Abstract

We simulate multishot intensity-and-phase measurements of unstable trains of complex ultrashort pulses using second-harmonic-generation (SHG) frequency-resolved optical gating (FROG) and spectral-phase interferometry for direct electric-field reconstruction (SPIDER). Both techniques fail to see the pulse structure. But FROG yields the correct average pulse duration and suggests the instability by exhibiting significant disagreement between measured and retrieved traces. SPIDER retrieves the correct average spectral phase but significantly underestimates the average pulse duration. In short, SPIDER measures only the coherent artifact. An analytical calculation confirms this last fact.

© 2012 Optical Society of America

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References

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    [CrossRef]

2008 (1)

2004 (1)

2003 (3)

F. Quéré, J. Itatani, G. Yudin, and P. Corkum, Phys. Rev. Lett. 90, 073902 (2003).
[CrossRef]

K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, K. Weber, and R. S. Windeler, Phys. Rev. Lett. 90, 113904 (2003).
[CrossRef]

X. Gu, M. Kimmel, A. P. Shreenath, R. Trebino, J. Dudley, S. Coen, and R. S. Windeler, Opt. Express 11, 2697 (2003).
[CrossRef]

2002 (1)

1998 (1)

1982 (1)

1979 (1)

E. W. Van Stryland, Opt. Commun. 31, 93 (1979).
[CrossRef]

1969 (1)

R. A. Fisher and J. A. Fleck, Appl. Phys. Lett. 15, 287 (1969).
[CrossRef]

Coen, S.

X. Gu, M. Kimmel, A. P. Shreenath, R. Trebino, J. Dudley, S. Coen, and R. S. Windeler, Opt. Express 11, 2697 (2003).
[CrossRef]

K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, K. Weber, and R. S. Windeler, Phys. Rev. Lett. 90, 113904 (2003).
[CrossRef]

Corkum, P.

F. Quéré, J. Itatani, G. Yudin, and P. Corkum, Phys. Rev. Lett. 90, 073902 (2003).
[CrossRef]

Corwin, K. L.

K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, K. Weber, and R. S. Windeler, Phys. Rev. Lett. 90, 113904 (2003).
[CrossRef]

Diddams, S. A.

K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, K. Weber, and R. S. Windeler, Phys. Rev. Lett. 90, 113904 (2003).
[CrossRef]

Dudley, J.

Dudley, J. M.

K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, K. Weber, and R. S. Windeler, Phys. Rev. Lett. 90, 113904 (2003).
[CrossRef]

Fisher, R. A.

R. A. Fisher and J. A. Fleck, Appl. Phys. Lett. 15, 287 (1969).
[CrossRef]

Fleck, J. A.

R. A. Fisher and J. A. Fleck, Appl. Phys. Lett. 15, 287 (1969).
[CrossRef]

Gu, X.

Hirasawa, M.

Iaconis, C.

Ina, H.

Itatani, J.

F. Quéré, J. Itatani, G. Yudin, and P. Corkum, Phys. Rev. Lett. 90, 073902 (2003).
[CrossRef]

Kimmel, M.

Kobayashi, S.

Morita, R.

Nakagawa, N.

Newbury, N. R.

K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, K. Weber, and R. S. Windeler, Phys. Rev. Lett. 90, 113904 (2003).
[CrossRef]

O’Shea, P.

Oka, K.

Quéré, F.

F. Quéré, J. Itatani, G. Yudin, and P. Corkum, Phys. Rev. Lett. 90, 073902 (2003).
[CrossRef]

Shreenath, A. P.

Suguro, A.

Takeda, M.

Trebino, R.

Van Stryland, E. W.

E. W. Van Stryland, Opt. Commun. 31, 93 (1979).
[CrossRef]

Walmsley, I. A.

Weber, K.

K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, K. Weber, and R. S. Windeler, Phys. Rev. Lett. 90, 113904 (2003).
[CrossRef]

Windeler, R. S.

Xu, L.

Yamamoto, K.

Yamashita, M.

Yudin, G.

F. Quéré, J. Itatani, G. Yudin, and P. Corkum, Phys. Rev. Lett. 90, 073902 (2003).
[CrossRef]

Zeek, E.

Appl. Phys. Lett. (1)

R. A. Fisher and J. A. Fleck, Appl. Phys. Lett. 15, 287 (1969).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Opt. Commun. (1)

E. W. Van Stryland, Opt. Commun. 31, 93 (1979).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. Lett. (2)

F. Quéré, J. Itatani, G. Yudin, and P. Corkum, Phys. Rev. Lett. 90, 073902 (2003).
[CrossRef]

K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, K. Weber, and R. S. Windeler, Phys. Rev. Lett. 90, 113904 (2003).
[CrossRef]

Other (1)

R. Trebino, Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses (Kluwer, 2002).

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Figures (2)

Fig. 1.
Fig. 1.

Top: double pulse and its autocorrelation. Bottom: a train of variably spaced double pulses and their multishot autocorrelation. The coherent artifact results from the short nonrandom coherent component of the double pulses (a single pulse), while the broader background results from the overall average pulse length (the combination of both pulses). This trace is typical of autocorrelations of nearly all trains of unstable complex pulses.

Fig. 2.
Fig. 2.

Nonrandom- and random-pulse trains of varying complexity, and simulated multishot SPIDER and SHG FROG measurements of them. Top row: nonrandom train of identical Gaussian flat-phase pulses. Middle and bottom rows: random-pulse trains of different average complexity and duration. Red curves are intensity, blue phase, green spectrum, and purple spectral phase. The black dotted SPIDER traces are fits assuming flat-phase Gaussian pulses and benign SPIDER-device misalignment: unequal SPIDER double-pulse energies. For all three pulse trains, SPIDER retrieves only the nonrandom pulse component, 12δt long, and exhibits decreasing fringe visibility (100%, 98%, and 90%, respectively). FROG exhibits an autocorrelationlike coherent artifact: the narrow blue spikes in the measured traces for the two random trains. Like SPIDER, FROG does not see the pulse structure, but it does yield the correct durations. More importantly, measured and retrieved FROG traces disagree for the random trains, and their rms differences (G errors) are large: 0.0083 and 0.014, respectively, for the 256×256 traces. In all plots, all temporal units are in δt, and all frequency units are in 2π/(Nδt), where N is the SPIDER array size (4096).

Equations (2)

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SSPIDER|E(ω)+E(ω+δω)exp(iωT)+Erand(ω)+Erand(ω+δω)exp(iωT)|2,
SSPIDER=S(ω)+S(ω+δω)+Srand(ω)+Srand(ω+δω)+2S(ω)S(ω+δω)cos[δωτ(ω)+ωT]+2Srand(ω)Srand(ω+δω)cos[δωτrand(ω)+ωT].

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