Abstract

Frequency-resolved optical gating (FROG) is a technique used to measure the intensity and phase of ultrashort laser pulses through the optical construction of a spectrogram of the pulse. To obtain quantitative information about the pulse from its spectrogram, an iterative two-dimensional phase-retrieval algorithm must be used. Current algorithms are quite robust, but retrieval of all the pulse information can be slow. Previous real-time FROG trace inversion work focused on second-harmonic-generation FROG, which has an ambiguity in the direction of time, and required digital signal processors (DSPs). We develop a simplified real-time FROG device based on a single-shot geometry that no longer requires DSPs. We use it and apply the principal component generalized projections algorithm to invert polarization gate FROG traces at rates as high as 20 Hz.

© 2003 Optical Society of America

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References

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    [CrossRef]
  2. D. J. Kane, R. Trebino, “Single-shot measurement of the intensity and phase of an arbitrary ultrashort pulse by using frequency-resolved optical gating,” Opt. Lett. 18, 823–825 (1993).
    [CrossRef] [PubMed]
  3. R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
    [CrossRef]
  4. D. J. Kane, G. Rodriguez, A. J. Taylor, T. S. Clement, “Simultaneous measurement of two ultrashort laser pulses from a single spectrogram in a single shot,” J. Opt. Soc. Am. 14, 935–943 (1997).
    [CrossRef]
  5. D. J. Kane, “Real-time measurement of ultrashort laser pulses using principal component generalized projections,” IEEE J. Sel. Top. Quantum Electron. 4, 278–284 (1998).
    [CrossRef]
  6. D. J. Kane, “Recent progress toward real-time measurement of ultrashort laser pulses,” IEEE J. Quantum Electron. 35, 421–431 (1999).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  21. V. Wong, I. A. Walmsley, “Ultrashort-pulse characterization from dynamic spectrograms by iterative phase retrieval,” J. Opt. Soc. Am. B 14, 944–949 (1997).
    [CrossRef]
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2000 (1)

1999 (4)

1998 (2)

D. J. Kane, “Real-time measurement of ultrashort laser pulses using principal component generalized projections,” IEEE J. Sel. Top. Quantum Electron. 4, 278–284 (1998).
[CrossRef]

C. Iaconis, V. Wong, I. A. Walmsley, “Direct interferometric techniques for characterizing ultrashort optical pulses,” IEEE J. Sel. Top. Quantum Electron. 4, 285–294 (1998).
[CrossRef]

1997 (4)

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

D. J. Kane, G. Rodriguez, A. J. Taylor, T. S. Clement, “Simultaneous measurement of two ultrashort laser pulses from a single spectrogram in a single shot,” J. Opt. Soc. Am. 14, 935–943 (1997).
[CrossRef]

V. Wong, I. A. Walmsley, “Ultrashort-pulse characterization from dynamic spectrograms by iterative phase retrieval,” J. Opt. Soc. Am. B 14, 944–949 (1997).
[CrossRef]

C. W. Siders, A. J. Taylor, M. C. Downer, “Multipulse interferometric frequency-resolved optical gating: real-time phase-sensitive imaging of ultrafast dynamics,” Opt. Lett. 22, 624–626 (1997).
[CrossRef] [PubMed]

1993 (3)

1991 (1)

1989 (1)

L. Cohen, “Time-frequency distributions—a review,” Proc. IEEE 77, 941–981 (1989).
[CrossRef]

1987 (2)

1984 (1)

1971 (1)

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

Anderson, M. E.

Bromage, J.

Chilla, J. L. A.

Clement, T. S.

D. J. Kane, G. Rodriguez, A. J. Taylor, T. S. Clement, “Simultaneous measurement of two ultrashort laser pulses from a single spectrogram in a single shot,” J. Opt. Soc. Am. 14, 935–943 (1997).
[CrossRef]

Cohen, L.

L. Cohen, “Time-frequency distributions—a review,” Proc. IEEE 77, 941–981 (1989).
[CrossRef]

DeLong, K. W.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

Downer, M. C.

Fienup, J. R.

Fittinghoff, D. N.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipies in C: The Art of Scientific Computing, 2nd ed. (Cambridge University, Cambridge, England, 1995).

Gallmann, L.

Habetler, G. J.

Iaconis, C.

Jain, A. K.

A. K. Jain, Fundamentals of Digital Image Processing, 1st ed. (Prentice-Hall, Englewood Cliffs, N.J., 1989).

Kane, D. J.

D. J. Kane, F. G. Omenetto, A. J. Taylor, “Convergence test for inversion of frequency-resolved optical gating spectrograms,” Opt. Lett. 25, 1216–1218 (2000).
[CrossRef]

D. J. Kane, “Recent progress toward real-time measurement of ultrashort laser pulses,” IEEE J. Quantum Electron. 35, 421–431 (1999).
[CrossRef]

D. J. Kane, “Real-time measurement of ultrashort laser pulses using principal component generalized projections,” IEEE J. Sel. Top. Quantum Electron. 4, 278–284 (1998).
[CrossRef]

D. J. Kane, G. Rodriguez, A. J. Taylor, T. S. Clement, “Simultaneous measurement of two ultrashort laser pulses from a single spectrogram in a single shot,” J. Opt. Soc. Am. 14, 935–943 (1997).
[CrossRef]

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

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

R. Trebino, D. J. Kane, “Using phase retrieval to measure the intensity and phase of ultrashort laser pulses: frequency-resolved optical gating,” J. Opt. Soc. Am. A 10, 1101–1111 (1993).
[CrossRef]

D. J. Kane, R. Trebino, “Single-shot measurement of the intensity and phase of an arbitrary ultrashort pulse by using frequency-resolved optical gating,” Opt. Lett. 18, 823–825 (1993).
[CrossRef] [PubMed]

Keller, U.

Krumbügel, M. A.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

Levi, A.

Martinez, O. E.

Matuschek, N.

Omenetto, F. G.

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipies in C: The Art of Scientific Computing, 2nd ed. (Cambridge University, Cambridge, England, 1995).

Reid, D. T.

D. T. Reid, “Algorithm for complete and rapid retrieval of ultrashort pulse amplitude and phase from a sonogram,” IEEE J. Quantum Electron. 35, 1584–1589 (1999).
[CrossRef]

Richman, B. A.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

Rodriguez, G.

D. J. Kane, G. Rodriguez, A. J. Taylor, T. S. Clement, “Simultaneous measurement of two ultrashort laser pulses from a single spectrogram in a single shot,” J. Opt. Soc. Am. 14, 935–943 (1997).
[CrossRef]

Shuman, T. M.

Siders, C. W.

Stark, H.

Steinmeyer, G.

Sutter, D. H.

Sweetser, J. N.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

Taylor, A. J.

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipies in C: The Art of Scientific Computing, 2nd ed. (Cambridge University, Cambridge, England, 1995).

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.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

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

R. Trebino, D. J. Kane, “Using phase retrieval to measure the intensity and phase of ultrashort laser pulses: frequency-resolved optical gating,” J. Opt. Soc. Am. A 10, 1101–1111 (1993).
[CrossRef]

D. J. Kane, R. Trebino, “Single-shot measurement of the intensity and phase of an arbitrary ultrashort pulse by using frequency-resolved optical gating,” Opt. Lett. 18, 823–825 (1993).
[CrossRef] [PubMed]

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipies in C: The Art of Scientific Computing, 2nd ed. (Cambridge University, Cambridge, England, 1995).

Walmsley, I. A.

Waxer, L.

Wong, V.

C. Iaconis, V. Wong, I. A. Walmsley, “Direct interferometric techniques for characterizing ultrashort optical pulses,” IEEE J. Sel. Top. Quantum Electron. 4, 285–294 (1998).
[CrossRef]

V. Wong, I. A. Walmsley, “Ultrashort-pulse characterization from dynamic spectrograms by iterative phase retrieval,” J. Opt. Soc. Am. B 14, 944–949 (1997).
[CrossRef]

Yudilevich, E.

IEEE J. Quantum Electron. (3)

D. J. Kane, “Recent progress toward real-time measurement of ultrashort laser pulses,” IEEE J. Quantum Electron. 35, 421–431 (1999).
[CrossRef]

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

D. T. Reid, “Algorithm for complete and rapid retrieval of ultrashort pulse amplitude and phase from a sonogram,” IEEE J. Quantum Electron. 35, 1584–1589 (1999).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

C. Iaconis, V. Wong, I. A. Walmsley, “Direct interferometric techniques for characterizing ultrashort optical pulses,” IEEE J. Sel. Top. Quantum Electron. 4, 285–294 (1998).
[CrossRef]

D. J. Kane, “Real-time measurement of ultrashort laser pulses using principal component generalized projections,” IEEE J. Sel. Top. Quantum Electron. 4, 278–284 (1998).
[CrossRef]

J. Appl. Phys. (1)

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. (1)

D. J. Kane, G. Rodriguez, A. J. Taylor, T. S. Clement, “Simultaneous measurement of two ultrashort laser pulses from a single spectrogram in a single shot,” J. Opt. Soc. Am. 14, 935–943 (1997).
[CrossRef]

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

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

Opt. Express (1)

Opt. Lett. (5)

Proc. IEEE (1)

L. Cohen, “Time-frequency distributions—a review,” Proc. IEEE 77, 941–981 (1989).
[CrossRef]

Rev. Sci. Instrum. (1)

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

Other (2)

A. K. Jain, Fundamentals of Digital Image Processing, 1st ed. (Prentice-Hall, Englewood Cliffs, N.J., 1989).

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipies in C: The Art of Scientific Computing, 2nd ed. (Cambridge University, Cambridge, England, 1995).

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Figures (4)

Fig. 1
Fig. 1

Schematic of the PCGP algorithm.

Fig. 2
Fig. 2

Schematic diagram of a single-shot PG FROG device. The input pulse is split into two replicas, the pulse and the gate, that cross at an angle to map the time delay to a spatial coordinate. A cylindrical lens focuses the gate and probe into the nonlinear medium (quartz). A polarizer is used to set the polarization of the probe to 45 deg relative to the gate. The gate pulse induces birefringence in the nonlinear medium, rotating the polarization of the probe. The signal leaks through the second polarizer, set at 90 deg relative to the first, and is spectrally resolved with an imaging spectrometer. The inset shows the signal pulse’s functional relationship to the probe and the gate pulses.

Fig. 3
Fig. 3

Screen data from the real-time FROG program. The large plot on the left side is the raw spectrogram directly from the video camera. The square around the spectrogram indicates the portion of the raw FROG trace used for the pulse retrieval. The plots on the right show the retrieved pulse intensity and phase. The FWHM of the pulse is 98.9 fs and the bandwidth is 5.37 THz. The actual retrieval rate was 19.4 retrievals/s with eight iterations of the algorithm between updates.

Fig. 4
Fig. 4

Example of retrieved data: (a) resampled FROG trace; (b) intensity and phase of the retrieved pulse; (c) weights. The nearly straight line indicates close to noise-limited convergence.

Equations (3)

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probein+1=Oij Oji* probejn, gatein+1=Oji* Oijgatejn,
Oij=probeigatej+Γ-1 gatei Γ probej,
Δt=NtNfΔf1/2, Δf=1NresampledΔt,

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