Abstract

We develop a modified version of the dynamic spectrogram that permits complete characterization of an ultrashort optical pulse with fewer approximations than do other schemes. The experimental procedure for such a measurement uses a second-order optical nonlinearity and yet yields an intuitive spectrogram with no inherent symmetry constraints or ambiguity. We describe and demonstrate pulse-shape reconstruction from this type of spectrogram. Phase retrieval is performed by means of an iterative algorithm.

© 1997 Optical Society of America

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References

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  1. J. L. A. Chilla and O. E. Martinez, “Analysis of a method of phase measurement of ultrashort pulses in the frequency domain,” IEEE J. Quantum Electron. 27, 1228–1235 (1991).
    [CrossRef]
  2. D. J. Kane and R. Trebino, “Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating,” IEEE J. Quantum Electron. 29, 571–579 (1993).
    [CrossRef]
  3. J.-P. Foing, J.-P. Likforman, M. Joffre, and A. Migus, “Femtosecond pulse phase measurement by spectrally resolved up-conversion: application to continuum compression,” IEEE J. Quantum Electron. 28, 2285–2290 (1992).
    [CrossRef]
  4. S. P. LeBlanc and R. Sauerbrey, “Ultrashort pulse characterization using plasma-induced cross-phase-modulation,” Opt. Commun. 111, 297–302 (1994).
    [CrossRef]
  5. J.-K. Rhee, T. S. Sosnowski, A.-C. Tien, and T. B. Norris, “Real-time characterization of femtosecond laser pulses using a spectrally and temporally resolved upconversion technique,” in Conference on Lasers and Electro-Optics, Vol. 15 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper CPD39.
  6. K. C. Chu, J. P. Heritage, R. S. Grant, K. X. Liu, A. Dienes, W. E. White, and A. Sullivan, “Direct measurement of the spectral phase of femtosecond pulses,” Opt. Lett. 20, 904–906 (1995).
    [CrossRef] [PubMed]
  7. K. W. DeLong, R. Trebino, J. Hunter, and W. E. White, “Frequency-resolved optical gating with the use of second-harmonic generation,” J. Opt. Soc. Am. B 11, 2206–2215 (1994).
    [CrossRef]
  8. B. S. Prade, J. M. Schins, E. T. J. Nibbering, M. A. Franco, and A. Mysyrowicz, “A simple method for the determination of the intensity and phase of ultrashort optical pulses,” Opt. Commun. 113, 79–84 (1994).
    [CrossRef]
  9. E. B. Treacy, “Measurement and interpretation of dynamic spectrograms of picosecond light pulses,” J. Appl. Phys. 42, 3848–3858 (1971).
    [CrossRef]
  10. V. Wong and I. A. Walmsley, “Linear filter analysis of methods for ultrashort pulse-shape measurements,” J. Opt. Soc. Am. B 12, 1491–1499 (1995).
    [CrossRef]
  11. J. Paye, M. Ramaswamy, J. G. Fujimoto, and E. P. Ippen, “Measurement of the amplitude and phase of ultrashort light pulses from spectrally resolved autocorrelation,” Opt. Lett. 18, 1946–1948 (1993).
    [CrossRef] [PubMed]
  12. G. Taft, A. Rundquist, M. M. Murnane, H. C. Kapteyn, K. W. DeLong, R. Trebino, and I. P. Christov, “Ultrashort optical waveform measurements using frequency-resolved optical gating,” Opt. Lett. 20, 483–485 (1995)
    [CrossRef]
  13. I. A. Walmsley and V. Wong, “Characterization of noisy trains of ultrashort pulses,” in Generation, Amplification, and Measurement of Ultrashort Laser Pulses III, W. E. White and D. H. Reitze, eds., Proc. SPIE 2701, 133–139 (1996)
    [CrossRef]
  14. M. Beck, I. A. Walmsley, and J. D. Kafka, “Group delay measurements of optical components near 800 nm,” IEEE J. Quantum Electron. 27, 2074–2081 (1991).
    [CrossRef]
  15. K. W. DeLong, D. N. Fittinghoff, R. Trebino, B. Kohler, and K. Wilson, “Pulse retrieval in frequency-resolved optical gating using the method of generalized projections,” Opt. Lett. 19, 2152–2154 (1994).
    [CrossRef] [PubMed]
  16. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1992), p. 301.

1996

I. A. Walmsley and V. Wong, “Characterization of noisy trains of ultrashort pulses,” in Generation, Amplification, and Measurement of Ultrashort Laser Pulses III, W. E. White and D. H. Reitze, eds., Proc. SPIE 2701, 133–139 (1996)
[CrossRef]

1995

1994

K. W. DeLong, R. Trebino, J. Hunter, and W. E. White, “Frequency-resolved optical gating with the use of second-harmonic generation,” J. Opt. Soc. Am. B 11, 2206–2215 (1994).
[CrossRef]

B. S. Prade, J. M. Schins, E. T. J. Nibbering, M. A. Franco, and A. Mysyrowicz, “A simple method for the determination of the intensity and phase of ultrashort optical pulses,” Opt. Commun. 113, 79–84 (1994).
[CrossRef]

S. P. LeBlanc and R. Sauerbrey, “Ultrashort pulse characterization using plasma-induced cross-phase-modulation,” Opt. Commun. 111, 297–302 (1994).
[CrossRef]

K. W. DeLong, D. N. Fittinghoff, R. Trebino, B. Kohler, and K. Wilson, “Pulse retrieval in frequency-resolved optical gating using the method of generalized projections,” Opt. Lett. 19, 2152–2154 (1994).
[CrossRef] [PubMed]

1993

J. Paye, M. Ramaswamy, J. G. Fujimoto, and E. P. Ippen, “Measurement of the amplitude and phase of ultrashort light pulses from spectrally resolved autocorrelation,” Opt. Lett. 18, 1946–1948 (1993).
[CrossRef] [PubMed]

D. J. Kane and R. Trebino, “Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating,” IEEE J. Quantum Electron. 29, 571–579 (1993).
[CrossRef]

1992

J.-P. Foing, J.-P. Likforman, M. Joffre, and A. Migus, “Femtosecond pulse phase measurement by spectrally resolved up-conversion: application to continuum compression,” IEEE J. Quantum Electron. 28, 2285–2290 (1992).
[CrossRef]

1991

J. L. A. Chilla and O. E. Martinez, “Analysis of a method of phase measurement of ultrashort pulses in the frequency domain,” IEEE J. Quantum Electron. 27, 1228–1235 (1991).
[CrossRef]

M. Beck, I. A. Walmsley, and J. D. Kafka, “Group delay measurements of optical components near 800 nm,” IEEE J. Quantum Electron. 27, 2074–2081 (1991).
[CrossRef]

1971

E. B. Treacy, “Measurement and interpretation of dynamic spectrograms of picosecond light pulses,” J. Appl. Phys. 42, 3848–3858 (1971).
[CrossRef]

Beck, M.

M. Beck, I. A. Walmsley, and J. D. Kafka, “Group delay measurements of optical components near 800 nm,” IEEE J. Quantum Electron. 27, 2074–2081 (1991).
[CrossRef]

Chilla, J. L. A.

J. L. A. Chilla and O. E. Martinez, “Analysis of a method of phase measurement of ultrashort pulses in the frequency domain,” IEEE J. Quantum Electron. 27, 1228–1235 (1991).
[CrossRef]

Christov, I. P.

Chu, K. C.

DeLong, K. W.

Dienes, A.

Fittinghoff, D. N.

Foing, J.-P.

J.-P. Foing, J.-P. Likforman, M. Joffre, and A. Migus, “Femtosecond pulse phase measurement by spectrally resolved up-conversion: application to continuum compression,” IEEE J. Quantum Electron. 28, 2285–2290 (1992).
[CrossRef]

Franco, M. A.

B. S. Prade, J. M. Schins, E. T. J. Nibbering, M. A. Franco, and A. Mysyrowicz, “A simple method for the determination of the intensity and phase of ultrashort optical pulses,” Opt. Commun. 113, 79–84 (1994).
[CrossRef]

Fujimoto, J. G.

Grant, R. S.

Heritage, J. P.

Hunter, J.

Ippen, E. P.

Joffre, M.

J.-P. Foing, J.-P. Likforman, M. Joffre, and A. Migus, “Femtosecond pulse phase measurement by spectrally resolved up-conversion: application to continuum compression,” IEEE J. Quantum Electron. 28, 2285–2290 (1992).
[CrossRef]

Kafka, J. D.

M. Beck, I. A. Walmsley, and J. D. Kafka, “Group delay measurements of optical components near 800 nm,” IEEE J. Quantum Electron. 27, 2074–2081 (1991).
[CrossRef]

Kane, D. J.

D. J. Kane and R. Trebino, “Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating,” IEEE J. Quantum Electron. 29, 571–579 (1993).
[CrossRef]

Kapteyn, H. C.

Kohler, B.

LeBlanc, S. P.

S. P. LeBlanc and R. Sauerbrey, “Ultrashort pulse characterization using plasma-induced cross-phase-modulation,” Opt. Commun. 111, 297–302 (1994).
[CrossRef]

Likforman, J.-P.

J.-P. Foing, J.-P. Likforman, M. Joffre, and A. Migus, “Femtosecond pulse phase measurement by spectrally resolved up-conversion: application to continuum compression,” IEEE J. Quantum Electron. 28, 2285–2290 (1992).
[CrossRef]

Liu, K. X.

Martinez, O. E.

J. L. A. Chilla and O. E. Martinez, “Analysis of a method of phase measurement of ultrashort pulses in the frequency domain,” IEEE J. Quantum Electron. 27, 1228–1235 (1991).
[CrossRef]

Migus, A.

J.-P. Foing, J.-P. Likforman, M. Joffre, and A. Migus, “Femtosecond pulse phase measurement by spectrally resolved up-conversion: application to continuum compression,” IEEE J. Quantum Electron. 28, 2285–2290 (1992).
[CrossRef]

Murnane, M. M.

Mysyrowicz, A.

B. S. Prade, J. M. Schins, E. T. J. Nibbering, M. A. Franco, and A. Mysyrowicz, “A simple method for the determination of the intensity and phase of ultrashort optical pulses,” Opt. Commun. 113, 79–84 (1994).
[CrossRef]

Nibbering, E. T. J.

B. S. Prade, J. M. Schins, E. T. J. Nibbering, M. A. Franco, and A. Mysyrowicz, “A simple method for the determination of the intensity and phase of ultrashort optical pulses,” Opt. Commun. 113, 79–84 (1994).
[CrossRef]

Paye, J.

Prade, B. S.

B. S. Prade, J. M. Schins, E. T. J. Nibbering, M. A. Franco, and A. Mysyrowicz, “A simple method for the determination of the intensity and phase of ultrashort optical pulses,” Opt. Commun. 113, 79–84 (1994).
[CrossRef]

Ramaswamy, M.

Rundquist, A.

Sauerbrey, R.

S. P. LeBlanc and R. Sauerbrey, “Ultrashort pulse characterization using plasma-induced cross-phase-modulation,” Opt. Commun. 111, 297–302 (1994).
[CrossRef]

Schins, J. M.

B. S. Prade, J. M. Schins, E. T. J. Nibbering, M. A. Franco, and A. Mysyrowicz, “A simple method for the determination of the intensity and phase of ultrashort optical pulses,” Opt. Commun. 113, 79–84 (1994).
[CrossRef]

Sullivan, A.

Taft, G.

Treacy, E. B.

E. B. Treacy, “Measurement and interpretation of dynamic spectrograms of picosecond light pulses,” J. Appl. Phys. 42, 3848–3858 (1971).
[CrossRef]

Trebino, R.

Walmsley, I. A.

I. A. Walmsley and V. Wong, “Characterization of noisy trains of ultrashort pulses,” in Generation, Amplification, and Measurement of Ultrashort Laser Pulses III, W. E. White and D. H. Reitze, eds., Proc. SPIE 2701, 133–139 (1996)
[CrossRef]

V. Wong and I. A. Walmsley, “Linear filter analysis of methods for ultrashort pulse-shape measurements,” J. Opt. Soc. Am. B 12, 1491–1499 (1995).
[CrossRef]

M. Beck, I. A. Walmsley, and J. D. Kafka, “Group delay measurements of optical components near 800 nm,” IEEE J. Quantum Electron. 27, 2074–2081 (1991).
[CrossRef]

White, W. E.

Wilson, K.

Wong, V.

I. A. Walmsley and V. Wong, “Characterization of noisy trains of ultrashort pulses,” in Generation, Amplification, and Measurement of Ultrashort Laser Pulses III, W. E. White and D. H. Reitze, eds., Proc. SPIE 2701, 133–139 (1996)
[CrossRef]

Wong, V.

IEEE J. Quantum Electron.

J. L. A. Chilla and O. E. Martinez, “Analysis of a method of phase measurement of ultrashort pulses in the frequency domain,” IEEE J. Quantum Electron. 27, 1228–1235 (1991).
[CrossRef]

D. J. Kane and R. Trebino, “Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating,” IEEE J. Quantum Electron. 29, 571–579 (1993).
[CrossRef]

J.-P. Foing, J.-P. Likforman, M. Joffre, and A. Migus, “Femtosecond pulse phase measurement by spectrally resolved up-conversion: application to continuum compression,” IEEE J. Quantum Electron. 28, 2285–2290 (1992).
[CrossRef]

M. Beck, I. A. Walmsley, and J. D. Kafka, “Group delay measurements of optical components near 800 nm,” IEEE J. Quantum Electron. 27, 2074–2081 (1991).
[CrossRef]

J. Appl. Phys.

E. B. Treacy, “Measurement and interpretation of dynamic spectrograms of picosecond light pulses,” J. Appl. Phys. 42, 3848–3858 (1971).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

B. S. Prade, J. M. Schins, E. T. J. Nibbering, M. A. Franco, and A. Mysyrowicz, “A simple method for the determination of the intensity and phase of ultrashort optical pulses,” Opt. Commun. 113, 79–84 (1994).
[CrossRef]

S. P. LeBlanc and R. Sauerbrey, “Ultrashort pulse characterization using plasma-induced cross-phase-modulation,” Opt. Commun. 111, 297–302 (1994).
[CrossRef]

Opt. Lett.

Proc. SPIE

I. A. Walmsley and V. Wong, “Characterization of noisy trains of ultrashort pulses,” in Generation, Amplification, and Measurement of Ultrashort Laser Pulses III, W. E. White and D. H. Reitze, eds., Proc. SPIE 2701, 133–139 (1996)
[CrossRef]

Other

J.-K. Rhee, T. S. Sosnowski, A.-C. Tien, and T. B. Norris, “Real-time characterization of femtosecond laser pulses using a spectrally and temporally resolved upconversion technique,” in Conference on Lasers and Electro-Optics, Vol. 15 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper CPD39.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1992), p. 301.

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Figures (5)

Fig. 1
Fig. 1

Multishot experimental apparatus for recording dynamic spectrograms from temporal analysis of spectral components.

Fig. 2
Fig. 2

Dynamic spectrogram as a function of ωc and τ of Kerr-lens mode-locked Ti:sapphire pulses after they have traversed an optical isolator.

Fig. 3
Fig. 3

Iterative phase-retrieval algorithm making use of the method of generalized projection. The algorithm starts with an initial guess for the spectral phase ϕ(ω) and iterates according to the loop shown. FT, Fourier transform.

Fig. 4
Fig. 4

(a) Retrieved input spectral phase (circles) and its second-order fit (dotted curve), along with the measured input spectrum (solid curve). (b) Reconstructed input intensity.

Fig. 5
Fig. 5

(a) Measured (circles) and reconstructed (solid curve) autocorrelations. (b) Measured (circles) and reconstructed (solid curve) cross correlations obtained with the slit completely opened.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

If(t)=dωE˜in(ω)H˜(ω; ωc)exp(-iωt)2,
S(ωc, τ)=dtIf(t)Iin(t-τ)
=dtIin(t-τ)×dωE˜in(ω)H˜(ω; ωc)exp(-iωt)2.
S(ωc, τ)dωE˜in(ω)H˜(ω; ωc)exp(-iωτ)2.
S(ωc, τ)|E˜in(ωc)|2h(τ-ϕωc)|2,
E˜f(ω; ωc)=|E˜in(ω)|exp[iϕ(ω)]H˜(ω; ωc).
i=1Nj=1N|E˜f(ωj; ωci)
-|E˜in(ωj)|exp[iϕ(ωj)]H˜(ωj; ωci)|2,

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