–1415 (1998).
[CrossRef] [PubMed]

Balcou, P.

P. Balcou, P. Salières, A. L’Huillier, and M. Lewenstein, “Generalized phase-matching conditions for high harmonics: The role of field-gradient forces,” Phys. Rev. A 55, 3204–3210 (1997).
[CrossRef]

A. L’Huillier, P. Balcou, S. Candel, k. J. Schafer, and K. C. Kulander, “Calculations of high-order harmonic-generation processes in xenon at 1064 nm,” Phys. Rev. A 46, 2778 (1992).
[CrossRef]

Balcou, Ph.

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

Bartels, R. A.

R. A. Bartels, A. Paul, H. Green, H. C. Kapteyn, M. M. Murnane, S. Backus, I. P. Christov, Y. Liu, D. Attwood, and C. Jacobsen, “Generation of Spatially Coherent Light at Extreme Ultraviolet Wavelengths,” Science 297, 376–378 (2002).
[PubMed]

Biegert, J.

T. Auguste, P. Salières, A. S. Wyatt, A. Monmayrant, I. A. Walmsley, E. Cormier, A. Zaïr, M. Holler, A. Guandalini, F. Schapper, J. Biegert, L. Gallmann, and U. Keller, “Theoretical and experimental analysis of quantum path interferences in high-order harmonic generation,” Phys. Rev. A 80, 033817 (2009).
[CrossRef]

A. Zaïr, M. Holler, A. Guandalini, F. Schapper, J. Biegert, L. Gallmann, U. Keller, A. S. Wyatt, A. Monmayrant, I. A. Walmsley, E. Cormier, T. Auguste, J. P. Caumes, and P. Salières, “Quantum Path Interferences in High-Order Harmonic Generation,” Phys. Rev. Lett. 100, 143902 (2008).
[CrossRef] [PubMed]

Brabec, T.

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414, 509–513 (2001).
[CrossRef] [PubMed]

Breger, P.

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L C. Dinu, P. Monchicourt, P. Breger, M. Kovac̆ev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft X-rays,” Science 302, 1540 (2003).
[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-dimensional model of high-order harmonic generation in the few-optical-cycle regime,” Phys. Rev. A 61, 063801 (2000).
[CrossRef]

Candel, S.

A. L’Huillier, P. Balcou, S. Candel, k. J. Schafer, and K. C. Kulander, “Calculations of high-order harmonic-generation processes in xenon at 1064 nm,” Phys. Rev. A 46, 2778 (1992).
[CrossRef]

Cao, W.

W. Cao, P. Lu, P. Lan, W. Hong, and X. Wang, “Control of quntum pahts in high-order harmonic generation via a ω + 3ω bichromatic laser field,” J. Phys. B 40, 869–875 (2007).
[CrossRef]

P. Lan, P. Lu, W. Cao, Y. Li, and X. Wang, “Attosecond ionization gating for isolated attosecond electron wave packet and broadband attosecond xuv pulses,” Phys. Rev. A 76, 051801 (2007).
[CrossRef]

W. Cao, P. Lu, X. Wang, and G. Yang, “Single-attosecond pulse generation with an intense multicycle driving pulse,” Phys. Rev. A 74, 063821 (2006).
[CrossRef]

P. Lan, P. Lu, W. Cao, X. Wang, and G. Yang, “Phase-locked high-order-harmonic and sub-100-as pulse generation grom stretched molecules,” Phys. Rev. A 74, 063411 (2006).
[CrossRef]

Carré, B.

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L C. Dinu, P. Monchicourt, P. Breger, M. Kovac̆ev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft X-rays,” Science 302, 1540 (2003).
[CrossRef] [PubMed]

Caumes, J. P.

A. Zaïr, M. Holler, A. Guandalini, F. Schapper, J. Biegert, L. Gallmann, U. Keller, A. S. Wyatt, A. Monmayrant, I. A. Walmsley, E. Cormier, T. Auguste, J. P. Caumes, and P. Salières, “Quantum Path Interferences in High-Order Harmonic Generation,” Phys. Rev. Lett. 100, 143902 (2008).
[CrossRef] [PubMed]

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-dimensional 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-dimensional model of high-order harmonic generation in the few-optical-cycle regime,” Phys. Rev. A 61, 063801 (2000).
[CrossRef]

Chang, Z.

A. Rundquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Phase-Matched Generation of Coherent Soft X-rays,” Science 280, 1412–1415 (1998).
[CrossRef] [PubMed]

Christov, I. P.

R. A. Bartels, A. Paul, H. Green, H. C. Kapteyn, M. M. Murnane, S. Backus, I. P. Christov, Y. Liu, D. Attwood, and C. Jacobsen, “Generation of Spatially Coherent Light at Extreme Ultraviolet Wavelengths,” Science 297, 376–378 (2002).
[PubMed]

Corkum, P.

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414, 509–513 (2001).
[CrossRef] [PubMed]

Corkum, P. B.

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

P. B. Corkum, “Plasma Perspective on Strong-Field Multiphoton Ionization,” Phys. Rev. Lett. 71,1994 (1993).
[CrossRef] [PubMed]

Cormier, E.

T. Auguste, P. Salières, A. S. Wyatt, A. Monmayrant, I. A. Walmsley, E. Cormier, A. Zaïr, M. Holler, A. Guandalini, F. Schapper, J. Biegert, L. Gallmann, and U. Keller, “Theoretical and experimental analysis of quantum path interferences in high-order harmonic generation,” Phys. Rev. A 80, 033817 (2009).
[CrossRef]

M. Holler, A. Zaïr, F. Schapper, T. Auguste, E. Cormier, A. Wyatt, A. Monmayrant, I. A. Walmsley, L. Gallmann, P. Salières, and U. Keller, “Ionization effects on spectral signatures of quantum-path interference in high-harmonic generation,” Opt. Express 17, 5716–5722 (2009).
[CrossRef] [PubMed]

A. Zaïr, M. Holler, A. Guandalini, F. Schapper, J. Biegert, L. Gallmann, U. Keller, A. S. Wyatt, A. Monmayrant, I. A. Walmsley, E. Cormier, T. Auguste, J. P. Caumes, and P. Salières, “Quantum Path Interferences in High-Order Harmonic Generation,” Phys. Rev. Lett. 100, 143902 (2008).
[CrossRef] [PubMed]

de Bohan, A.

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L C. Dinu, P. Monchicourt, P. Breger, M. Kovac̆ev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft X-rays,” Science 302, 1540 (2003).
[CrossRef] [PubMed]

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 (1986).

Dinu, L C.

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L C. Dinu, P. Monchicourt, P. Breger, M. Kovac̆ev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft X-rays,” Science 302, 1540 (2003).
[CrossRef] [PubMed]

Drescher, M.

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414, 509–513 (2001).
[CrossRef] [PubMed]

Durfee, C. G.

A. Rundquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Phase-Matched Generation of Coherent Soft X-rays,” Science 280, 1412–1415 (1998).
[CrossRef] [PubMed]

Frasinski, L. J.

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L C. Dinu, P. Monchicourt, P. Breger, M. Kovac̆ev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft X-rays,” Science 302, 1540 (2003).
[CrossRef] [PubMed]

Gaarde, M. B.

M. B. Gaarde and K. J. Schafer, “Space-Time Considerations in the Phase Locking of High Harmonics,” Phys. Rev. Lett. 89, 213901 (2002).
[CrossRef] [PubMed]

Gallmann, L.

F. Schapper, M. Holler, T. Auguste, A. Zaïr, M. Weger, P. Salières, L. Gallmann, and U. Keller, “Spatial finger-print of quantum path interferences in high order harmonic generation,” Opt. Express 18, 2987–2994 (2010).
[CrossRef] [PubMed]

T. Auguste, P. Salières, A. S. Wyatt, A. Monmayrant, I. A. Walmsley, E. Cormier, A. Zaïr, M. Holler, A. Guandalini, F. Schapper, J. Biegert, L. Gallmann, and U. Keller, “Theoretical and experimental analysis of quantum path interferences in high-order harmonic generation,” Phys. Rev. A 80, 033817 (2009).
[CrossRef]

M. Holler, A. Zaïr, F. Schapper, T. Auguste, E. Cormier, A. Wyatt, A. Monmayrant, I. A. Walmsley, L. Gallmann, P. Salières, and U. Keller, “Ionization effects on spectral signatures of quantum-path interference in high-harmonic generation,” Opt. Express 17, 5716–5722 (2009).
[CrossRef] [PubMed]

A. Zaïr, M. Holler, A. Guandalini, F. Schapper, J. Biegert, L. Gallmann, U. Keller, A. S. Wyatt, A. Monmayrant, I. A. Walmsley, E. Cormier, T. Auguste, J. P. Caumes, and P. Salières, “Quantum Path Interferences in High-Order Harmonic Generation,” Phys. Rev. Lett. 100, 143902 (2008).
[CrossRef] [PubMed]

T. Pfeifer, L. Gallmann, M. J. Abel, P. M. Nagel, D. M. Neumark, and S. R. Leone, “Heterodyne Mixing of Laser Fields for Temporal Gating of High-order Harmonic Generation,” Phys. Rev. Lett. 97, 163901 (2006).
[CrossRef] [PubMed]

Green, H.

R. A. Bartels, A. Paul, H. Green, H. C. Kapteyn, M. M. Murnane, S. Backus, I. P. Christov, Y. Liu, D. Attwood, and C. Jacobsen, “Generation of Spatially Coherent Light at Extreme Ultraviolet Wavelengths,” Science 297, 376–378 (2002).
[PubMed]

Guandalini, A.

T. Auguste, P. Salières, A. S. Wyatt, A. Monmayrant, I. A. Walmsley, E. Cormier, A. Zaïr, M. Holler, A. Guandalini, F. Schapper, J. Biegert, L. Gallmann, and U. Keller, “Theoretical and experimental analysis of quantum path interferences in high-order harmonic generation,” Phys. Rev. A 80, 033817 (2009).
[CrossRef]

A. Zaïr, M. Holler, A. Guandalini, F. Schapper, J. Biegert, L. Gallmann, U. Keller, A. S. Wyatt, A. Monmayrant, I. A. Walmsley, E. Cormier, T. Auguste, J. P. Caumes, and P. Salières, “Quantum Path Interferences in High-Order Harmonic Generation,” Phys. Rev. Lett. 100, 143902 (2008).
[CrossRef] [PubMed]

Heinzmann, U.

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414, 509–513 (2001).
[CrossRef] [PubMed]

Hentschel, M.

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414, 509–513 (2001).
[CrossRef] [PubMed]

Herne, C.

A. Rundquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Phase-Matched Generation of Coherent Soft X-rays,” Science 280, 1412–1415 (1998).
[CrossRef] [PubMed]

Holler, M.

F. Schapper, M. Holler, T. Auguste, A. Zaïr, M. Weger, P. Salières, L. Gallmann, and U. Keller, “Spatial finger-print of quantum path interferences in high order harmonic generation,” Opt. Express 18, 2987–2994 (2010).
[CrossRef] [PubMed]

M. Holler, A. Zaïr, F. Schapper, T. Auguste, E. Cormier, A. Wyatt, A. Monmayrant, I. A. Walmsley, L. Gallmann, P. Salières, and U. Keller, “Ionization effects on spectral signatures of quantum-path interference in high-harmonic generation,” Opt. Express 17, 5716–5722 (2009).
[CrossRef] [PubMed]

T. Auguste, P. Salières, A. S. Wyatt, A. Monmayrant, I. A. Walmsley, E. Cormier, A. Zaïr, M. Holler, A. Guandalini, F. Schapper, J. Biegert, L. Gallmann, and U. Keller, “Theoretical and experimental analysis of quantum path interferences in high-order harmonic generation,” Phys. Rev. A 80, 033817 (2009).
[CrossRef]

A. Zaïr, M. Holler, A. Guandalini, F. Schapper, J. Biegert, L. Gallmann, U. Keller, A. S. Wyatt, A. Monmayrant, I. A. Walmsley, E. Cormier, T. Auguste, J. P. Caumes, and P. Salières, “Quantum Path Interferences in High-Order Harmonic Generation,” Phys. Rev. Lett. 100, 143902 (2008).
[CrossRef] [PubMed]

Hong, W.

W. Hong, Q. Zhang, Z. Yang, and P. Lu, “Electron dynamic control for the quantum path in the midinfrared regime using a weak near-infrared pulse,” Phys. Rev. A 80, 053407 (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, P. Lan, Q. Li, Q. Zhang, Z. Yang, and X. Wang, “Method to generate directly a broadband isolated attosecond pulse with stable pulse duration and high signal-to-noise ratio,” Phys. Rev. A 78, 063407 (2008).
[CrossRef]

W. Cao, P. Lu, P. Lan, W. Hong, and X. Wang, “Control of quntum pahts in high-order harmonic generation via a ω + 3ω bichromatic laser field,” J. Phys. B 40, 869–875 (2007).
[CrossRef]

Ivanov, M. Yu.

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

Jacobsen, C.

R. A. Bartels, A. Paul, H. Green, H. C. Kapteyn, M. M. Murnane, S. Backus, I. P. Christov, Y. Liu, D. Attwood, and C. Jacobsen, “Generation of Spatially Coherent Light at Extreme Ultraviolet Wavelengths,” Science 297, 376–378 (2002).
[PubMed]

Kapteyn, H. C.

R. A. Bartels, A. Paul, H. Green, H. C. Kapteyn, M. M. Murnane, S. Backus, I. P. Christov, Y. Liu, D. Attwood, and C. Jacobsen, “Generation of Spatially Coherent Light at Extreme Ultraviolet Wavelengths,” Science 297, 376–378 (2002).
[PubMed]

A. Rundquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Phase-Matched Generation of Coherent Soft X-rays,” Science 280, 1412–1415 (1998).
[CrossRef] [PubMed]

Keller, U.

F. Schapper, M. Holler, T. Auguste, A. Zaïr, M. Weger, P. Salières, L. Gallmann, and U. Keller, “Spatial finger-print of quantum path interferences in high order harmonic generation,” Opt. Express 18, 2987–2994 (2010).
[CrossRef] [PubMed]

T. Auguste, P. Salières, A. S. Wyatt, A. Monmayrant, I. A. Walmsley, E. Cormier, A. Zaïr, M. Holler, A. Guandalini, F. Schapper, J. Biegert, L. Gallmann, and U. Keller, “Theoretical and experimental analysis of quantum path interferences in high-order harmonic generation,” Phys. Rev. A 80, 033817 (2009).
[CrossRef]

M. Holler, A. Zaïr, F. Schapper, T. Auguste, E. Cormier, A. Wyatt, A. Monmayrant, I. A. Walmsley, L. Gallmann, P. Salières, and U. Keller, “Ionization effects on spectral signatures of quantum-path interference in high-harmonic generation,” Opt. Express 17, 5716–5722 (2009).
[CrossRef] [PubMed]

A. Zaïr, M. Holler, A. Guandalini, F. Schapper, J. Biegert, L. Gallmann, U. Keller, A. S. Wyatt, A. Monmayrant, I. A. Walmsley, E. Cormier, T. Auguste, J. P. Caumes, and P. Salières, “Quantum Path Interferences in High-Order Harmonic Generation,” Phys. Rev. Lett. 100, 143902 (2008).
[CrossRef] [PubMed]

Kienberger, R.

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414, 509–513 (2001).
[CrossRef] [PubMed]

Kovac?ev, M.

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L C. Dinu, P. Monchicourt, P. Breger, M. Kovac̆ev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft X-rays,” Science 302, 1540 (2003).
[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 (1986).

Krausz, F.

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414, 509–513 (2001).
[CrossRef] [PubMed]

Kulander, K. C.

A. L’Huillier, P. Balcou, S. Candel, k. J. Schafer, and K. C. Kulander, “Calculations of high-order harmonic-generation processes in xenon at 1064 nm,” Phys. Rev. A 46, 2778 (1992).
[CrossRef]

L’Huillier, A.

P. Balcou, P. Salières, A. L’Huillier, and M. Lewenstein, “Generalized phase-matching conditions for high harmonics: The role of field-gradient forces,” Phys. Rev. A 55, 3204–3210 (1997).
[CrossRef]

P. Antoine, A. L’Huillier, and M. Lewenstein, “Attosecond Pulse Trains Using High-Order Harmonics,” Phys. Rev. Lett. 77, 1234–1237 (1996).
[CrossRef] [PubMed]

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

A. L’Huillier, P. Balcou, S. Candel, k. J. Schafer, and K. C. Kulander, “Calculations of high-order harmonic-generation processes in xenon at 1064 nm,” Phys. Rev. A 46, 2778 (1992).
[CrossRef]

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, P. Lu, P. Lan, Q. Li, Q. Zhang, Z. Yang, and X. Wang, “Method to generate directly a broadband isolated attosecond pulse with stable pulse duration and high signal-to-noise ratio,” Phys. Rev. A 78, 063407 (2008).
[CrossRef]

W. Cao, P. Lu, P. Lan, W. Hong, and X. Wang, “Control of quntum pahts in high-order harmonic generation via a ω + 3ω bichromatic laser field,” J. Phys. B 40, 869–875 (2007).
[CrossRef]

P. Lan, P. Lu, W. Cao, Y. Li, and X. Wang, “Attosecond ionization gating for isolated attosecond electron wave packet and broadband attosecond xuv pulses,” Phys. Rev. A 76, 051801 (2007).
[CrossRef]

P. Lan, P. Lu, W. Cao, X. Wang, and G. Yang, “Phase-locked high-order-harmonic and sub-100-as pulse generation grom stretched molecules,” Phys. Rev. A 74, 063411 (2006).
[CrossRef]

Leone, S. R.

T. Pfeifer, L. Gallmann, M. J. Abel, P. M. Nagel, D. M. Neumark, and S. R. Leone, “Heterodyne Mixing of Laser Fields for Temporal Gating of High-order Harmonic Generation,” Phys. Rev. Lett. 97, 163901 (2006).
[CrossRef] [PubMed]

Lewenstein, M.

P. Balcou, P. Salières, A. L’Huillier, and M. Lewenstein, “Generalized phase-matching conditions for high harmonics: The role of field-gradient forces,” Phys. Rev. A 55, 3204–3210 (1997).
[CrossRef]

P. Antoine, A. L’Huillier, and M. Lewenstein, “Attosecond Pulse Trains Using High-Order Harmonics,” Phys. Rev. Lett. 77, 1234–1237 (1996).
[CrossRef] [PubMed]

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

Li, Q.

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, P. Lan, Q. Li, Q. Zhang, Z. Yang, and X. Wang, “Method to generate directly a broadband isolated attosecond pulse with stable pulse duration and high signal-to-noise ratio,” Phys. Rev. A 78, 063407 (2008).
[CrossRef]

Li, Y.

P. Lan, P. Lu, W. Cao, Y. Li, and X. Wang, “Attosecond ionization gating for isolated attosecond electron wave packet and broadband attosecond xuv pulses,” Phys. Rev. A 76, 051801 (2007).
[CrossRef]

Lisio, C. De.

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-dimensional model of high-order harmonic generation in the few-optical-cycle regime,” Phys. Rev. A 61, 063801 (2000).
[CrossRef]

Liu, Y.

R. A. Bartels, A. Paul, H. Green, H. C. Kapteyn, M. M. Murnane, S. Backus, I. P. Christov, Y. Liu, D. Attwood, and C. Jacobsen, “Generation of Spatially Coherent Light at Extreme Ultraviolet Wavelengths,” Science 297, 376–378 (2002).
[PubMed]

Lu, P.

W. Hong, Q. Zhang, Z. Yang, and P. Lu, “Electron dynamic control for the quantum path in the midinfrared regime using a weak near-infrared pulse,” Phys. Rev. A 80, 053407 (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, P. Lan, Q. Li, Q. Zhang, Z. Yang, and X. Wang, “Method to generate directly a broadband isolated attosecond pulse with stable pulse duration and high signal-to-noise ratio,” Phys. Rev. A 78, 063407 (2008).
[CrossRef]

W. Cao, P. Lu, P. Lan, W. Hong, and X. Wang, “Control of quntum pahts in high-order harmonic generation via a ω + 3ω bichromatic laser field,” J. Phys. B 40, 869–875 (2007).
[CrossRef]

P. Lan, P. Lu, W. Cao, Y. Li, and X. Wang, “Attosecond ionization gating for isolated attosecond electron wave packet and broadband attosecond xuv pulses,” Phys. Rev. A 76, 051801 (2007).
[CrossRef]

W. Cao, P. Lu, X. Wang, and G. Yang, “Single-attosecond pulse generation with an intense multicycle driving pulse,” Phys. Rev. A 74, 063821 (2006).
[CrossRef]

P. Lan, P. Lu, W. Cao, X. Wang, and G. Yang, “Phase-locked high-order-harmonic and sub-100-as pulse generation grom stretched molecules,” Phys. Rev. A 74, 063411 (2006).
[CrossRef]

Mairesse, Y.

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L C. Dinu, P. Monchicourt, P. Breger, M. Kovac̆ev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft X-rays,” Science 302, 1540 (2003).
[CrossRef] [PubMed]

Merdji, H.

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L C. Dinu, P. Monchicourt, P. Breger, M. Kovac̆ev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft X-rays,” Science 302, 1540 (2003).
[CrossRef] [PubMed]

Milosevic, N.

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414, 509–513 (2001).
[CrossRef] [PubMed]

Monchicourt, P.

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L C. Dinu, P. Monchicourt, P. Breger, M. Kovac̆ev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft X-rays,” Science 302, 1540 (2003).
[CrossRef] [PubMed]

Monmayrant, A.

T. Auguste, P. Salières, A. S. Wyatt, A. Monmayrant, I. A. Walmsley, E. Cormier, A. Zaïr, M. Holler, A. Guandalini, F. Schapper, J. Biegert, L. Gallmann, and U. Keller, “Theoretical and experimental analysis of quantum path interferences in high-order harmonic generation,” Phys. Rev. A 80, 033817 (2009).
[CrossRef]

M. Holler, A. Zaïr, F. Schapper, T. Auguste, E. Cormier, A. Wyatt, A. Monmayrant, I. A. Walmsley, L. Gallmann, P. Salières, and U. Keller, “Ionization effects on spectral signatures of quantum-path interference in high-harmonic generation,” Opt. Express 17, 5716–5722 (2009).
[CrossRef] [PubMed]

A. Zaïr, M. Holler, A. Guandalini, F. Schapper, J. Biegert, L. Gallmann, U. Keller, A. S. Wyatt, A. Monmayrant, I. A. Walmsley, E. Cormier, T. Auguste, J. P. Caumes, and P. Salières, “Quantum Path Interferences in High-Order Harmonic Generation,” Phys. Rev. Lett. 100, 143902 (2008).
[CrossRef] [PubMed]

Muller, H. G.

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L C. Dinu, P. Monchicourt, P. Breger, M. Kovac̆ev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft X-rays,” Science 302, 1540 (2003).
[CrossRef] [PubMed]

Murnane, M. M.

R. A. Bartels, A. Paul, H. Green, H. C. Kapteyn, M. M. Murnane, S. Backus, I. P. Christov, Y. Liu, D. Attwood, and C. Jacobsen, “Generation of Spatially Coherent Light at Extreme Ultraviolet Wavelengths,” Science 297, 376–378 (2002).
[PubMed]

A. Rundquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Phase-Matched Generation of Coherent Soft X-rays,” Science 280, 1412–1415 (1998).
[CrossRef] [PubMed]

Nagel, P. M.

T. Pfeifer, L. Gallmann, M. J. Abel, P. M. Nagel, D. M. Neumark, and S. R. Leone, “Heterodyne Mixing of Laser Fields for Temporal Gating of High-order Harmonic Generation,” Phys. Rev. Lett. 97, 163901 (2006).
[CrossRef] [PubMed]

Neumark, D. M.

T. Pfeifer, L. Gallmann, M. J. Abel, P. M. Nagel, D. M. Neumark, and S. R. Leone, “Heterodyne Mixing of Laser Fields for Temporal Gating of High-order Harmonic Generation,” Phys. Rev. Lett. 97, 163901 (2006).
[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-dimensional model of high-order harmonic generation in the few-optical-cycle regime,” Phys. Rev. A 61, 063801 (2000).
[CrossRef]

Paul, A.

R. A. Bartels, A. Paul, H. Green, H. C. Kapteyn, M. M. Murnane, S. Backus, I. P. Christov, Y. Liu, D. Attwood, and C. Jacobsen, “Generation of Spatially Coherent Light at Extreme Ultraviolet Wavelengths,” Science 297, 376–378 (2002).
[PubMed]

Pfeifer, T.

T. Pfeifer, L. Gallmann, M. J. Abel, P. M. Nagel, D. M. Neumark, and S. R. Leone, “Heterodyne Mixing of Laser Fields for Temporal Gating of High-order Harmonic Generation,” Phys. Rev. Lett. 97, 163901 (2006).
[CrossRef] [PubMed]

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-dimensional 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-dimensional model of high-order harmonic generation in the few-optical-cycle regime,” Phys. Rev. A 61, 063801 (2000).
[CrossRef]

Reider, G. A.

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414, 509–513 (2001).
[CrossRef] [PubMed]

Rundquist, A.

A. Rundquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Phase-Matched Generation of Coherent Soft X-rays,” Science 280, 1412–1415 (1998).
[CrossRef] [PubMed]

Salières, P.

F. Schapper, M. Holler, T. Auguste, A. Zaïr, M. Weger, P. Salières, L. Gallmann, and U. Keller, “Spatial finger-print of quantum path interferences in high order harmonic generation,” Opt. Express 18, 2987–2994 (2010).
[CrossRef] [PubMed]

T. Auguste, P. Salières, A. S. Wyatt, A. Monmayrant, I. A. Walmsley, E. Cormier, A. Zaïr, M. Holler, A. Guandalini, F. Schapper, J. Biegert, L. Gallmann, and U. Keller, “Theoretical and experimental analysis of quantum path interferences in high-order harmonic generation,” Phys. Rev. A 80, 033817 (2009).
[CrossRef]

M. Holler, A. Zaïr, F. Schapper, T. Auguste, E. Cormier, A. Wyatt, A. Monmayrant, I. A. Walmsley, L. Gallmann, P. Salières, and U. Keller, “Ionization effects on spectral signatures of quantum-path interference in high-harmonic generation,” Opt. Express 17, 5716–5722 (2009).
[CrossRef] [PubMed]

A. Zaïr, M. Holler, A. Guandalini, F. Schapper, J. Biegert, L. Gallmann, U. Keller, A. S. Wyatt, A. Monmayrant, I. A. Walmsley, E. Cormier, T. Auguste, J. P. Caumes, and P. Salières, “Quantum Path Interferences in High-Order Harmonic Generation,” Phys. Rev. Lett. 100, 143902 (2008).
[CrossRef] [PubMed]

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L C. Dinu, P. Monchicourt, P. Breger, M. Kovac̆ev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft X-rays,” Science 302, 1540 (2003).
[CrossRef] [PubMed]

P. Balcou, P. Salières, A. L’Huillier, and M. Lewenstein, “Generalized phase-matching conditions for high harmonics: The role of field-gradient forces,” Phys. Rev. A 55, 3204–3210 (1997).
[CrossRef]

Schafer, K. J.

M. B. Gaarde and K. J. Schafer, “Space-Time Considerations in the Phase Locking of High Harmonics,” Phys. Rev. Lett. 89, 213901 (2002).
[CrossRef] [PubMed]

A. L’Huillier, P. Balcou, S. Candel, k. J. Schafer, and K. C. Kulander, “Calculations of high-order harmonic-generation processes in xenon at 1064 nm,” Phys. Rev. A 46, 2778 (1992).
[CrossRef]

Schapper, F.

F. Schapper, M. Holler, T. Auguste, A. Zaïr, M. Weger, P. Salières, L. Gallmann, and U. Keller, “Spatial finger-print of quantum path interferences in high order harmonic generation,” Opt. Express 18, 2987–2994 (2010).
[CrossRef] [PubMed]

M. Holler, A. Zaïr, F. Schapper, T. Auguste, E. Cormier, A. Wyatt, A. Monmayrant, I. A. Walmsley, L. Gallmann, P. Salières, and U. Keller, “Ionization effects on spectral signatures of quantum-path interference in high-harmonic generation,” Opt. Express 17, 5716–5722 (2009).
[CrossRef] [PubMed]

T. Auguste, P. Salières, A. S. Wyatt, A. Monmayrant, I. A. Walmsley, E. Cormier, A. Zaïr, M. Holler, A. Guandalini, F. Schapper, J. Biegert, L. Gallmann, and U. Keller, “Theoretical and experimental analysis of quantum path interferences in high-order harmonic generation,” Phys. Rev. A 80, 033817 (2009).
[CrossRef]

A. Zaïr, M. Holler, A. Guandalini, F. Schapper, J. Biegert, L. Gallmann, U. Keller, A. S. Wyatt, A. Monmayrant, I. A. Walmsley, E. Cormier, T. Auguste, J. P. Caumes, and P. Salières, “Quantum Path Interferences in High-Order Harmonic Generation,” Phys. Rev. Lett. 100, 143902 (2008).
[CrossRef] [PubMed]

Silvestri, S. De.

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-dimensional model of high-order harmonic generation in the few-optical-cycle regime,” Phys. Rev. A 61, 063801 (2000).
[CrossRef]

Spielmann, Ch.

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414, 509–513 (2001).
[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-dimensional model of high-order harmonic generation in the few-optical-cycle regime,” Phys. Rev. A 61, 063801 (2000).
[CrossRef]

Taïeb, R.

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L C. Dinu, P. Monchicourt, P. Breger, M. Kovac̆ev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft X-rays,” Science 302, 1540 (2003).
[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-dimensional model of high-order harmonic generation in the few-optical-cycle regime,” Phys. Rev. A 61, 063801 (2000).
[CrossRef]

Walmsley, I. A.

M. Holler, A. Zaïr, F. Schapper, T. Auguste, E. Cormier, A. Wyatt, A. Monmayrant, I. A. Walmsley, L. Gallmann, P. Salières, and U. Keller, “Ionization effects on spectral signatures of quantum-path interference in high-harmonic generation,” Opt. Express 17, 5716–5722 (2009).
[CrossRef] [PubMed]

T. Auguste, P. Salières, A. S. Wyatt, A. Monmayrant, I. A. Walmsley, E. Cormier, A. Zaïr, M. Holler, A. Guandalini, F. Schapper, J. Biegert, L. Gallmann, and U. Keller, “Theoretical and experimental analysis of quantum path interferences in high-order harmonic generation,” Phys. Rev. A 80, 033817 (2009).
[CrossRef]

A. Zaïr, M. Holler, A. Guandalini, F. Schapper, J. Biegert, L. Gallmann, U. Keller, A. S. Wyatt, A. Monmayrant, I. A. Walmsley, E. Cormier, T. Auguste, J. P. Caumes, and P. Salières, “Quantum Path Interferences in High-Order Harmonic Generation,” Phys. Rev. Lett. 100, 143902 (2008).
[CrossRef] [PubMed]

Wang, X.

W. Hong, P. Lu, P. Lan, Q. Li, Q. Zhang, Z. Yang, and X. Wang, “Method to generate directly a broadband isolated attosecond pulse with stable pulse duration and high signal-to-noise ratio,” Phys. Rev. A 78, 063407 (2008).
[CrossRef]

W. Cao, P. Lu, P. Lan, W. Hong, and X. Wang, “Control of quntum pahts in high-order harmonic generation via a ω + 3ω bichromatic laser field,” J. Phys. B 40, 869–875 (2007).
[CrossRef]

P. Lan, P. Lu, W. Cao, Y. Li, and X. Wang, “Attosecond ionization gating for isolated attosecond electron wave packet and broadband attosecond xuv pulses,” Phys. Rev. A 76, 051801 (2007).
[CrossRef]

W. Cao, P. Lu, X. Wang, and G. Yang, “Single-attosecond pulse generation with an intense multicycle driving pulse,” Phys. Rev. A 74, 063821 (2006).
[CrossRef]

P. Lan, P. Lu, W. Cao, X. Wang, and G. Yang, “Phase-locked high-order-harmonic and sub-100-as pulse generation grom stretched molecules,” Phys. Rev. A 74, 063411 (2006).
[CrossRef]

Weger, M.

Wyatt, A.

Wyatt, A. S.

T. Auguste, P. Salières, A. S. Wyatt, A. Monmayrant, I. A. Walmsley, E. Cormier, A. Zaïr, M. Holler, A. Guandalini, F. Schapper, J. Biegert, L. Gallmann, and U. Keller, “Theoretical and experimental analysis of quantum path interferences in high-order harmonic generation,” Phys. Rev. A 80, 033817 (2009).
[CrossRef]

A. Zaïr, M. Holler, A. Guandalini, F. Schapper, J. Biegert, L. Gallmann, U. Keller, A. S. Wyatt, A. Monmayrant, I. A. Walmsley, E. Cormier, T. Auguste, J. P. Caumes, and P. Salières, “Quantum Path Interferences in High-Order Harmonic Generation,” Phys. Rev. Lett. 100, 143902 (2008).
[CrossRef] [PubMed]

Yang, G.

W. Cao, P. Lu, X. Wang, and G. Yang, “Single-attosecond pulse generation with an intense multicycle driving pulse,” Phys. Rev. A 74, 063821 (2006).
[CrossRef]

P. Lan, P. Lu, W. Cao, X. Wang, and G. Yang, “Phase-locked high-order-harmonic and sub-100-as pulse generation grom stretched molecules,” Phys. Rev. A 74, 063411 (2006).
[CrossRef]

Yang, Z.

W. Hong, Q. Zhang, Z. Yang, and P. Lu, “Electron dynamic control for the quantum path in the midinfrared regime using a weak near-infrared pulse,” Phys. Rev. A 80, 053407 (2009).
[CrossRef]

W. Hong, P. Lu, P. Lan, Q. Li, Q. Zhang, Z. Yang, and X. Wang, “Method to generate directly a broadband isolated attosecond pulse with stable pulse duration and high signal-to-noise ratio,” Phys. Rev. A 78, 063407 (2008).
[CrossRef]

Zaïr, A.

F. Schapper, M. Holler, T. Auguste, A. Zaïr, M. Weger, P. Salières, L. Gallmann, and U. Keller, “Spatial finger-print of quantum path interferences in high order harmonic generation,” Opt. Express 18, 2987–2994 (2010).
[CrossRef] [PubMed]

T. Auguste, P. Salières, A. S. Wyatt, A. Monmayrant, I. A. Walmsley, E. Cormier, A. Zaïr, M. Holler, A. Guandalini, F. Schapper, J. Biegert, L. Gallmann, and U. Keller, “Theoretical and experimental analysis of quantum path interferences in high-order harmonic generation,” Phys. Rev. A 80, 033817 (2009).
[CrossRef]

M. Holler, A. Zaïr, F. Schapper, T. Auguste, E. Cormier, A. Wyatt, A. Monmayrant, I. A. Walmsley, L. Gallmann, P. Salières, and U. Keller, “Ionization effects on spectral signatures of quantum-path interference in high-harmonic generation,” Opt. Express 17, 5716–5722 (2009).
[CrossRef] [PubMed]

A. Zaïr, M. Holler, A. Guandalini, F. Schapper, J. Biegert, L. Gallmann, U. Keller, A. S. Wyatt, A. Monmayrant, I. A. Walmsley, E. Cormier, T. Auguste, J. P. Caumes, and P. Salières, “Quantum Path Interferences in High-Order Harmonic Generation,” Phys. Rev. Lett. 100, 143902 (2008).
[CrossRef] [PubMed]

Zhang, Q.

W. Hong, Q. Zhang, Z. Yang, and P. Lu, “Electron dynamic control for the quantum path in the midinfrared regime using a weak near-infrared pulse,” Phys. Rev. A 80, 053407 (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, P. Lan, Q. Li, Q. Zhang, Z. Yang, and X. Wang, “Method to generate directly a broadband isolated attosecond pulse with stable pulse duration and high signal-to-noise ratio,” Phys. Rev. A 78, 063407 (2008).
[CrossRef]

J. Phys. B (1)

W. Cao, P. Lu, P. Lan, W. Hong, and X. Wang, “Control of quntum pahts in high-order harmonic generation via a ω + 3ω bichromatic laser field,” J. Phys. B 40, 869–875 (2007).
[CrossRef]

Nature (1)

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414, 509–513 (2001).
[CrossRef] [PubMed]

Opt. Express (2)

Phys. Rev. A (11)

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

W. Cao, P. Lu, X. Wang, and G. Yang, “Single-attosecond pulse generation with an intense multicycle driving pulse,” Phys. Rev. A 74, 063821 (2006).
[CrossRef]

W. Hong, P. Lu, P. Lan, Q. Li, Q. Zhang, Z. Yang, and X. Wang, “Method to generate directly a broadband isolated attosecond pulse with stable pulse duration and high signal-to-noise ratio,” Phys. Rev. A 78, 063407 (2008).
[CrossRef]

W. Hong, Q. Zhang, Z. Yang, and P. Lu, “Electron dynamic control for the quantum path in the midinfrared regime using a weak near-infrared pulse,” Phys. Rev. A 80, 053407 (2009).
[CrossRef]

P. Lan, P. Lu, W. Cao, Y. Li, and X. Wang, “Attosecond ionization gating for isolated attosecond electron wave packet and broadband attosecond xuv pulses,” Phys. Rev. A 76, 051801 (2007).
[CrossRef]

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-dimensional model of high-order harmonic generation in the few-optical-cycle regime,” Phys. Rev. A 61, 063801 (2000).
[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]

A. L’Huillier, P. Balcou, S. Candel, k. J. Schafer, and K. C. Kulander, “Calculations of high-order harmonic-generation processes in xenon at 1064 nm,” Phys. Rev. A 46, 2778 (1992).
[CrossRef]

P. Balcou, P. Salières, A. L’Huillier, and M. Lewenstein, “Generalized phase-matching conditions for high harmonics: The role of field-gradient forces,” Phys. Rev. A 55, 3204–3210 (1997).
[CrossRef]

P. Lan, P. Lu, W. Cao, X. Wang, and G. Yang, “Phase-locked high-order-harmonic and sub-100-as pulse generation grom stretched molecules,” Phys. Rev. A 74, 063411 (2006).
[CrossRef]

T. Auguste, P. Salières, A. S. Wyatt, A. Monmayrant, I. A. Walmsley, E. Cormier, A. Zaïr, M. Holler, A. Guandalini, F. Schapper, J. Biegert, L. Gallmann, and U. Keller, “Theoretical and experimental analysis of quantum path interferences in high-order harmonic generation,” Phys. Rev. A 80, 033817 (2009).
[CrossRef]

Phys. Rev. Lett. (5)

M. B. Gaarde and K. J. Schafer, “Space-Time Considerations in the Phase Locking of High Harmonics,” Phys. Rev. Lett. 89, 213901 (2002).
[CrossRef] [PubMed]

P. B. Corkum, “Plasma Perspective on Strong-Field Multiphoton Ionization,” Phys. Rev. Lett. 71,1994 (1993).
[CrossRef] [PubMed]

T. Pfeifer, L. Gallmann, M. J. Abel, P. M. Nagel, D. M. Neumark, and S. R. Leone, “Heterodyne Mixing of Laser Fields for Temporal Gating of High-order Harmonic Generation,” Phys. Rev. Lett. 97, 163901 (2006).
[CrossRef] [PubMed]

A. Zaïr, M. Holler, A. Guandalini, F. Schapper, J. Biegert, L. Gallmann, U. Keller, A. S. Wyatt, A. Monmayrant, I. A. Walmsley, E. Cormier, T. Auguste, J. P. Caumes, and P. Salières, “Quantum Path Interferences in High-Order Harmonic Generation,” Phys. Rev. Lett. 100, 143902 (2008).
[CrossRef] [PubMed]

P. Antoine, A. L’Huillier, and M. Lewenstein, “Attosecond Pulse Trains Using High-Order Harmonics,” Phys. Rev. Lett. 77, 1234–1237 (1996).
[CrossRef] [PubMed]

Science (3)

A. Rundquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Phase-Matched Generation of Coherent Soft X-rays,” Science 280, 1412–1415 (1998).
[CrossRef] [PubMed]

R. A. Bartels, A. Paul, H. Green, H. C. Kapteyn, M. M. Murnane, S. Backus, I. P. Christov, Y. Liu, D. Attwood, and C. Jacobsen, “Generation of Spatially Coherent Light at Extreme Ultraviolet Wavelengths,” Science 297, 376–378 (2002).
[PubMed]

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L C. Dinu, P. Monchicourt, P. Breger, M. Kovac̆ev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft X-rays,” Science 302, 1540 (2003).
[CrossRef] [PubMed]

Sov. Phys. JETP (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 (1986).

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Figures (5)

Fig. 1
Fig. 1

The ionization (blue circles) and recombination times (green crosses) as a function of the return kinetic energy in unit of the harmonic order in the two-color (a) and one-color fields (b). The electric field (red dashed) and the tunnel ionization rate (grey filled curve) in the two-color (c) and one-color fields (d).

Fig. 2
Fig. 2

The time-frequency images of high order harmonics after propagation in the two-color fields (a–b) and the driving fields alone (c–d). The beam waists of the driving field and the controlling field at the focus are both 25 μm (a) or 35 μm and 25 μm (b), respectively.

Fig. 3
Fig. 3

The phase-mismatching maps for the different quantum path contributions to the 22nd harmonic in the two-color fields (a–c) and the one-color fields (d–f). The white areas correspond to very poor phase matching and the dark areas to very good phase matching. (c and f) The phase-mismatching maps for the short trajectories. (a,b,d and e) The phase-mismatching maps for the long trajectories. For the two-color field, the beam waists of the driving field and the controlling field at the focus are both 25 μm (a) or 35 μm and 25 μm (b and c), respectively. For the one-color field, the beam waists of the one-color field at the focus are 25 μm (d) or 35 μm (e and f), respectively.

Fig. 4
Fig. 4

(a) The near-field spatial distribution of the contribution ratio between the two trajectories as a function of the laser intensity. The harmonics from 20th to 25th are superposed to generate the attosecond pulse. (b) The near-field interference fringe image in the two-color field by using a spatial near-field filter.

Fig. 5
Fig. 5

The dependence of the 22nd and 23rd harmonics on the laser intensity in the far field without (a) and with (b) the near-field filtering.

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

d n l ( t ) = i t d t [ π ɛ + i ( t t ) / 2 ] 3 / 2 g * ( t ) × d * [ p s t ( t , t ) A ( t ) ] d [ p s t ( t , t ) A ( t ) ] × exp [ i S s t ( t , t ) ] E ( t ) g ( t ) + c . c ..
p s t ( t , t ) = 1 t t t t A ( t ) d t ,
S s t ( t , t ) = ( t t ) I p 1 2 p s t 2 ( t , t ) ( t t ) + 1 2 t t A 2 ( t ) d t ,
d ( p ) = i 2 7 / 2 π ( 2 I p ) 5 / 4 p ( p 2 + 2 I p ) 3 .
g ( t ) = exp [ t ω ( t ) d t ] .
ω ( t ) = w e | C n * | 2 ( 4 w e ω t ) 2 n * 1 exp ( 4 w e 3 ω t ) ,
d ( p ) = i 2 7 / 2 π ( 2 I p ) 5 / 4 p ( p 2 + 2 I p ) 3 .
w e = I p h ¯ , ω t = e | E l ( t ) | 2 m e I p , n * = Z ( I p h I p ) 1 / 2 , | C n * | 2 = 2 2 n * n * Γ ( n * + 1 ) Γ ( n * ) ,
2 E l ( r , z , t ) 1 c 2 2 E l ( r , z , t ) t 2 = ω p ( r , z , t ) 2 c 2 E l ( r , z , t ) ,
2 E h ( r , z , t ) 1 c 2 2 E h ( r , z , t ) t 2 = ω p ( r , z , t ) 2 c 2 E h ( r , z , t ) + μ 0 2 P n l ( r , z , t ) t 2 ,
ω p = e n e ( r , z , t ) m ɛ 0
n e ( t ) = n 0 [ 1 exp ( t ω ( t ) d t ) ] ,
E ( t ) = E 0 f ( t ) cos [ ω 0 t ] + E 1 f ( t ) cos [ 2 ω 0 t + ϕ 0 ] ,
η = τ N d t I X U V ( t ) T 0 / 2 d t I X U V ( t ) .

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