Abstract

The technique of second-harmonic generation frequency-resolved optical gating is applied to measure the intensity and the phase of 4.5-fs pulses resulting from the fiber-compressed output of a cavity-dumped Ti:sapphire laser. Characterization of even shorter optical pulses by this method should also be feasible.

© 1998 Optical Society of America

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References

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  1. A. Baltuška, Z. Wei, M. S. Pshenichnikov, and D. A. Wiersma, Opt. Lett. 22, 102 (1997); Appl. Phys. B 65, 175 (1997).
    [Crossref]
  2. M. Nisoli, S. De Silvestri, O. Svelto, R. Szipöcs, K. Ferencz, S. Sartania, Ch. Spielmann, and F. Krausz, Opt. Lett. 22, 522 (1997); M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, M. Lenzner, Ch. Spielmann, and F. Krausz, Appl. Phys. B 65, 189 (1997).
    [Crossref] [PubMed]
  3. D. J. Kane and R. Trebino, IEEE J. Quantum Electron. 29, 571 (1993).
    [Crossref]
  4. K. W. DeLong, R. Trebino, and D. J. Kane, J. Opt. Soc. Am. B 11, 1595 (1994).
    [Crossref]
  5. K. W. DeLong, R. Trebino, J. Hunter, and W. E. White, J. Opt. Soc. Am. B 11, 2206 (1994).
    [Crossref]
  6. G. Taft, A. Rundquist, M. M. Murnane, H. C. Kapteyn, K. W. DeLong, R. Trebino, and I. Christov, Opt. Lett. 20, 743 (1995).
    [Crossref] [PubMed]
  7. G. Taft, A. Rundquist, M. M. Murnane, I. P. Christov, H. C. Kapteyn, K. W. DeLong, D. N. Fittinghoff, M. A. Krumbügel, J. N. Sweetser, and R. Trebino, IEEE J. Sel. Topics Quantum Electron. 2, 575 (1996).
    [Crossref]
  8. T. Brabec and F. Krausz, Phys. Rev. Lett. 78, 3282 (1997).
    [Crossref]
  9. From refractive-index dispersion of ?-barium borate we estimated that the effective second-order nonlinearity deff changes no more than 5% within the SH bandwidth. For details see Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984), Chap. 2.
  10. K. W. DeLong, C. L. Ladera, R. Trebino, B. Kohler, and K. R. Wilson, Opt. Lett. 20, 486 (1995).
    [Crossref] [PubMed]
  11. A. M. Weiner, IEEE J. Quantum Electron. 19, 1276 (1983).
    [Crossref]
  12. S. Feng, H. G. Winful, and R. W. Hellwarth, Opt. Lett. 23, 385 (1998).
    [Crossref]
  13. K. W. DeLong, D. N. Fittinghoff, R. Trebino, B. Kohler, and K. Wilson, Opt. Lett. 19, 2152 (1994).
    [Crossref] [PubMed]
  14. Note that relation (3) is a much better approximation for type I phase matching than for type II.
  15. The correct value for ?t is smaller by a factor of 2 than the one derived in Ref. 7.
  16. R. Trebino, Sandia National Laboratories, Livermore, Calif. 94551 (personal communication, 1997).
  17. J. Squier, D. Fittinghoff, C. P. Barty, K. R. Wilson, M. Müller, and G. J. Brakenhoff, Opt. Commun. 147, 153 (1998).
    [Crossref]
  18. V. Kabelka and A. V. Masalov, Opt. Commun. 100, 482 (1993).
    [Crossref]

1998 (2)

S. Feng, H. G. Winful, and R. W. Hellwarth, Opt. Lett. 23, 385 (1998).
[Crossref]

J. Squier, D. Fittinghoff, C. P. Barty, K. R. Wilson, M. Müller, and G. J. Brakenhoff, Opt. Commun. 147, 153 (1998).
[Crossref]

1997 (3)

1996 (1)

G. Taft, A. Rundquist, M. M. Murnane, I. P. Christov, H. C. Kapteyn, K. W. DeLong, D. N. Fittinghoff, M. A. Krumbügel, J. N. Sweetser, and R. Trebino, IEEE J. Sel. Topics Quantum Electron. 2, 575 (1996).
[Crossref]

1995 (2)

1994 (3)

1993 (2)

V. Kabelka and A. V. Masalov, Opt. Commun. 100, 482 (1993).
[Crossref]

D. J. Kane and R. Trebino, IEEE J. Quantum Electron. 29, 571 (1993).
[Crossref]

1983 (1)

A. M. Weiner, IEEE J. Quantum Electron. 19, 1276 (1983).
[Crossref]

Baltuška, A.

Barty, C. P.

J. Squier, D. Fittinghoff, C. P. Barty, K. R. Wilson, M. Müller, and G. J. Brakenhoff, Opt. Commun. 147, 153 (1998).
[Crossref]

Brabec, T.

T. Brabec and F. Krausz, Phys. Rev. Lett. 78, 3282 (1997).
[Crossref]

Brakenhoff, G. J.

J. Squier, D. Fittinghoff, C. P. Barty, K. R. Wilson, M. Müller, and G. J. Brakenhoff, Opt. Commun. 147, 153 (1998).
[Crossref]

Christov, I.

Christov, I. P.

G. Taft, A. Rundquist, M. M. Murnane, I. P. Christov, H. C. Kapteyn, K. W. DeLong, D. N. Fittinghoff, M. A. Krumbügel, J. N. Sweetser, and R. Trebino, IEEE J. Sel. Topics Quantum Electron. 2, 575 (1996).
[Crossref]

De Silvestri, S.

DeLong, K. W.

Feng, S.

Ferencz, K.

Fittinghoff, D.

J. Squier, D. Fittinghoff, C. P. Barty, K. R. Wilson, M. Müller, and G. J. Brakenhoff, Opt. Commun. 147, 153 (1998).
[Crossref]

Fittinghoff, D. N.

G. Taft, A. Rundquist, M. M. Murnane, I. P. Christov, H. C. Kapteyn, K. W. DeLong, D. N. Fittinghoff, M. A. Krumbügel, J. N. Sweetser, and R. Trebino, IEEE J. Sel. Topics Quantum Electron. 2, 575 (1996).
[Crossref]

K. W. DeLong, D. N. Fittinghoff, R. Trebino, B. Kohler, and K. Wilson, Opt. Lett. 19, 2152 (1994).
[Crossref] [PubMed]

Hellwarth, R. W.

Hunter, J.

Kabelka, V.

V. Kabelka and A. V. Masalov, Opt. Commun. 100, 482 (1993).
[Crossref]

Kane, D. J.

K. W. DeLong, R. Trebino, and D. J. Kane, J. Opt. Soc. Am. B 11, 1595 (1994).
[Crossref]

D. J. Kane and R. Trebino, IEEE J. Quantum Electron. 29, 571 (1993).
[Crossref]

Kapteyn, H. C.

G. Taft, A. Rundquist, M. M. Murnane, I. P. Christov, H. C. Kapteyn, K. W. DeLong, D. N. Fittinghoff, M. A. Krumbügel, J. N. Sweetser, and R. Trebino, IEEE J. Sel. Topics Quantum Electron. 2, 575 (1996).
[Crossref]

G. Taft, A. Rundquist, M. M. Murnane, H. C. Kapteyn, K. W. DeLong, R. Trebino, and I. Christov, Opt. Lett. 20, 743 (1995).
[Crossref] [PubMed]

Kohler, B.

Krausz, F.

Krumbügel, M. A.

G. Taft, A. Rundquist, M. M. Murnane, I. P. Christov, H. C. Kapteyn, K. W. DeLong, D. N. Fittinghoff, M. A. Krumbügel, J. N. Sweetser, and R. Trebino, IEEE J. Sel. Topics Quantum Electron. 2, 575 (1996).
[Crossref]

Ladera, C. L.

Masalov, A. V.

V. Kabelka and A. V. Masalov, Opt. Commun. 100, 482 (1993).
[Crossref]

Müller, M.

J. Squier, D. Fittinghoff, C. P. Barty, K. R. Wilson, M. Müller, and G. J. Brakenhoff, Opt. Commun. 147, 153 (1998).
[Crossref]

Murnane, M. M.

G. Taft, A. Rundquist, M. M. Murnane, I. P. Christov, H. C. Kapteyn, K. W. DeLong, D. N. Fittinghoff, M. A. Krumbügel, J. N. Sweetser, and R. Trebino, IEEE J. Sel. Topics Quantum Electron. 2, 575 (1996).
[Crossref]

G. Taft, A. Rundquist, M. M. Murnane, H. C. Kapteyn, K. W. DeLong, R. Trebino, and I. Christov, Opt. Lett. 20, 743 (1995).
[Crossref] [PubMed]

Nisoli, M.

Pshenichnikov, M. S.

Rundquist, A.

G. Taft, A. Rundquist, M. M. Murnane, I. P. Christov, H. C. Kapteyn, K. W. DeLong, D. N. Fittinghoff, M. A. Krumbügel, J. N. Sweetser, and R. Trebino, IEEE J. Sel. Topics Quantum Electron. 2, 575 (1996).
[Crossref]

G. Taft, A. Rundquist, M. M. Murnane, H. C. Kapteyn, K. W. DeLong, R. Trebino, and I. Christov, Opt. Lett. 20, 743 (1995).
[Crossref] [PubMed]

Sartania, S.

Shen, Y. R.

From refractive-index dispersion of ?-barium borate we estimated that the effective second-order nonlinearity deff changes no more than 5% within the SH bandwidth. For details see Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984), Chap. 2.

Spielmann, Ch.

Squier, J.

J. Squier, D. Fittinghoff, C. P. Barty, K. R. Wilson, M. Müller, and G. J. Brakenhoff, Opt. Commun. 147, 153 (1998).
[Crossref]

Svelto, O.

Sweetser, J. N.

G. Taft, A. Rundquist, M. M. Murnane, I. P. Christov, H. C. Kapteyn, K. W. DeLong, D. N. Fittinghoff, M. A. Krumbügel, J. N. Sweetser, and R. Trebino, IEEE J. Sel. Topics Quantum Electron. 2, 575 (1996).
[Crossref]

Szipöcs, R.

Taft, G.

G. Taft, A. Rundquist, M. M. Murnane, I. P. Christov, H. C. Kapteyn, K. W. DeLong, D. N. Fittinghoff, M. A. Krumbügel, J. N. Sweetser, and R. Trebino, IEEE J. Sel. Topics Quantum Electron. 2, 575 (1996).
[Crossref]

G. Taft, A. Rundquist, M. M. Murnane, H. C. Kapteyn, K. W. DeLong, R. Trebino, and I. Christov, Opt. Lett. 20, 743 (1995).
[Crossref] [PubMed]

Trebino, R.

Wei, Z.

Weiner, A. M.

A. M. Weiner, IEEE J. Quantum Electron. 19, 1276 (1983).
[Crossref]

White, W. E.

Wiersma, D. A.

Wilson, K.

Wilson, K. R.

J. Squier, D. Fittinghoff, C. P. Barty, K. R. Wilson, M. Müller, and G. J. Brakenhoff, Opt. Commun. 147, 153 (1998).
[Crossref]

K. W. DeLong, C. L. Ladera, R. Trebino, B. Kohler, and K. R. Wilson, Opt. Lett. 20, 486 (1995).
[Crossref] [PubMed]

Winful, H. G.

IEEE J. Quantum Electron. (2)

D. J. Kane and R. Trebino, IEEE J. Quantum Electron. 29, 571 (1993).
[Crossref]

A. M. Weiner, IEEE J. Quantum Electron. 19, 1276 (1983).
[Crossref]

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

G. Taft, A. Rundquist, M. M. Murnane, I. P. Christov, H. C. Kapteyn, K. W. DeLong, D. N. Fittinghoff, M. A. Krumbügel, J. N. Sweetser, and R. Trebino, IEEE J. Sel. Topics Quantum Electron. 2, 575 (1996).
[Crossref]

J. Opt. Soc. Am. B (2)

Opt. Commun. (2)

J. Squier, D. Fittinghoff, C. P. Barty, K. R. Wilson, M. Müller, and G. J. Brakenhoff, Opt. Commun. 147, 153 (1998).
[Crossref]

V. Kabelka and A. V. Masalov, Opt. Commun. 100, 482 (1993).
[Crossref]

Opt. Lett. (6)

Phys. Rev. Lett. (1)

T. Brabec and F. Krausz, Phys. Rev. Lett. 78, 3282 (1997).
[Crossref]

Other (4)

From refractive-index dispersion of ?-barium borate we estimated that the effective second-order nonlinearity deff changes no more than 5% within the SH bandwidth. For details see Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984), Chap. 2.

Note that relation (3) is a much better approximation for type I phase matching than for type II.

The correct value for ?t is smaller by a factor of 2 than the one derived in Ref. 7.

R. Trebino, Sandia National Laboratories, Livermore, Calif. 94551 (personal communication, 1997).

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Figures (4)

Fig. 1
Fig. 1

Conversion efficiency RΩ (solid curves) and the ratio of FROG signals as given by relation (1) and Eq. (5) (dotted and dashed curves) for (a) a transform-limited 5-fs Gaussian pulse and (b) a linearly chirped 150-fs pulse with the same bandwidth. A 10- µm-thick β-barium borate doubling crystal is cut at θ=33.4° for type I phase matching. The detector’s spectral sensitivity is QΩ=1.

Fig. 2
Fig. 2

Experimentally measured and retrieved SHG FROG traces of compressed pulses. The traces are shown as density plots with overlaid contour lines at the levels 0.02, 0.05, 0.1, 0.2, 0.4, 0.6, and 0.8 of peak SH intensity.

Fig. 3
Fig. 3

(a) Temporal marginal (filled circles) and independently measured autocorrelation of 4.5-fs pulses (solid curves) and (b) frequency marginal and autoconvolution of the fundamental spectrum.

Fig. 4
Fig. 4

Retrieved pulse parameters in (a) the time and (b) the frequency domains. Shaded contours show field intensities; dashed curves indicate phases. The experimental spectrum of the pulse (filled circles) is depicted for comparison.

Equations (5)

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SΩ,τ,LΩ2nΩ2QΩ-+EωEΩ-ω×ω1-ωΩ1/2 expiωτ+iΔkω,Ω-ωL2×sinc Δkω,Ω-ωL2dω2,
Δkω,Ω-ω=koω+koΩ-ω-keΩ
SΩ,τ,LRΩSFROGSHGΩ,τ,
RΩ=Ω3nΩ2QΩsinc2ΔkΩ2,Ω2L2,
SFROGSHGΩ,τ=-+EωEΩ-ωexpiωτdω2.

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