Abstract

We study the effects of dispersive media and structures on the carrier-envelope phase (CEP) shift of focused few-cycles pulses. For phase-sensitive interactions with matter requiring focusing in vacuum, the variation of the CEP through the focal region can be significantly slow down by inserting a dispersive slab of adequate thickness between the focusing system and the focus. The focal CEP shift can also be slow down in experiments requiring focusing in a dispersive medium by a suitable choice of the dispersive propagation distance up to the focus.

© 2009 Optical Society of America

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  1. A. Apolonski, P. Dombi, G.G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgdörfer, T.W. Hänsch, and F. Krausz, “Observation of light-phase-sensitive photoemission from a metal,” Phys. Rev. Lett. 92, 073902 (2004).
    [CrossRef] [PubMed]
  2. F. Lindner, G.G. Paulus, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy phase shift for few-cycle laser pulses,” Phys. Rev. Lett. 92, 113001 (2004).
    [CrossRef] [PubMed]
  3. T. Tritschler, K. D. Hof, M. W. Klein, and M. Wegener, “Variation of the carrier-envelope phase of few-cycle laser pulses owing to the Gouy phase: a solid-state-based measurement,” Opt. Lett. 30, 753–755 (2005).
    [CrossRef] [PubMed]
  4. P. Dombi, A. Apolonski, Ch. Lemell, G. G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, K. Torizuka, J. Burgdörfer, T.W. Hänsch, and F. Krausz, “Direct measurement and analysis of the carrier-envelope phase in light pulses approaching the single-cycle regime,” New J. Phys. 6, 39 (2004).
    [CrossRef]
  5. F. Krausz and Misha Yu. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81, 161–234 (2009).
    [CrossRef]
  6. A. Baltuska, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hansch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421, 611 (2003).
    [CrossRef] [PubMed]
  7. T.M. Fortier, P. A. Roos, D. J. Jones, S.T. Cundiff, R. D. R. Bhat, and J. E. Sipe, “Carrier-envelope phase-controlled quantum interference of injected photocurrents in semiconductors,” Phys. Rev. Lett. 92, 147403 (2004).
    [CrossRef] [PubMed]
  8. P. A. Roos, Q. Qraishi, S. T. Cundiff, R. D. R. Bhat, and J. E. Sipe, “Characterization of quantum interference control of injected currents in LT-GaAs for carrier-envelope phase measurements,” Opt. Express 11, 2081–2090 (2003).
    [CrossRef] [PubMed]
  9. O. D. Mücke, T. Tritschler, M. Wegener, F. X. Kaertner, U. Morgner, G. Khitrova, and H. M. Gibbs, “Carrier wave Rabi flopping: role of the carrier-envelope phase,” Opt. Lett. 29, 2160–2162 (2004).
    [CrossRef] [PubMed]
  10. S. E. Irvine, P. Dombi, G. Farkas, and A. Y. Elezzabi, “Influence of the carrier-envelope phase of few-cycle pulses on ponderomotive surface-plasmon electron acceleration,” Phys. Rev. Lett. 97, 146801 (2006).
    [CrossRef] [PubMed]
  11. P. Dombi and P. Rácz, “Ultrafast monoenergetic electron source by optical waveform control of surface plasmons,” Opt. Express 16, 2887–2893 (2008).
    [CrossRef] [PubMed]
  12. A. Cavalieri, “Attosecond spectroscopy in condensed matter,” Nature 449, 1029–1032 (2007).
    [CrossRef] [PubMed]
  13. D. Faccio, A. Lotti, M. Kolesik, J.V. Moloney, S. Tzortzakis, A. Couairon, and P. Di Trapani, “Spontaneous emergence of pulses with constant carrier-envelope phase in femtosecond filamentation,” Opt. Express 16, 11103 (2008).
    [CrossRef] [PubMed]
  14. C. J. Zapata-Rodríguez and M. A. Porras, “Controlling the carrier-envelope phase of few-cycle focused laser beams with a dispersive beam expander,” Opt. Express 16, 22090 (2008).
    [CrossRef] [PubMed]
  15. M. A. Porras, “Characterization of the electric field of focused pulsed Gaussian beams for phase-sensitive interactions with matter,” Opt. Lett. 34, 1546–1548 (2009).
    [CrossRef] [PubMed]
  16. A. E. Siegman, “Lasers,” University Science books, Mill Valley, California (1986).
  17. M. A. Porras, “Diffraction effects in few-cycle optical pulses,” Phys. Rev. E 65, 026606 (2002).
    [CrossRef]
  18. S. Feng and H. G. Winful, “Spatiotemporal structure of isodiffracting ultrashort electromagnetic pulses,” Phys. Rev. E 61, 862–873 (2000).
    [CrossRef]

2009 (2)

2008 (3)

2007 (1)

A. Cavalieri, “Attosecond spectroscopy in condensed matter,” Nature 449, 1029–1032 (2007).
[CrossRef] [PubMed]

2006 (1)

S. E. Irvine, P. Dombi, G. Farkas, and A. Y. Elezzabi, “Influence of the carrier-envelope phase of few-cycle pulses on ponderomotive surface-plasmon electron acceleration,” Phys. Rev. Lett. 97, 146801 (2006).
[CrossRef] [PubMed]

2005 (1)

2004 (5)

O. D. Mücke, T. Tritschler, M. Wegener, F. X. Kaertner, U. Morgner, G. Khitrova, and H. M. Gibbs, “Carrier wave Rabi flopping: role of the carrier-envelope phase,” Opt. Lett. 29, 2160–2162 (2004).
[CrossRef] [PubMed]

P. Dombi, A. Apolonski, Ch. Lemell, G. G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, K. Torizuka, J. Burgdörfer, T.W. Hänsch, and F. Krausz, “Direct measurement and analysis of the carrier-envelope phase in light pulses approaching the single-cycle regime,” New J. Phys. 6, 39 (2004).
[CrossRef]

T.M. Fortier, P. A. Roos, D. J. Jones, S.T. Cundiff, R. D. R. Bhat, and J. E. Sipe, “Carrier-envelope phase-controlled quantum interference of injected photocurrents in semiconductors,” Phys. Rev. Lett. 92, 147403 (2004).
[CrossRef] [PubMed]

A. Apolonski, P. Dombi, G.G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgdörfer, T.W. Hänsch, and F. Krausz, “Observation of light-phase-sensitive photoemission from a metal,” Phys. Rev. Lett. 92, 073902 (2004).
[CrossRef] [PubMed]

F. Lindner, G.G. Paulus, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy phase shift for few-cycle laser pulses,” Phys. Rev. Lett. 92, 113001 (2004).
[CrossRef] [PubMed]

2003 (2)

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

P. A. Roos, Q. Qraishi, S. T. Cundiff, R. D. R. Bhat, and J. E. Sipe, “Characterization of quantum interference control of injected currents in LT-GaAs for carrier-envelope phase measurements,” Opt. Express 11, 2081–2090 (2003).
[CrossRef] [PubMed]

2002 (1)

M. A. Porras, “Diffraction effects in few-cycle optical pulses,” Phys. Rev. E 65, 026606 (2002).
[CrossRef]

2000 (1)

S. Feng and H. G. Winful, “Spatiotemporal structure of isodiffracting ultrashort electromagnetic pulses,” Phys. Rev. E 61, 862–873 (2000).
[CrossRef]

Apolonski, A.

P. Dombi, A. Apolonski, Ch. Lemell, G. G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, K. Torizuka, J. Burgdörfer, T.W. Hänsch, and F. Krausz, “Direct measurement and analysis of the carrier-envelope phase in light pulses approaching the single-cycle regime,” New J. Phys. 6, 39 (2004).
[CrossRef]

A. Apolonski, P. Dombi, G.G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgdörfer, T.W. Hänsch, and F. Krausz, “Observation of light-phase-sensitive photoemission from a metal,” Phys. Rev. Lett. 92, 073902 (2004).
[CrossRef] [PubMed]

Baltuska, A.

F. Lindner, G.G. Paulus, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy phase shift for few-cycle laser pulses,” Phys. Rev. Lett. 92, 113001 (2004).
[CrossRef] [PubMed]

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

Bhat, R. D. R.

T.M. Fortier, P. A. Roos, D. J. Jones, S.T. Cundiff, R. D. R. Bhat, and J. E. Sipe, “Carrier-envelope phase-controlled quantum interference of injected photocurrents in semiconductors,” Phys. Rev. Lett. 92, 147403 (2004).
[CrossRef] [PubMed]

P. A. Roos, Q. Qraishi, S. T. Cundiff, R. D. R. Bhat, and J. E. Sipe, “Characterization of quantum interference control of injected currents in LT-GaAs for carrier-envelope phase measurements,” Opt. Express 11, 2081–2090 (2003).
[CrossRef] [PubMed]

Burgdörfer, J.

A. Apolonski, P. Dombi, G.G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgdörfer, T.W. Hänsch, and F. Krausz, “Observation of light-phase-sensitive photoemission from a metal,” Phys. Rev. Lett. 92, 073902 (2004).
[CrossRef] [PubMed]

P. Dombi, A. Apolonski, Ch. Lemell, G. G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, K. Torizuka, J. Burgdörfer, T.W. Hänsch, and F. Krausz, “Direct measurement and analysis of the carrier-envelope phase in light pulses approaching the single-cycle regime,” New J. Phys. 6, 39 (2004).
[CrossRef]

Cavalieri, A.

A. Cavalieri, “Attosecond spectroscopy in condensed matter,” Nature 449, 1029–1032 (2007).
[CrossRef] [PubMed]

Couairon, A.

Cundiff, S. T.

Cundiff, S.T.

T.M. Fortier, P. A. Roos, D. J. Jones, S.T. Cundiff, R. D. R. Bhat, and J. E. Sipe, “Carrier-envelope phase-controlled quantum interference of injected photocurrents in semiconductors,” Phys. Rev. Lett. 92, 147403 (2004).
[CrossRef] [PubMed]

Di Trapani, P.

Dombi, P.

P. Dombi and P. Rácz, “Ultrafast monoenergetic electron source by optical waveform control of surface plasmons,” Opt. Express 16, 2887–2893 (2008).
[CrossRef] [PubMed]

S. E. Irvine, P. Dombi, G. Farkas, and A. Y. Elezzabi, “Influence of the carrier-envelope phase of few-cycle pulses on ponderomotive surface-plasmon electron acceleration,” Phys. Rev. Lett. 97, 146801 (2006).
[CrossRef] [PubMed]

P. Dombi, A. Apolonski, Ch. Lemell, G. G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, K. Torizuka, J. Burgdörfer, T.W. Hänsch, and F. Krausz, “Direct measurement and analysis of the carrier-envelope phase in light pulses approaching the single-cycle regime,” New J. Phys. 6, 39 (2004).
[CrossRef]

A. Apolonski, P. Dombi, G.G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgdörfer, T.W. Hänsch, and F. Krausz, “Observation of light-phase-sensitive photoemission from a metal,” Phys. Rev. Lett. 92, 073902 (2004).
[CrossRef] [PubMed]

Elezzabi, A. Y.

S. E. Irvine, P. Dombi, G. Farkas, and A. Y. Elezzabi, “Influence of the carrier-envelope phase of few-cycle pulses on ponderomotive surface-plasmon electron acceleration,” Phys. Rev. Lett. 97, 146801 (2006).
[CrossRef] [PubMed]

Faccio, D.

Farkas, G.

S. E. Irvine, P. Dombi, G. Farkas, and A. Y. Elezzabi, “Influence of the carrier-envelope phase of few-cycle pulses on ponderomotive surface-plasmon electron acceleration,” Phys. Rev. Lett. 97, 146801 (2006).
[CrossRef] [PubMed]

Feng, S.

S. Feng and H. G. Winful, “Spatiotemporal structure of isodiffracting ultrashort electromagnetic pulses,” Phys. Rev. E 61, 862–873 (2000).
[CrossRef]

Fortier, T.M.

T.M. Fortier, P. A. Roos, D. J. Jones, S.T. Cundiff, R. D. R. Bhat, and J. E. Sipe, “Carrier-envelope phase-controlled quantum interference of injected photocurrents in semiconductors,” Phys. Rev. Lett. 92, 147403 (2004).
[CrossRef] [PubMed]

Gibbs, H. M.

Gohle, Ch.

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

Goulielmakis, E.

F. Lindner, G.G. Paulus, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy phase shift for few-cycle laser pulses,” Phys. Rev. Lett. 92, 113001 (2004).
[CrossRef] [PubMed]

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

Hansch, T. W.

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

Hänsch, T.W.

P. Dombi, A. Apolonski, Ch. Lemell, G. G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, K. Torizuka, J. Burgdörfer, T.W. Hänsch, and F. Krausz, “Direct measurement and analysis of the carrier-envelope phase in light pulses approaching the single-cycle regime,” New J. Phys. 6, 39 (2004).
[CrossRef]

A. Apolonski, P. Dombi, G.G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgdörfer, T.W. Hänsch, and F. Krausz, “Observation of light-phase-sensitive photoemission from a metal,” Phys. Rev. Lett. 92, 073902 (2004).
[CrossRef] [PubMed]

Hentschel, M.

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

Hof, K. D.

Holzwarth, R.

P. Dombi, A. Apolonski, Ch. Lemell, G. G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, K. Torizuka, J. Burgdörfer, T.W. Hänsch, and F. Krausz, “Direct measurement and analysis of the carrier-envelope phase in light pulses approaching the single-cycle regime,” New J. Phys. 6, 39 (2004).
[CrossRef]

A. Apolonski, P. Dombi, G.G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgdörfer, T.W. Hänsch, and F. Krausz, “Observation of light-phase-sensitive photoemission from a metal,” Phys. Rev. Lett. 92, 073902 (2004).
[CrossRef] [PubMed]

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

Irvine, S. E.

S. E. Irvine, P. Dombi, G. Farkas, and A. Y. Elezzabi, “Influence of the carrier-envelope phase of few-cycle pulses on ponderomotive surface-plasmon electron acceleration,” Phys. Rev. Lett. 97, 146801 (2006).
[CrossRef] [PubMed]

Ivanov, Misha Yu.

F. Krausz and Misha Yu. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81, 161–234 (2009).
[CrossRef]

Jones, D. J.

T.M. Fortier, P. A. Roos, D. J. Jones, S.T. Cundiff, R. D. R. Bhat, and J. E. Sipe, “Carrier-envelope phase-controlled quantum interference of injected photocurrents in semiconductors,” Phys. Rev. Lett. 92, 147403 (2004).
[CrossRef] [PubMed]

Kaertner, F. X.

Kakehata, M.

P. Dombi, A. Apolonski, Ch. Lemell, G. G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, K. Torizuka, J. Burgdörfer, T.W. Hänsch, and F. Krausz, “Direct measurement and analysis of the carrier-envelope phase in light pulses approaching the single-cycle regime,” New J. Phys. 6, 39 (2004).
[CrossRef]

A. Apolonski, P. Dombi, G.G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgdörfer, T.W. Hänsch, and F. Krausz, “Observation of light-phase-sensitive photoemission from a metal,” Phys. Rev. Lett. 92, 073902 (2004).
[CrossRef] [PubMed]

Khitrova, G.

Klein, M. W.

Kolesik, M.

Krausz, F.

F. Krausz and Misha Yu. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81, 161–234 (2009).
[CrossRef]

A. Apolonski, P. Dombi, G.G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgdörfer, T.W. Hänsch, and F. Krausz, “Observation of light-phase-sensitive photoemission from a metal,” Phys. Rev. Lett. 92, 073902 (2004).
[CrossRef] [PubMed]

P. Dombi, A. Apolonski, Ch. Lemell, G. G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, K. Torizuka, J. Burgdörfer, T.W. Hänsch, and F. Krausz, “Direct measurement and analysis of the carrier-envelope phase in light pulses approaching the single-cycle regime,” New J. Phys. 6, 39 (2004).
[CrossRef]

F. Lindner, G.G. Paulus, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy phase shift for few-cycle laser pulses,” Phys. Rev. Lett. 92, 113001 (2004).
[CrossRef] [PubMed]

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

Lemell, Ch.

P. Dombi, A. Apolonski, Ch. Lemell, G. G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, K. Torizuka, J. Burgdörfer, T.W. Hänsch, and F. Krausz, “Direct measurement and analysis of the carrier-envelope phase in light pulses approaching the single-cycle regime,” New J. Phys. 6, 39 (2004).
[CrossRef]

A. Apolonski, P. Dombi, G.G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgdörfer, T.W. Hänsch, and F. Krausz, “Observation of light-phase-sensitive photoemission from a metal,” Phys. Rev. Lett. 92, 073902 (2004).
[CrossRef] [PubMed]

Lezius, M.

F. Lindner, G.G. Paulus, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy phase shift for few-cycle laser pulses,” Phys. Rev. Lett. 92, 113001 (2004).
[CrossRef] [PubMed]

Lindner, F.

F. Lindner, G.G. Paulus, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy phase shift for few-cycle laser pulses,” Phys. Rev. Lett. 92, 113001 (2004).
[CrossRef] [PubMed]

Lotti, A.

Moloney, J.V.

Morgner, U.

Mücke, O. D.

Paulus, G. G.

P. Dombi, A. Apolonski, Ch. Lemell, G. G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, K. Torizuka, J. Burgdörfer, T.W. Hänsch, and F. Krausz, “Direct measurement and analysis of the carrier-envelope phase in light pulses approaching the single-cycle regime,” New J. Phys. 6, 39 (2004).
[CrossRef]

Paulus, G.G.

F. Lindner, G.G. Paulus, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy phase shift for few-cycle laser pulses,” Phys. Rev. Lett. 92, 113001 (2004).
[CrossRef] [PubMed]

A. Apolonski, P. Dombi, G.G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgdörfer, T.W. Hänsch, and F. Krausz, “Observation of light-phase-sensitive photoemission from a metal,” Phys. Rev. Lett. 92, 073902 (2004).
[CrossRef] [PubMed]

Porras, M. A.

Qraishi, Q.

Rácz, P.

Roos, P. A.

T.M. Fortier, P. A. Roos, D. J. Jones, S.T. Cundiff, R. D. R. Bhat, and J. E. Sipe, “Carrier-envelope phase-controlled quantum interference of injected photocurrents in semiconductors,” Phys. Rev. Lett. 92, 147403 (2004).
[CrossRef] [PubMed]

P. A. Roos, Q. Qraishi, S. T. Cundiff, R. D. R. Bhat, and J. E. Sipe, “Characterization of quantum interference control of injected currents in LT-GaAs for carrier-envelope phase measurements,” Opt. Express 11, 2081–2090 (2003).
[CrossRef] [PubMed]

Scrinzi, A.

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

Siegman, A. E.

A. E. Siegman, “Lasers,” University Science books, Mill Valley, California (1986).

Sipe, J. E.

T.M. Fortier, P. A. Roos, D. J. Jones, S.T. Cundiff, R. D. R. Bhat, and J. E. Sipe, “Carrier-envelope phase-controlled quantum interference of injected photocurrents in semiconductors,” Phys. Rev. Lett. 92, 147403 (2004).
[CrossRef] [PubMed]

P. A. Roos, Q. Qraishi, S. T. Cundiff, R. D. R. Bhat, and J. E. Sipe, “Characterization of quantum interference control of injected currents in LT-GaAs for carrier-envelope phase measurements,” Opt. Express 11, 2081–2090 (2003).
[CrossRef] [PubMed]

Torizuka, K.

A. Apolonski, P. Dombi, G.G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgdörfer, T.W. Hänsch, and F. Krausz, “Observation of light-phase-sensitive photoemission from a metal,” Phys. Rev. Lett. 92, 073902 (2004).
[CrossRef] [PubMed]

P. Dombi, A. Apolonski, Ch. Lemell, G. G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, K. Torizuka, J. Burgdörfer, T.W. Hänsch, and F. Krausz, “Direct measurement and analysis of the carrier-envelope phase in light pulses approaching the single-cycle regime,” New J. Phys. 6, 39 (2004).
[CrossRef]

Tritschler, T.

Tzortzakis, S.

Udem, Th.

P. Dombi, A. Apolonski, Ch. Lemell, G. G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, K. Torizuka, J. Burgdörfer, T.W. Hänsch, and F. Krausz, “Direct measurement and analysis of the carrier-envelope phase in light pulses approaching the single-cycle regime,” New J. Phys. 6, 39 (2004).
[CrossRef]

A. Apolonski, P. Dombi, G.G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgdörfer, T.W. Hänsch, and F. Krausz, “Observation of light-phase-sensitive photoemission from a metal,” Phys. Rev. Lett. 92, 073902 (2004).
[CrossRef] [PubMed]

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

Uiberacker, M.

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

Walther, H.

F. Lindner, G.G. Paulus, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy phase shift for few-cycle laser pulses,” Phys. Rev. Lett. 92, 113001 (2004).
[CrossRef] [PubMed]

Wegener, M.

Winful, H. G.

S. Feng and H. G. Winful, “Spatiotemporal structure of isodiffracting ultrashort electromagnetic pulses,” Phys. Rev. E 61, 862–873 (2000).
[CrossRef]

Yakovlev, V. S.

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

Zapata-Rodríguez, C. J.

Nature (2)

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

A. Cavalieri, “Attosecond spectroscopy in condensed matter,” Nature 449, 1029–1032 (2007).
[CrossRef] [PubMed]

New J. Phys. (1)

P. Dombi, A. Apolonski, Ch. Lemell, G. G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, K. Torizuka, J. Burgdörfer, T.W. Hänsch, and F. Krausz, “Direct measurement and analysis of the carrier-envelope phase in light pulses approaching the single-cycle regime,” New J. Phys. 6, 39 (2004).
[CrossRef]

Opt. Express (4)

Opt. Lett. (3)

Phys. Rev. E (2)

M. A. Porras, “Diffraction effects in few-cycle optical pulses,” Phys. Rev. E 65, 026606 (2002).
[CrossRef]

S. Feng and H. G. Winful, “Spatiotemporal structure of isodiffracting ultrashort electromagnetic pulses,” Phys. Rev. E 61, 862–873 (2000).
[CrossRef]

Phys. Rev. Lett. (4)

T.M. Fortier, P. A. Roos, D. J. Jones, S.T. Cundiff, R. D. R. Bhat, and J. E. Sipe, “Carrier-envelope phase-controlled quantum interference of injected photocurrents in semiconductors,” Phys. Rev. Lett. 92, 147403 (2004).
[CrossRef] [PubMed]

A. Apolonski, P. Dombi, G.G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgdörfer, T.W. Hänsch, and F. Krausz, “Observation of light-phase-sensitive photoemission from a metal,” Phys. Rev. Lett. 92, 073902 (2004).
[CrossRef] [PubMed]

F. Lindner, G.G. Paulus, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy phase shift for few-cycle laser pulses,” Phys. Rev. Lett. 92, 113001 (2004).
[CrossRef] [PubMed]

S. E. Irvine, P. Dombi, G. Farkas, and A. Y. Elezzabi, “Influence of the carrier-envelope phase of few-cycle pulses on ponderomotive surface-plasmon electron acceleration,” Phys. Rev. Lett. 97, 146801 (2006).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

F. Krausz and Misha Yu. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81, 161–234 (2009).
[CrossRef]

Other (1)

A. E. Siegman, “Lasers,” University Science books, Mill Valley, California (1986).

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Figures (5)

Fig. 1.
Fig. 1.

Focusing (a) in vacuum through a dispersive slab, and (b) in a dispersive medium.

Fig. 2.
Fig. 2.

On-axis CEP shift ΔΦ(z) as given by Eq. (21) for the indicated values of g and γ. The dashed curves correspond to γ=0 (no dispersion-induced focal shift).

Fig. 3.
Fig. 3.

(a) Pulse forms at the focus z f (black solid curve) and at zf +2LR (red dashed curve), and (b) axial CEP shifts from Eq. (21) (solid curve) and numerically calculated (open circles) for focusing in vacuum without insertion of slab. (c) and (d), and (e) and (f) show the same physical quantities as (a) and (b) but with the insertion of a slab in the focusing path. In (c) and (d) second- and third-order dispersion introduced by the slab were compensated in the input pulse; in (e) and (f) only second-order dispersion was compensated. Details of the focusing geometry, slab material and input pulse are given in the text.

Fig. 4.
Fig. 4.

CEP shift from Eq. (23) for the indicated values of g and nLR /L 1. For the dashed curves γ=0, and for the solid curves γ takes the value resulting in a horizontal flex point.

Fig. 5.
Fig. 5.

For focusing of a two-cycle pulse in fused silica: (a) Caustics surfaces s(z) about the focus for the carrier-frequency (black curve) and sideband red and blue frequencies (red and blue curves). (b) CEP shifts numerically calculated (open circles), from Eq. (23) (solid curve), and from Eq. (23) neglecting the effect of dispersion-induced focal shift (dashed curve). (c) Pulse forms at the focus z f (solid black curve) and at zf +nLR (dashed red curve). See the text for the focusing geometry, input pulse and medium thickness.

Equations (26)

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Ein (ω,r)=p(ω)exp(iωr22cq̂in),
(ABCD) = (1BfB1f1) ,
zf = [fdjnj(ω)] n (ω)
b=Bf=djnj(ω)+zn(ω)f=zzfn(ω)Zn(ω),
E (ω,r,z)=p(ω)A+Bq̂inexp(iωr22cq̂)exp(iωcS)
q̂ = b+f1+iLf,
E (ω,r,z)=p(ω)q̂(f)q̂exp(iωr22cq̂)exp(iωcS),
q̂ b i f2 L = b iLR ,
E (ω,r,z)p(ω)(f)q̂exp(iωr22cq̂)exp(iωcS).
R̂ = b+LR2/b,s2=sf2(1+b2/LR2),
E (t,r,z)=12πE(ω,r,z)exp(iωt)=12πa(ω,r,z)exp{i[ωtφ(ω,r,z)]},
a (ω,r,z)=fLR11+(bLR)2exp(r2s2),
φ (ω,r,z)=π2tan1(bLR)+ωr22cR̂+ωcS.
A (t,r,z)=12πdωp(ω)a(ω,r,z)exp{i[φ(ω,r,z)φ0(r,z)]}exp{i(ωω0)t}.
A (τ,r,z)=12πdωp(ω)a(ω,r,z)exp{i[12φ0(r,z)(ωω0)2+]}exp{i(ωω0)τ} ,
Δ Φ (r,z)=[ω0φ0(r,z)+φ0(r,z)][ω0φ0(0,zf,0)+φ0(0,zf,0)].
ω0 φ0 (r,z)+φ0(r,z)=ω0cS0ω0π2tan1(b0LR,0)
(LR,0LR,0ω0) b0LR,01+(b0LR,0)2 (12r2s02)
+ ω0b0LR,0 [11+(b0LR,0)2(12r2s02)+r2s02] ,
Δ Φ (r,z)=Z0L1,0tan1(Z0n0LR,0)
+ 11+(Z0n0LR,0)2 [g0(Z0n0LR,0)+γ0(Z0n0LR,0)2] (12r2s02) + γ0 r2s02 .
g0 = L0L0 ω0 ,
γ0 = zf,0n0LR,0 ω0
Δ Φ (z)=tan1(ZLR)+gZLR1+(ZLR)2+γ(ZLR)21+(ZLR)2,
δ n LR k L1 .
Δ Φ (z)=ZL1tan1(ZnLR)+gZnLR1+(ZnLR)2+γ(ZnLR)21+(ZnLR)2

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