Abstract

We have experimentally investigated the frequency modulation of high-order harmonics in an orthogonally polarized two-color laser field consisting of a mid-infrared 1800nm fundamental pulse and its second harmonic pulse. It is demonstrated that the high harmonic spectra can be fine-tuned as we slightly change the relative delay of the two-color laser pulses. By analyzing the relative frequency shift of each harmonic at different two-color delays, the nonadiabatic spectral shift induced by the rapid variation of the intensity-dependent intrinsic dipole phase can be distinguished from the blueshift induced by the change of the refractive index during self-phase modulation (SPM). Our comprehensive analysis shows that the frequency modulation pattern is a reflection of the average emission time of high-order harmonic generation (HHG), thus offering a simple method to fine-tune the spectra of the harmonics on a sub-cycle time scale.

© 2016 Optical Society of America

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  1. T. Ditmire, E. T. Gumbrell, R. A. Smith, J. W. G. Tisch, D. D. Meyerhofer, and M. H. R. Hutchinson, “Spatial coherence measurement of soft X-ray radiation produced by high order harmonic generation,” Phys. Rev. Lett. 77(23), 4756–4759 (1996).
    [Crossref] [PubMed]
  2. M. Bellini, C. Lyngå, A. Tozzi, M. B. Gaarde, T. W. Hänsch, A. L’Huillier, and C. G. Wahlström, “Temporal coherence of ultrashort high-order harmonic pulses,” Phys. Rev. Lett. 81(2), 297–300 (1998).
    [Crossref]
  3. P. Salières, A. L’Huillier, and M. Lewenstein, “Coherence control of high-order harmonics,” Phys. Rev. Lett. 74(19), 3776–3779 (1995).
    [Crossref] [PubMed]
  4. Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft x-rays,” Science 302(5650), 1540–1543 (2003).
    [Crossref] [PubMed]
  5. H. Niikura, H. J. Wörner, D. M. Villeneuve, and P. B. Corkum, “Probing the spatial structure of a molecular attosecond electron wave packet using shaped recollision trajectories,” Phys. Rev. Lett. 107(9), 093004 (2011).
    [Crossref] [PubMed]
  6. M. Kitzler and M. Lezius, “Spatial control of recollision wave packets with attosecond precision,” Phys. Rev. Lett. 95(25), 253001 (2005).
    [Crossref] [PubMed]
  7. A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003).
    [Crossref] [PubMed]
  8. D. Shafir, Y. Mairesse, D. M. Villeneuve, P. B. Corkum, and N. Dudovich, “Atomic wavefunctions probed through strong-field light–matter interaction,” Nat. Phys. 5(6), 412–416 (2009).
    [Crossref]
  9. P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71(13), 1994–1997 (1993).
    [Crossref] [PubMed]
  10. M. Lewenstein, P. 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(3), 2117–2132 (1994).
    [Crossref] [PubMed]
  11. X.-M. Tong and S.-I. Chu, “Probing the spectral and temporal structures of high-order harmonic generation in intense laser pulses,” Phys. Rev. A 61(2), 021802 (2000).
    [Crossref]
  12. W. M. Wood, C. W. Siders, and M. C. Downer, “Measurement of femtosecond ionization dynamics of atmospheric density gases by spectral blueshifting,” Phys. Rev. Lett. 67(25), 3523–3526 (1991).
    [Crossref] [PubMed]
  13. H. J. Shin, D. G. Lee, Y. H. Cha, K. H. Hong, and C. H. Nam, “Generation of nonadiabatic blueshift of high harmonics in an intense femtosecond laser field,” Phys. Rev. Lett. 83(13), 2544–2547 (1999).
    [Crossref]
  14. H. J. Shin, G. L. Dong, Y. H. Cha, J.-H. Kim, K. H. Hong, and C. H. Nam, “Nonadiabatic blueshift of high-order harmonics from Ar and Ne atoms in an intense femtosecond laser field,” Phys. Rev. A 63(5), 053407 (2001).
    [Crossref]
  15. J. B. Watson, A. Sanpera, and K. Burnett, “Pulse-shape effects and blueshifting in the single-atom harmonic generation from neutral species and ions,” Phys. Rev. A 51(2), 1458–1463 (1995).
    [Crossref] [PubMed]
  16. K. J. Schafer and K. C. Kulander, “High harmonic generation from ultrafast pump lasers,” Phys. Rev. Lett. 78(4), 638–641 (1997).
    [Crossref]
  17. M. Geissler, G. Tempea, and T. Brabec, “Phase-matched high-order harmonic generation in the nonadiabatic limit,” Phys. Rev. A 62(3), 033817 (2000).
    [Crossref]
  18. H. Du, S. Xue, H. Wang, Z. Zhang, and B. Hu, “Nonadiabatic spectral redshift of h- igh-order harmonics with the help of a VUV pulse,” Phys. Rev. A 91(6), 063844 (2015).
    [Crossref]
  19. S. C. Rae and K. Burnett, “Detailed simulations of plasma-induced spectral blueshifting,” Phys. Rev. A 46(2), 1084–1090 (1992).
    [Crossref] [PubMed]
  20. D. J. Hoffmann, C. Hutchison, A. Zaïr, and J. P. Marangos, “Control of temporal mapping and harmonic intensity modulation using two-color orthogonally polarized fields,” Phys. Rev. A 89(2), 023423 (2014).
    [Crossref]
  21. C. M. Kim, I. J. Kim, and C. H. Nam, “Generation of a strong attosecond pulse train with an orthogonally polarized two-color laser field,” Phys. Rev. A 72(3), 033817 (2005).
    [Crossref]
  22. L. Brugnera, D. J. Hoffmann, T. Siegel, F. Frank, A. Zaïr, J. W. G. Tisch, and J. P. Marangos, “Trajectory selection in high harmonic generation by controlling the phase between orthogonal two-color fields,” Phys. Rev. Lett. 107(15), 153902 (2011).
    [Crossref] [PubMed]
  23. M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and atomic ions in electromagnetic field,” Sov. Phys. JETP 64(3), 1191–1194 (1986).
  24. H. Merdji, M. Kovačev, W. Boutu, P. Salières, F. Vernay, and B. Carré, “Macroscopic control of high-order harmonics quantum-path components for the generation of attosecond pulses,” Phys. Rev. A 74(4), 043804 (2006).
    [Crossref]
  25. 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(14), 143902 (2008).
    [Crossref] [PubMed]
  26. I. Jong Kim, C. M Kim, H. T Kim, G. H Lee, Y. S. Lee, J. Y Park, D. J Cho, and C. H Nam, “Highly efficient high-harmonic generation in an orthogonally polarized two-color laser field,” Phys. Rev. Lett. 94(24), 243901 (2005).
    [Crossref] [PubMed]
  27. Y. Zheng, H. Diao, Z. Zeng, X. Ge, R. Li, and Z. Xu, “Manipulating electron-ion recollision in a midinfrared laser field,” Phys. Rev. A 92(3), 033417 (2015).
    [Crossref]
  28. J.-H. Kim, H. J. Shin, G. L. Dong, and C. H. Nam, “Enhanced spectral resolution of high-order harmonics by the coherent sum of dipole spectra,” Phys. Rev. A 62(5), 055402 (2000).
    [Crossref]
  29. M. B. Gaarde and K. J. Schafer, “Quantum path distributions for high-order harmonics in rare gas atoms,” Phys. Rev. A 65(3), 031406 (2002).
    [Crossref]
  30. J. Xu, “Isolated short attosecond pulse generation in an orthogonally polarized multicycle chirped laser field,” Phys. Rev. A 83(3), 033823 (2011).
    [Crossref]

2015 (2)

H. Du, S. Xue, H. Wang, Z. Zhang, and B. Hu, “Nonadiabatic spectral redshift of h- igh-order harmonics with the help of a VUV pulse,” Phys. Rev. A 91(6), 063844 (2015).
[Crossref]

Y. Zheng, H. Diao, Z. Zeng, X. Ge, R. Li, and Z. Xu, “Manipulating electron-ion recollision in a midinfrared laser field,” Phys. Rev. A 92(3), 033417 (2015).
[Crossref]

2014 (1)

D. J. Hoffmann, C. Hutchison, A. Zaïr, and J. P. Marangos, “Control of temporal mapping and harmonic intensity modulation using two-color orthogonally polarized fields,” Phys. Rev. A 89(2), 023423 (2014).
[Crossref]

2011 (3)

L. Brugnera, D. J. Hoffmann, T. Siegel, F. Frank, A. Zaïr, J. W. G. Tisch, and J. P. Marangos, “Trajectory selection in high harmonic generation by controlling the phase between orthogonal two-color fields,” Phys. Rev. Lett. 107(15), 153902 (2011).
[Crossref] [PubMed]

J. Xu, “Isolated short attosecond pulse generation in an orthogonally polarized multicycle chirped laser field,” Phys. Rev. A 83(3), 033823 (2011).
[Crossref]

H. Niikura, H. J. Wörner, D. M. Villeneuve, and P. B. Corkum, “Probing the spatial structure of a molecular attosecond electron wave packet using shaped recollision trajectories,” Phys. Rev. Lett. 107(9), 093004 (2011).
[Crossref] [PubMed]

2009 (1)

D. Shafir, Y. Mairesse, D. M. Villeneuve, P. B. Corkum, and N. Dudovich, “Atomic wavefunctions probed through strong-field light–matter interaction,” Nat. Phys. 5(6), 412–416 (2009).
[Crossref]

2008 (1)

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(14), 143902 (2008).
[Crossref] [PubMed]

2006 (1)

H. Merdji, M. Kovačev, W. Boutu, P. Salières, F. Vernay, and B. Carré, “Macroscopic control of high-order harmonics quantum-path components for the generation of attosecond pulses,” Phys. Rev. A 74(4), 043804 (2006).
[Crossref]

2005 (3)

I. Jong Kim, C. M Kim, H. T Kim, G. H Lee, Y. S. Lee, J. Y Park, D. J Cho, and C. H Nam, “Highly efficient high-harmonic generation in an orthogonally polarized two-color laser field,” Phys. Rev. Lett. 94(24), 243901 (2005).
[Crossref] [PubMed]

C. M. Kim, I. J. Kim, and C. H. Nam, “Generation of a strong attosecond pulse train with an orthogonally polarized two-color laser field,” Phys. Rev. A 72(3), 033817 (2005).
[Crossref]

M. Kitzler and M. Lezius, “Spatial control of recollision wave packets with attosecond precision,” Phys. Rev. Lett. 95(25), 253001 (2005).
[Crossref] [PubMed]

2003 (2)

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003).
[Crossref] [PubMed]

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft x-rays,” Science 302(5650), 1540–1543 (2003).
[Crossref] [PubMed]

2002 (1)

M. B. Gaarde and K. J. Schafer, “Quantum path distributions for high-order harmonics in rare gas atoms,” Phys. Rev. A 65(3), 031406 (2002).
[Crossref]

2001 (1)

H. J. Shin, G. L. Dong, Y. H. Cha, J.-H. Kim, K. H. Hong, and C. H. Nam, “Nonadiabatic blueshift of high-order harmonics from Ar and Ne atoms in an intense femtosecond laser field,” Phys. Rev. A 63(5), 053407 (2001).
[Crossref]

2000 (3)

M. Geissler, G. Tempea, and T. Brabec, “Phase-matched high-order harmonic generation in the nonadiabatic limit,” Phys. Rev. A 62(3), 033817 (2000).
[Crossref]

X.-M. Tong and S.-I. Chu, “Probing the spectral and temporal structures of high-order harmonic generation in intense laser pulses,” Phys. Rev. A 61(2), 021802 (2000).
[Crossref]

J.-H. Kim, H. J. Shin, G. L. Dong, and C. H. Nam, “Enhanced spectral resolution of high-order harmonics by the coherent sum of dipole spectra,” Phys. Rev. A 62(5), 055402 (2000).
[Crossref]

1999 (1)

H. J. Shin, D. G. Lee, Y. H. Cha, K. H. Hong, and C. H. Nam, “Generation of nonadiabatic blueshift of high harmonics in an intense femtosecond laser field,” Phys. Rev. Lett. 83(13), 2544–2547 (1999).
[Crossref]

1998 (1)

M. Bellini, C. Lyngå, A. Tozzi, M. B. Gaarde, T. W. Hänsch, A. L’Huillier, and C. G. Wahlström, “Temporal coherence of ultrashort high-order harmonic pulses,” Phys. Rev. Lett. 81(2), 297–300 (1998).
[Crossref]

1997 (1)

K. J. Schafer and K. C. Kulander, “High harmonic generation from ultrafast pump lasers,” Phys. Rev. Lett. 78(4), 638–641 (1997).
[Crossref]

1996 (1)

T. Ditmire, E. T. Gumbrell, R. A. Smith, J. W. G. Tisch, D. D. Meyerhofer, and M. H. R. Hutchinson, “Spatial coherence measurement of soft X-ray radiation produced by high order harmonic generation,” Phys. Rev. Lett. 77(23), 4756–4759 (1996).
[Crossref] [PubMed]

1995 (2)

P. Salières, A. L’Huillier, and M. Lewenstein, “Coherence control of high-order harmonics,” Phys. Rev. Lett. 74(19), 3776–3779 (1995).
[Crossref] [PubMed]

J. B. Watson, A. Sanpera, and K. Burnett, “Pulse-shape effects and blueshifting in the single-atom harmonic generation from neutral species and ions,” Phys. Rev. A 51(2), 1458–1463 (1995).
[Crossref] [PubMed]

1994 (1)

M. Lewenstein, P. 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(3), 2117–2132 (1994).
[Crossref] [PubMed]

1993 (1)

P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71(13), 1994–1997 (1993).
[Crossref] [PubMed]

1992 (1)

S. C. Rae and K. Burnett, “Detailed simulations of plasma-induced spectral blueshifting,” Phys. Rev. A 46(2), 1084–1090 (1992).
[Crossref] [PubMed]

1991 (1)

W. M. Wood, C. W. Siders, and M. C. Downer, “Measurement of femtosecond ionization dynamics of atmospheric density gases by spectral blueshifting,” Phys. Rev. Lett. 67(25), 3523–3526 (1991).
[Crossref] [PubMed]

1986 (1)

M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and atomic ions in electromagnetic field,” Sov. Phys. JETP 64(3), 1191–1194 (1986).

Agostini, P.

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft x-rays,” Science 302(5650), 1540–1543 (2003).
[Crossref] [PubMed]

Ammosov, M. V.

M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and atomic ions in electromagnetic field,” Sov. Phys. JETP 64(3), 1191–1194 (1986).

Auguste, T.

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(14), 143902 (2008).
[Crossref] [PubMed]

Balcou, P.

M. Lewenstein, P. 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(3), 2117–2132 (1994).
[Crossref] [PubMed]

Baltuška, A.

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003).
[Crossref] [PubMed]

Bellini, M.

M. Bellini, C. Lyngå, A. Tozzi, M. B. Gaarde, T. W. Hänsch, A. L’Huillier, and C. G. Wahlström, “Temporal coherence of ultrashort high-order harmonic pulses,” Phys. Rev. Lett. 81(2), 297–300 (1998).
[Crossref]

Biegert, J.

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(14), 143902 (2008).
[Crossref] [PubMed]

Boutu, W.

H. Merdji, M. Kovačev, W. Boutu, P. Salières, F. Vernay, and B. Carré, “Macroscopic control of high-order harmonics quantum-path components for the generation of attosecond pulses,” Phys. Rev. A 74(4), 043804 (2006).
[Crossref]

Brabec, T.

M. Geissler, G. Tempea, and T. Brabec, “Phase-matched high-order harmonic generation in the nonadiabatic limit,” Phys. Rev. A 62(3), 033817 (2000).
[Crossref]

Breger, P.

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft x-rays,” Science 302(5650), 1540–1543 (2003).
[Crossref] [PubMed]

Brugnera, L.

L. Brugnera, D. J. Hoffmann, T. Siegel, F. Frank, A. Zaïr, J. W. G. Tisch, and J. P. Marangos, “Trajectory selection in high harmonic generation by controlling the phase between orthogonal two-color fields,” Phys. Rev. Lett. 107(15), 153902 (2011).
[Crossref] [PubMed]

Burnett, K.

J. B. Watson, A. Sanpera, and K. Burnett, “Pulse-shape effects and blueshifting in the single-atom harmonic generation from neutral species and ions,” Phys. Rev. A 51(2), 1458–1463 (1995).
[Crossref] [PubMed]

S. C. Rae and K. Burnett, “Detailed simulations of plasma-induced spectral blueshifting,” Phys. Rev. A 46(2), 1084–1090 (1992).
[Crossref] [PubMed]

Carré, B.

H. Merdji, M. Kovačev, W. Boutu, P. Salières, F. Vernay, and B. Carré, “Macroscopic control of high-order harmonics quantum-path components for the generation of attosecond pulses,” Phys. Rev. A 74(4), 043804 (2006).
[Crossref]

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft x-rays,” Science 302(5650), 1540–1543 (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(14), 143902 (2008).
[Crossref] [PubMed]

Cha, Y. H.

H. J. Shin, G. L. Dong, Y. H. Cha, J.-H. Kim, K. H. Hong, and C. H. Nam, “Nonadiabatic blueshift of high-order harmonics from Ar and Ne atoms in an intense femtosecond laser field,” Phys. Rev. A 63(5), 053407 (2001).
[Crossref]

H. J. Shin, D. G. Lee, Y. H. Cha, K. H. Hong, and C. H. Nam, “Generation of nonadiabatic blueshift of high harmonics in an intense femtosecond laser field,” Phys. Rev. Lett. 83(13), 2544–2547 (1999).
[Crossref]

Cho, D. J

I. Jong Kim, C. M Kim, H. T Kim, G. H Lee, Y. S. Lee, J. Y Park, D. J Cho, and C. H Nam, “Highly efficient high-harmonic generation in an orthogonally polarized two-color laser field,” Phys. Rev. Lett. 94(24), 243901 (2005).
[Crossref] [PubMed]

Chu, S.-I.

X.-M. Tong and S.-I. Chu, “Probing the spectral and temporal structures of high-order harmonic generation in intense laser pulses,” Phys. Rev. A 61(2), 021802 (2000).
[Crossref]

Corkum, P. B.

H. Niikura, H. J. Wörner, D. M. Villeneuve, and P. B. Corkum, “Probing the spatial structure of a molecular attosecond electron wave packet using shaped recollision trajectories,” Phys. Rev. Lett. 107(9), 093004 (2011).
[Crossref] [PubMed]

D. Shafir, Y. Mairesse, D. M. Villeneuve, P. B. Corkum, and N. Dudovich, “Atomic wavefunctions probed through strong-field light–matter interaction,” Nat. Phys. 5(6), 412–416 (2009).
[Crossref]

M. Lewenstein, P. 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(3), 2117–2132 (1994).
[Crossref] [PubMed]

P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71(13), 1994–1997 (1993).
[Crossref] [PubMed]

Cormier, E.

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(14), 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. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft x-rays,” Science 302(5650), 1540–1543 (2003).
[Crossref] [PubMed]

Delone, N. B.

M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and atomic ions in electromagnetic field,” Sov. Phys. JETP 64(3), 1191–1194 (1986).

Diao, H.

Y. Zheng, H. Diao, Z. Zeng, X. Ge, R. Li, and Z. Xu, “Manipulating electron-ion recollision in a midinfrared laser field,” Phys. Rev. A 92(3), 033417 (2015).
[Crossref]

Dinu, L. C.

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft x-rays,” Science 302(5650), 1540–1543 (2003).
[Crossref] [PubMed]

Ditmire, T.

T. Ditmire, E. T. Gumbrell, R. A. Smith, J. W. G. Tisch, D. D. Meyerhofer, and M. H. R. Hutchinson, “Spatial coherence measurement of soft X-ray radiation produced by high order harmonic generation,” Phys. Rev. Lett. 77(23), 4756–4759 (1996).
[Crossref] [PubMed]

Dong, G. L.

H. J. Shin, G. L. Dong, Y. H. Cha, J.-H. Kim, K. H. Hong, and C. H. Nam, “Nonadiabatic blueshift of high-order harmonics from Ar and Ne atoms in an intense femtosecond laser field,” Phys. Rev. A 63(5), 053407 (2001).
[Crossref]

J.-H. Kim, H. J. Shin, G. L. Dong, and C. H. Nam, “Enhanced spectral resolution of high-order harmonics by the coherent sum of dipole spectra,” Phys. Rev. A 62(5), 055402 (2000).
[Crossref]

Downer, M. C.

W. M. Wood, C. W. Siders, and M. C. Downer, “Measurement of femtosecond ionization dynamics of atmospheric density gases by spectral blueshifting,” Phys. Rev. Lett. 67(25), 3523–3526 (1991).
[Crossref] [PubMed]

Du, H.

H. Du, S. Xue, H. Wang, Z. Zhang, and B. Hu, “Nonadiabatic spectral redshift of h- igh-order harmonics with the help of a VUV pulse,” Phys. Rev. A 91(6), 063844 (2015).
[Crossref]

Dudovich, N.

D. Shafir, Y. Mairesse, D. M. Villeneuve, P. B. Corkum, and N. Dudovich, “Atomic wavefunctions probed through strong-field light–matter interaction,” Nat. Phys. 5(6), 412–416 (2009).
[Crossref]

Frank, F.

L. Brugnera, D. J. Hoffmann, T. Siegel, F. Frank, A. Zaïr, J. W. G. Tisch, and J. P. Marangos, “Trajectory selection in high harmonic generation by controlling the phase between orthogonal two-color fields,” Phys. Rev. Lett. 107(15), 153902 (2011).
[Crossref] [PubMed]

Frasinski, L. J.

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft x-rays,” Science 302(5650), 1540–1543 (2003).
[Crossref] [PubMed]

Gaarde, M. B.

M. B. Gaarde and K. J. Schafer, “Quantum path distributions for high-order harmonics in rare gas atoms,” Phys. Rev. A 65(3), 031406 (2002).
[Crossref]

M. Bellini, C. Lyngå, A. Tozzi, M. B. Gaarde, T. W. Hänsch, A. L’Huillier, and C. G. Wahlström, “Temporal coherence of ultrashort high-order harmonic pulses,” Phys. Rev. Lett. 81(2), 297–300 (1998).
[Crossref]

Gallmann, L.

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(14), 143902 (2008).
[Crossref] [PubMed]

Ge, X.

Y. Zheng, H. Diao, Z. Zeng, X. Ge, R. Li, and Z. Xu, “Manipulating electron-ion recollision in a midinfrared laser field,” Phys. Rev. A 92(3), 033417 (2015).
[Crossref]

Geissler, M.

M. Geissler, G. Tempea, and T. Brabec, “Phase-matched high-order harmonic generation in the nonadiabatic limit,” Phys. Rev. A 62(3), 033817 (2000).
[Crossref]

Gohle, Ch.

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003).
[Crossref] [PubMed]

Goulielmakis, E.

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003).
[Crossref] [PubMed]

Guandalini, A.

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(14), 143902 (2008).
[Crossref] [PubMed]

Gumbrell, E. T.

T. Ditmire, E. T. Gumbrell, R. A. Smith, J. W. G. Tisch, D. D. Meyerhofer, and M. H. R. Hutchinson, “Spatial coherence measurement of soft X-ray radiation produced by high order harmonic generation,” Phys. Rev. Lett. 77(23), 4756–4759 (1996).
[Crossref] [PubMed]

Hänsch, T. W.

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003).
[Crossref] [PubMed]

M. Bellini, C. Lyngå, A. Tozzi, M. B. Gaarde, T. W. Hänsch, A. L’Huillier, and C. G. Wahlström, “Temporal coherence of ultrashort high-order harmonic pulses,” Phys. Rev. Lett. 81(2), 297–300 (1998).
[Crossref]

Hentschel, M.

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003).
[Crossref] [PubMed]

Hoffmann, D. J.

D. J. Hoffmann, C. Hutchison, A. Zaïr, and J. P. Marangos, “Control of temporal mapping and harmonic intensity modulation using two-color orthogonally polarized fields,” Phys. Rev. A 89(2), 023423 (2014).
[Crossref]

L. Brugnera, D. J. Hoffmann, T. Siegel, F. Frank, A. Zaïr, J. W. G. Tisch, and J. P. Marangos, “Trajectory selection in high harmonic generation by controlling the phase between orthogonal two-color fields,” Phys. Rev. Lett. 107(15), 153902 (2011).
[Crossref] [PubMed]

Holler, M.

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(14), 143902 (2008).
[Crossref] [PubMed]

Holzwarth, R.

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003).
[Crossref] [PubMed]

Hong, K. H.

H. J. Shin, G. L. Dong, Y. H. Cha, J.-H. Kim, K. H. Hong, and C. H. Nam, “Nonadiabatic blueshift of high-order harmonics from Ar and Ne atoms in an intense femtosecond laser field,” Phys. Rev. A 63(5), 053407 (2001).
[Crossref]

H. J. Shin, D. G. Lee, Y. H. Cha, K. H. Hong, and C. H. Nam, “Generation of nonadiabatic blueshift of high harmonics in an intense femtosecond laser field,” Phys. Rev. Lett. 83(13), 2544–2547 (1999).
[Crossref]

Hu, B.

H. Du, S. Xue, H. Wang, Z. Zhang, and B. Hu, “Nonadiabatic spectral redshift of h- igh-order harmonics with the help of a VUV pulse,” Phys. Rev. A 91(6), 063844 (2015).
[Crossref]

Hutchinson, M. H. R.

T. Ditmire, E. T. Gumbrell, R. A. Smith, J. W. G. Tisch, D. D. Meyerhofer, and M. H. R. Hutchinson, “Spatial coherence measurement of soft X-ray radiation produced by high order harmonic generation,” Phys. Rev. Lett. 77(23), 4756–4759 (1996).
[Crossref] [PubMed]

Hutchison, C.

D. J. Hoffmann, C. Hutchison, A. Zaïr, and J. P. Marangos, “Control of temporal mapping and harmonic intensity modulation using two-color orthogonally polarized fields,” Phys. Rev. A 89(2), 023423 (2014).
[Crossref]

Ivanov, M. Yu.

M. Lewenstein, P. 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(3), 2117–2132 (1994).
[Crossref] [PubMed]

Jong Kim, I.

I. Jong Kim, C. M Kim, H. T Kim, G. H Lee, Y. S. Lee, J. Y Park, D. J Cho, and C. H Nam, “Highly efficient high-harmonic generation in an orthogonally polarized two-color laser field,” Phys. Rev. Lett. 94(24), 243901 (2005).
[Crossref] [PubMed]

Keller, U.

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(14), 143902 (2008).
[Crossref] [PubMed]

Kim, C. M

I. Jong Kim, C. M Kim, H. T Kim, G. H Lee, Y. S. Lee, J. Y Park, D. J Cho, and C. H Nam, “Highly efficient high-harmonic generation in an orthogonally polarized two-color laser field,” Phys. Rev. Lett. 94(24), 243901 (2005).
[Crossref] [PubMed]

Kim, C. M.

C. M. Kim, I. J. Kim, and C. H. Nam, “Generation of a strong attosecond pulse train with an orthogonally polarized two-color laser field,” Phys. Rev. A 72(3), 033817 (2005).
[Crossref]

Kim, H. T

I. Jong Kim, C. M Kim, H. T Kim, G. H Lee, Y. S. Lee, J. Y Park, D. J Cho, and C. H Nam, “Highly efficient high-harmonic generation in an orthogonally polarized two-color laser field,” Phys. Rev. Lett. 94(24), 243901 (2005).
[Crossref] [PubMed]

Kim, I. J.

C. M. Kim, I. J. Kim, and C. H. Nam, “Generation of a strong attosecond pulse train with an orthogonally polarized two-color laser field,” Phys. Rev. A 72(3), 033817 (2005).
[Crossref]

Kim, J.-H.

H. J. Shin, G. L. Dong, Y. H. Cha, J.-H. Kim, K. H. Hong, and C. H. Nam, “Nonadiabatic blueshift of high-order harmonics from Ar and Ne atoms in an intense femtosecond laser field,” Phys. Rev. A 63(5), 053407 (2001).
[Crossref]

J.-H. Kim, H. J. Shin, G. L. Dong, and C. H. Nam, “Enhanced spectral resolution of high-order harmonics by the coherent sum of dipole spectra,” Phys. Rev. A 62(5), 055402 (2000).
[Crossref]

Kitzler, M.

M. Kitzler and M. Lezius, “Spatial control of recollision wave packets with attosecond precision,” Phys. Rev. Lett. 95(25), 253001 (2005).
[Crossref] [PubMed]

Kovacev, M.

H. Merdji, M. Kovačev, W. Boutu, P. Salières, F. Vernay, and B. Carré, “Macroscopic control of high-order harmonics quantum-path components for the generation of attosecond pulses,” Phys. Rev. A 74(4), 043804 (2006).
[Crossref]

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft x-rays,” Science 302(5650), 1540–1543 (2003).
[Crossref] [PubMed]

Krainov, V. P.

M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and atomic ions in electromagnetic field,” Sov. Phys. JETP 64(3), 1191–1194 (1986).

Krausz, F.

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003).
[Crossref] [PubMed]

Kulander, K. C.

K. J. Schafer and K. C. Kulander, “High harmonic generation from ultrafast pump lasers,” Phys. Rev. Lett. 78(4), 638–641 (1997).
[Crossref]

L’Huillier, A.

M. Bellini, C. Lyngå, A. Tozzi, M. B. Gaarde, T. W. Hänsch, A. L’Huillier, and C. G. Wahlström, “Temporal coherence of ultrashort high-order harmonic pulses,” Phys. Rev. Lett. 81(2), 297–300 (1998).
[Crossref]

P. Salières, A. L’Huillier, and M. Lewenstein, “Coherence control of high-order harmonics,” Phys. Rev. Lett. 74(19), 3776–3779 (1995).
[Crossref] [PubMed]

M. Lewenstein, P. 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(3), 2117–2132 (1994).
[Crossref] [PubMed]

Lee, D. G.

H. J. Shin, D. G. Lee, Y. H. Cha, K. H. Hong, and C. H. Nam, “Generation of nonadiabatic blueshift of high harmonics in an intense femtosecond laser field,” Phys. Rev. Lett. 83(13), 2544–2547 (1999).
[Crossref]

Lee, G. H

I. Jong Kim, C. M Kim, H. T Kim, G. H Lee, Y. S. Lee, J. Y Park, D. J Cho, and C. H Nam, “Highly efficient high-harmonic generation in an orthogonally polarized two-color laser field,” Phys. Rev. Lett. 94(24), 243901 (2005).
[Crossref] [PubMed]

Lee, Y. S.

I. Jong Kim, C. M Kim, H. T Kim, G. H Lee, Y. S. Lee, J. Y Park, D. J Cho, and C. H Nam, “Highly efficient high-harmonic generation in an orthogonally polarized two-color laser field,” Phys. Rev. Lett. 94(24), 243901 (2005).
[Crossref] [PubMed]

Lewenstein, M.

P. Salières, A. L’Huillier, and M. Lewenstein, “Coherence control of high-order harmonics,” Phys. Rev. Lett. 74(19), 3776–3779 (1995).
[Crossref] [PubMed]

M. Lewenstein, P. 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(3), 2117–2132 (1994).
[Crossref] [PubMed]

Lezius, M.

M. Kitzler and M. Lezius, “Spatial control of recollision wave packets with attosecond precision,” Phys. Rev. Lett. 95(25), 253001 (2005).
[Crossref] [PubMed]

Li, R.

Y. Zheng, H. Diao, Z. Zeng, X. Ge, R. Li, and Z. Xu, “Manipulating electron-ion recollision in a midinfrared laser field,” Phys. Rev. A 92(3), 033417 (2015).
[Crossref]

Lyngå, C.

M. Bellini, C. Lyngå, A. Tozzi, M. B. Gaarde, T. W. Hänsch, A. L’Huillier, and C. G. Wahlström, “Temporal coherence of ultrashort high-order harmonic pulses,” Phys. Rev. Lett. 81(2), 297–300 (1998).
[Crossref]

Mairesse, Y.

D. Shafir, Y. Mairesse, D. M. Villeneuve, P. B. Corkum, and N. Dudovich, “Atomic wavefunctions probed through strong-field light–matter interaction,” Nat. Phys. 5(6), 412–416 (2009).
[Crossref]

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft x-rays,” Science 302(5650), 1540–1543 (2003).
[Crossref] [PubMed]

Marangos, J. P.

D. J. Hoffmann, C. Hutchison, A. Zaïr, and J. P. Marangos, “Control of temporal mapping and harmonic intensity modulation using two-color orthogonally polarized fields,” Phys. Rev. A 89(2), 023423 (2014).
[Crossref]

L. Brugnera, D. J. Hoffmann, T. Siegel, F. Frank, A. Zaïr, J. W. G. Tisch, and J. P. Marangos, “Trajectory selection in high harmonic generation by controlling the phase between orthogonal two-color fields,” Phys. Rev. Lett. 107(15), 153902 (2011).
[Crossref] [PubMed]

Merdji, H.

H. Merdji, M. Kovačev, W. Boutu, P. Salières, F. Vernay, and B. Carré, “Macroscopic control of high-order harmonics quantum-path components for the generation of attosecond pulses,” Phys. Rev. A 74(4), 043804 (2006).
[Crossref]

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft x-rays,” Science 302(5650), 1540–1543 (2003).
[Crossref] [PubMed]

Meyerhofer, D. D.

T. Ditmire, E. T. Gumbrell, R. A. Smith, J. W. G. Tisch, D. D. Meyerhofer, and M. H. R. Hutchinson, “Spatial coherence measurement of soft X-ray radiation produced by high order harmonic generation,” Phys. Rev. Lett. 77(23), 4756–4759 (1996).
[Crossref] [PubMed]

Monchicourt, P.

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft x-rays,” Science 302(5650), 1540–1543 (2003).
[Crossref] [PubMed]

Monmayrant, A.

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(14), 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. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft x-rays,” Science 302(5650), 1540–1543 (2003).
[Crossref] [PubMed]

Nam, C. H

I. Jong Kim, C. M Kim, H. T Kim, G. H Lee, Y. S. Lee, J. Y Park, D. J Cho, and C. H Nam, “Highly efficient high-harmonic generation in an orthogonally polarized two-color laser field,” Phys. Rev. Lett. 94(24), 243901 (2005).
[Crossref] [PubMed]

Nam, C. H.

C. M. Kim, I. J. Kim, and C. H. Nam, “Generation of a strong attosecond pulse train with an orthogonally polarized two-color laser field,” Phys. Rev. A 72(3), 033817 (2005).
[Crossref]

H. J. Shin, G. L. Dong, Y. H. Cha, J.-H. Kim, K. H. Hong, and C. H. Nam, “Nonadiabatic blueshift of high-order harmonics from Ar and Ne atoms in an intense femtosecond laser field,” Phys. Rev. A 63(5), 053407 (2001).
[Crossref]

J.-H. Kim, H. J. Shin, G. L. Dong, and C. H. Nam, “Enhanced spectral resolution of high-order harmonics by the coherent sum of dipole spectra,” Phys. Rev. A 62(5), 055402 (2000).
[Crossref]

H. J. Shin, D. G. Lee, Y. H. Cha, K. H. Hong, and C. H. Nam, “Generation of nonadiabatic blueshift of high harmonics in an intense femtosecond laser field,” Phys. Rev. Lett. 83(13), 2544–2547 (1999).
[Crossref]

Niikura, H.

H. Niikura, H. J. Wörner, D. M. Villeneuve, and P. B. Corkum, “Probing the spatial structure of a molecular attosecond electron wave packet using shaped recollision trajectories,” Phys. Rev. Lett. 107(9), 093004 (2011).
[Crossref] [PubMed]

Park, J. Y

I. Jong Kim, C. M Kim, H. T Kim, G. H Lee, Y. S. Lee, J. Y Park, D. J Cho, and C. H Nam, “Highly efficient high-harmonic generation in an orthogonally polarized two-color laser field,” Phys. Rev. Lett. 94(24), 243901 (2005).
[Crossref] [PubMed]

Rae, S. C.

S. C. Rae and K. Burnett, “Detailed simulations of plasma-induced spectral blueshifting,” Phys. Rev. A 46(2), 1084–1090 (1992).
[Crossref] [PubMed]

Salières, 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(14), 143902 (2008).
[Crossref] [PubMed]

H. Merdji, M. Kovačev, W. Boutu, P. Salières, F. Vernay, and B. Carré, “Macroscopic control of high-order harmonics quantum-path components for the generation of attosecond pulses,” Phys. Rev. A 74(4), 043804 (2006).
[Crossref]

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft x-rays,” Science 302(5650), 1540–1543 (2003).
[Crossref] [PubMed]

P. Salières, A. L’Huillier, and M. Lewenstein, “Coherence control of high-order harmonics,” Phys. Rev. Lett. 74(19), 3776–3779 (1995).
[Crossref] [PubMed]

Sanpera, A.

J. B. Watson, A. Sanpera, and K. Burnett, “Pulse-shape effects and blueshifting in the single-atom harmonic generation from neutral species and ions,” Phys. Rev. A 51(2), 1458–1463 (1995).
[Crossref] [PubMed]

Schafer, K. J.

M. B. Gaarde and K. J. Schafer, “Quantum path distributions for high-order harmonics in rare gas atoms,” Phys. Rev. A 65(3), 031406 (2002).
[Crossref]

K. J. Schafer and K. C. Kulander, “High harmonic generation from ultrafast pump lasers,” Phys. Rev. Lett. 78(4), 638–641 (1997).
[Crossref]

Schapper, F.

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(14), 143902 (2008).
[Crossref] [PubMed]

Scrinzi, A.

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003).
[Crossref] [PubMed]

Shafir, D.

D. Shafir, Y. Mairesse, D. M. Villeneuve, P. B. Corkum, and N. Dudovich, “Atomic wavefunctions probed through strong-field light–matter interaction,” Nat. Phys. 5(6), 412–416 (2009).
[Crossref]

Shin, H. J.

H. J. Shin, G. L. Dong, Y. H. Cha, J.-H. Kim, K. H. Hong, and C. H. Nam, “Nonadiabatic blueshift of high-order harmonics from Ar and Ne atoms in an intense femtosecond laser field,” Phys. Rev. A 63(5), 053407 (2001).
[Crossref]

J.-H. Kim, H. J. Shin, G. L. Dong, and C. H. Nam, “Enhanced spectral resolution of high-order harmonics by the coherent sum of dipole spectra,” Phys. Rev. A 62(5), 055402 (2000).
[Crossref]

H. J. Shin, D. G. Lee, Y. H. Cha, K. H. Hong, and C. H. Nam, “Generation of nonadiabatic blueshift of high harmonics in an intense femtosecond laser field,” Phys. Rev. Lett. 83(13), 2544–2547 (1999).
[Crossref]

Siders, C. W.

W. M. Wood, C. W. Siders, and M. C. Downer, “Measurement of femtosecond ionization dynamics of atmospheric density gases by spectral blueshifting,” Phys. Rev. Lett. 67(25), 3523–3526 (1991).
[Crossref] [PubMed]

Siegel, T.

L. Brugnera, D. J. Hoffmann, T. Siegel, F. Frank, A. Zaïr, J. W. G. Tisch, and J. P. Marangos, “Trajectory selection in high harmonic generation by controlling the phase between orthogonal two-color fields,” Phys. Rev. Lett. 107(15), 153902 (2011).
[Crossref] [PubMed]

Smith, R. A.

T. Ditmire, E. T. Gumbrell, R. A. Smith, J. W. G. Tisch, D. D. Meyerhofer, and M. H. R. Hutchinson, “Spatial coherence measurement of soft X-ray radiation produced by high order harmonic generation,” Phys. Rev. Lett. 77(23), 4756–4759 (1996).
[Crossref] [PubMed]

Taïeb, R.

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft x-rays,” Science 302(5650), 1540–1543 (2003).
[Crossref] [PubMed]

Tempea, G.

M. Geissler, G. Tempea, and T. Brabec, “Phase-matched high-order harmonic generation in the nonadiabatic limit,” Phys. Rev. A 62(3), 033817 (2000).
[Crossref]

Tisch, J. W. G.

L. Brugnera, D. J. Hoffmann, T. Siegel, F. Frank, A. Zaïr, J. W. G. Tisch, and J. P. Marangos, “Trajectory selection in high harmonic generation by controlling the phase between orthogonal two-color fields,” Phys. Rev. Lett. 107(15), 153902 (2011).
[Crossref] [PubMed]

T. Ditmire, E. T. Gumbrell, R. A. Smith, J. W. G. Tisch, D. D. Meyerhofer, and M. H. R. Hutchinson, “Spatial coherence measurement of soft X-ray radiation produced by high order harmonic generation,” Phys. Rev. Lett. 77(23), 4756–4759 (1996).
[Crossref] [PubMed]

Tong, X.-M.

X.-M. Tong and S.-I. Chu, “Probing the spectral and temporal structures of high-order harmonic generation in intense laser pulses,” Phys. Rev. A 61(2), 021802 (2000).
[Crossref]

Tozzi, A.

M. Bellini, C. Lyngå, A. Tozzi, M. B. Gaarde, T. W. Hänsch, A. L’Huillier, and C. G. Wahlström, “Temporal coherence of ultrashort high-order harmonic pulses,” Phys. Rev. Lett. 81(2), 297–300 (1998).
[Crossref]

Udem, T.

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003).
[Crossref] [PubMed]

Uiberacker, M.

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003).
[Crossref] [PubMed]

Vernay, F.

H. Merdji, M. Kovačev, W. Boutu, P. Salières, F. Vernay, and B. Carré, “Macroscopic control of high-order harmonics quantum-path components for the generation of attosecond pulses,” Phys. Rev. A 74(4), 043804 (2006).
[Crossref]

Villeneuve, D. M.

H. Niikura, H. J. Wörner, D. M. Villeneuve, and P. B. Corkum, “Probing the spatial structure of a molecular attosecond electron wave packet using shaped recollision trajectories,” Phys. Rev. Lett. 107(9), 093004 (2011).
[Crossref] [PubMed]

D. Shafir, Y. Mairesse, D. M. Villeneuve, P. B. Corkum, and N. Dudovich, “Atomic wavefunctions probed through strong-field light–matter interaction,” Nat. Phys. 5(6), 412–416 (2009).
[Crossref]

Wahlström, C. G.

M. Bellini, C. Lyngå, A. Tozzi, M. B. Gaarde, T. W. Hänsch, A. L’Huillier, and C. G. Wahlström, “Temporal coherence of ultrashort high-order harmonic pulses,” Phys. Rev. Lett. 81(2), 297–300 (1998).
[Crossref]

Walmsley, I. A.

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(14), 143902 (2008).
[Crossref] [PubMed]

Wang, H.

H. Du, S. Xue, H. Wang, Z. Zhang, and B. Hu, “Nonadiabatic spectral redshift of h- igh-order harmonics with the help of a VUV pulse,” Phys. Rev. A 91(6), 063844 (2015).
[Crossref]

Watson, J. B.

J. B. Watson, A. Sanpera, and K. Burnett, “Pulse-shape effects and blueshifting in the single-atom harmonic generation from neutral species and ions,” Phys. Rev. A 51(2), 1458–1463 (1995).
[Crossref] [PubMed]

Wood, W. M.

W. M. Wood, C. W. Siders, and M. C. Downer, “Measurement of femtosecond ionization dynamics of atmospheric density gases by spectral blueshifting,” Phys. Rev. Lett. 67(25), 3523–3526 (1991).
[Crossref] [PubMed]

Wörner, H. J.

H. Niikura, H. J. Wörner, D. M. Villeneuve, and P. B. Corkum, “Probing the spatial structure of a molecular attosecond electron wave packet using shaped recollision trajectories,” Phys. Rev. Lett. 107(9), 093004 (2011).
[Crossref] [PubMed]

Wyatt, A. S.

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(14), 143902 (2008).
[Crossref] [PubMed]

Xu, J.

J. Xu, “Isolated short attosecond pulse generation in an orthogonally polarized multicycle chirped laser field,” Phys. Rev. A 83(3), 033823 (2011).
[Crossref]

Xu, Z.

Y. Zheng, H. Diao, Z. Zeng, X. Ge, R. Li, and Z. Xu, “Manipulating electron-ion recollision in a midinfrared laser field,” Phys. Rev. A 92(3), 033417 (2015).
[Crossref]

Xue, S.

H. Du, S. Xue, H. Wang, Z. Zhang, and B. Hu, “Nonadiabatic spectral redshift of h- igh-order harmonics with the help of a VUV pulse,” Phys. Rev. A 91(6), 063844 (2015).
[Crossref]

Yakovlev, V. S.

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003).
[Crossref] [PubMed]

Zaïr, A.

D. J. Hoffmann, C. Hutchison, A. Zaïr, and J. P. Marangos, “Control of temporal mapping and harmonic intensity modulation using two-color orthogonally polarized fields,” Phys. Rev. A 89(2), 023423 (2014).
[Crossref]

L. Brugnera, D. J. Hoffmann, T. Siegel, F. Frank, A. Zaïr, J. W. G. Tisch, and J. P. Marangos, “Trajectory selection in high harmonic generation by controlling the phase between orthogonal two-color fields,” Phys. Rev. Lett. 107(15), 153902 (2011).
[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(14), 143902 (2008).
[Crossref] [PubMed]

Zeng, Z.

Y. Zheng, H. Diao, Z. Zeng, X. Ge, R. Li, and Z. Xu, “Manipulating electron-ion recollision in a midinfrared laser field,” Phys. Rev. A 92(3), 033417 (2015).
[Crossref]

Zhang, Z.

H. Du, S. Xue, H. Wang, Z. Zhang, and B. Hu, “Nonadiabatic spectral redshift of h- igh-order harmonics with the help of a VUV pulse,” Phys. Rev. A 91(6), 063844 (2015).
[Crossref]

Zheng, Y.

Y. Zheng, H. Diao, Z. Zeng, X. Ge, R. Li, and Z. Xu, “Manipulating electron-ion recollision in a midinfrared laser field,” Phys. Rev. A 92(3), 033417 (2015).
[Crossref]

Nat. Phys. (1)

D. Shafir, Y. Mairesse, D. M. Villeneuve, P. B. Corkum, and N. Dudovich, “Atomic wavefunctions probed through strong-field light–matter interaction,” Nat. Phys. 5(6), 412–416 (2009).
[Crossref]

Nature (1)

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003).
[Crossref] [PubMed]

Phys. Rev. A (14)

H. J. Shin, G. L. Dong, Y. H. Cha, J.-H. Kim, K. H. Hong, and C. H. Nam, “Nonadiabatic blueshift of high-order harmonics from Ar and Ne atoms in an intense femtosecond laser field,” Phys. Rev. A 63(5), 053407 (2001).
[Crossref]

J. B. Watson, A. Sanpera, and K. Burnett, “Pulse-shape effects and blueshifting in the single-atom harmonic generation from neutral species and ions,” Phys. Rev. A 51(2), 1458–1463 (1995).
[Crossref] [PubMed]

H. Merdji, M. Kovačev, W. Boutu, P. Salières, F. Vernay, and B. Carré, “Macroscopic control of high-order harmonics quantum-path components for the generation of attosecond pulses,” Phys. Rev. A 74(4), 043804 (2006).
[Crossref]

Y. Zheng, H. Diao, Z. Zeng, X. Ge, R. Li, and Z. Xu, “Manipulating electron-ion recollision in a midinfrared laser field,” Phys. Rev. A 92(3), 033417 (2015).
[Crossref]

J.-H. Kim, H. J. Shin, G. L. Dong, and C. H. Nam, “Enhanced spectral resolution of high-order harmonics by the coherent sum of dipole spectra,” Phys. Rev. A 62(5), 055402 (2000).
[Crossref]

M. B. Gaarde and K. J. Schafer, “Quantum path distributions for high-order harmonics in rare gas atoms,” Phys. Rev. A 65(3), 031406 (2002).
[Crossref]

J. Xu, “Isolated short attosecond pulse generation in an orthogonally polarized multicycle chirped laser field,” Phys. Rev. A 83(3), 033823 (2011).
[Crossref]

M. Lewenstein, P. 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(3), 2117–2132 (1994).
[Crossref] [PubMed]

X.-M. Tong and S.-I. Chu, “Probing the spectral and temporal structures of high-order harmonic generation in intense laser pulses,” Phys. Rev. A 61(2), 021802 (2000).
[Crossref]

M. Geissler, G. Tempea, and T. Brabec, “Phase-matched high-order harmonic generation in the nonadiabatic limit,” Phys. Rev. A 62(3), 033817 (2000).
[Crossref]

H. Du, S. Xue, H. Wang, Z. Zhang, and B. Hu, “Nonadiabatic spectral redshift of h- igh-order harmonics with the help of a VUV pulse,” Phys. Rev. A 91(6), 063844 (2015).
[Crossref]

S. C. Rae and K. Burnett, “Detailed simulations of plasma-induced spectral blueshifting,” Phys. Rev. A 46(2), 1084–1090 (1992).
[Crossref] [PubMed]

D. J. Hoffmann, C. Hutchison, A. Zaïr, and J. P. Marangos, “Control of temporal mapping and harmonic intensity modulation using two-color orthogonally polarized fields,” Phys. Rev. A 89(2), 023423 (2014).
[Crossref]

C. M. Kim, I. J. Kim, and C. H. Nam, “Generation of a strong attosecond pulse train with an orthogonally polarized two-color laser field,” Phys. Rev. A 72(3), 033817 (2005).
[Crossref]

Phys. Rev. Lett. (12)

L. Brugnera, D. J. Hoffmann, T. Siegel, F. Frank, A. Zaïr, J. W. G. Tisch, and J. P. Marangos, “Trajectory selection in high harmonic generation by controlling the phase between orthogonal two-color fields,” Phys. Rev. Lett. 107(15), 153902 (2011).
[Crossref] [PubMed]

W. M. Wood, C. W. Siders, and M. C. Downer, “Measurement of femtosecond ionization dynamics of atmospheric density gases by spectral blueshifting,” Phys. Rev. Lett. 67(25), 3523–3526 (1991).
[Crossref] [PubMed]

H. J. Shin, D. G. Lee, Y. H. Cha, K. H. Hong, and C. H. Nam, “Generation of nonadiabatic blueshift of high harmonics in an intense femtosecond laser field,” Phys. Rev. Lett. 83(13), 2544–2547 (1999).
[Crossref]

P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71(13), 1994–1997 (1993).
[Crossref] [PubMed]

H. Niikura, H. J. Wörner, D. M. Villeneuve, and P. B. Corkum, “Probing the spatial structure of a molecular attosecond electron wave packet using shaped recollision trajectories,” Phys. Rev. Lett. 107(9), 093004 (2011).
[Crossref] [PubMed]

M. Kitzler and M. Lezius, “Spatial control of recollision wave packets with attosecond precision,” Phys. Rev. Lett. 95(25), 253001 (2005).
[Crossref] [PubMed]

T. Ditmire, E. T. Gumbrell, R. A. Smith, J. W. G. Tisch, D. D. Meyerhofer, and M. H. R. Hutchinson, “Spatial coherence measurement of soft X-ray radiation produced by high order harmonic generation,” Phys. Rev. Lett. 77(23), 4756–4759 (1996).
[Crossref] [PubMed]

M. Bellini, C. Lyngå, A. Tozzi, M. B. Gaarde, T. W. Hänsch, A. L’Huillier, and C. G. Wahlström, “Temporal coherence of ultrashort high-order harmonic pulses,” Phys. Rev. Lett. 81(2), 297–300 (1998).
[Crossref]

P. Salières, A. L’Huillier, and M. Lewenstein, “Coherence control of high-order harmonics,” Phys. Rev. Lett. 74(19), 3776–3779 (1995).
[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(14), 143902 (2008).
[Crossref] [PubMed]

I. Jong Kim, C. M Kim, H. T Kim, G. H Lee, Y. S. Lee, J. Y Park, D. J Cho, and C. H Nam, “Highly efficient high-harmonic generation in an orthogonally polarized two-color laser field,” Phys. Rev. Lett. 94(24), 243901 (2005).
[Crossref] [PubMed]

K. J. Schafer and K. C. Kulander, “High harmonic generation from ultrafast pump lasers,” Phys. Rev. Lett. 78(4), 638–641 (1997).
[Crossref]

Science (1)

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft x-rays,” Science 302(5650), 1540–1543 (2003).
[Crossref] [PubMed]

Sov. Phys. JETP (1)

M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and atomic ions in electromagnetic field,” Sov. Phys. JETP 64(3), 1191–1194 (1986).

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Figures (5)

Fig. 1
Fig. 1 Schematic diagram of the MIR-OTC experiment. SM: silver mirror; CM: concave mirror; BBO: barium borate crystal; CCD: charge coupled device.
Fig. 2
Fig. 2 Experimental harmonic spectra as a function of the two-color delay ranging from −20fs~20fs (a) and its enlarged spectra 0.4fs~1fs (b) obtained by the MIR-OTC scheme from Ar. The dashed black lines indicate the unshifted harmonic positions on the CCD camera, while the solid black lines indicate the spectral centers of each harmonic at different time delays. Harmonic spectra around H52 (c) and the relative spectral shifts of H52 (d) at delay A, delay B, delay C, delay D and delay E, corresponding to the time delays of 0.145T,0.135T,0.125T,0.115T and 0.105T,respectively. Note that the experimental spectral shifts of H52 in (d) are obtained by taking the spectrum of delay C as a reference.
Fig. 3
Fig. 3 The time frequency distribution of HHG at five different time delays (a) delay A(0.145T); (b) delay B(0.135T); (c) delay C(0.125T); (d) delay D(0.115T); (e) delay E(0.105T), respectively.
Fig. 4
Fig. 4 (a) Laser intensities of the synthesized pulses of the OTC field (solid red line), the fundamental pulse (dashed blue line), and the SH pulse (dashed black line) when the delay is 0.125T. (b) The calculated nonadiabatic spectral shift corresponding to the laser pulse in Fig. 4(a). (c) The relative spectral shifts of H52 obtained by simulation (blue line) and experiment (red line, the same as in Fig. 2 (d)). It is worth noting that both the experimental and the simulated relative spectral shifts are obtained by taking the spectrum at delay C as the reference.
Fig. 5
Fig. 5 (a)Calculated average emission times of different harmonic orders at delay B (blue line), delay C (red line) and delay D (green line). (b)The order dependence of relative spectral shifts obtained by experimental results at delay B (solid blue line) and delay D (solid green line), calculated relative spectral shifts with considering the propagation effect and the nonadiabatic effect at delay B (dashed blue line) and delay D (dashed green line).Noteworthy is the fact that both the experimental and the theoretical relative spectral shifts are obtained by taking the spectrum at delay C as the reference.

Equations (15)

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δ n e e 2 2 ε 0 m ω 2 N e ,
Δ ω 1 , e ( t , τ ) = 2 π L λ 1 d ( δ n e ) d t = λ 1 e 2 L ρ 0 4 π ε 0 m c 2 n e ( t , τ ) t λ 1 e 2 L ρ 0 4 π ε 0 m c 2 n e ( t , τ ) τ p ,
Δ ω t o t , e = q Δ ω 1 , e + Δ ω q ( q + 1 q ) Δ ω 1 , e ( t , τ ) .
δ n a e 2 2 ε 0 m N a ω r 2 ω 2 ,
Δ ω 1 , a ( t , τ ) = 2 π L λ 1 d ( δ n a ) d t = π e 2 ρ 0 L ε 0 m λ 1 1 ω r 2 ω 1 2 n e t ,
Δ ω q , a ( t , τ ) = π e 2 ρ 0 L ε 0 m λ q 1 ω r 2 ω q 2 n e t ,
Δ ω t o t , a = q Δ ω 1 , a + Δ ω q , a λ 1 e 2 L ρ 0 4 π ε 0 m c 2 ( q ( ω r ω 1 ) 2 1 + q ( ω r ω 1 ) 2 q 2 ) n e ( t , τ ) t ,
Δ ω t o t , q = Δ ω t o t , e + Δ ω t o t , a λ 1 e 2 L ρ 0 4 π ε 0 m c 2 n e ( t , τ ) τ p ( q + 1 q + q ( ω r ω 1 ) 2 1 + q ( ω r ω 1 ) 2 q 2 ) .
E s ( t ) = E x f ( t ) cos ( ω t ) x + E y f ( t + τ ) cos [ 2 ω ( t + τ ) ] y ,
S ( t q , r ) = 1 t q , i t q , r d t [ 1 2 m ( v x ( t ) 2 + v y ( t ) 2 ) + I p ] .
ϕ int = S α q , i I s ,
Δ ω int ( q , τ ) α q , i d I s d t ,
t q , e = | A ( t , q ω 1 ) | 2 t d t | A ( t , q ω 1 ) | 2 d t ,
Δ ω int ( q , τ ) α q , i d I s d t | t = t q , e .
A ( t , ω ) = d h ' ' ( t ' ) W t , ω ( t ' ) d t ' ,

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