Abstract

The space and time distribution of electromagnetic energy is essential information for any laser pulse applications that require precision. Although many instruments quantify the temporal profile of ultrashort laser pulses, they are generally limited to space-averaged measurement. In this work, we present an extremely simple technique to characterize the spatial distribution of fluence, pulse duration and chirp of ultrashort light pulses. This technique is based upon imaging the two-photon fluorescence distribution generated by the laser pulse as it propagates through a dispersive medium. It is expected that this technique will provide to less specialized users a precise in-situ analysis of their ultrashort laser beam.

© 2006 Optical Society of America

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  1. M. Drescher, M. Hentschel, R. Kienberger, M. Uiberacker, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, and F. Krausz, "Time-resolved atomic inner-shell spectroscopy," Nature 419,803-807 (2002).
    [CrossRef] [PubMed]
  2. S. Chelkowski, A. D. Bandrauk, and P. B. Corkum, "Efficient molecular dissociation by a chirped ultrashort infrared laser pulse," Phys. Rev. Lett. 65, 2355-2358 (1990).
    [CrossRef] [PubMed]
  3. B. Broers, H. B. van Linden van den Heuvell, and L. D. Noordam, "Efficient population transfer in a three-level ladder system by frequency-swept ultrashort laser pulses," Phys. Rev. Lett. 69, 2062-2065 (1992).
    [CrossRef] [PubMed]
  4. A. Monmayrant, B. Chatel, and B. Girard, "Quantum state measurement using coherent transients," Phys. Rev. Lett. 96,103002 (2006).
    [CrossRef] [PubMed]
  5. F. Mao, Q. Xing, K. Wang, L. Lang, Z. Wang, L. Chai, and Q. Wang, "Optical trapping of red blood cells and two-photon excitation-based photodynamic study using a femtosecond laser," Opt. Commun. 256, 358-363 (2005).
    [CrossRef]
  6. E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, "Direct measurement of Light Waves," Science 27,1267-1269 (2004).
    [CrossRef]
  7. P. O’Shea, M. Kimmel, X. Gu, and R. Trebino, "Highly simplified device for ultrashort-pulse measurement," Opt. Lett. 26, 932-934 (2001).
    [CrossRef]
  8. C. Iaconis and I. A. Walmsley, "Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses," Opt. Lett. 23, 792-794 (1998).
    [CrossRef]
  9. D. Kane and R. P. Trebino, "Single-shot measurement of the intensity and phase of a femtosecond laser pulse," in Ultrafast Pulse Generation and Spectroscopy, T. R. Gosnell, A. J. Taylor, K. A. Nelson, M. C. Downer, eds., Proc. SPIE 1861, 150-160 (1993).
    [CrossRef]
  10. P. Gabolde and R. Trebino, "Self-referenced measurement of the complete electric field of ultrashort pulses," Opt. Express 12, 4423-4429 (2004).
    [CrossRef] [PubMed]
  11. C. Dorrer, E. M. Kosik and I. A. Walmsley, "Direct space-time characterization of the electric fields of ultrashort optical pulses," Opt. Lett. 27, 548-550 (2002).
    [CrossRef]
  12. D. Anderson and M. Lisak, "Analytic study of pulse broadening in dispersive optical fibers," Phys. Rev. A 35,184-187 (1987).
    [CrossRef] [PubMed]
  13. S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schröder, "The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges," Can. J. Phys. 83, 863-905 (2005).
    [CrossRef]
  14. G. P. Agrawal, Nonlinear Fiber Optics, P. L. Kelley, I. P. Kaminow, G. P. Agrawal, eds., (Academic Press, New York, 2001).

2006 (1)

A. Monmayrant, B. Chatel, and B. Girard, "Quantum state measurement using coherent transients," Phys. Rev. Lett. 96,103002 (2006).
[CrossRef] [PubMed]

2005 (2)

F. Mao, Q. Xing, K. Wang, L. Lang, Z. Wang, L. Chai, and Q. Wang, "Optical trapping of red blood cells and two-photon excitation-based photodynamic study using a femtosecond laser," Opt. Commun. 256, 358-363 (2005).
[CrossRef]

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schröder, "The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges," Can. J. Phys. 83, 863-905 (2005).
[CrossRef]

2004 (2)

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, "Direct measurement of Light Waves," Science 27,1267-1269 (2004).
[CrossRef]

P. Gabolde and R. Trebino, "Self-referenced measurement of the complete electric field of ultrashort pulses," Opt. Express 12, 4423-4429 (2004).
[CrossRef] [PubMed]

2002 (2)

C. Dorrer, E. M. Kosik and I. A. Walmsley, "Direct space-time characterization of the electric fields of ultrashort optical pulses," Opt. Lett. 27, 548-550 (2002).
[CrossRef]

M. Drescher, M. Hentschel, R. Kienberger, M. Uiberacker, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, and F. Krausz, "Time-resolved atomic inner-shell spectroscopy," Nature 419,803-807 (2002).
[CrossRef] [PubMed]

2001 (1)

1998 (1)

1992 (1)

B. Broers, H. B. van Linden van den Heuvell, and L. D. Noordam, "Efficient population transfer in a three-level ladder system by frequency-swept ultrashort laser pulses," Phys. Rev. Lett. 69, 2062-2065 (1992).
[CrossRef] [PubMed]

1990 (1)

S. Chelkowski, A. D. Bandrauk, and P. B. Corkum, "Efficient molecular dissociation by a chirped ultrashort infrared laser pulse," Phys. Rev. Lett. 65, 2355-2358 (1990).
[CrossRef] [PubMed]

1987 (1)

D. Anderson and M. Lisak, "Analytic study of pulse broadening in dispersive optical fibers," Phys. Rev. A 35,184-187 (1987).
[CrossRef] [PubMed]

Aközbek, N.

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schröder, "The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges," Can. J. Phys. 83, 863-905 (2005).
[CrossRef]

Anderson, D.

D. Anderson and M. Lisak, "Analytic study of pulse broadening in dispersive optical fibers," Phys. Rev. A 35,184-187 (1987).
[CrossRef] [PubMed]

Baltuska, A.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, "Direct measurement of Light Waves," Science 27,1267-1269 (2004).
[CrossRef]

Bandrauk, A. D.

S. Chelkowski, A. D. Bandrauk, and P. B. Corkum, "Efficient molecular dissociation by a chirped ultrashort infrared laser pulse," Phys. Rev. Lett. 65, 2355-2358 (1990).
[CrossRef] [PubMed]

Becker, A.

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schröder, "The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges," Can. J. Phys. 83, 863-905 (2005).
[CrossRef]

Broers, B.

B. Broers, H. B. van Linden van den Heuvell, and L. D. Noordam, "Efficient population transfer in a three-level ladder system by frequency-swept ultrashort laser pulses," Phys. Rev. Lett. 69, 2062-2065 (1992).
[CrossRef] [PubMed]

Chai, L.

F. Mao, Q. Xing, K. Wang, L. Lang, Z. Wang, L. Chai, and Q. Wang, "Optical trapping of red blood cells and two-photon excitation-based photodynamic study using a femtosecond laser," Opt. Commun. 256, 358-363 (2005).
[CrossRef]

Chatel, B.

A. Monmayrant, B. Chatel, and B. Girard, "Quantum state measurement using coherent transients," Phys. Rev. Lett. 96,103002 (2006).
[CrossRef] [PubMed]

Chelkowski, S.

S. Chelkowski, A. D. Bandrauk, and P. B. Corkum, "Efficient molecular dissociation by a chirped ultrashort infrared laser pulse," Phys. Rev. Lett. 65, 2355-2358 (1990).
[CrossRef] [PubMed]

Chin, S. L.

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schröder, "The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges," Can. J. Phys. 83, 863-905 (2005).
[CrossRef]

Corkum, P. B.

S. Chelkowski, A. D. Bandrauk, and P. B. Corkum, "Efficient molecular dissociation by a chirped ultrashort infrared laser pulse," Phys. Rev. Lett. 65, 2355-2358 (1990).
[CrossRef] [PubMed]

Dorrer, C.

Drescher, M.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, "Direct measurement of Light Waves," Science 27,1267-1269 (2004).
[CrossRef]

M. Drescher, M. Hentschel, R. Kienberger, M. Uiberacker, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, and F. Krausz, "Time-resolved atomic inner-shell spectroscopy," Nature 419,803-807 (2002).
[CrossRef] [PubMed]

Gabolde, P.

Girard, B.

A. Monmayrant, B. Chatel, and B. Girard, "Quantum state measurement using coherent transients," Phys. Rev. Lett. 96,103002 (2006).
[CrossRef] [PubMed]

Goulielmakis, E.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, "Direct measurement of Light Waves," Science 27,1267-1269 (2004).
[CrossRef]

Gu, X.

Heinzmann, U.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, "Direct measurement of Light Waves," Science 27,1267-1269 (2004).
[CrossRef]

M. Drescher, M. Hentschel, R. Kienberger, M. Uiberacker, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, and F. Krausz, "Time-resolved atomic inner-shell spectroscopy," Nature 419,803-807 (2002).
[CrossRef] [PubMed]

Hentschel, M.

M. Drescher, M. Hentschel, R. Kienberger, M. Uiberacker, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, and F. Krausz, "Time-resolved atomic inner-shell spectroscopy," Nature 419,803-807 (2002).
[CrossRef] [PubMed]

Hosseini, S. A.

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schröder, "The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges," Can. J. Phys. 83, 863-905 (2005).
[CrossRef]

Iaconis, C.

Kandidov, V. P.

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schröder, "The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges," Can. J. Phys. 83, 863-905 (2005).
[CrossRef]

Kienberger, R.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, "Direct measurement of Light Waves," Science 27,1267-1269 (2004).
[CrossRef]

M. Drescher, M. Hentschel, R. Kienberger, M. Uiberacker, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, and F. Krausz, "Time-resolved atomic inner-shell spectroscopy," Nature 419,803-807 (2002).
[CrossRef] [PubMed]

Kimmel, M.

Kleineberg, U.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, "Direct measurement of Light Waves," Science 27,1267-1269 (2004).
[CrossRef]

M. Drescher, M. Hentschel, R. Kienberger, M. Uiberacker, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, and F. Krausz, "Time-resolved atomic inner-shell spectroscopy," Nature 419,803-807 (2002).
[CrossRef] [PubMed]

Kosareva, O. G.

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schröder, "The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges," Can. J. Phys. 83, 863-905 (2005).
[CrossRef]

Kosik, E. M.

Krausz, F.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, "Direct measurement of Light Waves," Science 27,1267-1269 (2004).
[CrossRef]

M. Drescher, M. Hentschel, R. Kienberger, M. Uiberacker, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, and F. Krausz, "Time-resolved atomic inner-shell spectroscopy," Nature 419,803-807 (2002).
[CrossRef] [PubMed]

Lang, L.

F. Mao, Q. Xing, K. Wang, L. Lang, Z. Wang, L. Chai, and Q. Wang, "Optical trapping of red blood cells and two-photon excitation-based photodynamic study using a femtosecond laser," Opt. Commun. 256, 358-363 (2005).
[CrossRef]

Lisak, M.

D. Anderson and M. Lisak, "Analytic study of pulse broadening in dispersive optical fibers," Phys. Rev. A 35,184-187 (1987).
[CrossRef] [PubMed]

Liu, W.

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schröder, "The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges," Can. J. Phys. 83, 863-905 (2005).
[CrossRef]

Luo, Q.

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schröder, "The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges," Can. J. Phys. 83, 863-905 (2005).
[CrossRef]

Mao, F.

F. Mao, Q. Xing, K. Wang, L. Lang, Z. Wang, L. Chai, and Q. Wang, "Optical trapping of red blood cells and two-photon excitation-based photodynamic study using a femtosecond laser," Opt. Commun. 256, 358-363 (2005).
[CrossRef]

Monmayrant, A.

A. Monmayrant, B. Chatel, and B. Girard, "Quantum state measurement using coherent transients," Phys. Rev. Lett. 96,103002 (2006).
[CrossRef] [PubMed]

O’Shea, P.

Schröder, H.

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schröder, "The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges," Can. J. Phys. 83, 863-905 (2005).
[CrossRef]

Scrinzi, A.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, "Direct measurement of Light Waves," Science 27,1267-1269 (2004).
[CrossRef]

M. Drescher, M. Hentschel, R. Kienberger, M. Uiberacker, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, and F. Krausz, "Time-resolved atomic inner-shell spectroscopy," Nature 419,803-807 (2002).
[CrossRef] [PubMed]

Théberge, F.

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schröder, "The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges," Can. J. Phys. 83, 863-905 (2005).
[CrossRef]

Trebino, R.

Uiberacker, M.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, "Direct measurement of Light Waves," Science 27,1267-1269 (2004).
[CrossRef]

M. Drescher, M. Hentschel, R. Kienberger, M. Uiberacker, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, and F. Krausz, "Time-resolved atomic inner-shell spectroscopy," Nature 419,803-807 (2002).
[CrossRef] [PubMed]

Walmsley, I. A.

Wang, K.

F. Mao, Q. Xing, K. Wang, L. Lang, Z. Wang, L. Chai, and Q. Wang, "Optical trapping of red blood cells and two-photon excitation-based photodynamic study using a femtosecond laser," Opt. Commun. 256, 358-363 (2005).
[CrossRef]

Wang, Q.

F. Mao, Q. Xing, K. Wang, L. Lang, Z. Wang, L. Chai, and Q. Wang, "Optical trapping of red blood cells and two-photon excitation-based photodynamic study using a femtosecond laser," Opt. Commun. 256, 358-363 (2005).
[CrossRef]

Wang, Z.

F. Mao, Q. Xing, K. Wang, L. Lang, Z. Wang, L. Chai, and Q. Wang, "Optical trapping of red blood cells and two-photon excitation-based photodynamic study using a femtosecond laser," Opt. Commun. 256, 358-363 (2005).
[CrossRef]

Westerwalbesloh, Th.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, "Direct measurement of Light Waves," Science 27,1267-1269 (2004).
[CrossRef]

M. Drescher, M. Hentschel, R. Kienberger, M. Uiberacker, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, and F. Krausz, "Time-resolved atomic inner-shell spectroscopy," Nature 419,803-807 (2002).
[CrossRef] [PubMed]

Xing, Q.

F. Mao, Q. Xing, K. Wang, L. Lang, Z. Wang, L. Chai, and Q. Wang, "Optical trapping of red blood cells and two-photon excitation-based photodynamic study using a femtosecond laser," Opt. Commun. 256, 358-363 (2005).
[CrossRef]

Yakovlev, V.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, "Direct measurement of Light Waves," Science 27,1267-1269 (2004).
[CrossRef]

M. Drescher, M. Hentschel, R. Kienberger, M. Uiberacker, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, and F. Krausz, "Time-resolved atomic inner-shell spectroscopy," Nature 419,803-807 (2002).
[CrossRef] [PubMed]

Can. J. Phys. (1)

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schröder, "The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges," Can. J. Phys. 83, 863-905 (2005).
[CrossRef]

Nature (1)

M. Drescher, M. Hentschel, R. Kienberger, M. Uiberacker, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, and F. Krausz, "Time-resolved atomic inner-shell spectroscopy," Nature 419,803-807 (2002).
[CrossRef] [PubMed]

Opt. Commun. (1)

F. Mao, Q. Xing, K. Wang, L. Lang, Z. Wang, L. Chai, and Q. Wang, "Optical trapping of red blood cells and two-photon excitation-based photodynamic study using a femtosecond laser," Opt. Commun. 256, 358-363 (2005).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. A (1)

D. Anderson and M. Lisak, "Analytic study of pulse broadening in dispersive optical fibers," Phys. Rev. A 35,184-187 (1987).
[CrossRef] [PubMed]

Phys. Rev. Lett. (3)

S. Chelkowski, A. D. Bandrauk, and P. B. Corkum, "Efficient molecular dissociation by a chirped ultrashort infrared laser pulse," Phys. Rev. Lett. 65, 2355-2358 (1990).
[CrossRef] [PubMed]

B. Broers, H. B. van Linden van den Heuvell, and L. D. Noordam, "Efficient population transfer in a three-level ladder system by frequency-swept ultrashort laser pulses," Phys. Rev. Lett. 69, 2062-2065 (1992).
[CrossRef] [PubMed]

A. Monmayrant, B. Chatel, and B. Girard, "Quantum state measurement using coherent transients," Phys. Rev. Lett. 96,103002 (2006).
[CrossRef] [PubMed]

Science (1)

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, "Direct measurement of Light Waves," Science 27,1267-1269 (2004).
[CrossRef]

Other (2)

D. Kane and R. P. Trebino, "Single-shot measurement of the intensity and phase of a femtosecond laser pulse," in Ultrafast Pulse Generation and Spectroscopy, T. R. Gosnell, A. J. Taylor, K. A. Nelson, M. C. Downer, eds., Proc. SPIE 1861, 150-160 (1993).
[CrossRef]

G. P. Agrawal, Nonlinear Fiber Optics, P. L. Kelley, I. P. Kaminow, G. P. Agrawal, eds., (Academic Press, New York, 2001).

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Figures (5)

Fig. 1.
Fig. 1.

(a) Illustration of the measurement setup. The fluorescence induced by the femtosecond laser pulse propagating in dye solution is imaged by the CCD camera. The slit is used to characterize individually each slice of the beam profile. The dimensions of the slit are adjusted such that the diffraction is negligible. (b)–(d) Simulated two-photon fluorescence distribution induces by a laser pulse of 7 fs at full width at half maximum, centered at 737 nm and propagating in methanol/dye solution. (b) The initial chirp is positive (ζ0=+3), that is, with the longer wavelengths on the leading edge of the pulse and the shorter ones on the trailing edge. (c) The laser pulse is transform limited (ζ0=0). (d) The initial chirp is negative (ζ0=-3), that is, with the shorter wavelengths on the leading edge of the pulse and the longer ones on the trailing edge.

Fig. 2.
Fig. 2.

(a) Spectral distribution of the laser pulse. (b) Measured (black) longitudinal distribution of the fluorescence and (red) fitted curve. (c)–(d) Test of the fit stability. Each panel corresponds to different fits of the measured fluorescence by varying (c) the chirp of the laser pulse and (d) the pulse duration. arb.unit, arbitrary unit.

Fig. 3.
Fig. 3.

(a) Spectral distribution of the laser pulse. (b) Autocorrelation signal. The retrieved pulse duration from (b) is 7±1 fs at full width at half maximum. We note from the autocorrelation trace that there is a pedestal pulse of unknown duration that is superposed with the short laser pulse. arb.unit, arbitrary unit.

Fig. 4.
Fig. 4.

Characterization of a few-cycle laser pulse. (a) False color representation of two-photon fluorescence induced by a laser pulse (7±1 fs measured with an autocorrelator and the central wavelength is 737 nm) propagating in a solution of Fluorescein 27 dissolved in methanol (concentration 2.4×1017 molecules/cm3). The measured (black line) longitudinal fluorescence distribution at the center of the beam is shown in (b). The purple curve (Sum of fits) is the best fit. The red, green and deep blue curves in (b) correspond to the fluorescence induced by individual pulses. The transverse distribution of pulse duration, chirp and laser fluence for the few-cycle and pedestal laser pulses are shown in (c).

Fig. 5.
Fig. 5.

The longitudinal two-photon fluorescence distribution (black line) of the laser beam is shown in (a) for a laser pulse centered at 560 nm and generated through four-wave mixing in air. The dye solution was Coumarin 440 dissolved in methanol at 4×10-4 mol/L; (b) for the output pulse from a Ti:sapphire oscillator centered at 800 nm. The dye solution was Fluorescein 27 dissolved in methanol at 4×10-4 mol/L; (c) for an infrared pulse centered at 1.32 µm and generated from an optical parametric amplifier. The dye solution was Nile Blue dissolved in methanol at 10-3 mol/L. The red curves are the best fits and the parameters are indicated on the graphs. The normalized spectral intensity distribution of the laser pulse are shown in (d) for the four-wave mixing pulse, (e) for the Ti:sapphire laser pulse and (f) for the optical parametric laser pulse. arb.unit, arbitrary unit.

Equations (2)

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F ( x , y , z ) σ ( 2 ) [ S 0 ( x , y ) ] 2 exp ( 2 α z ) t 0 ( x , y ) ( [ t 0 ( x , y ) ] 2 + ς 0 ( x , y ) k 2 z 4 ln 2 ) 2 + ( k 2 z 4 ln 2 ) 2
z = ς 0 1 + ς 0 2 ( t 0 2 k 2 4 ln 2 )

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