Abstract

We investigate the nonlinear optical phenomenon of self-focusing in air with phase-stabilized few-cycle light pulses. This investigation looks at the role of the carrier-envelope phase by observing a filament in air, a nonlinear phenomenon that can be utilized for few-cycle pulse compression [Appl. Phys. B 79, 673 (2004) ]. We were able to measure the critical power for self-focusing in air to be 18±1  GW for a 6.3 fs pulse centered at 800 nm. Using this value and a basic first-order theory, we predicted that the self-focusing distance should deviate by 790μm as the carrier-envelope phase is shifted from 0 to π/2  rad. In contrast, the experimental results showed no deviation in the focus distance with a 3σ upper limit of 180μm. These counterintuitive results show the need for further study of self-focusing dynamics in the few-cycle regime.

© 2010 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. T. Brabec and F. Krausz, Rev. Mod. Phys. 72, 545 (2000).
    [CrossRef]
  2. T. Udem, R. Holzwarth, and T. W. Hansch, Nature 416, 233 (2002).
    [CrossRef] [PubMed]
  3. J. H. Marburger, Prog. Quantum Electron. 4, 35 (1975).
    [CrossRef]
  4. V. I. Talanov, JETP Lett. 11, 199 (1970).
  5. A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. A. Mourou, Opt. Lett. 20, 73 (1995).
    [CrossRef] [PubMed]
  6. X. Chen, X. Li, J. Liu, P. Wei, X. Ge, R. Li, and Z. Xu, Opt. Lett. 32, 2402 (2007).
    [CrossRef] [PubMed]
  7. A. Guandalini, P. Eckle, M. Anscombe, P. Schlup, J. Biegert, and U. Keller, J. Phys. B 39, S257 (2006).
    [CrossRef]
  8. D. Faccio, A. Lotti, M. Kolesik, J. V. Moloney, S. Tzortzakis, A. Couairon, and P. Di Trapani, Opt. Express 16, 11103 (2008).
    [CrossRef] [PubMed]
  9. C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, Appl. Phys. B 79, 673 (2004).
    [CrossRef]
  10. J. Ripoche, G. Grillon, B. Prade, M. Franco, E. Nibbering, R. Lange, and A. Mysyrowicz, Opt. Commun. 135, 310 (1997).
    [CrossRef]
  11. W. Liu and S. L. Chin, Opt. Express 13, 5750 (2005).
    [CrossRef] [PubMed]
  12. A. Baltuska, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakoviev, A. Scrinzi, T. W. Hansch, and F. Krausz, IEEE J. Sel. Top. Quantum Electron. 9, 972 (2003).
    [CrossRef]

2008 (1)

2007 (1)

2006 (1)

A. Guandalini, P. Eckle, M. Anscombe, P. Schlup, J. Biegert, and U. Keller, J. Phys. B 39, S257 (2006).
[CrossRef]

2005 (1)

2004 (1)

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, Appl. Phys. B 79, 673 (2004).
[CrossRef]

2003 (1)

A. Baltuska, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakoviev, A. Scrinzi, T. W. Hansch, and F. Krausz, IEEE J. Sel. Top. Quantum Electron. 9, 972 (2003).
[CrossRef]

2002 (1)

T. Udem, R. Holzwarth, and T. W. Hansch, Nature 416, 233 (2002).
[CrossRef] [PubMed]

2000 (1)

T. Brabec and F. Krausz, Rev. Mod. Phys. 72, 545 (2000).
[CrossRef]

1997 (1)

J. Ripoche, G. Grillon, B. Prade, M. Franco, E. Nibbering, R. Lange, and A. Mysyrowicz, Opt. Commun. 135, 310 (1997).
[CrossRef]

1995 (1)

1975 (1)

J. H. Marburger, Prog. Quantum Electron. 4, 35 (1975).
[CrossRef]

1970 (1)

V. I. Talanov, JETP Lett. 11, 199 (1970).

Anscombe, M.

A. Guandalini, P. Eckle, M. Anscombe, P. Schlup, J. Biegert, and U. Keller, J. Phys. B 39, S257 (2006).
[CrossRef]

Baltuska, A.

A. Baltuska, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakoviev, A. Scrinzi, T. W. Hansch, and F. Krausz, IEEE J. Sel. Top. Quantum Electron. 9, 972 (2003).
[CrossRef]

Biegert, J.

A. Guandalini, P. Eckle, M. Anscombe, P. Schlup, J. Biegert, and U. Keller, J. Phys. B 39, S257 (2006).
[CrossRef]

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, Appl. Phys. B 79, 673 (2004).
[CrossRef]

Brabec, T.

T. Brabec and F. Krausz, Rev. Mod. Phys. 72, 545 (2000).
[CrossRef]

Braun, A.

Chen, X.

Chin, S. L.

Couairon, A.

D. Faccio, A. Lotti, M. Kolesik, J. V. Moloney, S. Tzortzakis, A. Couairon, and P. Di Trapani, Opt. Express 16, 11103 (2008).
[CrossRef] [PubMed]

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, Appl. Phys. B 79, 673 (2004).
[CrossRef]

Di Trapani, P.

Du, D.

Eckle, P.

A. Guandalini, P. Eckle, M. Anscombe, P. Schlup, J. Biegert, and U. Keller, J. Phys. B 39, S257 (2006).
[CrossRef]

Faccio, D.

Franco, M.

J. Ripoche, G. Grillon, B. Prade, M. Franco, E. Nibbering, R. Lange, and A. Mysyrowicz, Opt. Commun. 135, 310 (1997).
[CrossRef]

Ge, X.

Gohle, C.

A. Baltuska, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakoviev, A. Scrinzi, T. W. Hansch, and F. Krausz, IEEE J. Sel. Top. Quantum Electron. 9, 972 (2003).
[CrossRef]

Goulielmakis, E.

A. Baltuska, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakoviev, A. Scrinzi, T. W. Hansch, and F. Krausz, IEEE J. Sel. Top. Quantum Electron. 9, 972 (2003).
[CrossRef]

Grillon, G.

J. Ripoche, G. Grillon, B. Prade, M. Franco, E. Nibbering, R. Lange, and A. Mysyrowicz, Opt. Commun. 135, 310 (1997).
[CrossRef]

Guandalini, A.

A. Guandalini, P. Eckle, M. Anscombe, P. Schlup, J. Biegert, and U. Keller, J. Phys. B 39, S257 (2006).
[CrossRef]

Hansch, T. W.

A. Baltuska, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakoviev, A. Scrinzi, T. W. Hansch, and F. Krausz, IEEE J. Sel. Top. Quantum Electron. 9, 972 (2003).
[CrossRef]

T. Udem, R. Holzwarth, and T. W. Hansch, Nature 416, 233 (2002).
[CrossRef] [PubMed]

Hauri, C. P.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, Appl. Phys. B 79, 673 (2004).
[CrossRef]

Heinrich, A.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, Appl. Phys. B 79, 673 (2004).
[CrossRef]

Helbing, F. W.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, Appl. Phys. B 79, 673 (2004).
[CrossRef]

Hentschel, M.

A. Baltuska, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakoviev, A. Scrinzi, T. W. Hansch, and F. Krausz, IEEE J. Sel. Top. Quantum Electron. 9, 972 (2003).
[CrossRef]

Holzwarth, R.

A. Baltuska, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakoviev, A. Scrinzi, T. W. Hansch, and F. Krausz, IEEE J. Sel. Top. Quantum Electron. 9, 972 (2003).
[CrossRef]

T. Udem, R. Holzwarth, and T. W. Hansch, Nature 416, 233 (2002).
[CrossRef] [PubMed]

Keller, U.

A. Guandalini, P. Eckle, M. Anscombe, P. Schlup, J. Biegert, and U. Keller, J. Phys. B 39, S257 (2006).
[CrossRef]

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, Appl. Phys. B 79, 673 (2004).
[CrossRef]

Kolesik, M.

Korn, G.

Kornelis, W.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, Appl. Phys. B 79, 673 (2004).
[CrossRef]

Krausz, F.

A. Baltuska, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakoviev, A. Scrinzi, T. W. Hansch, and F. Krausz, IEEE J. Sel. Top. Quantum Electron. 9, 972 (2003).
[CrossRef]

T. Brabec and F. Krausz, Rev. Mod. Phys. 72, 545 (2000).
[CrossRef]

Lange, R.

J. Ripoche, G. Grillon, B. Prade, M. Franco, E. Nibbering, R. Lange, and A. Mysyrowicz, Opt. Commun. 135, 310 (1997).
[CrossRef]

Li, R.

Li, X.

Liu, J.

Liu, W.

Liu, X.

Lotti, A.

Marburger, J. H.

J. H. Marburger, Prog. Quantum Electron. 4, 35 (1975).
[CrossRef]

Moloney, J. V.

Mourou, G. A.

Mysyrowicz, A.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, Appl. Phys. B 79, 673 (2004).
[CrossRef]

J. Ripoche, G. Grillon, B. Prade, M. Franco, E. Nibbering, R. Lange, and A. Mysyrowicz, Opt. Commun. 135, 310 (1997).
[CrossRef]

Nibbering, E.

J. Ripoche, G. Grillon, B. Prade, M. Franco, E. Nibbering, R. Lange, and A. Mysyrowicz, Opt. Commun. 135, 310 (1997).
[CrossRef]

Prade, B.

J. Ripoche, G. Grillon, B. Prade, M. Franco, E. Nibbering, R. Lange, and A. Mysyrowicz, Opt. Commun. 135, 310 (1997).
[CrossRef]

Ripoche, J.

J. Ripoche, G. Grillon, B. Prade, M. Franco, E. Nibbering, R. Lange, and A. Mysyrowicz, Opt. Commun. 135, 310 (1997).
[CrossRef]

Schlup, P.

A. Guandalini, P. Eckle, M. Anscombe, P. Schlup, J. Biegert, and U. Keller, J. Phys. B 39, S257 (2006).
[CrossRef]

Scrinzi, A.

A. Baltuska, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakoviev, A. Scrinzi, T. W. Hansch, and F. Krausz, IEEE J. Sel. Top. Quantum Electron. 9, 972 (2003).
[CrossRef]

Squier, J.

Talanov, V. I.

V. I. Talanov, JETP Lett. 11, 199 (1970).

Tzortzakis, S.

Udem, T.

A. Baltuska, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakoviev, A. Scrinzi, T. W. Hansch, and F. Krausz, IEEE J. Sel. Top. Quantum Electron. 9, 972 (2003).
[CrossRef]

T. Udem, R. Holzwarth, and T. W. Hansch, Nature 416, 233 (2002).
[CrossRef] [PubMed]

Uiberacker, M.

A. Baltuska, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakoviev, A. Scrinzi, T. W. Hansch, and F. Krausz, IEEE J. Sel. Top. Quantum Electron. 9, 972 (2003).
[CrossRef]

Wei, P.

Xu, Z.

Yakoviev, V. S.

A. Baltuska, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakoviev, A. Scrinzi, T. W. Hansch, and F. Krausz, IEEE J. Sel. Top. Quantum Electron. 9, 972 (2003).
[CrossRef]

Appl. Phys. B (1)

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, Appl. Phys. B 79, 673 (2004).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

A. Baltuska, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakoviev, A. Scrinzi, T. W. Hansch, and F. Krausz, IEEE J. Sel. Top. Quantum Electron. 9, 972 (2003).
[CrossRef]

J. Phys. B (1)

A. Guandalini, P. Eckle, M. Anscombe, P. Schlup, J. Biegert, and U. Keller, J. Phys. B 39, S257 (2006).
[CrossRef]

JETP Lett. (1)

V. I. Talanov, JETP Lett. 11, 199 (1970).

Nature (1)

T. Udem, R. Holzwarth, and T. W. Hansch, Nature 416, 233 (2002).
[CrossRef] [PubMed]

Opt. Commun. (1)

J. Ripoche, G. Grillon, B. Prade, M. Franco, E. Nibbering, R. Lange, and A. Mysyrowicz, Opt. Commun. 135, 310 (1997).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Prog. Quantum Electron. (1)

J. H. Marburger, Prog. Quantum Electron. 4, 35 (1975).
[CrossRef]

Rev. Mod. Phys. (1)

T. Brabec and F. Krausz, Rev. Mod. Phys. 72, 545 (2000).
[CrossRef]

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 (4)

Fig. 1
Fig. 1

A 6 fs pulse with a central wavelength of 800 nm will have a smaller peak E-field when the CEP is π / 2 compared with zero. The dashed curve represents the envelope of the pulse, the solid curves represent the carriers, and the dotted line shows the decrease in the E-field for a phase of π / 2   rad .

Fig. 2
Fig. 2

Image of the plasma formed at the focus as captured by the CCD camera. The intensity distribution of the plasma is found from graphing the intensity of the pixels on the brightest horizontal row.

Fig. 3
Fig. 3

Measuring the critical power for self-focusing in air to be 18 ± 1   GW for a 6.3 fs pulse. The graph scale is log–log with crosses representing data, and the line is a fit to show the deviation point. The vertical axis was not calibrated to length, but a smaller pixel number implies that the center of the plasma is closer to the focusing mirror.

Fig. 4
Fig. 4

Deviation in the onset of the plasma as the CEP is shifted through a 2 π   rad range. Crosses are data, the gray band represents the amplitude of the sin fit, and the phase axis is not absolute. The total observed shift in focus position, with a 3 σ confidence level, is 180 μ m , considerably smaller than the calculated 790 μ m .

Equations (2)

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

z sf = 0.367 k a 2 ( P P cr 0.852 ) 2 0.0219 + θ ,
Δ z sf z sf 2 1.362 ( P P cr 0.852 ) Δ P k a 2 ( P P cr 0.852 ) 2 0.0219 P P cr P cr ,

Metrics