Abstract

The ac-Stark shift of the A 2Σ+ n=2X 2r n=0 two-photon Bohr resonance of nitric oxide at 409.8 nm is utilized to autocorrelate intense, ultrashort optical pulses at 400 nm. When they are temporally and spatially overlapped, two identical pulses shift the absorption into transient resonance with the applied two-photon energy. Interferometric autocorrelation traces are obtained by detection of A 2Σ+ n=2X 2r n=2 fluorescence as a function of the time delay between the two pulses: The method is background free and highly nonlinear. Experimental measurements are simulated through solutions to the time-dependent Schrödinger equation for one-dimensional motion of an electron in an electric field, which procedure yields a measure of the incident pulse width.

© 2002 Optical Society of America

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    [CrossRef]
  22. A. Fürbach, T. Le, C. Spielmann, and F. Krausz, “Generation of 8 fs pulses at 390 nm,” Appl. Phys. B 70, S37–S40 (2000).
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  23. M. Hacker, T. Feurer, R. Sauerbrey, T. Lucza, and G. Szabo, “Programmable femtosecond laser pulses in the ultraviolet,” J. Opt. Soc. Am. B 18, 866–871 (2001).
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  25. Some authors (e.g., in Ref. 34 below, p. 367) define an intensity correlation of order (n+1) as An(τD)=∫-∞∞ Is(t)Irn(t-τD)dt, for which Irn(t)→δ(t) and An(τD)→Is(t) as n→∞, where Is(t)=|Es(t)|2 and Ir(t)=|Er(t)|2 are the signal and the reference pulse intensity envelopes, respectively.
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    [CrossRef]
  27. We write the fluorescence signal as SF[I(t)], as opposed to SF[I0], to emphasize excitation of fluorescent population throughout the entire pulse duration and to indicate the possibility of extracting I(t) from SF[I(t)], as discussed in Section 3 below.
  28. L. G. Piper and L. M. Cowles, “Einstein coefficients and transition moment variation for the NO(A 2Σ+–X 2∏r) transition,” J. Chem. Phys. 85, 2419–2422 (1986).
    [CrossRef]
  29. J. Luque and D. R. Crosley, “Transition probabilities and electronic transition moments of the A 2Σ+–X 2∏ and D 2Σ+–X 2∏ systems of nitric oxide,” J. Chem. Phys. 111, 7405–7415 (1999), and references therein.
    [CrossRef]
  30. R. B. López-Martens, T. W. Schmidt, and G. Roberts, “ac Stark shifts in Rydberg NO levels induced by intense laser pulses,” Phys. Rev. A 62, 013414:1–9 (2000).
  31. B. W. Shore, The Theory of Coherent Atomic Excitation (Wiley, New York, 1990), Vol. 1, Chap. 4, pp. 268–274; Chap. 10, pp. 590–604.
  32. T. W. Schmidt, R. B. López-Martens, and G. Roberts, “Time-resolved spectroscopy of the dynamic Stark effect,” submitted to Phys. Rev. A.
  33. K. P. Huber and G. Herzberg, Molecular Structure and Molecular Spectra IV: Constants of Diatomic Molecules (Van Nostrand Reinhold, New York, 1979), pp. 466–480.
  34. J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic, San Diego, Calif.1995), Chap. 1, pp. 9–10; Chap. 8, pp. 365–380.
  35. R. A. Kaindl, M. Wurm, K. Reimann, P. Hamm, A. M. Weiner, and M. Wörner, “Generation, shaping and characterization of intense femtosecond pulses tunable from 3 to 20 µm,” J. Opt. Soc. Am. B 17, 2086–2094 (2000).
    [CrossRef]
  36. C. G. Durfee, S. Backus, H. C. Kapteyn, and M. M. Murnane, “Intense 8-fs pulse generation in the deep ultraviolet,” Opt. Lett. 24, 697–699 (1999).
    [CrossRef]
  37. For ease of analysis in detecting a total ion signal, the absorption of photons that results in population of divers Rydberg levels is probably best avoided; otherwise the Stark shifts of all such levels must be taken into account in the analysis. Owing to the ease by which highly excited Rydberg states close to the ionization potential are shifted into resonance during multiphoton absorption, we suspect that the present method, when it is combined with ion detection, may not be optimally applied to map out the transient response of lower-lying bound states to which multiphoton (above-threshold) resonance ionization processes are accessed en route to the departure of an electron.
  38. Z. H. Chang, A. Rundquist, H. W. Wang, M. M. Murnane, and H. C. Kapteyn, “Generation of coherent soft x-rays at 2.7 nm using high harmonics,” Phys. Rev. Lett. 79, 2967–2970 (1997).
    [CrossRef]
  39. P. Dietrich, F. Krausz, and P. B. Corkum, “Determining the absolute carrier phase of a few-cycle laser pulse,” Opt. Lett. 25, 16–18 (2000).
    [CrossRef]
  40. M. Mehendale, S. A. Mitchell, J. P. Likforman, D. M. Villeneuve, and P. B. Corkum, “Method for single-shot measurement of the carrier envelope phase of a few-cycle laser pulse,” Opt. Lett. 25, 1672–1674 (2000).
    [CrossRef]
  41. See, for example, A. Braun, J. V. Rudd, H. Cheng, G. Mourou, D. Kopf, I. D. Jung, K. J. Weingarten, and U. Keller, “Characterization of short-pulse oscillators by means of a high-dynamic-range autocorrelation measurement,” Opt. Lett. 20, 1889–1891 (1995).
    [CrossRef] [PubMed]
  42. See, for example, I. D. Jung, F. X. Kärtner, J. Henkmann, G. Zhang, and U. Keller, “High-dynamic-range characterization of ultrashort pulses,” Appl. Phys. B 65, 307–310 (1997).
    [CrossRef]
  43. P. H. Bucksbaum, R. R. Freeman, M. Bashkansky, and T. J. McIlrath, “Role of the ponderomotive potential in above-threshold ionization,” J. Opt. Soc. Am. B 4, 760–764 (1987).
    [CrossRef]
  44. R. R. Freeman, P. H. Bucksbaum, H. Milchberg, S. Darack, D. Schumacher, and M. E. Geusic, “Above-threshold ionization with subpicosecond laser pulses,” Phys. Rev. Lett. 59, 1092–1095 (1987).
    [CrossRef] [PubMed]
  45. I. Walmsley, L. Waxer, and C. Dorrer, “The role of dispersion in ultrafast optics,” Rev. Sci. Instrum. 72, 1–29 (2001).
    [CrossRef]
  46. For nitric oxide, and other gases, this information may be found in “Optische konstanten, part 8 of Eigenschaften der Materie in ihren Aggregatzuständen,” Landholt–Börnstein: Zahlenwerte und Funktion en aus Physik, Chenie, Astronomie, Geophysik und Technik, 6th ed., K.-H. Hellwege and A. M. Hellwege, eds. (Springer-Verlag, Berlin, 1962), Table 4a, pp. 6-882–6-884.
  47. See, for example, D. B. Milošević, S. Hu, and W. Becker, “Quantum mechanical model for ultrahigh-order harmonic generation in the moderately relativistic regime,” Phys. Rev. A63, 011403(R):1–4 (2001).
    [CrossRef]
  48. M. Brewczyk and K. Rzazewski, “Interaction of a multi-electron atom with intense radiation in the VUV range: beyond the conventional model for high harmonic generation,” J. Phys. B 34, L289–L296 (2001).
    [CrossRef]
  49. P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
    [CrossRef] [PubMed]
  50. E. Constant, V. D. Taranukhin, A. Stolow, and P. B. Corkum, “Methods for the measurement of the duration of high-harmonic pulses,” Phys. Rev. A 56, 3870–3878 (1997).
    [CrossRef]

2001 (4)

M. Hacker, T. Feurer, R. Sauerbrey, T. Lucza, and G. Szabo, “Programmable femtosecond laser pulses in the ultraviolet,” J. Opt. Soc. Am. B 18, 866–871 (2001).
[CrossRef]

I. Walmsley, L. Waxer, and C. Dorrer, “The role of dispersion in ultrafast optics,” Rev. Sci. Instrum. 72, 1–29 (2001).
[CrossRef]

M. Brewczyk and K. Rzazewski, “Interaction of a multi-electron atom with intense radiation in the VUV range: beyond the conventional model for high harmonic generation,” J. Phys. B 34, L289–L296 (2001).
[CrossRef]

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[CrossRef] [PubMed]

2000 (10)

A. Fürbach, T. Le, C. Spielmann, and F. Krausz, “Generation of 8 fs pulses at 390 nm,” Appl. Phys. B 70, S37–S40 (2000).
[CrossRef]

R. B. López-Martens, T. W. Schmidt, and G. Roberts, “ac Stark shifts in Rydberg NO levels induced by intense laser pulses,” Phys. Rev. A 62, 013414:1–9 (2000).

R. A. Kaindl, M. Wurm, K. Reimann, P. Hamm, A. M. Weiner, and M. Wörner, “Generation, shaping and characterization of intense femtosecond pulses tunable from 3 to 20 µm,” J. Opt. Soc. Am. B 17, 2086–2094 (2000).
[CrossRef]

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

M. Mehendale, S. A. Mitchell, J. P. Likforman, D. M. Villeneuve, and P. B. Corkum, “Method for single-shot measurement of the carrier envelope phase of a few-cycle laser pulse,” Opt. Lett. 25, 1672–1674 (2000).
[CrossRef]

P. O’Shea, M. Kimmel, X. Gu, and R. Trebino, “Increased bandwidth in ultrashort-pulse measurement using an angle-dithered nonlinear-optical crystal,” Opt. Express 7, 342–349 (2000), http://www.opticsexpress.org .
[CrossRef]

L. Gallmann, D. H. Sutter, N. Matuschek, G. Steinmeyer, and U. Keller, “Techniques for the characterization of sub-10 fs optical pulses: a comparison,” Appl. Phys. B 70, S67–S75 (2000).
[CrossRef]

For a recent extension of this approach and its connection to FROG see C. Radzewicz, P. Wasylczyk, and J. S. Krasinksi, “A poor man’s FROG,” Opt. Commun. 186, 329–333 (2000).
[CrossRef]

See, for example, P. Loza-Alvaréz, W. Sibbett, and D. T. Reid, “Autocorrelation of femtosecond pulses from 415–630 nm using GaN laser diode,” Electron. Lett. 36, 631–633 (2000).
[CrossRef]

Y. Kobayashi, T. Ohno, T. Sekikawa, Y. Nabekawa, and S. Watanabe, “Pulse width measurement of high-order harmonics by autocorrelation,” Appl. Phys. B 70, 389–394 (2000).
[CrossRef]

1999 (3)

C. G. Durfee, S. Backus, H. C. Kapteyn, and M. M. Murnane, “Intense 8-fs pulse generation in the deep ultraviolet,” Opt. Lett. 24, 697–699 (1999).
[CrossRef]

J. Luque and D. R. Crosley, “Transition probabilities and electronic transition moments of the A 2Σ+–X 2∏ and D 2Σ+–X 2∏ systems of nitric oxide,” J. Chem. Phys. 111, 7405–7415 (1999), and references therein.
[CrossRef]

N. B. Delone and V. P. Krainov, “ac Stark shift of atomic energy levels,” Usp. Fiz. Nauk 42, 669–687 (1999).
[CrossRef]

1998 (4)

1997 (4)

See, for example, J. K. Ranka, A. L. Gaeta, A. Baltuska, M. S. Pschenichnikov, and D. A. Wiersma, “Autocorrelation measurement of 6-fs pulses based on the two-photon-induced photocurrent in a GaAsP photodiode,” Opt. Lett. 22, 1344–1346 (1997).
[CrossRef]

Z. H. Chang, A. Rundquist, H. W. Wang, M. M. Murnane, and H. C. Kapteyn, “Generation of coherent soft x-rays at 2.7 nm using high harmonics,” Phys. Rev. Lett. 79, 2967–2970 (1997).
[CrossRef]

See, for example, I. D. Jung, F. X. Kärtner, J. Henkmann, G. Zhang, and U. Keller, “High-dynamic-range characterization of ultrashort pulses,” Appl. Phys. B 65, 307–310 (1997).
[CrossRef]

E. Constant, V. D. Taranukhin, A. Stolow, and P. B. Corkum, “Methods for the measurement of the duration of high-harmonic pulses,” Phys. Rev. A 56, 3870–3878 (1997).
[CrossRef]

1996 (2)

1995 (1)

1994 (2)

P. Heist and T. Kleinschmidt, “Measurement of ultraviolet subpicosecond pulses based on ultrafast beam deflection,” Opt. Lett. 19, 1961–1963 (1994).
[CrossRef] [PubMed]

K. W. DeLong, D. N. Fittinghoff, and R. Trebino, “Practical issues in ultrashort laser pulse measurement using frequency-resolved optical gating,” IEEE J. Quantum Electron. 32, 1253–1264 (1994).
[CrossRef]

1993 (3)

1991 (2)

1987 (3)

E. S. Kintzer and C. Rempel, “Near-surface second-harmonic generation for autocorrelation measurements in the UV,” Appl. Phys. B 42, 91–95 (1987).
[CrossRef]

P. H. Bucksbaum, R. R. Freeman, M. Bashkansky, and T. J. McIlrath, “Role of the ponderomotive potential in above-threshold ionization,” J. Opt. Soc. Am. B 4, 760–764 (1987).
[CrossRef]

R. R. Freeman, P. H. Bucksbaum, H. Milchberg, S. Darack, D. Schumacher, and M. E. Geusic, “Above-threshold ionization with subpicosecond laser pulses,” Phys. Rev. Lett. 59, 1092–1095 (1987).
[CrossRef] [PubMed]

1986 (1)

L. G. Piper and L. M. Cowles, “Einstein coefficients and transition moment variation for the NO(A 2Σ+–X 2∏r) transition,” J. Chem. Phys. 85, 2419–2422 (1986).
[CrossRef]

1967 (1)

H. P. Weber, “Method for pulsewidth measurement of ultrashort light pulses generated by phase-locked lasers using nonlinear optics,” J. Appl. Phys. 38, 2231–2234 (1967).
[CrossRef]

Agostini, P.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[CrossRef] [PubMed]

Albrecht, H. S.

Augé, F.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[CrossRef] [PubMed]

Backus, S.

Balcou, Ph.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[CrossRef] [PubMed]

Baltuska, A.

Bashkansky, M.

Becker, W.

See, for example, D. B. Milošević, S. Hu, and W. Becker, “Quantum mechanical model for ultrahigh-order harmonic generation in the moderately relativistic regime,” Phys. Rev. A63, 011403(R):1–4 (2001).
[CrossRef]

Bowie, J. L.

Braun, A.

Breger, P.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[CrossRef] [PubMed]

Brewczyk, M.

M. Brewczyk and K. Rzazewski, “Interaction of a multi-electron atom with intense radiation in the VUV range: beyond the conventional model for high harmonic generation,” J. Phys. B 34, L289–L296 (2001).
[CrossRef]

Bucksbaum, P. H.

P. H. Bucksbaum, R. R. Freeman, M. Bashkansky, and T. J. McIlrath, “Role of the ponderomotive potential in above-threshold ionization,” J. Opt. Soc. Am. B 4, 760–764 (1987).
[CrossRef]

R. R. Freeman, P. H. Bucksbaum, H. Milchberg, S. Darack, D. Schumacher, and M. E. Geusic, “Above-threshold ionization with subpicosecond laser pulses,” Phys. Rev. Lett. 59, 1092–1095 (1987).
[CrossRef] [PubMed]

Cantosaid, E. J.

Chang, Z. H.

Z. H. Chang, A. Rundquist, H. W. Wang, M. M. Murnane, and H. C. Kapteyn, “Generation of coherent soft x-rays at 2.7 nm using high harmonics,” Phys. Rev. Lett. 79, 2967–2970 (1997).
[CrossRef]

Cheng, H.

Constant, E.

E. Constant, V. D. Taranukhin, A. Stolow, and P. B. Corkum, “Methods for the measurement of the duration of high-harmonic pulses,” Phys. Rev. A 56, 3870–3878 (1997).
[CrossRef]

Corkum, P. B.

Cowles, L. M.

L. G. Piper and L. M. Cowles, “Einstein coefficients and transition moment variation for the NO(A 2Σ+–X 2∏r) transition,” J. Chem. Phys. 85, 2419–2422 (1986).
[CrossRef]

Crosley, D. R.

J. Luque and D. R. Crosley, “Transition probabilities and electronic transition moments of the A 2Σ+–X 2∏ and D 2Σ+–X 2∏ systems of nitric oxide,” J. Chem. Phys. 111, 7405–7415 (1999), and references therein.
[CrossRef]

Dadap, J. I.

Darack, S.

R. R. Freeman, P. H. Bucksbaum, H. Milchberg, S. Darack, D. Schumacher, and M. E. Geusic, “Above-threshold ionization with subpicosecond laser pulses,” Phys. Rev. Lett. 59, 1092–1095 (1987).
[CrossRef] [PubMed]

Delone, N. B.

N. B. Delone and V. P. Krainov, “ac Stark shift of atomic energy levels,” Usp. Fiz. Nauk 42, 669–687 (1999).
[CrossRef]

DeLong, K. W.

D. N. Fittinghoff, J. L. Bowie, J. N. Sweetser, R. T. Jennings, M. A. Krumbügel, K. W. DeLong, R. Trebino, and I. A. Walmsley, “Measurement of the intensity and phase of ultraweak, ultrashort laser pulses,” Opt. Lett. 21, 884–886 (1996).
[CrossRef] [PubMed]

K. W. DeLong, D. N. Fittinghoff, and R. Trebino, “Practical issues in ultrashort laser pulse measurement using frequency-resolved optical gating,” IEEE J. Quantum Electron. 32, 1253–1264 (1994).
[CrossRef]

Diels, J.-C.

J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic, San Diego, Calif.1995), Chap. 1, pp. 9–10; Chap. 8, pp. 365–380.

Dietrich, P.

Dorrer, C.

I. Walmsley, L. Waxer, and C. Dorrer, “The role of dispersion in ultrafast optics,” Rev. Sci. Instrum. 72, 1–29 (2001).
[CrossRef]

Downer, M. C.

Durfee, C. G.

Fernsler, R.

K. Michelmann, T. Feurer, R. Fernsler, and R. Sauerbrey, “Frequency resolved optical gating using the electronic Kerr effect,” Appl. Phys. B 63, 485–489 (1996).
[CrossRef]

Feurer, T.

M. Hacker, T. Feurer, R. Sauerbrey, T. Lucza, and G. Szabo, “Programmable femtosecond laser pulses in the ultraviolet,” J. Opt. Soc. Am. B 18, 866–871 (2001).
[CrossRef]

K. Michelmann, T. Feurer, R. Fernsler, and R. Sauerbrey, “Frequency resolved optical gating using the electronic Kerr effect,” Appl. Phys. B 63, 485–489 (1996).
[CrossRef]

Fittinghoff, D. N.

D. N. Fittinghoff, J. L. Bowie, J. N. Sweetser, R. T. Jennings, M. A. Krumbügel, K. W. DeLong, R. Trebino, and I. A. Walmsley, “Measurement of the intensity and phase of ultraweak, ultrashort laser pulses,” Opt. Lett. 21, 884–886 (1996).
[CrossRef] [PubMed]

K. W. DeLong, D. N. Fittinghoff, and R. Trebino, “Practical issues in ultrashort laser pulse measurement using frequency-resolved optical gating,” IEEE J. Quantum Electron. 32, 1253–1264 (1994).
[CrossRef]

Focht, G. B.

Freeman, R. R.

P. H. Bucksbaum, R. R. Freeman, M. Bashkansky, and T. J. McIlrath, “Role of the ponderomotive potential in above-threshold ionization,” J. Opt. Soc. Am. B 4, 760–764 (1987).
[CrossRef]

R. R. Freeman, P. H. Bucksbaum, H. Milchberg, S. Darack, D. Schumacher, and M. E. Geusic, “Above-threshold ionization with subpicosecond laser pulses,” Phys. Rev. Lett. 59, 1092–1095 (1987).
[CrossRef] [PubMed]

Fürbach, A.

A. Fürbach, T. Le, C. Spielmann, and F. Krausz, “Generation of 8 fs pulses at 390 nm,” Appl. Phys. B 70, S37–S40 (2000).
[CrossRef]

Gaeta, A. L.

A. M. Streltsov, J. K. Ranka, and A. L. Gaeta, “Femtosecond ultraviolet autocorrelation measurements based on two-photon conductivity in fused silica,” Opt. Lett. 23, 790–800 (1998).
[CrossRef]

See, for example, J. K. Ranka, A. L. Gaeta, A. Baltuska, M. S. Pschenichnikov, and D. A. Wiersma, “Autocorrelation measurement of 6-fs pulses based on the two-photon-induced photocurrent in a GaAsP photodiode,” Opt. Lett. 22, 1344–1346 (1997).
[CrossRef]

Gallmann, L.

L. Gallmann, D. H. Sutter, N. Matuschek, G. Steinmeyer, and U. Keller, “Techniques for the characterization of sub-10 fs optical pulses: a comparison,” Appl. Phys. B 70, S67–S75 (2000).
[CrossRef]

Geusic, M. E.

R. R. Freeman, P. H. Bucksbaum, H. Milchberg, S. Darack, D. Schumacher, and M. E. Geusic, “Above-threshold ionization with subpicosecond laser pulses,” Phys. Rev. Lett. 59, 1092–1095 (1987).
[CrossRef] [PubMed]

Gu, X.

P. O’Shea, M. Kimmel, X. Gu, and R. Trebino, “Increased bandwidth in ultrashort-pulse measurement using an angle-dithered nonlinear-optical crystal,” Opt. Express 7, 342–349 (2000), http://www.opticsexpress.org .
[CrossRef]

P. O’Shea, M. Kimmel, X. Gu, and R. Trebino, “Highly simplified ultrashort pulse measurement,” in Ultrafast Phenomena XII, T. Elsaesser, S. Mukamel, M. M. Murnane, and N. F. Scherer, eds. (Springer-Verlag, Berlin, 2001), pp. 123–125.

Hacker, M.

Hamm, P.

Heist, P.

Henkmann, J.

See, for example, I. D. Jung, F. X. Kärtner, J. Henkmann, G. Zhang, and U. Keller, “High-dynamic-range characterization of ultrashort pulses,” Appl. Phys. B 65, 307–310 (1997).
[CrossRef]

Herzberg, G.

K. P. Huber and G. Herzberg, Molecular Structure and Molecular Spectra IV: Constants of Diatomic Molecules (Van Nostrand Reinhold, New York, 1979), pp. 466–480.

Hu, S.

See, for example, D. B. Milošević, S. Hu, and W. Becker, “Quantum mechanical model for ultrahigh-order harmonic generation in the moderately relativistic regime,” Phys. Rev. A63, 011403(R):1–4 (2001).
[CrossRef]

Huber, K. P.

K. P. Huber and G. Herzberg, Molecular Structure and Molecular Spectra IV: Constants of Diatomic Molecules (Van Nostrand Reinhold, New York, 1979), pp. 466–480.

Iaconis, C.

Ishiguro, M.

Jennings, R. T.

Jordan, C.

Jung, I. D.

Kaindl, R. A.

Kapteyn, H. C.

C. G. Durfee, S. Backus, H. C. Kapteyn, and M. M. Murnane, “Intense 8-fs pulse generation in the deep ultraviolet,” Opt. Lett. 24, 697–699 (1999).
[CrossRef]

Z. H. Chang, A. Rundquist, H. W. Wang, M. M. Murnane, and H. C. Kapteyn, “Generation of coherent soft x-rays at 2.7 nm using high harmonics,” Phys. Rev. Lett. 79, 2967–2970 (1997).
[CrossRef]

Kärtner, F. X.

See, for example, I. D. Jung, F. X. Kärtner, J. Henkmann, G. Zhang, and U. Keller, “High-dynamic-range characterization of ultrashort pulses,” Appl. Phys. B 65, 307–310 (1997).
[CrossRef]

Kawasumi, T.

Keller, U.

L. Gallmann, D. H. Sutter, N. Matuschek, G. Steinmeyer, and U. Keller, “Techniques for the characterization of sub-10 fs optical pulses: a comparison,” Appl. Phys. B 70, S67–S75 (2000).
[CrossRef]

See, for example, I. D. Jung, F. X. Kärtner, J. Henkmann, G. Zhang, and U. Keller, “High-dynamic-range characterization of ultrashort pulses,” Appl. Phys. B 65, 307–310 (1997).
[CrossRef]

See, for example, A. Braun, J. V. Rudd, H. Cheng, G. Mourou, D. Kopf, I. D. Jung, K. J. Weingarten, and U. Keller, “Characterization of short-pulse oscillators by means of a high-dynamic-range autocorrelation measurement,” Opt. Lett. 20, 1889–1891 (1995).
[CrossRef] [PubMed]

Kimmel, M.

P. O’Shea, M. Kimmel, X. Gu, and R. Trebino, “Increased bandwidth in ultrashort-pulse measurement using an angle-dithered nonlinear-optical crystal,” Opt. Express 7, 342–349 (2000), http://www.opticsexpress.org .
[CrossRef]

P. O’Shea, M. Kimmel, X. Gu, and R. Trebino, “Highly simplified ultrashort pulse measurement,” in Ultrafast Phenomena XII, T. Elsaesser, S. Mukamel, M. M. Murnane, and N. F. Scherer, eds. (Springer-Verlag, Berlin, 2001), pp. 123–125.

Kintzer, E. S.

E. S. Kintzer and C. Rempel, “Near-surface second-harmonic generation for autocorrelation measurements in the UV,” Appl. Phys. B 42, 91–95 (1987).
[CrossRef]

Kleinschmidt, J.

Kleinschmidt, T.

Kobayashi, Y.

Y. Kobayashi, T. Ohno, T. Sekikawa, Y. Nabekawa, and S. Watanabe, “Pulse width measurement of high-order harmonics by autocorrelation,” Appl. Phys. B 70, 389–394 (2000).
[CrossRef]

Y. Kobayashi, T. Sekikawa, Y. Nabekawa, and S. Watanabe, “27 fs extreme ultraviolet pulse generation by high-order harmonics,” Opt. Lett. 23, 64–66 (1998).
[CrossRef]

Kopf, D.

Krainov, V. P.

N. B. Delone and V. P. Krainov, “ac Stark shift of atomic energy levels,” Usp. Fiz. Nauk 42, 669–687 (1999).
[CrossRef]

Krasinksi, J. S.

For a recent extension of this approach and its connection to FROG see C. Radzewicz, P. Wasylczyk, and J. S. Krasinksi, “A poor man’s FROG,” Opt. Commun. 186, 329–333 (2000).
[CrossRef]

Krausz, F.

A. Fürbach, T. Le, C. Spielmann, and F. Krausz, “Generation of 8 fs pulses at 390 nm,” Appl. Phys. B 70, S37–S40 (2000).
[CrossRef]

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

Krumbügel, M. A.

Le, T.

A. Fürbach, T. Le, C. Spielmann, and F. Krausz, “Generation of 8 fs pulses at 390 nm,” Appl. Phys. B 70, S37–S40 (2000).
[CrossRef]

Le Blanc, S. P.

Likforman, J. P.

López-Martens, R. B.

R. B. López-Martens, T. W. Schmidt, and G. Roberts, “ac Stark shifts in Rydberg NO levels induced by intense laser pulses,” Phys. Rev. A 62, 013414:1–9 (2000).

T. W. Schmidt, R. B. López-Martens, and G. Roberts, “Time-resolved spectroscopy of the dynamic Stark effect,” submitted to Phys. Rev. A.

Loza-Alvaréz, P.

See, for example, P. Loza-Alvaréz, W. Sibbett, and D. T. Reid, “Autocorrelation of femtosecond pulses from 415–630 nm using GaN laser diode,” Electron. Lett. 36, 631–633 (2000).
[CrossRef]

Lucza, T.

Luque, J.

J. Luque and D. R. Crosley, “Transition probabilities and electronic transition moments of the A 2Σ+–X 2∏ and D 2Σ+–X 2∏ systems of nitric oxide,” J. Chem. Phys. 111, 7405–7415 (1999), and references therein.
[CrossRef]

Marowsky, G.

Matuschek, N.

L. Gallmann, D. H. Sutter, N. Matuschek, G. Steinmeyer, and U. Keller, “Techniques for the characterization of sub-10 fs optical pulses: a comparison,” Appl. Phys. B 70, S67–S75 (2000).
[CrossRef]

McIlrath, T. J.

Mehendale, M.

Michelmann, K.

K. Michelmann, T. Feurer, R. Fernsler, and R. Sauerbrey, “Frequency resolved optical gating using the electronic Kerr effect,” Appl. Phys. B 63, 485–489 (1996).
[CrossRef]

Milchberg, H.

R. R. Freeman, P. H. Bucksbaum, H. Milchberg, S. Darack, D. Schumacher, and M. E. Geusic, “Above-threshold ionization with subpicosecond laser pulses,” Phys. Rev. Lett. 59, 1092–1095 (1987).
[CrossRef] [PubMed]

Miloševic, D. B.

See, for example, D. B. Milošević, S. Hu, and W. Becker, “Quantum mechanical model for ultrahigh-order harmonic generation in the moderately relativistic regime,” Phys. Rev. A63, 011403(R):1–4 (2001).
[CrossRef]

Mitchell, S. A.

Mourou, G.

Muller, H. G.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[CrossRef] [PubMed]

Mullot, G.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[CrossRef] [PubMed]

Murnane, M. M.

C. G. Durfee, S. Backus, H. C. Kapteyn, and M. M. Murnane, “Intense 8-fs pulse generation in the deep ultraviolet,” Opt. Lett. 24, 697–699 (1999).
[CrossRef]

Z. H. Chang, A. Rundquist, H. W. Wang, M. M. Murnane, and H. C. Kapteyn, “Generation of coherent soft x-rays at 2.7 nm using high harmonics,” Phys. Rev. Lett. 79, 2967–2970 (1997).
[CrossRef]

Nabekawa, Y.

Y. Kobayashi, T. Ohno, T. Sekikawa, Y. Nabekawa, and S. Watanabe, “Pulse width measurement of high-order harmonics by autocorrelation,” Appl. Phys. B 70, 389–394 (2000).
[CrossRef]

Y. Kobayashi, T. Sekikawa, Y. Nabekawa, and S. Watanabe, “27 fs extreme ultraviolet pulse generation by high-order harmonics,” Opt. Lett. 23, 64–66 (1998).
[CrossRef]

Nishiok, H.

O’Shea, P.

P. O’Shea, M. Kimmel, X. Gu, and R. Trebino, “Increased bandwidth in ultrashort-pulse measurement using an angle-dithered nonlinear-optical crystal,” Opt. Express 7, 342–349 (2000), http://www.opticsexpress.org .
[CrossRef]

P. O’Shea, M. Kimmel, X. Gu, and R. Trebino, “Highly simplified ultrashort pulse measurement,” in Ultrafast Phenomena XII, T. Elsaesser, S. Mukamel, M. M. Murnane, and N. F. Scherer, eds. (Springer-Verlag, Berlin, 2001), pp. 123–125.

Ohno, T.

Y. Kobayashi, T. Ohno, T. Sekikawa, Y. Nabekawa, and S. Watanabe, “Pulse width measurement of high-order harmonics by autocorrelation,” Appl. Phys. B 70, 389–394 (2000).
[CrossRef]

Paul, P. M.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[CrossRef] [PubMed]

Peatross, J.

Piper, L. G.

L. G. Piper and L. M. Cowles, “Einstein coefficients and transition moment variation for the NO(A 2Σ+–X 2∏r) transition,” J. Chem. Phys. 85, 2419–2422 (1986).
[CrossRef]

Pschenichnikov, M. S.

Radzewicz, C.

For a recent extension of this approach and its connection to FROG see C. Radzewicz, P. Wasylczyk, and J. S. Krasinksi, “A poor man’s FROG,” Opt. Commun. 186, 329–333 (2000).
[CrossRef]

Ranka, J. K.

A. M. Streltsov, J. K. Ranka, and A. L. Gaeta, “Femtosecond ultraviolet autocorrelation measurements based on two-photon conductivity in fused silica,” Opt. Lett. 23, 790–800 (1998).
[CrossRef]

See, for example, J. K. Ranka, A. L. Gaeta, A. Baltuska, M. S. Pschenichnikov, and D. A. Wiersma, “Autocorrelation measurement of 6-fs pulses based on the two-photon-induced photocurrent in a GaAsP photodiode,” Opt. Lett. 22, 1344–1346 (1997).
[CrossRef]

Reid, D. T.

See, for example, P. Loza-Alvaréz, W. Sibbett, and D. T. Reid, “Autocorrelation of femtosecond pulses from 415–630 nm using GaN laser diode,” Electron. Lett. 36, 631–633 (2000).
[CrossRef]

Reimann, K.

Reitze, D. H.

Rempel, C.

E. S. Kintzer and C. Rempel, “Near-surface second-harmonic generation for autocorrelation measurements in the UV,” Appl. Phys. B 42, 91–95 (1987).
[CrossRef]

Roberts, G.

R. B. López-Martens, T. W. Schmidt, and G. Roberts, “ac Stark shifts in Rydberg NO levels induced by intense laser pulses,” Phys. Rev. A 62, 013414:1–9 (2000).

T. W. Schmidt, R. B. López-Martens, and G. Roberts, “Time-resolved spectroscopy of the dynamic Stark effect,” submitted to Phys. Rev. A.

Rudd, J. V.

Rudolph, W.

J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic, San Diego, Calif.1995), Chap. 1, pp. 9–10; Chap. 8, pp. 365–380.

Rundquist, A.

J. Peatross and A. Rundquist, “Temporal decorrelation of short laser pulses,” J. Opt. Soc. Am. B 15, 216–222 (1998).
[CrossRef]

Z. H. Chang, A. Rundquist, H. W. Wang, M. M. Murnane, and H. C. Kapteyn, “Generation of coherent soft x-rays at 2.7 nm using high harmonics,” Phys. Rev. Lett. 79, 2967–2970 (1997).
[CrossRef]

Rzazewski, K.

M. Brewczyk and K. Rzazewski, “Interaction of a multi-electron atom with intense radiation in the VUV range: beyond the conventional model for high harmonic generation,” J. Phys. B 34, L289–L296 (2001).
[CrossRef]

Sauerbrey, R.

Schmidt, T. W.

R. B. López-Martens, T. W. Schmidt, and G. Roberts, “ac Stark shifts in Rydberg NO levels induced by intense laser pulses,” Phys. Rev. A 62, 013414:1–9 (2000).

T. W. Schmidt, R. B. López-Martens, and G. Roberts, “Time-resolved spectroscopy of the dynamic Stark effect,” submitted to Phys. Rev. A.

Schröder, T.

Schumacher, D.

R. R. Freeman, P. H. Bucksbaum, H. Milchberg, S. Darack, D. Schumacher, and M. E. Geusic, “Above-threshold ionization with subpicosecond laser pulses,” Phys. Rev. Lett. 59, 1092–1095 (1987).
[CrossRef] [PubMed]

Sekikawa, T.

Y. Kobayashi, T. Ohno, T. Sekikawa, Y. Nabekawa, and S. Watanabe, “Pulse width measurement of high-order harmonics by autocorrelation,” Appl. Phys. B 70, 389–394 (2000).
[CrossRef]

Y. Kobayashi, T. Sekikawa, Y. Nabekawa, and S. Watanabe, “27 fs extreme ultraviolet pulse generation by high-order harmonics,” Opt. Lett. 23, 64–66 (1998).
[CrossRef]

Shore, B. W.

B. W. Shore, The Theory of Coherent Atomic Excitation (Wiley, New York, 1990), Vol. 1, Chap. 4, pp. 268–274; Chap. 10, pp. 590–604.

Sibbett, W.

See, for example, P. Loza-Alvaréz, W. Sibbett, and D. T. Reid, “Autocorrelation of femtosecond pulses from 415–630 nm using GaN laser diode,” Electron. Lett. 36, 631–633 (2000).
[CrossRef]

Simon, P.

Spielmann, C.

A. Fürbach, T. Le, C. Spielmann, and F. Krausz, “Generation of 8 fs pulses at 390 nm,” Appl. Phys. B 70, S37–S40 (2000).
[CrossRef]

Steinmeyer, G.

L. Gallmann, D. H. Sutter, N. Matuschek, G. Steinmeyer, and U. Keller, “Techniques for the characterization of sub-10 fs optical pulses: a comparison,” Appl. Phys. B 70, S67–S75 (2000).
[CrossRef]

Stolow, A.

E. Constant, V. D. Taranukhin, A. Stolow, and P. B. Corkum, “Methods for the measurement of the duration of high-harmonic pulses,” Phys. Rev. A 56, 3870–3878 (1997).
[CrossRef]

Streltsov, A. M.

A. M. Streltsov, J. K. Ranka, and A. L. Gaeta, “Femtosecond ultraviolet autocorrelation measurements based on two-photon conductivity in fused silica,” Opt. Lett. 23, 790–800 (1998).
[CrossRef]

Sutter, D. H.

L. Gallmann, D. H. Sutter, N. Matuschek, G. Steinmeyer, and U. Keller, “Techniques for the characterization of sub-10 fs optical pulses: a comparison,” Appl. Phys. B 70, S67–S75 (2000).
[CrossRef]

Sweetser, J. N.

Szabo, G.

Takuma, H.

Taranukhin, V. D.

E. Constant, V. D. Taranukhin, A. Stolow, and P. B. Corkum, “Methods for the measurement of the duration of high-harmonic pulses,” Phys. Rev. A 56, 3870–3878 (1997).
[CrossRef]

Toma, E. S.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[CrossRef] [PubMed]

Trebino, R.

P. O’Shea, M. Kimmel, X. Gu, and R. Trebino, “Increased bandwidth in ultrashort-pulse measurement using an angle-dithered nonlinear-optical crystal,” Opt. Express 7, 342–349 (2000), http://www.opticsexpress.org .
[CrossRef]

D. N. Fittinghoff, J. L. Bowie, J. N. Sweetser, R. T. Jennings, M. A. Krumbügel, K. W. DeLong, R. Trebino, and I. A. Walmsley, “Measurement of the intensity and phase of ultraweak, ultrashort laser pulses,” Opt. Lett. 21, 884–886 (1996).
[CrossRef] [PubMed]

K. W. DeLong, D. N. Fittinghoff, and R. Trebino, “Practical issues in ultrashort laser pulse measurement using frequency-resolved optical gating,” IEEE J. Quantum Electron. 32, 1253–1264 (1994).
[CrossRef]

P. O’Shea, M. Kimmel, X. Gu, and R. Trebino, “Highly simplified ultrashort pulse measurement,” in Ultrafast Phenomena XII, T. Elsaesser, S. Mukamel, M. M. Murnane, and N. F. Scherer, eds. (Springer-Verlag, Berlin, 2001), pp. 123–125.

Udea, K.

van Lap, D.

Villeneuve, D. M.

Walmsley, I.

I. Walmsley, L. Waxer, and C. Dorrer, “The role of dispersion in ultrafast optics,” Rev. Sci. Instrum. 72, 1–29 (2001).
[CrossRef]

Walmsley, I. A.

Wang, H. W.

Z. H. Chang, A. Rundquist, H. W. Wang, M. M. Murnane, and H. C. Kapteyn, “Generation of coherent soft x-rays at 2.7 nm using high harmonics,” Phys. Rev. Lett. 79, 2967–2970 (1997).
[CrossRef]

Wasylczyk, P.

For a recent extension of this approach and its connection to FROG see C. Radzewicz, P. Wasylczyk, and J. S. Krasinksi, “A poor man’s FROG,” Opt. Commun. 186, 329–333 (2000).
[CrossRef]

Watanabe, S.

Y. Kobayashi, T. Ohno, T. Sekikawa, Y. Nabekawa, and S. Watanabe, “Pulse width measurement of high-order harmonics by autocorrelation,” Appl. Phys. B 70, 389–394 (2000).
[CrossRef]

Y. Kobayashi, T. Sekikawa, Y. Nabekawa, and S. Watanabe, “27 fs extreme ultraviolet pulse generation by high-order harmonics,” Opt. Lett. 23, 64–66 (1998).
[CrossRef]

Waxer, L.

I. Walmsley, L. Waxer, and C. Dorrer, “The role of dispersion in ultrafast optics,” Rev. Sci. Instrum. 72, 1–29 (2001).
[CrossRef]

Weber, H. P.

H. P. Weber, “Method for pulsewidth measurement of ultrashort light pulses generated by phase-locked lasers using nonlinear optics,” J. Appl. Phys. 38, 2231–2234 (1967).
[CrossRef]

Weiner, A. M.

Weingarten, K. J.

Wiersma, D. A.

Wörner, M.

Wurm, M.

Zhang, G.

See, for example, I. D. Jung, F. X. Kärtner, J. Henkmann, G. Zhang, and U. Keller, “High-dynamic-range characterization of ultrashort pulses,” Appl. Phys. B 65, 307–310 (1997).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (6)

Y. Kobayashi, T. Ohno, T. Sekikawa, Y. Nabekawa, and S. Watanabe, “Pulse width measurement of high-order harmonics by autocorrelation,” Appl. Phys. B 70, 389–394 (2000).
[CrossRef]

L. Gallmann, D. H. Sutter, N. Matuschek, G. Steinmeyer, and U. Keller, “Techniques for the characterization of sub-10 fs optical pulses: a comparison,” Appl. Phys. B 70, S67–S75 (2000).
[CrossRef]

E. S. Kintzer and C. Rempel, “Near-surface second-harmonic generation for autocorrelation measurements in the UV,” Appl. Phys. B 42, 91–95 (1987).
[CrossRef]

K. Michelmann, T. Feurer, R. Fernsler, and R. Sauerbrey, “Frequency resolved optical gating using the electronic Kerr effect,” Appl. Phys. B 63, 485–489 (1996).
[CrossRef]

A. Fürbach, T. Le, C. Spielmann, and F. Krausz, “Generation of 8 fs pulses at 390 nm,” Appl. Phys. B 70, S37–S40 (2000).
[CrossRef]

See, for example, I. D. Jung, F. X. Kärtner, J. Henkmann, G. Zhang, and U. Keller, “High-dynamic-range characterization of ultrashort pulses,” Appl. Phys. B 65, 307–310 (1997).
[CrossRef]

Electron. Lett. (1)

See, for example, P. Loza-Alvaréz, W. Sibbett, and D. T. Reid, “Autocorrelation of femtosecond pulses from 415–630 nm using GaN laser diode,” Electron. Lett. 36, 631–633 (2000).
[CrossRef]

IEEE J. Quantum Electron. (1)

K. W. DeLong, D. N. Fittinghoff, and R. Trebino, “Practical issues in ultrashort laser pulse measurement using frequency-resolved optical gating,” IEEE J. Quantum Electron. 32, 1253–1264 (1994).
[CrossRef]

J. Appl. Phys. (1)

H. P. Weber, “Method for pulsewidth measurement of ultrashort light pulses generated by phase-locked lasers using nonlinear optics,” J. Appl. Phys. 38, 2231–2234 (1967).
[CrossRef]

J. Chem. Phys. (2)

L. G. Piper and L. M. Cowles, “Einstein coefficients and transition moment variation for the NO(A 2Σ+–X 2∏r) transition,” J. Chem. Phys. 85, 2419–2422 (1986).
[CrossRef]

J. Luque and D. R. Crosley, “Transition probabilities and electronic transition moments of the A 2Σ+–X 2∏ and D 2Σ+–X 2∏ systems of nitric oxide,” J. Chem. Phys. 111, 7405–7415 (1999), and references therein.
[CrossRef]

J. Opt. Soc. Am. B (4)

J. Phys. B (1)

M. Brewczyk and K. Rzazewski, “Interaction of a multi-electron atom with intense radiation in the VUV range: beyond the conventional model for high harmonic generation,” J. Phys. B 34, L289–L296 (2001).
[CrossRef]

Opt. Commun. (1)

For a recent extension of this approach and its connection to FROG see C. Radzewicz, P. Wasylczyk, and J. S. Krasinksi, “A poor man’s FROG,” Opt. Commun. 186, 329–333 (2000).
[CrossRef]

Opt. Express (1)

Opt. Lett. (14)

C. Iaconis and I. A. Walmsley, “Spectral phase interferometer for direct electric-field reconstruction,” Opt. Lett. 23, 792–794 (1998).
[CrossRef]

D. N. Fittinghoff, J. L. Bowie, J. N. Sweetser, R. T. Jennings, M. A. Krumbügel, K. W. DeLong, R. Trebino, and I. A. Walmsley, “Measurement of the intensity and phase of ultraweak, ultrashort laser pulses,” Opt. Lett. 21, 884–886 (1996).
[CrossRef] [PubMed]

E. J. Cantosaid, P. Simon, C. Jordan, and G. Marowsky, “Surface second-harmonic generation in Si(111) for autocorrelation measurements of 248 nm femtosecond pulses,” Opt. Lett. 18, 2038–2040 (1993).
[CrossRef]

See, for example, J. K. Ranka, A. L. Gaeta, A. Baltuska, M. S. Pschenichnikov, and D. A. Wiersma, “Autocorrelation measurement of 6-fs pulses based on the two-photon-induced photocurrent in a GaAsP photodiode,” Opt. Lett. 22, 1344–1346 (1997).
[CrossRef]

Y. Kobayashi, T. Sekikawa, Y. Nabekawa, and S. Watanabe, “27 fs extreme ultraviolet pulse generation by high-order harmonics,” Opt. Lett. 23, 64–66 (1998).
[CrossRef]

P. Heist and T. Kleinschmidt, “Measurement of ultraviolet subpicosecond pulses based on ultrafast beam deflection,” Opt. Lett. 19, 1961–1963 (1994).
[CrossRef] [PubMed]

J. I. Dadap, G. B. Focht, D. H. Reitze, and M. C. Downer, “Two-photon absorption in diamond and its application to ultraviolet femtosecond pulse-width measurement,” Opt. Lett. 16, 499–501 (1991).
[CrossRef] [PubMed]

S. P. Le Blanc, G. Szabo, and R. Sauerbrey, “Femtosecond single-shot phase-sensitive autocorrelator for the ultraviolet,” Opt. Lett. 16, 1508–1510 (1991).
[CrossRef] [PubMed]

H. Nishiok, M. Ishiguro, T. Kawasumi, K. Udea, and H. Takuma, “Single-shot UV autocorrelator that uses a two-photon-induced photoacoustic signal in water,” Opt. Lett. 18, 45–47 (1993).
[CrossRef]

A. M. Streltsov, J. K. Ranka, and A. L. Gaeta, “Femtosecond ultraviolet autocorrelation measurements based on two-photon conductivity in fused silica,” Opt. Lett. 23, 790–800 (1998).
[CrossRef]

C. G. Durfee, S. Backus, H. C. Kapteyn, and M. M. Murnane, “Intense 8-fs pulse generation in the deep ultraviolet,” Opt. Lett. 24, 697–699 (1999).
[CrossRef]

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

M. Mehendale, S. A. Mitchell, J. P. Likforman, D. M. Villeneuve, and P. B. Corkum, “Method for single-shot measurement of the carrier envelope phase of a few-cycle laser pulse,” Opt. Lett. 25, 1672–1674 (2000).
[CrossRef]

See, for example, A. Braun, J. V. Rudd, H. Cheng, G. Mourou, D. Kopf, I. D. Jung, K. J. Weingarten, and U. Keller, “Characterization of short-pulse oscillators by means of a high-dynamic-range autocorrelation measurement,” Opt. Lett. 20, 1889–1891 (1995).
[CrossRef] [PubMed]

Phys. Rev. A (2)

E. Constant, V. D. Taranukhin, A. Stolow, and P. B. Corkum, “Methods for the measurement of the duration of high-harmonic pulses,” Phys. Rev. A 56, 3870–3878 (1997).
[CrossRef]

R. B. López-Martens, T. W. Schmidt, and G. Roberts, “ac Stark shifts in Rydberg NO levels induced by intense laser pulses,” Phys. Rev. A 62, 013414:1–9 (2000).

Phys. Rev. Lett. (2)

R. R. Freeman, P. H. Bucksbaum, H. Milchberg, S. Darack, D. Schumacher, and M. E. Geusic, “Above-threshold ionization with subpicosecond laser pulses,” Phys. Rev. Lett. 59, 1092–1095 (1987).
[CrossRef] [PubMed]

Z. H. Chang, A. Rundquist, H. W. Wang, M. M. Murnane, and H. C. Kapteyn, “Generation of coherent soft x-rays at 2.7 nm using high harmonics,” Phys. Rev. Lett. 79, 2967–2970 (1997).
[CrossRef]

Rev. Sci. Instrum. (1)

I. Walmsley, L. Waxer, and C. Dorrer, “The role of dispersion in ultrafast optics,” Rev. Sci. Instrum. 72, 1–29 (2001).
[CrossRef]

Science (1)

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[CrossRef] [PubMed]

Usp. Fiz. Nauk (1)

N. B. Delone and V. P. Krainov, “ac Stark shift of atomic energy levels,” Usp. Fiz. Nauk 42, 669–687 (1999).
[CrossRef]

Other (10)

We write the fluorescence signal as SF[I(t)], as opposed to SF[I0], to emphasize excitation of fluorescent population throughout the entire pulse duration and to indicate the possibility of extracting I(t) from SF[I(t)], as discussed in Section 3 below.

For ease of analysis in detecting a total ion signal, the absorption of photons that results in population of divers Rydberg levels is probably best avoided; otherwise the Stark shifts of all such levels must be taken into account in the analysis. Owing to the ease by which highly excited Rydberg states close to the ionization potential are shifted into resonance during multiphoton absorption, we suspect that the present method, when it is combined with ion detection, may not be optimally applied to map out the transient response of lower-lying bound states to which multiphoton (above-threshold) resonance ionization processes are accessed en route to the departure of an electron.

For nitric oxide, and other gases, this information may be found in “Optische konstanten, part 8 of Eigenschaften der Materie in ihren Aggregatzuständen,” Landholt–Börnstein: Zahlenwerte und Funktion en aus Physik, Chenie, Astronomie, Geophysik und Technik, 6th ed., K.-H. Hellwege and A. M. Hellwege, eds. (Springer-Verlag, Berlin, 1962), Table 4a, pp. 6-882–6-884.

See, for example, D. B. Milošević, S. Hu, and W. Becker, “Quantum mechanical model for ultrahigh-order harmonic generation in the moderately relativistic regime,” Phys. Rev. A63, 011403(R):1–4 (2001).
[CrossRef]

B. W. Shore, The Theory of Coherent Atomic Excitation (Wiley, New York, 1990), Vol. 1, Chap. 4, pp. 268–274; Chap. 10, pp. 590–604.

T. W. Schmidt, R. B. López-Martens, and G. Roberts, “Time-resolved spectroscopy of the dynamic Stark effect,” submitted to Phys. Rev. A.

K. P. Huber and G. Herzberg, Molecular Structure and Molecular Spectra IV: Constants of Diatomic Molecules (Van Nostrand Reinhold, New York, 1979), pp. 466–480.

J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic, San Diego, Calif.1995), Chap. 1, pp. 9–10; Chap. 8, pp. 365–380.

Some authors (e.g., in Ref. 34 below, p. 367) define an intensity correlation of order (n+1) as An(τD)=∫-∞∞ Is(t)Irn(t-τD)dt, for which Irn(t)→δ(t) and An(τD)→Is(t) as n→∞, where Is(t)=|Es(t)|2 and Ir(t)=|Er(t)|2 are the signal and the reference pulse intensity envelopes, respectively.

P. O’Shea, M. Kimmel, X. Gu, and R. Trebino, “Highly simplified ultrashort pulse measurement,” in Ultrafast Phenomena XII, T. Elsaesser, S. Mukamel, M. M. Murnane, and N. F. Scherer, eds. (Springer-Verlag, Berlin, 2001), pp. 123–125.

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Figures (7)

Fig. 1
Fig. 1

Autocorrelation behavior as a function of the nonlinear order coefficient n of the correlation integral. (a)–(c) Autocorrelation integral Gn(τD)=-[Es(t)Er*(t-τD)]ndt as defined by Eq. (3) (solid curves), |Es(t)|2 (dashed curves), and |Es(t)|2n (dotted–dashed curves) for the values of n indicated, where Eq(t)=Eq0(t)exp[iωqt+ϕq(t)] (q=s=r) are two identical E fields with Eq0(t)=exp(-t2/4σq2), ωq=0.6 fs-1, ϕq(t)=0 for all t, and σq=8.5 fs. The designation of time on the abscissa refers to τD for Gn(τD) and to t for |Es(t)|2 and |Es(t)|2n. (a) Shows that for n=2 the FWHM of G2(τD) is 21/2 times larger than the FWHM (τP=20 fs) of |Es(t)|2=|Er(t)|2, as expected for Gaussian functions. (b), (c) Show that Gn(τD)|Es(t)|2n as n attains large values. (d)–(f ) Illustrate An(τD) defined by Eq. (1) (solid curves), |Es(t)|2 (dashed curves), and |Es(t)|2n (dotted–dashed curves) for values of n as indicated, where Es(t) and Er(t) have the forms, and the abscissa has the meaning, given above. (d) Familiar second-order autocorrelation interferogram for n=2. (e), (f) Show how An(τD) tends in the limit n to a single interferometric peak with a FWHM approaching that of |Es(t)|2n. [For the arbitrary values of ωq, ϕq(t), and σq chosen here, An(τD) is dominated by a single peak, with two side maxima at τD=±1.7 fs reaching 6% of the amplitude of the center, when n=200.]

Fig. 2
Fig. 2

(a) Electronic and vibrational energy levels of NO that pertain to this research as a function of internuclear coordinate. Off-resonant two-photon excitation of the A 2Σ+ n=2X 2r n=0 Bohr transition at λ=400 nm (ωR=3.026 eV) leads to dynamic Stark shifting of the optically connected levels, which is monitored in real time by detection of A 2Σ+ n=2X 2r n=2 γ-band fluorescence at λ=222 nm (shown as a zigzag arrow). The differences between twice the energy supplied by the incoming photons, represented by the vertical arrow, and the n=2 vibrational level of the A 2Σ+ state, and that between the n=0 and the n=2 vibrational levels of the X 2r state, are exaggerated for clarity. The potential curve labeled X 1Σ+ represents the ground state of NO+. (b) Schematic diagram of the optical arrangement of an ac-Stark autocorrelator. Ultrafast light pulses from an amplified Ti:sapphire laser at λ=800 nm are frequency doubled by type I phase matching in a 0.5-mm BBO crystal. The second-harmonic beam is directed via a Michelson interferometer before collinear focusing at one side (to minimize fluorescence quenching) in a quartz cell containing a slow flow of NO gas. The λ/2 plate and the polarizer control the energy of input pulses. Detector D represents the combination of a monochromator and a photomultiplier tube for collection of fluorescence emitted perpendicular to the direction of propagation of the laser beam.

Fig. 3
Fig. 3

(a) Experimental NO A 2Σ+ n=2X 2r n=2 fluorescence signal excited by ultrafast laser pulses at 400 nm as a function of pulse energy P. The observed fluorescence exhibits a threshold as the A 2Σ+ n=2X 2r n=0 absorption is shifted to within the two-photon bandwidth of the applied laser field, and it then increases nonlinearly, with a slight shoulder at P170180 µJ per pulse. (b) |a2(t0)|2, the calculated fluorescent population in the first excited state of an electron confined to a one-dimensional box, versus peak intensity of a Gaussian pulse with temporal duration (FWHM) τP=97 fs.

Fig. 4
Fig. 4

Interferometric autocorrelation traces obtained from dynamic Stark shifting of the NO A 2Σ+ n=2X 2r n=0 two-photon Bohr resonance by laser pulses at λ=400 nm and total incident energies of (a) P=60 and (b) P=140 µJ. The autocorrelation envelope in (a) is fitted to a Gaussian function characterized by a FWHM of 76±6 fs; that in (b) is characterized by an average time duration of 138±11 fs derived from the second moment of the fluorescence energy density - SF[I(t)]dt.

Fig. 5
Fig. 5

Close-up of interferometric autocorrelation traces obtained with laser pulses at λ=400 nm and total incident energies of (a) P=40, (b) P=92, and (c) P=140 µJ. At lower energies the trace exhibits peaks with a shark-tooth shape as the laser pulses constructively interfere. At higher energies the individual peaks become sinusoidal as a result of saturation due to Rabi cycling of population between the A 2Σ+ n=2 and the X 2r n=0 levels at various instantaneous Stark shifts of the two-photon transition that optically connects them.

Fig. 6
Fig. 6

Calculated interferometric autocorrelation traces derived from dynamic Stark shifting of NO A 2Σ+ n=2X 2r n=0 for identical Gaussian pulses with τP=97 fs and peak intensities at a maximum space–time overlap of (a) I0=15 and (b) I0=35 TW cm-2. The autocorrelation envelope in (a) is fitted to a Gaussian function with a FWHM of 50 fs; that in (b) is characterized by an average time duration of 77 fs derived from the second moment of the fluorescence energy density -SF[I(t)]dt.

Fig. 7
Fig. 7

Calculated interferometric autocorrelation traces for identical Gaussian pulses with τP=97 fs and peak intensities at a maximum space–time overlap of (a) I0=1.0, (b) I0=2.8, and (c) 4.3 TW cm-2.

Equations (14)

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An(τD)=-|[Es(t)+Er(t-τD)]2|ndt,
A2(τD)=-[|Es0(t)|4+|Er0(t-τD)|4+4|Es0(t)|2×|Er0(t-τD)|2]dt+2 exp(iω0τD)×-[|Es0(t)|2+|Er0(t-τD)|2]×Es0(t)Er0*(t-τD)
×exp{i[ϕs(t)-ϕr(t)]}dt+c.c.
+exp(2iω0τD)- Es02(t)(Er0*)2(t-τD)×exp{2i[ϕs(t)-ϕr(t)]}dt+c.c.,
Gn(τD)=-[f1(t)f2*(t-τD)]ndt
Gn(τD)largenEs2n(t)nδs(t),
dSF[I(t)]=f[I(t)]dt.
i ddt|Ψ(t)=H(t)|Ψ(t).
i ddt|Ψ(t)=H(t)i ci(t)|ϕi(t)=i i(t)ci(t)|ϕi(t).
i ddt|Ψ(t)=H(t)j aj(t)|ψj=ij i(t)aj(t)ϕi(t)|ψj|ϕi(t)
ak(t0)=ψk|Ψ(t0)=-iψk|-t0 dt i,j i(t)aj(t)ϕi(t)|ψj|ϕi(t).
H(t)=Tˆ+V+E(t)(x-L/2),
E(t)=E0{exp[-4 ln(2)t2/τP2]cos(ω0t)+exp[-4 ln(2)(t-τD)2/τP2]cos[ω0(t-τD)]}.
|ψj=2/L sin(jπx/L)0<x<L0elsewhere,

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