Abstract

We extend to the ultraviolet frequency-resolved optical gating a new method for measuring the intensity and phase evolution of an individual ultrashort pulse without assumption. Using frequency-resolved optical gating, we measure a 310-fs, 308-nm pulse, whose phase is approximately cubic in time. We show that this phase distortion probably results from self-phase modulation and amplifier detuning.

© 1994 Optical Society of America

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References

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  1. K. Naganuma, K. Mogi, H. Yamada, IEEE J. Quantum Electron. 25, 1225 (1989).
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  2. C. Yan, J.-C. Diels, J. Opt. Soc. Am. B 8, 1259 (1991).
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  4. D. J. Kane, R. Trebino, IEEE J. Quantum Electron. 29, 571 (1993).
    [CrossRef]
  5. D. J. Kane, R. Trebino, Opt. Lett. 18, 823 (1993).
    [CrossRef] [PubMed]
  6. R. Trebino, D. J. Kane, J. Opt. Soc. Am. A 10, 1101 (1993).
    [CrossRef]
  7. H. Schultz, H. Schüler, T. Engers, D. von der Linde, IEEE J. Quantum Electron. 25, 2580 (1989).
    [CrossRef]
  8. J. I. Dadap, G. B. Focht, D. H. Reitze, M. C. Downer, Opt. Lett. 16, 499 (1991).
    [CrossRef] [PubMed]
  9. S. P. Le Blanc, G. Szabo, R. Sauerbrey, Opt. Lett. 16, 1508 (1991).
    [CrossRef] [PubMed]
  10. E. S. Kintzer, C. Rempel, Appl. Phys. B 42, 91 (1987).
    [CrossRef]
  11. H.-St. Albrecht, P. Heist, J. Kleinschmidt, D. van Lap, T. Schröder, Appl. Phys. B 55, 362 (1992), and references therein.
    [CrossRef]
  12. K. W. DeLong, R. Trebino, D. J. Kane, “Comparison of ultrashort-pulse frequency-resolved optical gating traces for three common beam geometries,” submitted toJ. Opt. Soc. Am. B.
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  16. R. A. Altes, J. Acoust. Soc. Am. 67, 1232 (1980).
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  17. L. Cohen, Proc. IEEE 77, 941 (1989).
    [CrossRef]
  18. W. Koenig, H. K. Dunn, L. Y. Lacy, J. Acoust. Soc. Am. 18, 19 (1946).
    [CrossRef]
  19. K. W. DeLong, R. Trebino, “Improved ultrashort-pulse-retrieval algorithm for frequency-resolved optical gating,” J. Opt. Soc. Am. A (to be published).
  20. A. J. Taylor, C. R. Tallman, J. P. Roberts, C. S. Lesker, T. R. Gosnell, R. H. Y. Lee, G. A. Kyrala, Opt. Lett. 15, 39 (1990).
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  21. F. Kannari, M. Obara, J. Opt. Soc. Am. B 7, 1493 (1990), and references therein.
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  22. K. W. DeLong, J. Yumoto, J. Opt. Soc. Am. B 9, 1593 (1992).
    [CrossRef]

1993 (3)

1992 (2)

K. W. DeLong, J. Yumoto, J. Opt. Soc. Am. B 9, 1593 (1992).
[CrossRef]

H.-St. Albrecht, P. Heist, J. Kleinschmidt, D. van Lap, T. Schröder, Appl. Phys. B 55, 362 (1992), and references therein.
[CrossRef]

1991 (5)

1990 (3)

1989 (3)

L. Cohen, Proc. IEEE 77, 941 (1989).
[CrossRef]

K. Naganuma, K. Mogi, H. Yamada, IEEE J. Quantum Electron. 25, 1225 (1989).
[CrossRef]

H. Schultz, H. Schüler, T. Engers, D. von der Linde, IEEE J. Quantum Electron. 25, 2580 (1989).
[CrossRef]

1987 (1)

E. S. Kintzer, C. Rempel, Appl. Phys. B 42, 91 (1987).
[CrossRef]

1982 (1)

P. B. Corkum, R. S. Taylor, IEEE J. Quantum Electron. QE-18, 1962 (1982).
[CrossRef]

1980 (1)

R. A. Altes, J. Acoust. Soc. Am. 67, 1232 (1980).
[CrossRef]

1946 (1)

W. Koenig, H. K. Dunn, L. Y. Lacy, J. Acoust. Soc. Am. 18, 19 (1946).
[CrossRef]

Albrecht, H.-St.

H.-St. Albrecht, P. Heist, J. Kleinschmidt, D. van Lap, T. Schröder, Appl. Phys. B 55, 362 (1992), and references therein.
[CrossRef]

Altes, R. A.

R. A. Altes, J. Acoust. Soc. Am. 67, 1232 (1980).
[CrossRef]

Chilla, J. L. A.

Cohen, L.

L. Cohen, Proc. IEEE 77, 941 (1989).
[CrossRef]

Corkum, P. B.

P. B. Corkum, R. S. Taylor, IEEE J. Quantum Electron. QE-18, 1962 (1982).
[CrossRef]

Dadap, J. I.

DeLong, K. W.

K. W. DeLong, J. Yumoto, J. Opt. Soc. Am. B 9, 1593 (1992).
[CrossRef]

K. W. DeLong, R. Trebino, “Improved ultrashort-pulse-retrieval algorithm for frequency-resolved optical gating,” J. Opt. Soc. Am. A (to be published).

K. W. DeLong, R. Trebino, D. J. Kane, “Comparison of ultrashort-pulse frequency-resolved optical gating traces for three common beam geometries,” submitted toJ. Opt. Soc. Am. B.

Diels, J.-C.

Downer, M. C.

Dunn, H. K.

W. Koenig, H. K. Dunn, L. Y. Lacy, J. Acoust. Soc. Am. 18, 19 (1946).
[CrossRef]

Engers, T.

H. Schultz, H. Schüler, T. Engers, D. von der Linde, IEEE J. Quantum Electron. 25, 2580 (1989).
[CrossRef]

Focht, G. B.

Gosnell, T. R.

Heist, P.

H.-St. Albrecht, P. Heist, J. Kleinschmidt, D. van Lap, T. Schröder, Appl. Phys. B 55, 362 (1992), and references therein.
[CrossRef]

Kane, D. J.

D. J. Kane, R. Trebino, Opt. Lett. 18, 823 (1993).
[CrossRef] [PubMed]

R. Trebino, D. J. Kane, J. Opt. Soc. Am. A 10, 1101 (1993).
[CrossRef]

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

K. W. DeLong, R. Trebino, D. J. Kane, “Comparison of ultrashort-pulse frequency-resolved optical gating traces for three common beam geometries,” submitted toJ. Opt. Soc. Am. B.

Kannari, F.

Kintzer, E. S.

E. S. Kintzer, C. Rempel, Appl. Phys. B 42, 91 (1987).
[CrossRef]

Kleinschmidt, J.

H.-St. Albrecht, P. Heist, J. Kleinschmidt, D. van Lap, T. Schröder, Appl. Phys. B 55, 362 (1992), and references therein.
[CrossRef]

Koenig, W.

W. Koenig, H. K. Dunn, L. Y. Lacy, J. Acoust. Soc. Am. 18, 19 (1946).
[CrossRef]

Kyrala, G. A.

Lacy, L. Y.

W. Koenig, H. K. Dunn, L. Y. Lacy, J. Acoust. Soc. Am. 18, 19 (1946).
[CrossRef]

Le Blanc, S. P.

Lee, R. H. Y.

Lesker, C. S.

MacPherson, D. C.

Martinez, O. E.

Mogi, K.

K. Naganuma, K. Mogi, H. Yamada, IEEE J. Quantum Electron. 25, 1225 (1989).
[CrossRef]

Naganuma, K.

K. Naganuma, K. Mogi, H. Yamada, IEEE J. Quantum Electron. 25, 1225 (1989).
[CrossRef]

Obara, M.

Reitze, D. H.

Rempel, C.

E. S. Kintzer, C. Rempel, Appl. Phys. B 42, 91 (1987).
[CrossRef]

Roberts, J. P.

Sauerbrey, R.

Schröder, T.

H.-St. Albrecht, P. Heist, J. Kleinschmidt, D. van Lap, T. Schröder, Appl. Phys. B 55, 362 (1992), and references therein.
[CrossRef]

Schüler, H.

H. Schultz, H. Schüler, T. Engers, D. von der Linde, IEEE J. Quantum Electron. 25, 2580 (1989).
[CrossRef]

Schultz, H.

H. Schultz, H. Schüler, T. Engers, D. von der Linde, IEEE J. Quantum Electron. 25, 2580 (1989).
[CrossRef]

Szabo, G.

Tallman, C. R.

Taylor, A. J.

Taylor, R. S.

P. B. Corkum, R. S. Taylor, IEEE J. Quantum Electron. QE-18, 1962 (1982).
[CrossRef]

Trebino, R.

D. J. Kane, R. Trebino, Opt. Lett. 18, 823 (1993).
[CrossRef] [PubMed]

R. Trebino, D. J. Kane, J. Opt. Soc. Am. A 10, 1101 (1993).
[CrossRef]

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

K. W. DeLong, R. Trebino, D. J. Kane, “Comparison of ultrashort-pulse frequency-resolved optical gating traces for three common beam geometries,” submitted toJ. Opt. Soc. Am. B.

K. W. DeLong, R. Trebino, “Improved ultrashort-pulse-retrieval algorithm for frequency-resolved optical gating,” J. Opt. Soc. Am. A (to be published).

van Lap, D.

H.-St. Albrecht, P. Heist, J. Kleinschmidt, D. van Lap, T. Schröder, Appl. Phys. B 55, 362 (1992), and references therein.
[CrossRef]

von der Linde, D.

H. Schultz, H. Schüler, T. Engers, D. von der Linde, IEEE J. Quantum Electron. 25, 2580 (1989).
[CrossRef]

Yamada, H.

K. Naganuma, K. Mogi, H. Yamada, IEEE J. Quantum Electron. 25, 1225 (1989).
[CrossRef]

Yan, C.

Yumoto, J.

Appl. Phys. B (2)

E. S. Kintzer, C. Rempel, Appl. Phys. B 42, 91 (1987).
[CrossRef]

H.-St. Albrecht, P. Heist, J. Kleinschmidt, D. van Lap, T. Schröder, Appl. Phys. B 55, 362 (1992), and references therein.
[CrossRef]

IEEE J. Quantum Electron. (4)

H. Schultz, H. Schüler, T. Engers, D. von der Linde, IEEE J. Quantum Electron. 25, 2580 (1989).
[CrossRef]

K. Naganuma, K. Mogi, H. Yamada, IEEE J. Quantum Electron. 25, 1225 (1989).
[CrossRef]

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

P. B. Corkum, R. S. Taylor, IEEE J. Quantum Electron. QE-18, 1962 (1982).
[CrossRef]

J. Acoust. Soc. Am. (2)

R. A. Altes, J. Acoust. Soc. Am. 67, 1232 (1980).
[CrossRef]

W. Koenig, H. K. Dunn, L. Y. Lacy, J. Acoust. Soc. Am. 18, 19 (1946).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (3)

Opt. Lett. (7)

Proc. IEEE (1)

L. Cohen, Proc. IEEE 77, 941 (1989).
[CrossRef]

Other (2)

K. W. DeLong, R. Trebino, “Improved ultrashort-pulse-retrieval algorithm for frequency-resolved optical gating,” J. Opt. Soc. Am. A (to be published).

K. W. DeLong, R. Trebino, D. J. Kane, “Comparison of ultrashort-pulse frequency-resolved optical gating traces for three common beam geometries,” submitted toJ. Opt. Soc. Am. B.

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Figures (6)

Fig. 1
Fig. 1

Experimental arrangement for single-shot FROG. The delay is mapped onto position horizontally across the nonlinear-optical medium. At the spectrometer entrance the delay (τ) varies horizontally along the slits. Thus, at the output, delay is the horizontal axis, and frequency (ω) is the vertical axis. The camera therefore measures IFROG(ω, τ) in a single shot. Inset: schematic of the FROG interaction of two smooth Gaussian pulses for a given delay (i.e., position at the sample). The signal pulse indicates the approximate instantaneous frequency of E(t) at 2τ/3.

Fig. 2
Fig. 2

Experimental single-shot FROG trace for a ~308-nm pulse, which has a duration of ~310 fs and a quadratic instantaneous frequency versus time, i.e., a cubic phase versus time.

Fig. 3
Fig. 3

Derived intensity (thick curve) and phase (thin curve) evolutions for the pulse whose FROG trace is shown in Fig. 2. The cubic dependence of the phase evolution in time indicates the quadratic dependence of the instantaneous frequency in time.

Fig. 4
Fig. 4

Experimental and derived third-order intensity autocorrelations for the pulse of Figs. 2 and 3.

Fig. 5
Fig. 5

How a cubic phase versus time can occur: the solid curve is the frequency versus time for a self-phase-modulated pulse that is to be amplified. The shaded region shows the region of gain of the amplifier. The resulting pulse frequency versus time will be roughly quadratic in time, and hence the phase will be cubic in time.

Fig. 6
Fig. 6

Theoretical (a) intensity and phase and (b) FROG trace of a self-phase-modulated pulse amplified by a narrow-band, detuned amplifier. We did this calculation by multiplying E(ω) for a Gaussian pulse, spectrally broadened by a factor of 2.58 because of self-phase modulation, by a gain function in the form of a Gaussian with the same bandwidth as the broadened pulse but detuned by 70% of its width. Fourier transforming yielded E(t), which was then used to generate the FROG trace.

Equations (2)

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E sig ( t , τ ) E ( t ) E ( t - τ ) 2 ,
I FROG ( ω , τ ) | - E sig ( t , τ ) exp ( - i ω t ) d t | 2 .

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