Abstract

Attosecond angular streaking is a new technique to achieve unsurpassed time accuracy of only a few attoseconds. Recently this has been successfully used to set an upper limit on the electron tunneling delay time in strong laser field ionization. The measurement technique can be modeled with either the time-dependent Schrödinger equation (TDSE) or a more simple semiclassical approach that describes the process in two steps in analogy to the three-step model in high harmonic generation (HHG): step one is the tunnel ionization and step two is the classical motion in the strong laser field. Here we describe in detail a semiclassical model which is based on the ADK theory for the tunneling step, with subsequent classical propagation of the electron in the laser field. We take into account different ellipticities of the laser field and a possible wavelength-dependent ellipticity that is typically observed for pulses in the two-optical-cycle regime. This semiclassical model shows excellent agreement with the experimental result.

© 2010 OSA

Full Article  |  PDF Article

Corrections

M. Smolarski, P. Eckle, U. Keller, and R. Dörner, "Semiclassical model for attosecond angular streaking: errata," Opt. Express 19, 25319-25319 (2011)
https://www.osapublishing.org/oe/abstract.cfm?uri=oe-19-25-25319

References

  • View by:
  • |
  • |
  • |

  1. L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Soviet Phys. JETP 20, 1307 (1965).
  2. H. R. Reiss, “Limits on tunneling theories of strong-field ionization,” Phys. Rev. Lett. 101(4), 043002 (2008).
    [CrossRef] [PubMed]
  3. P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71(13), 1994–1997 (1993).
    [CrossRef] [PubMed]
  4. H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69(4), 327–332 (1999).
    [CrossRef]
  5. G. G. Paulus, ““A Meter of the “Absolute” Phase of Few-Cycle Laser Pulses,” Laser Phys. 15, 843–854 (2005).
  6. P. Dietrich, F. Krausz, and P. B. Corkum, “Determining the absolute carrier phase of a few-cycle laser pulse,” Opt. Lett. 25(1), 16–18 (2000).
    [CrossRef]
  7. P. Eckle, M. Smolarski, P. Schlup, J. Biegert, A. Staudte, M. Schöffler, H. G. Muller, R. Dörner, and U. Keller, “Attosecond angular streaking,” Nat. Phys. 4(7), 565–570 (2008).
    [CrossRef]
  8. C. Smeenk, L. Arissian, A. Staudte, D. M. Villeneuve, and P. B. Corkum, “Momentum space tomographic imaging of photoelectrons,” J. Phys. B 42(18), 185402 (2009).
    [CrossRef]
  9. R. P. Feynman, “Space-Time Approach to Non-Relativistic Quantum Mechanics,” Rev. Mod. Phys. 20(2), 367–387 (1948).
    [CrossRef]
  10. P. Salières, B. Carré, L. Le Déroff, F. Grasbon, G. G. Paulus, H. Walther, R. Kopold, W. Becker, D. B. Milosević, A. Sanpera, and M. Lewenstein, “Feynman’s path-integral approach for intense-laser-atom interactions,” Science 292(5518), 902–905 (2001).
    [CrossRef] [PubMed]
  11. M. V. Ammosov, N. B. Delone, and V. P. Kraĭnov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64, 1191–1194 (1986).
  12. T. Gabriel, “Dispersion-Free Reflective Phase Retarder for Few-Cycle Femtosecond Pulses”, Paper FB6, Optical Interference Coatings Topical Meeting, Tuscon (AZ), June 6–11 2010.
  13. R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68(9), 3277–3295 (1997).
    [CrossRef]
  14. C. Iaconis and I. A. Walmsley, “Self-Referencing Spectral Interferometry for Measuring Ultrashort Optical Pulses,” IEEE J. Quantum Electron. 35(4), 501–509 (1999).
    [CrossRef]
  15. M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, M. Lenzner, C. Spielmann, and F. Krausz, “A novel high-energy pulse compression system: generation of multigigawatt sub-5-fs pulses,” Appl. Phys. B 65(2), 189–196 (1997).
    [CrossRef]
  16. C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79(6), 673–677 (2004).
    [CrossRef]
  17. G. Szivessy and C. Münster, “Über die Prüfung der Gitteroptik bei aktiven Kristallen,” Ann. Phys. 412(7), 703–736 (1934).
    [CrossRef]
  18. S. C. McClain, L. W. Hillman, and R. A. Chipman, “Polarization ray tracing in anisotropic optically active media. I. Algorithms,” J. Opt. Soc. Am. 10(11), 2371–2382 (1993).
    [CrossRef]
  19. S. C. McClain, L. W. Hillman, and R. A. Chipman, “Polarization ray tracing in anisotropic optically active media. II. Theory and physics,” J. Opt. Soc. Am. A 10(11), 2383–2393 (1993).
    [CrossRef]
  20. E. D. Palik, “Handbook of Optical Constants of Solids,” (Academic Press, 1985).
  21. M. J. Dodge, “Refractive properties of magnesium fluoride,” Appl. Opt. 23(12), 1980–1985 (1984).
    [CrossRef] [PubMed]
  22. P. Antoine, A. L’Huillier, M. Lewenstein, P. Salières, and B. Carré, “Theory of high-order harmonic generation by an elliptically polarized laser field,” Phys. Rev. A 53(3), 1725–1745 (1996).
    [CrossRef] [PubMed]
  23. N. B. Delone and V. P. Krainov, “Energy and angular electron spectra for the tunnel ionization of atoms by strong low-frequency radiation,” J. Opt. Soc. Am. B 8(6), 1207–1211 (1991).
    [CrossRef]
  24. H. R. Schwarz, “Numerische Mathematik,” B. G. Teubner, ed. (Verlag, 1997).
  25. M. Uiberacker, Th. Uphues, M. Schultze, A. J. Verhoef, V. Yakovlev, M. F. Kling, J. Rauschenberger, N. M. Kabachnik, H. Schröder, M. Lezius, K. L. Kompa, H.-G. Muller, M. J. J. Vrakking, S. Hendel, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond real-time observation of electron tunnelling in atoms,” Nature 446(7136), 627–632 (2007).
    [CrossRef] [PubMed]
  26. C. M. Maharjan, A. S. Alnaser, X. M. Tong, B. Ulrich, P. Ranitovic, S. Ghimire, Z. Chang, I. V. Litvinyuk, and C. L. Cocke, “Momentum imaging of doubly charged ions of Ne and Ar in the sequential ionization region,” Phys. Rev. A 72, 041403(R) (2005)
    [CrossRef]
  27. X. M. Tong and C. D. Lin, “Empirical formula for statistic field ionization rates of atoms and molecules by lasers in the barrier-suppression regime,” J. Phys. B 38(15), 2593–2600 (2005).
    [CrossRef]

2009 (1)

C. Smeenk, L. Arissian, A. Staudte, D. M. Villeneuve, and P. B. Corkum, “Momentum space tomographic imaging of photoelectrons,” J. Phys. B 42(18), 185402 (2009).
[CrossRef]

2008 (2)

H. R. Reiss, “Limits on tunneling theories of strong-field ionization,” Phys. Rev. Lett. 101(4), 043002 (2008).
[CrossRef] [PubMed]

P. Eckle, M. Smolarski, P. Schlup, J. Biegert, A. Staudte, M. Schöffler, H. G. Muller, R. Dörner, and U. Keller, “Attosecond angular streaking,” Nat. Phys. 4(7), 565–570 (2008).
[CrossRef]

2007 (1)

M. Uiberacker, Th. Uphues, M. Schultze, A. J. Verhoef, V. Yakovlev, M. F. Kling, J. Rauschenberger, N. M. Kabachnik, H. Schröder, M. Lezius, K. L. Kompa, H.-G. Muller, M. J. J. Vrakking, S. Hendel, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond real-time observation of electron tunnelling in atoms,” Nature 446(7136), 627–632 (2007).
[CrossRef] [PubMed]

2005 (3)

C. M. Maharjan, A. S. Alnaser, X. M. Tong, B. Ulrich, P. Ranitovic, S. Ghimire, Z. Chang, I. V. Litvinyuk, and C. L. Cocke, “Momentum imaging of doubly charged ions of Ne and Ar in the sequential ionization region,” Phys. Rev. A 72, 041403(R) (2005)
[CrossRef]

X. M. Tong and C. D. Lin, “Empirical formula for statistic field ionization rates of atoms and molecules by lasers in the barrier-suppression regime,” J. Phys. B 38(15), 2593–2600 (2005).
[CrossRef]

G. G. Paulus, ““A Meter of the “Absolute” Phase of Few-Cycle Laser Pulses,” Laser Phys. 15, 843–854 (2005).

2004 (1)

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79(6), 673–677 (2004).
[CrossRef]

2001 (1)

P. Salières, B. Carré, L. Le Déroff, F. Grasbon, G. G. Paulus, H. Walther, R. Kopold, W. Becker, D. B. Milosević, A. Sanpera, and M. Lewenstein, “Feynman’s path-integral approach for intense-laser-atom interactions,” Science 292(5518), 902–905 (2001).
[CrossRef] [PubMed]

2000 (1)

1999 (2)

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69(4), 327–332 (1999).
[CrossRef]

C. Iaconis and I. A. Walmsley, “Self-Referencing Spectral Interferometry for Measuring Ultrashort Optical Pulses,” IEEE J. Quantum Electron. 35(4), 501–509 (1999).
[CrossRef]

1997 (2)

M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, M. Lenzner, C. Spielmann, and F. Krausz, “A novel high-energy pulse compression system: generation of multigigawatt sub-5-fs pulses,” Appl. Phys. B 65(2), 189–196 (1997).
[CrossRef]

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68(9), 3277–3295 (1997).
[CrossRef]

1996 (1)

P. Antoine, A. L’Huillier, M. Lewenstein, P. Salières, and B. Carré, “Theory of high-order harmonic generation by an elliptically polarized laser field,” Phys. Rev. A 53(3), 1725–1745 (1996).
[CrossRef] [PubMed]

1993 (3)

S. C. McClain, L. W. Hillman, and R. A. Chipman, “Polarization ray tracing in anisotropic optically active media. I. Algorithms,” J. Opt. Soc. Am. 10(11), 2371–2382 (1993).
[CrossRef]

S. C. McClain, L. W. Hillman, and R. A. Chipman, “Polarization ray tracing in anisotropic optically active media. II. Theory and physics,” J. Opt. Soc. Am. A 10(11), 2383–2393 (1993).
[CrossRef]

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

1991 (1)

1986 (1)

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

1984 (1)

1965 (1)

L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Soviet Phys. JETP 20, 1307 (1965).

1948 (1)

R. P. Feynman, “Space-Time Approach to Non-Relativistic Quantum Mechanics,” Rev. Mod. Phys. 20(2), 367–387 (1948).
[CrossRef]

1934 (1)

G. Szivessy and C. Münster, “Über die Prüfung der Gitteroptik bei aktiven Kristallen,” Ann. Phys. 412(7), 703–736 (1934).
[CrossRef]

Alnaser, A. S.

C. M. Maharjan, A. S. Alnaser, X. M. Tong, B. Ulrich, P. Ranitovic, S. Ghimire, Z. Chang, I. V. Litvinyuk, and C. L. Cocke, “Momentum imaging of doubly charged ions of Ne and Ar in the sequential ionization region,” Phys. Rev. A 72, 041403(R) (2005)
[CrossRef]

Ammosov, M. V.

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

Antoine, P.

P. Antoine, A. L’Huillier, M. Lewenstein, P. Salières, and B. Carré, “Theory of high-order harmonic generation by an elliptically polarized laser field,” Phys. Rev. A 53(3), 1725–1745 (1996).
[CrossRef] [PubMed]

Arissian, L.

C. Smeenk, L. Arissian, A. Staudte, D. M. Villeneuve, and P. B. Corkum, “Momentum space tomographic imaging of photoelectrons,” J. Phys. B 42(18), 185402 (2009).
[CrossRef]

Becker, W.

P. Salières, B. Carré, L. Le Déroff, F. Grasbon, G. G. Paulus, H. Walther, R. Kopold, W. Becker, D. B. Milosević, A. Sanpera, and M. Lewenstein, “Feynman’s path-integral approach for intense-laser-atom interactions,” Science 292(5518), 902–905 (2001).
[CrossRef] [PubMed]

Biegert, J.

P. Eckle, M. Smolarski, P. Schlup, J. Biegert, A. Staudte, M. Schöffler, H. G. Muller, R. Dörner, and U. Keller, “Attosecond angular streaking,” Nat. Phys. 4(7), 565–570 (2008).
[CrossRef]

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79(6), 673–677 (2004).
[CrossRef]

Carré, B.

P. Salières, B. Carré, L. Le Déroff, F. Grasbon, G. G. Paulus, H. Walther, R. Kopold, W. Becker, D. B. Milosević, A. Sanpera, and M. Lewenstein, “Feynman’s path-integral approach for intense-laser-atom interactions,” Science 292(5518), 902–905 (2001).
[CrossRef] [PubMed]

P. Antoine, A. L’Huillier, M. Lewenstein, P. Salières, and B. Carré, “Theory of high-order harmonic generation by an elliptically polarized laser field,” Phys. Rev. A 53(3), 1725–1745 (1996).
[CrossRef] [PubMed]

Chang, Z.

C. M. Maharjan, A. S. Alnaser, X. M. Tong, B. Ulrich, P. Ranitovic, S. Ghimire, Z. Chang, I. V. Litvinyuk, and C. L. Cocke, “Momentum imaging of doubly charged ions of Ne and Ar in the sequential ionization region,” Phys. Rev. A 72, 041403(R) (2005)
[CrossRef]

Cheng, Z.

M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, M. Lenzner, C. Spielmann, and F. Krausz, “A novel high-energy pulse compression system: generation of multigigawatt sub-5-fs pulses,” Appl. Phys. B 65(2), 189–196 (1997).
[CrossRef]

Chipman, R. A.

S. C. McClain, L. W. Hillman, and R. A. Chipman, “Polarization ray tracing in anisotropic optically active media. I. Algorithms,” J. Opt. Soc. Am. 10(11), 2371–2382 (1993).
[CrossRef]

S. C. McClain, L. W. Hillman, and R. A. Chipman, “Polarization ray tracing in anisotropic optically active media. II. Theory and physics,” J. Opt. Soc. Am. A 10(11), 2383–2393 (1993).
[CrossRef]

Cocke, C. L.

C. M. Maharjan, A. S. Alnaser, X. M. Tong, B. Ulrich, P. Ranitovic, S. Ghimire, Z. Chang, I. V. Litvinyuk, and C. L. Cocke, “Momentum imaging of doubly charged ions of Ne and Ar in the sequential ionization region,” Phys. Rev. A 72, 041403(R) (2005)
[CrossRef]

Corkum, P. B.

C. Smeenk, L. Arissian, A. Staudte, D. M. Villeneuve, and P. B. Corkum, “Momentum space tomographic imaging of photoelectrons,” J. Phys. B 42(18), 185402 (2009).
[CrossRef]

P. Dietrich, F. Krausz, and P. B. Corkum, “Determining the absolute carrier phase of a few-cycle laser pulse,” Opt. Lett. 25(1), 16–18 (2000).
[CrossRef]

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

Couairon, A.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79(6), 673–677 (2004).
[CrossRef]

De Silvestri, S.

M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, M. Lenzner, C. Spielmann, and F. Krausz, “A novel high-energy pulse compression system: generation of multigigawatt sub-5-fs pulses,” Appl. Phys. B 65(2), 189–196 (1997).
[CrossRef]

Delone, N. B.

N. B. Delone and V. P. Krainov, “Energy and angular electron spectra for the tunnel ionization of atoms by strong low-frequency radiation,” J. Opt. Soc. Am. B 8(6), 1207–1211 (1991).
[CrossRef]

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

DeLong, K. W.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68(9), 3277–3295 (1997).
[CrossRef]

Dietrich, P.

Dodge, M. J.

Dörner, R.

P. Eckle, M. Smolarski, P. Schlup, J. Biegert, A. Staudte, M. Schöffler, H. G. Muller, R. Dörner, and U. Keller, “Attosecond angular streaking,” Nat. Phys. 4(7), 565–570 (2008).
[CrossRef]

Drescher, M.

M. Uiberacker, Th. Uphues, M. Schultze, A. J. Verhoef, V. Yakovlev, M. F. Kling, J. Rauschenberger, N. M. Kabachnik, H. Schröder, M. Lezius, K. L. Kompa, H.-G. Muller, M. J. J. Vrakking, S. Hendel, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond real-time observation of electron tunnelling in atoms,” Nature 446(7136), 627–632 (2007).
[CrossRef] [PubMed]

Dunlop, A. E.

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69(4), 327–332 (1999).
[CrossRef]

Eckle, P.

P. Eckle, M. Smolarski, P. Schlup, J. Biegert, A. Staudte, M. Schöffler, H. G. Muller, R. Dörner, and U. Keller, “Attosecond angular streaking,” Nat. Phys. 4(7), 565–570 (2008).
[CrossRef]

Feynman, R. P.

R. P. Feynman, “Space-Time Approach to Non-Relativistic Quantum Mechanics,” Rev. Mod. Phys. 20(2), 367–387 (1948).
[CrossRef]

Fittinghoff, D. N.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68(9), 3277–3295 (1997).
[CrossRef]

Ghimire, S.

C. M. Maharjan, A. S. Alnaser, X. M. Tong, B. Ulrich, P. Ranitovic, S. Ghimire, Z. Chang, I. V. Litvinyuk, and C. L. Cocke, “Momentum imaging of doubly charged ions of Ne and Ar in the sequential ionization region,” Phys. Rev. A 72, 041403(R) (2005)
[CrossRef]

Grasbon, F.

P. Salières, B. Carré, L. Le Déroff, F. Grasbon, G. G. Paulus, H. Walther, R. Kopold, W. Becker, D. B. Milosević, A. Sanpera, and M. Lewenstein, “Feynman’s path-integral approach for intense-laser-atom interactions,” Science 292(5518), 902–905 (2001).
[CrossRef] [PubMed]

Hauri, C. P.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79(6), 673–677 (2004).
[CrossRef]

Heinrich, A.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79(6), 673–677 (2004).
[CrossRef]

Heinzmann, U.

M. Uiberacker, Th. Uphues, M. Schultze, A. J. Verhoef, V. Yakovlev, M. F. Kling, J. Rauschenberger, N. M. Kabachnik, H. Schröder, M. Lezius, K. L. Kompa, H.-G. Muller, M. J. J. Vrakking, S. Hendel, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond real-time observation of electron tunnelling in atoms,” Nature 446(7136), 627–632 (2007).
[CrossRef] [PubMed]

Helbing, F. W.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79(6), 673–677 (2004).
[CrossRef]

Hendel, S.

M. Uiberacker, Th. Uphues, M. Schultze, A. J. Verhoef, V. Yakovlev, M. F. Kling, J. Rauschenberger, N. M. Kabachnik, H. Schröder, M. Lezius, K. L. Kompa, H.-G. Muller, M. J. J. Vrakking, S. Hendel, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond real-time observation of electron tunnelling in atoms,” Nature 446(7136), 627–632 (2007).
[CrossRef] [PubMed]

Hillman, L. W.

S. C. McClain, L. W. Hillman, and R. A. Chipman, “Polarization ray tracing in anisotropic optically active media. I. Algorithms,” J. Opt. Soc. Am. 10(11), 2371–2382 (1993).
[CrossRef]

S. C. McClain, L. W. Hillman, and R. A. Chipman, “Polarization ray tracing in anisotropic optically active media. II. Theory and physics,” J. Opt. Soc. Am. A 10(11), 2383–2393 (1993).
[CrossRef]

Iaconis, C.

C. Iaconis and I. A. Walmsley, “Self-Referencing Spectral Interferometry for Measuring Ultrashort Optical Pulses,” IEEE J. Quantum Electron. 35(4), 501–509 (1999).
[CrossRef]

Kabachnik, N. M.

M. Uiberacker, Th. Uphues, M. Schultze, A. J. Verhoef, V. Yakovlev, M. F. Kling, J. Rauschenberger, N. M. Kabachnik, H. Schröder, M. Lezius, K. L. Kompa, H.-G. Muller, M. J. J. Vrakking, S. Hendel, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond real-time observation of electron tunnelling in atoms,” Nature 446(7136), 627–632 (2007).
[CrossRef] [PubMed]

Kane, D. J.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68(9), 3277–3295 (1997).
[CrossRef]

Keldysh, L. V.

L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Soviet Phys. JETP 20, 1307 (1965).

Keller, U.

P. Eckle, M. Smolarski, P. Schlup, J. Biegert, A. Staudte, M. Schöffler, H. G. Muller, R. Dörner, and U. Keller, “Attosecond angular streaking,” Nat. Phys. 4(7), 565–570 (2008).
[CrossRef]

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79(6), 673–677 (2004).
[CrossRef]

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69(4), 327–332 (1999).
[CrossRef]

Kleineberg, U.

M. Uiberacker, Th. Uphues, M. Schultze, A. J. Verhoef, V. Yakovlev, M. F. Kling, J. Rauschenberger, N. M. Kabachnik, H. Schröder, M. Lezius, K. L. Kompa, H.-G. Muller, M. J. J. Vrakking, S. Hendel, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond real-time observation of electron tunnelling in atoms,” Nature 446(7136), 627–632 (2007).
[CrossRef] [PubMed]

Kling, M. F.

M. Uiberacker, Th. Uphues, M. Schultze, A. J. Verhoef, V. Yakovlev, M. F. Kling, J. Rauschenberger, N. M. Kabachnik, H. Schröder, M. Lezius, K. L. Kompa, H.-G. Muller, M. J. J. Vrakking, S. Hendel, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond real-time observation of electron tunnelling in atoms,” Nature 446(7136), 627–632 (2007).
[CrossRef] [PubMed]

Kompa, K. L.

M. Uiberacker, Th. Uphues, M. Schultze, A. J. Verhoef, V. Yakovlev, M. F. Kling, J. Rauschenberger, N. M. Kabachnik, H. Schröder, M. Lezius, K. L. Kompa, H.-G. Muller, M. J. J. Vrakking, S. Hendel, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond real-time observation of electron tunnelling in atoms,” Nature 446(7136), 627–632 (2007).
[CrossRef] [PubMed]

Kopold, R.

P. Salières, B. Carré, L. Le Déroff, F. Grasbon, G. G. Paulus, H. Walther, R. Kopold, W. Becker, D. B. Milosević, A. Sanpera, and M. Lewenstein, “Feynman’s path-integral approach for intense-laser-atom interactions,” Science 292(5518), 902–905 (2001).
[CrossRef] [PubMed]

Kornelis, W.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79(6), 673–677 (2004).
[CrossRef]

Krainov, V. P.

N. B. Delone and V. P. Krainov, “Energy and angular electron spectra for the tunnel ionization of atoms by strong low-frequency radiation,” J. Opt. Soc. Am. B 8(6), 1207–1211 (1991).
[CrossRef]

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

Krausz, F.

M. Uiberacker, Th. Uphues, M. Schultze, A. J. Verhoef, V. Yakovlev, M. F. Kling, J. Rauschenberger, N. M. Kabachnik, H. Schröder, M. Lezius, K. L. Kompa, H.-G. Muller, M. J. J. Vrakking, S. Hendel, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond real-time observation of electron tunnelling in atoms,” Nature 446(7136), 627–632 (2007).
[CrossRef] [PubMed]

P. Dietrich, F. Krausz, and P. B. Corkum, “Determining the absolute carrier phase of a few-cycle laser pulse,” Opt. Lett. 25(1), 16–18 (2000).
[CrossRef]

M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, M. Lenzner, C. Spielmann, and F. Krausz, “A novel high-energy pulse compression system: generation of multigigawatt sub-5-fs pulses,” Appl. Phys. B 65(2), 189–196 (1997).
[CrossRef]

Krumbügel, M. A.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68(9), 3277–3295 (1997).
[CrossRef]

L’Huillier, A.

P. Antoine, A. L’Huillier, M. Lewenstein, P. Salières, and B. Carré, “Theory of high-order harmonic generation by an elliptically polarized laser field,” Phys. Rev. A 53(3), 1725–1745 (1996).
[CrossRef] [PubMed]

Le Déroff, L.

P. Salières, B. Carré, L. Le Déroff, F. Grasbon, G. G. Paulus, H. Walther, R. Kopold, W. Becker, D. B. Milosević, A. Sanpera, and M. Lewenstein, “Feynman’s path-integral approach for intense-laser-atom interactions,” Science 292(5518), 902–905 (2001).
[CrossRef] [PubMed]

Lenzner, M.

M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, M. Lenzner, C. Spielmann, and F. Krausz, “A novel high-energy pulse compression system: generation of multigigawatt sub-5-fs pulses,” Appl. Phys. B 65(2), 189–196 (1997).
[CrossRef]

Lewenstein, M.

P. Salières, B. Carré, L. Le Déroff, F. Grasbon, G. G. Paulus, H. Walther, R. Kopold, W. Becker, D. B. Milosević, A. Sanpera, and M. Lewenstein, “Feynman’s path-integral approach for intense-laser-atom interactions,” Science 292(5518), 902–905 (2001).
[CrossRef] [PubMed]

P. Antoine, A. L’Huillier, M. Lewenstein, P. Salières, and B. Carré, “Theory of high-order harmonic generation by an elliptically polarized laser field,” Phys. Rev. A 53(3), 1725–1745 (1996).
[CrossRef] [PubMed]

Lezius, M.

M. Uiberacker, Th. Uphues, M. Schultze, A. J. Verhoef, V. Yakovlev, M. F. Kling, J. Rauschenberger, N. M. Kabachnik, H. Schröder, M. Lezius, K. L. Kompa, H.-G. Muller, M. J. J. Vrakking, S. Hendel, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond real-time observation of electron tunnelling in atoms,” Nature 446(7136), 627–632 (2007).
[CrossRef] [PubMed]

Lin, C. D.

X. M. Tong and C. D. Lin, “Empirical formula for statistic field ionization rates of atoms and molecules by lasers in the barrier-suppression regime,” J. Phys. B 38(15), 2593–2600 (2005).
[CrossRef]

Litvinyuk, I. V.

C. M. Maharjan, A. S. Alnaser, X. M. Tong, B. Ulrich, P. Ranitovic, S. Ghimire, Z. Chang, I. V. Litvinyuk, and C. L. Cocke, “Momentum imaging of doubly charged ions of Ne and Ar in the sequential ionization region,” Phys. Rev. A 72, 041403(R) (2005)
[CrossRef]

Maharjan, C. M.

C. M. Maharjan, A. S. Alnaser, X. M. Tong, B. Ulrich, P. Ranitovic, S. Ghimire, Z. Chang, I. V. Litvinyuk, and C. L. Cocke, “Momentum imaging of doubly charged ions of Ne and Ar in the sequential ionization region,” Phys. Rev. A 72, 041403(R) (2005)
[CrossRef]

McClain, S. C.

S. C. McClain, L. W. Hillman, and R. A. Chipman, “Polarization ray tracing in anisotropic optically active media. II. Theory and physics,” J. Opt. Soc. Am. A 10(11), 2383–2393 (1993).
[CrossRef]

S. C. McClain, L. W. Hillman, and R. A. Chipman, “Polarization ray tracing in anisotropic optically active media. I. Algorithms,” J. Opt. Soc. Am. 10(11), 2371–2382 (1993).
[CrossRef]

Milosevic, D. B.

P. Salières, B. Carré, L. Le Déroff, F. Grasbon, G. G. Paulus, H. Walther, R. Kopold, W. Becker, D. B. Milosević, A. Sanpera, and M. Lewenstein, “Feynman’s path-integral approach for intense-laser-atom interactions,” Science 292(5518), 902–905 (2001).
[CrossRef] [PubMed]

Muller, H. G.

P. Eckle, M. Smolarski, P. Schlup, J. Biegert, A. Staudte, M. Schöffler, H. G. Muller, R. Dörner, and U. Keller, “Attosecond angular streaking,” Nat. Phys. 4(7), 565–570 (2008).
[CrossRef]

Muller, H.-G.

M. Uiberacker, Th. Uphues, M. Schultze, A. J. Verhoef, V. Yakovlev, M. F. Kling, J. Rauschenberger, N. M. Kabachnik, H. Schröder, M. Lezius, K. L. Kompa, H.-G. Muller, M. J. J. Vrakking, S. Hendel, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond real-time observation of electron tunnelling in atoms,” Nature 446(7136), 627–632 (2007).
[CrossRef] [PubMed]

Münster, C.

G. Szivessy and C. Münster, “Über die Prüfung der Gitteroptik bei aktiven Kristallen,” Ann. Phys. 412(7), 703–736 (1934).
[CrossRef]

Mysyrowicz, A.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79(6), 673–677 (2004).
[CrossRef]

Nisoli, M.

M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, M. Lenzner, C. Spielmann, and F. Krausz, “A novel high-energy pulse compression system: generation of multigigawatt sub-5-fs pulses,” Appl. Phys. B 65(2), 189–196 (1997).
[CrossRef]

Paulus, G. G.

G. G. Paulus, ““A Meter of the “Absolute” Phase of Few-Cycle Laser Pulses,” Laser Phys. 15, 843–854 (2005).

P. Salières, B. Carré, L. Le Déroff, F. Grasbon, G. G. Paulus, H. Walther, R. Kopold, W. Becker, D. B. Milosević, A. Sanpera, and M. Lewenstein, “Feynman’s path-integral approach for intense-laser-atom interactions,” Science 292(5518), 902–905 (2001).
[CrossRef] [PubMed]

Ranitovic, P.

C. M. Maharjan, A. S. Alnaser, X. M. Tong, B. Ulrich, P. Ranitovic, S. Ghimire, Z. Chang, I. V. Litvinyuk, and C. L. Cocke, “Momentum imaging of doubly charged ions of Ne and Ar in the sequential ionization region,” Phys. Rev. A 72, 041403(R) (2005)
[CrossRef]

Rauschenberger, J.

M. Uiberacker, Th. Uphues, M. Schultze, A. J. Verhoef, V. Yakovlev, M. F. Kling, J. Rauschenberger, N. M. Kabachnik, H. Schröder, M. Lezius, K. L. Kompa, H.-G. Muller, M. J. J. Vrakking, S. Hendel, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond real-time observation of electron tunnelling in atoms,” Nature 446(7136), 627–632 (2007).
[CrossRef] [PubMed]

Reiss, H. R.

H. R. Reiss, “Limits on tunneling theories of strong-field ionization,” Phys. Rev. Lett. 101(4), 043002 (2008).
[CrossRef] [PubMed]

Richman, B. A.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68(9), 3277–3295 (1997).
[CrossRef]

Salières, P.

P. Salières, B. Carré, L. Le Déroff, F. Grasbon, G. G. Paulus, H. Walther, R. Kopold, W. Becker, D. B. Milosević, A. Sanpera, and M. Lewenstein, “Feynman’s path-integral approach for intense-laser-atom interactions,” Science 292(5518), 902–905 (2001).
[CrossRef] [PubMed]

P. Antoine, A. L’Huillier, M. Lewenstein, P. Salières, and B. Carré, “Theory of high-order harmonic generation by an elliptically polarized laser field,” Phys. Rev. A 53(3), 1725–1745 (1996).
[CrossRef] [PubMed]

Sanpera, A.

P. Salières, B. Carré, L. Le Déroff, F. Grasbon, G. G. Paulus, H. Walther, R. Kopold, W. Becker, D. B. Milosević, A. Sanpera, and M. Lewenstein, “Feynman’s path-integral approach for intense-laser-atom interactions,” Science 292(5518), 902–905 (2001).
[CrossRef] [PubMed]

Sartania, S.

M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, M. Lenzner, C. Spielmann, and F. Krausz, “A novel high-energy pulse compression system: generation of multigigawatt sub-5-fs pulses,” Appl. Phys. B 65(2), 189–196 (1997).
[CrossRef]

Schlup, P.

P. Eckle, M. Smolarski, P. Schlup, J. Biegert, A. Staudte, M. Schöffler, H. G. Muller, R. Dörner, and U. Keller, “Attosecond angular streaking,” Nat. Phys. 4(7), 565–570 (2008).
[CrossRef]

Schöffler, M.

P. Eckle, M. Smolarski, P. Schlup, J. Biegert, A. Staudte, M. Schöffler, H. G. Muller, R. Dörner, and U. Keller, “Attosecond angular streaking,” Nat. Phys. 4(7), 565–570 (2008).
[CrossRef]

Schröder, H.

M. Uiberacker, Th. Uphues, M. Schultze, A. J. Verhoef, V. Yakovlev, M. F. Kling, J. Rauschenberger, N. M. Kabachnik, H. Schröder, M. Lezius, K. L. Kompa, H.-G. Muller, M. J. J. Vrakking, S. Hendel, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond real-time observation of electron tunnelling in atoms,” Nature 446(7136), 627–632 (2007).
[CrossRef] [PubMed]

Schultze, M.

M. Uiberacker, Th. Uphues, M. Schultze, A. J. Verhoef, V. Yakovlev, M. F. Kling, J. Rauschenberger, N. M. Kabachnik, H. Schröder, M. Lezius, K. L. Kompa, H.-G. Muller, M. J. J. Vrakking, S. Hendel, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond real-time observation of electron tunnelling in atoms,” Nature 446(7136), 627–632 (2007).
[CrossRef] [PubMed]

Smeenk, C.

C. Smeenk, L. Arissian, A. Staudte, D. M. Villeneuve, and P. B. Corkum, “Momentum space tomographic imaging of photoelectrons,” J. Phys. B 42(18), 185402 (2009).
[CrossRef]

Smolarski, M.

P. Eckle, M. Smolarski, P. Schlup, J. Biegert, A. Staudte, M. Schöffler, H. G. Muller, R. Dörner, and U. Keller, “Attosecond angular streaking,” Nat. Phys. 4(7), 565–570 (2008).
[CrossRef]

Spielmann, C.

M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, M. Lenzner, C. Spielmann, and F. Krausz, “A novel high-energy pulse compression system: generation of multigigawatt sub-5-fs pulses,” Appl. Phys. B 65(2), 189–196 (1997).
[CrossRef]

Stagira, S.

M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, M. Lenzner, C. Spielmann, and F. Krausz, “A novel high-energy pulse compression system: generation of multigigawatt sub-5-fs pulses,” Appl. Phys. B 65(2), 189–196 (1997).
[CrossRef]

Staudte, A.

C. Smeenk, L. Arissian, A. Staudte, D. M. Villeneuve, and P. B. Corkum, “Momentum space tomographic imaging of photoelectrons,” J. Phys. B 42(18), 185402 (2009).
[CrossRef]

P. Eckle, M. Smolarski, P. Schlup, J. Biegert, A. Staudte, M. Schöffler, H. G. Muller, R. Dörner, and U. Keller, “Attosecond angular streaking,” Nat. Phys. 4(7), 565–570 (2008).
[CrossRef]

Steinmeyer, G.

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69(4), 327–332 (1999).
[CrossRef]

Stenger, J.

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69(4), 327–332 (1999).
[CrossRef]

Sutter, D. H.

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69(4), 327–332 (1999).
[CrossRef]

Svelto, O.

M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, M. Lenzner, C. Spielmann, and F. Krausz, “A novel high-energy pulse compression system: generation of multigigawatt sub-5-fs pulses,” Appl. Phys. B 65(2), 189–196 (1997).
[CrossRef]

Sweetser, J. N.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68(9), 3277–3295 (1997).
[CrossRef]

Szivessy, G.

G. Szivessy and C. Münster, “Über die Prüfung der Gitteroptik bei aktiven Kristallen,” Ann. Phys. 412(7), 703–736 (1934).
[CrossRef]

Telle, H. R.

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69(4), 327–332 (1999).
[CrossRef]

Tong, X. M.

X. M. Tong and C. D. Lin, “Empirical formula for statistic field ionization rates of atoms and molecules by lasers in the barrier-suppression regime,” J. Phys. B 38(15), 2593–2600 (2005).
[CrossRef]

C. M. Maharjan, A. S. Alnaser, X. M. Tong, B. Ulrich, P. Ranitovic, S. Ghimire, Z. Chang, I. V. Litvinyuk, and C. L. Cocke, “Momentum imaging of doubly charged ions of Ne and Ar in the sequential ionization region,” Phys. Rev. A 72, 041403(R) (2005)
[CrossRef]

Trebino, R.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68(9), 3277–3295 (1997).
[CrossRef]

Uiberacker, M.

M. Uiberacker, Th. Uphues, M. Schultze, A. J. Verhoef, V. Yakovlev, M. F. Kling, J. Rauschenberger, N. M. Kabachnik, H. Schröder, M. Lezius, K. L. Kompa, H.-G. Muller, M. J. J. Vrakking, S. Hendel, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond real-time observation of electron tunnelling in atoms,” Nature 446(7136), 627–632 (2007).
[CrossRef] [PubMed]

Ulrich, B.

C. M. Maharjan, A. S. Alnaser, X. M. Tong, B. Ulrich, P. Ranitovic, S. Ghimire, Z. Chang, I. V. Litvinyuk, and C. L. Cocke, “Momentum imaging of doubly charged ions of Ne and Ar in the sequential ionization region,” Phys. Rev. A 72, 041403(R) (2005)
[CrossRef]

Uphues, Th.

M. Uiberacker, Th. Uphues, M. Schultze, A. J. Verhoef, V. Yakovlev, M. F. Kling, J. Rauschenberger, N. M. Kabachnik, H. Schröder, M. Lezius, K. L. Kompa, H.-G. Muller, M. J. J. Vrakking, S. Hendel, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond real-time observation of electron tunnelling in atoms,” Nature 446(7136), 627–632 (2007).
[CrossRef] [PubMed]

Verhoef, A. J.

M. Uiberacker, Th. Uphues, M. Schultze, A. J. Verhoef, V. Yakovlev, M. F. Kling, J. Rauschenberger, N. M. Kabachnik, H. Schröder, M. Lezius, K. L. Kompa, H.-G. Muller, M. J. J. Vrakking, S. Hendel, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond real-time observation of electron tunnelling in atoms,” Nature 446(7136), 627–632 (2007).
[CrossRef] [PubMed]

Villeneuve, D. M.

C. Smeenk, L. Arissian, A. Staudte, D. M. Villeneuve, and P. B. Corkum, “Momentum space tomographic imaging of photoelectrons,” J. Phys. B 42(18), 185402 (2009).
[CrossRef]

Vrakking, M. J. J.

M. Uiberacker, Th. Uphues, M. Schultze, A. J. Verhoef, V. Yakovlev, M. F. Kling, J. Rauschenberger, N. M. Kabachnik, H. Schröder, M. Lezius, K. L. Kompa, H.-G. Muller, M. J. J. Vrakking, S. Hendel, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond real-time observation of electron tunnelling in atoms,” Nature 446(7136), 627–632 (2007).
[CrossRef] [PubMed]

Walmsley, I. A.

C. Iaconis and I. A. Walmsley, “Self-Referencing Spectral Interferometry for Measuring Ultrashort Optical Pulses,” IEEE J. Quantum Electron. 35(4), 501–509 (1999).
[CrossRef]

Walther, H.

P. Salières, B. Carré, L. Le Déroff, F. Grasbon, G. G. Paulus, H. Walther, R. Kopold, W. Becker, D. B. Milosević, A. Sanpera, and M. Lewenstein, “Feynman’s path-integral approach for intense-laser-atom interactions,” Science 292(5518), 902–905 (2001).
[CrossRef] [PubMed]

Yakovlev, V.

M. Uiberacker, Th. Uphues, M. Schultze, A. J. Verhoef, V. Yakovlev, M. F. Kling, J. Rauschenberger, N. M. Kabachnik, H. Schröder, M. Lezius, K. L. Kompa, H.-G. Muller, M. J. J. Vrakking, S. Hendel, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond real-time observation of electron tunnelling in atoms,” Nature 446(7136), 627–632 (2007).
[CrossRef] [PubMed]

Ann. Phys. (1)

G. Szivessy and C. Münster, “Über die Prüfung der Gitteroptik bei aktiven Kristallen,” Ann. Phys. 412(7), 703–736 (1934).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (3)

M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, M. Lenzner, C. Spielmann, and F. Krausz, “A novel high-energy pulse compression system: generation of multigigawatt sub-5-fs pulses,” Appl. Phys. B 65(2), 189–196 (1997).
[CrossRef]

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79(6), 673–677 (2004).
[CrossRef]

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69(4), 327–332 (1999).
[CrossRef]

IEEE J. Quantum Electron. (1)

C. Iaconis and I. A. Walmsley, “Self-Referencing Spectral Interferometry for Measuring Ultrashort Optical Pulses,” IEEE J. Quantum Electron. 35(4), 501–509 (1999).
[CrossRef]

J. Opt. Soc. Am. (1)

S. C. McClain, L. W. Hillman, and R. A. Chipman, “Polarization ray tracing in anisotropic optically active media. I. Algorithms,” J. Opt. Soc. Am. 10(11), 2371–2382 (1993).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

J. Phys. B (2)

X. M. Tong and C. D. Lin, “Empirical formula for statistic field ionization rates of atoms and molecules by lasers in the barrier-suppression regime,” J. Phys. B 38(15), 2593–2600 (2005).
[CrossRef]

C. Smeenk, L. Arissian, A. Staudte, D. M. Villeneuve, and P. B. Corkum, “Momentum space tomographic imaging of photoelectrons,” J. Phys. B 42(18), 185402 (2009).
[CrossRef]

Laser Phys. (1)

G. G. Paulus, ““A Meter of the “Absolute” Phase of Few-Cycle Laser Pulses,” Laser Phys. 15, 843–854 (2005).

Nat. Phys. (1)

P. Eckle, M. Smolarski, P. Schlup, J. Biegert, A. Staudte, M. Schöffler, H. G. Muller, R. Dörner, and U. Keller, “Attosecond angular streaking,” Nat. Phys. 4(7), 565–570 (2008).
[CrossRef]

Nature (1)

M. Uiberacker, Th. Uphues, M. Schultze, A. J. Verhoef, V. Yakovlev, M. F. Kling, J. Rauschenberger, N. M. Kabachnik, H. Schröder, M. Lezius, K. L. Kompa, H.-G. Muller, M. J. J. Vrakking, S. Hendel, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond real-time observation of electron tunnelling in atoms,” Nature 446(7136), 627–632 (2007).
[CrossRef] [PubMed]

Opt. Lett. (1)

Phys. Rev. A (2)

C. M. Maharjan, A. S. Alnaser, X. M. Tong, B. Ulrich, P. Ranitovic, S. Ghimire, Z. Chang, I. V. Litvinyuk, and C. L. Cocke, “Momentum imaging of doubly charged ions of Ne and Ar in the sequential ionization region,” Phys. Rev. A 72, 041403(R) (2005)
[CrossRef]

P. Antoine, A. L’Huillier, M. Lewenstein, P. Salières, and B. Carré, “Theory of high-order harmonic generation by an elliptically polarized laser field,” Phys. Rev. A 53(3), 1725–1745 (1996).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

H. R. Reiss, “Limits on tunneling theories of strong-field ionization,” Phys. Rev. Lett. 101(4), 043002 (2008).
[CrossRef] [PubMed]

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

Rev. Mod. Phys. (1)

R. P. Feynman, “Space-Time Approach to Non-Relativistic Quantum Mechanics,” Rev. Mod. Phys. 20(2), 367–387 (1948).
[CrossRef]

Rev. Sci. Instrum. (1)

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68(9), 3277–3295 (1997).
[CrossRef]

Science (1)

P. Salières, B. Carré, L. Le Déroff, F. Grasbon, G. G. Paulus, H. Walther, R. Kopold, W. Becker, D. B. Milosević, A. Sanpera, and M. Lewenstein, “Feynman’s path-integral approach for intense-laser-atom interactions,” Science 292(5518), 902–905 (2001).
[CrossRef] [PubMed]

Sov. Phys. JETP (1)

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

Soviet Phys. JETP (1)

L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Soviet Phys. JETP 20, 1307 (1965).

Other (3)

E. D. Palik, “Handbook of Optical Constants of Solids,” (Academic Press, 1985).

T. Gabriel, “Dispersion-Free Reflective Phase Retarder for Few-Cycle Femtosecond Pulses”, Paper FB6, Optical Interference Coatings Topical Meeting, Tuscon (AZ), June 6–11 2010.

H. R. Schwarz, “Numerische Mathematik,” B. G. Teubner, ed. (Verlag, 1997).

Supplementary Material (1)

» Media 1: MOV (2664 KB)     

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

(Media 1). Classical spatial trajectories in a perfect circularly polarized laser beam (i.e. ε = 1). Blue: Trajectory of an electron ionized 2.5 cycles before reaching the maximal intensity. Green: Direction of field at instant of ionization for purple trajectory. Red: Trajectory of an electron ionized at the instant of maximal intensity. Purple: Direction of field at instant of ionization for red trajectory. Black: Path of the electric field vector of a 5.9-fs Gaussian pulse in the range of ± 10 fs. (2663K)

Fig. 2
Fig. 2

Parameters of the λ/4 waveplate: a) Phaseshift δ, b) rotation angle α of the eigenmodes, c) ellipticity parameter ε.

Fig. 3
Fig. 3

a) Pulse shape (black curve, right scale) and ellipticity (red curve, left scale). b) zoom into central region of a). We used a typical pulse shape of the electric field of the laser pulses from experimental data. The time dependent ellipticity is expressed as the ratio of the two major axis of polarization; the sign represents the helicity.

Fig. 4
Fig. 4

a) to c): Helium ion momentum distribution, ionized at 3.92 1014 W/cm2. d) to f): as a) to c) but smoothed and normalized with respect to a smoothed distribution with random CEO phase. Panels g) to h): Helium ion angular distribution, comparison theory and experiment: Red - theory, black – experiment [7]. Distributions in each row have the same CEO – phase and the increment between the rows is 0.497 radian.

Fig. 5
Fig. 5

a): Surviving probability of Xenon for CEO phase stabilized, elliptically polarized laser pulse, FWHM of 5.9 fs and a peak intensity 1 1016 W/cm2. Result for measured pulse (blue) and for a Gaussian pulse matching ellipticity, CEO phase and wavelength of the measured pulse (red). Resulting momentum distribution for the measured pulse b) and for the Gaussian pulse c).

Fig. 6
Fig. 6

Total angular momentum in units of ħ (red line) and total kinetic energy (blue line) in units of h∙υ for the system of an electron and a Helium ion, ionized at t = 0 with a 5.9-fs Gaussian pulse shape and a peak intensity of 4 1014 W/cm2.

Tables (1)

Tables Icon

Table 1 Parameters in Eq. (6)

Equations (8)

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

Ψ ( x , t ) D x e i S Ψ ( x 0 , t 0 )    where S is the classical action: S = t 0 t 1 2 m p 2 ( x ( t ) ) V ( x ( t ) ) d t ,
E ( t ) = A ( t ) ( sin ( ω 0 t ) x + ε sin ( ω 0 t ) y ) .
p = t i F ( t ) d t = e t i E ( t ) d t = e t i A ( t ) ( sin ( ω 0 t ) x + ε cos ( ω 0 t ) y ) d t = e ω [ A ( t ) cos ( ω 0 t ) x + ε A ( t ) sin ( ω 0 t ) y ] t i + e ω t i ( d d t A ( t ) ) ( cos ( ω 0 t ) x + ε sin ( ω 0 t ) y ) d t e ω ( A ( t i ) cos ( ω 0 t i ) x ε A ( t i ) sin ( ω 0 t i ) y ) ,
P 1 = [ cos ( α ) sin ( α ) sin ( α ) cos ( α ) ] [ 1 1 + ε 2 i ε 1 + ε 2 ] ,
P 2 = [ cos ( α + π 2 ) sin ( α + π 2 ) sin ( α + π 2 ) cos ( α + π 2 ) ] [ 1 1 + ε 2 i ε 1 + ε 2 ] .
n i 2 1 = j = 1 6 A j λ 2 λ 2 λ j 2 .
w s ~ exp ( 3 1 3 E 2 3 [ 2 ε i + p 2 + ( p | | E * ω ) 2 ] )  with  E * = E 2 3 ( 2 ε i ) 1 2 3 1 3 .
L = r × p = t i t f t i t q E ( τ ) m d τ d t × t i t f q E ( ζ ) d ζ = q 2 m t i t f t i t E ( τ ) d τ d t × t i t f E ( ζ ) d ζ .

Metrics