Abstract

We introduce a new technique, frequency-resolved optical gating, for measuring the intensity I(t) and the phase ϕ(t) of an individual arbitrary ultrashort pulse. Using an instantaneous nonlinear-optical interaction of two variably delayed replicas of the pulse, frequency-resolved optical gating involves measuring the spectrum of the signal pulse versus relative delay. The resulting trace, a spectrogram, yields an intuitive full-information display of the pulse. Inversion of this trace to obtain the pulse intensity and phase is equivalent to the well-known two-dimensional phase-retrieval problem and thus yields essentially unambiguous results for I(t) and ϕ(t).

© 1993 Optical Society of America

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1993

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

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

1992

J. Paye, IEEE J. Quantum Electron, 28, 2262 (1992).
[CrossRef]

A. Brun, P. Georges, G. Le Saux, F. Salin, Rev. Sci. Instrum. 27, 1225 (1992).

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

1991

1990

1989

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

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

1988

1987

1986

J. Jansky, G. Corradi, Opt. Commun. 60, 251 (1986).
[CrossRef]

1985

1984

R. Barakat, G. Newsam, J. Math. Phys. 25, 3190 (1984).
[CrossRef]

1983

S. H. Nawab, T. F. Quatieri, J. S. Lim, IEEE Trans. Acoust. Speech Signal Process. ASSP-31, 986 (1983).
[CrossRef]

1982

1980

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

1975

E. P. Ippen, C. V. Shank, Appl. Phys. Lett. 27, 488 (1975).
[CrossRef]

1967

J. A. Armstrong, Appl. Phys. Lett. 10, 16 (1967).
[CrossRef]

1956

E. J. Akutowicz, Trans. Am. Math. Soc. 83, 234 (1956).

1946

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

Akutowicz, E. J.

E. J. Akutowicz, Trans. Am. Math. Soc. 83, 234 (1956).

Altes, R. A.

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

Armstrong, J. A.

J. A. Armstrong, Appl. Phys. Lett. 10, 16 (1967).
[CrossRef]

Barakat, R.

R. Barakat, G. Newsam, J. Math. Phys. 25, 3190 (1984).
[CrossRef]

Brun, A.

A. Brun, P. Georges, G. Le Saux, F. Salin, Rev. Sci. Instrum. 27, 1225 (1992).

Chilla, J. L. A.

Cohen, L.

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

Corradi, G.

J. Jansky, G. Corradi, Opt. Commun. 60, 251 (1986).
[CrossRef]

da Silva, V. L.

Delong, K. W.

Diels, J.-C. M.

Dunn, H. K.

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

Fienup, J. R.

Foing, J. P.

J. P. Foing, L. P. Likforman, M. Joffre, in Ultrafast Phenomena VIII, J. L. Martin, ed. (Springer-Verlag, Berlin, 1993), p. 44.

Fontaine, J. J.

Georges, P.

A. Brun, P. Georges, G. Le Saux, F. Salin, Rev. Sci. Instrum. 27, 1225 (1992).

Gomes, A. S. L.

Grischkowsky, D.

Hayden, C. C.

Heritage, J. P.

J. P. Heritage, A. M. Weiner, R. N. Thurston, in Ultrafast Phenomena V, G. R. Fleming, A. E. Siegman, eds. (Springer-Verlag, Berlin, 1986), p. 34.

Ippen, E. P.

E. P. Ippen, C. V. Shank, Appl. Phys. Lett. 27, 488 (1975).
[CrossRef]

Jansky, J.

J. Jansky, G. Corradi, Opt. Commun. 60, 251 (1986).
[CrossRef]

Joffre, M.

J. P. Foing, L. P. Likforman, M. Joffre, in Ultrafast Phenomena VIII, J. L. Martin, ed. (Springer-Verlag, Berlin, 1993), p. 44.

Johnson, A. M.

Kane, D. J.

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]

Koenig, W.

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

Lacy, L. Y.

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

Lane, R. G.

R. G. Lane, J. Mod. Opt. 38, 1797 (1991).
[CrossRef]

Le Saux, G.

A. Brun, P. Georges, G. Le Saux, F. Salin, Rev. Sci. Instrum. 27, 1225 (1992).

Levine, A. M.

Likforman, L. P.

J. P. Foing, L. P. Likforman, M. Joffre, in Ultrafast Phenomena VIII, J. L. Martin, ed. (Springer-Verlag, Berlin, 1993), p. 44.

Lim, J. S.

S. H. Nawab, T. F. Quatieri, J. S. Lim, IEEE Trans. Acoust. Speech Signal Process. ASSP-31, 986 (1983).
[CrossRef]

Martinez, O. E.

McMichael, I. C.

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]

Nawab, S. H.

S. H. Nawab, T. F. Quatieri, J. S. Lim, IEEE Trans. Acoust. Speech Signal Process. ASSP-31, 986 (1983).
[CrossRef]

Newsam, G.

R. Barakat, G. Newsam, J. Math. Phys. 25, 3190 (1984).
[CrossRef]

Paye, J.

J. Paye, IEEE J. Quantum Electron, 28, 2262 (1992).
[CrossRef]

Quatieri, T. F.

S. H. Nawab, T. F. Quatieri, J. S. Lim, IEEE Trans. Acoust. Speech Signal Process. ASSP-31, 986 (1983).
[CrossRef]

Rothenberg, J. E.

Salin, F.

A. Brun, P. Georges, G. Le Saux, F. Salin, Rev. Sci. Instrum. 27, 1225 (1992).

Seldin, J. H.

J. H. Seldin, J. R. Fienup, J. Opt. Am. A 7, 428 (1990).
[CrossRef]

Shank, C. V.

E. P. Ippen, C. V. Shank, Appl. Phys. Lett. 27, 488 (1975).
[CrossRef]

Shen, Y. R.

Y. R. Shen, G.-Z. Yang, in Supercontinuum Laser Source, R. R. Alfano, ed. (Springer-Verlag, New York, 1989), p. 16.

Simoni, F.

Simpson, W. M.

Stark, H.

H. Stark, Image Recovery: Theory and Application (Academic, Orlando, Fla., 1987).

Taylor, J. R.

Thurston, R. N.

J. P. Heritage, A. M. Weiner, R. N. Thurston, in Ultrafast Phenomena V, G. R. Fleming, A. E. Siegman, eds. (Springer-Verlag, Berlin, 1986), p. 34.

Trebino, R.

Weiner, A. M.

J. P. Heritage, A. M. Weiner, R. N. Thurston, in Ultrafast Phenomena V, G. R. Fleming, A. E. Siegman, eds. (Springer-Verlag, Berlin, 1986), p. 34.

Yamada, H.

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

Yang, G.-Z.

Y. R. Shen, G.-Z. Yang, in Supercontinuum Laser Source, R. R. Alfano, ed. (Springer-Verlag, New York, 1989), p. 16.

Yumoto, J.

Appl. Opt.

Appl. Phys. Lett.

J. A. Armstrong, Appl. Phys. Lett. 10, 16 (1967).
[CrossRef]

E. P. Ippen, C. V. Shank, Appl. Phys. Lett. 27, 488 (1975).
[CrossRef]

IEEE J. Quantum Electron,

J. Paye, IEEE J. Quantum Electron, 28, 2262 (1992).
[CrossRef]

IEEE J. Quantum Electron.

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

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

IEEE Trans. Acoust. Speech Signal Process.

S. H. Nawab, T. F. Quatieri, J. S. Lim, IEEE Trans. Acoust. Speech Signal Process. ASSP-31, 986 (1983).
[CrossRef]

J. Acoust. Soc. Am.

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. Math. Phys.

R. Barakat, G. Newsam, J. Math. Phys. 25, 3190 (1984).
[CrossRef]

J. Mod. Opt.

R. G. Lane, J. Mod. Opt. 38, 1797 (1991).
[CrossRef]

J. Opt. Am. A

J. H. Seldin, J. R. Fienup, J. Opt. Am. A 7, 428 (1990).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Opt. Commun.

J. Jansky, G. Corradi, Opt. Commun. 60, 251 (1986).
[CrossRef]

Opt. Lett.

Proc. IEEE

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

Rev. Sci. Instrum.

A. Brun, P. Georges, G. Le Saux, F. Salin, Rev. Sci. Instrum. 27, 1225 (1992).

Trans. Am. Math. Soc.

E. J. Akutowicz, Trans. Am. Math. Soc. 83, 234 (1956).

Other

H. Stark, Image Recovery: Theory and Application (Academic, Orlando, Fla., 1987).

J. P. Heritage, A. M. Weiner, R. N. Thurston, in Ultrafast Phenomena V, G. R. Fleming, A. E. Siegman, eds. (Springer-Verlag, Berlin, 1986), p. 34.

J. P. Foing, L. P. Likforman, M. Joffre, in Ultrafast Phenomena VIII, J. L. Martin, ed. (Springer-Verlag, Berlin, 1993), p. 44.

Y. R. Shen, G.-Z. Yang, in Supercontinuum Laser Source, R. R. Alfano, ed. (Springer-Verlag, New York, 1989), p. 16.

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Figures (6)

Fig. 1
Fig. 1

Experimental arrangement for single-shot FROG. Delay is mapped onto position horizontally across the nonlinear-optical medium. At the spectrometer, delay (τ) varies along the slits, and frequency (ω) varies in the direction perpendicular to this. The CCD camera therefore measures IFROG(ω, τ) in a single shot. Inset: schematic of the FROG interaction of two smooth pulses for a given delay (i.e., position at the sample). The signal pulse is centered at the time 2τ/3 and reflects the instantaneous frequency of E(t) at that time. For complex pulses, the signal pulse reflects the spectrum of a temporal slice of E(t) determined by the delay τ.

Fig. 2
Fig. 2

Density plots (bottom row) of FROG traces for negatively chirped, unchirped, and positively chirped Gaussian pulses. Top row: instantaneous frequency versus time for the pulses. Observe that the FROG trace reflects the instantaneous frequency of the pulse. This is the case for more complex phase evolutions also.

Fig. 3
Fig. 3

Iterative Fourier-transform algorithm for inverting a FROG trace to obtain a pulse intensity and phase.

Fig. 4
Fig. 4

Experimental single-shot FROG trace for an approximately linearly chirped pulse.

Fig. 5
Fig. 5

Derived intensity (thick curve) and phase (thin curve) evolutions for the pulse of Fig. 4. The inverted parabolic shape of the phase evolution indicates approximately linear positive chirp.

Fig. 6
Fig. 6

Experimental and derived third-order intensity autocorrelations for the pulse of Figs. 4 and 5.

Equations (4)

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

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