Abstract

We numerically simulate the performance of the ultrasimple frequency-resolved-optical-gating (FROG) technique, GRENOUILLE, for measuring ultrashort laser pulses. While simple in practice, GRENOUILLE has many theoretical subtleties because it involves the second-harmonic generation of relatively tightly focused and broadband pulses. In addition, these processes occur in a thick crystal, in which the phase-matching bandwidth is deliberately made narrow compared to the pulse bandwidth. In these simulations, we include all sum-frequency-generation processes, both collinear and noncollinear. We also include dispersion using the Sellmeier equation for the crystal BBO. Working in the frequency domain, we compute the GRENOUILLE trace for practical—and impractical—examples and show that accurate measurements are easily obtained for properly designed devices.

© 2007 Optical Society of America

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References

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  1. R. Trebino, Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses (Kluwer Academic Publishers, Boston, 2002).
  2. P. O'Shea, M. Kimmel, X. Gu, and R. Trebino, "Highly simplified device for ultrashort-pulse measurement," Opt. Lett. 26, 932-934(2001).
    [CrossRef]
  3. C. Radzewicz, P. Wasylczyk and J. S. Krasinski, "A poor man's FROG," Opt. Commun. 186,329-333(2000)
    [CrossRef]
  4. S. Akturk, M. Kimmel, P. O'Shea, and R. Trebino, "Measuring pulse-front tilt in ultrashort pulses using GRENOUILLE," Opt. Express 11, 491-501(2003).
    [CrossRef] [PubMed]
  5. S. Akturk, M. Kimmel, P. O'Shea, and R. Trebino, "Measuring spatial chirp in ultrashort pulses using single-shot Frequency-Resolved Optical Gating," Opt. Express 11, 68-78(2003).
    [CrossRef] [PubMed]
  6. P. O'Shea, S. Akturk, M. Kimmel, and R. Trebino, "Practical issues in ultra-short-pulse measurements with ‘GRENOUILLE’," Appl. Phys. B 79, 683-691(2004).
    [CrossRef]
  7. S. Akturk, M. Kimmel, P. O'Shea, and R. Trebino, "Extremely simple device for measuring 20 fs pulses," Opt. Lett. 29, 1025-1027(2004).
    [CrossRef] [PubMed]

2004 (2)

P. O'Shea, S. Akturk, M. Kimmel, and R. Trebino, "Practical issues in ultra-short-pulse measurements with ‘GRENOUILLE’," Appl. Phys. B 79, 683-691(2004).
[CrossRef]

S. Akturk, M. Kimmel, P. O'Shea, and R. Trebino, "Extremely simple device for measuring 20 fs pulses," Opt. Lett. 29, 1025-1027(2004).
[CrossRef] [PubMed]

2003 (2)

2001 (1)

2000 (1)

C. Radzewicz, P. Wasylczyk and J. S. Krasinski, "A poor man's FROG," Opt. Commun. 186,329-333(2000)
[CrossRef]

Akturk, S.

Gu, X.

Kimmel, M.

Krasinski, J. S.

C. Radzewicz, P. Wasylczyk and J. S. Krasinski, "A poor man's FROG," Opt. Commun. 186,329-333(2000)
[CrossRef]

O'Shea, P.

Radzewicz, C.

C. Radzewicz, P. Wasylczyk and J. S. Krasinski, "A poor man's FROG," Opt. Commun. 186,329-333(2000)
[CrossRef]

Trebino, R.

Wasylczyk, P.

C. Radzewicz, P. Wasylczyk and J. S. Krasinski, "A poor man's FROG," Opt. Commun. 186,329-333(2000)
[CrossRef]

Appl. Phys. B (1)

P. O'Shea, S. Akturk, M. Kimmel, and R. Trebino, "Practical issues in ultra-short-pulse measurements with ‘GRENOUILLE’," Appl. Phys. B 79, 683-691(2004).
[CrossRef]

Opt. Commun. (1)

C. Radzewicz, P. Wasylczyk and J. S. Krasinski, "A poor man's FROG," Opt. Commun. 186,329-333(2000)
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Other (1)

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

Supplementary Material (2)

» Media 1: AVI (2450 KB)     
» Media 2: AVI (2450 KB)     

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Figures (11)

Fig. 1.
Fig. 1.

(a). FROG (top) and its simpler cousin, GRENOUILLE (bottom). GRENOUILLE replaces the beam splitter and recombining apparatus with a Fresnel biprism. And it also replaces the thin crystal and spectrometer with a thick crystal.

Fig. 1.
Fig. 1.

(b). GRENOUILLE from above and the side.

Fig. 2.
Fig. 2.

(a). The Fresnel biprism and its use for splitting and crossing two replicas of the pulse to be measured. It maps delay onto transverse position of the crystal.

Fig. 2.
Fig. 2.

(b). Rough polar plots of the output SHG intensity of a given color vs. angle for a tightly focused broadband input pulse and SHG crystals of various thicknesses. The thick crystal autocorrelates the tightly focused input pulse and simultaneously angularly disperses the resulting second-harmonic pulse.

Fig. 3.
Fig. 3.

Diagram for the phase-mismatch calculation. The k-vector of grid q (k 3y , ω 3) is tilted from the z-axis by θ 3. θ 1 and θ 2 are the tilt angles of the k-vectors of the electric field pair P1(k 1y , ω 1) and P2(k 2y , ω 2).

Fig. 4.
Fig. 4.

(a) Ideal FROG trace for the 60fs flat phase pulse. (b) Simulated GRENOUILLE trace of a. (c) Retrieved GRENOUILLE trace. (d,e) The black lines show the retrieved temporal and spectral intensities and phases of the pulse. The red lines show the intensities and phases of the actual input pulse.

Fig. 5.
Fig. 5.

(a) Ideal FROG trace of a double chirped 50 fs pulse. (b) Simulated GRENOUILLE trace. (c) Retrieved GRENOUILLE trace. (d,e) The black curves show the retrieved temporal and spectral intensities and phases of the pulse. The red curves show the intensities and phases of the actual input pulse.

Fig. 6.
Fig. 6.

(2.45 MB) Movie of simulated GRENOUILLE traces for a 60-fs flat-phase pulse focused at the center of a 3.5 mm BBO with different focal-length lenses. In the movie, the focal spot size evolves from 10 to 100 μm. The weaker foci yield traces that are spectrally too narrow. [Media 1]

Fig. 7.
Fig. 7.

(2.45 MB) Movie of simulated GRENOUILLE trace for a 50-fs double chirped pulse focused down to the center of a BBO crystal with a 10-μm focal spot. In the movie, the thickness of the BBO crystal changes from 0.5 mm to 9.5 mm. [Media 2]

Fig. 8.
Fig. 8.

(a) Ideal FROG trace of a double chirped long pulse. (b) Simulated GRENOUILLE trace of the same pulse. (c) Retrieved GRENOUILLE trace. (d,e) The black curves show the retrieved temporal and spectral intensities and phases of the pulse. The red curves show the intensities and phases of the actual input pulse.

Fig. 9.
Fig. 9.

(a) Ideal FROG trace of a slightly chirped 20 fs double pulse. (b) Simulated GRENOUILLE trace of this pulse. (c) Retrieved GRENOUILLE trace. (d,e) The black curves show the retrieved temporal and spectral intensities and phases of the pulse. The red curves show the intensities and phases of the actual input pulse.

Equations (4)

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E 3 ( k 3 y , ω 3 , z ) z = i d eff ω 3 c n ˜ 3 exp ( i Δ k z z ) ×
E 1 ( k 1 y , ω 1 , z ) E 2 ( k 3 y k 1 y , ω 3 ω 1 , z ) d k 1 y d ω 1
Δ k qz = ω 3 n e ( ω 3 , θ 3 ) c cos θ 3 ω 1 n o ( ω 1 ) c cos θ 1 ω 2 n o ( ω 2 ) c cos θ 2
I FROG ( ω , τ ) = E ( t ) E ( t τ ) exp ( i ω t ) d t 2 .

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