Abstract

We perform numerical simulations of cross-correlation frequency-resolved optical gating with the nonlinearities, optical parametric amplification, and difference-frequency generation for measuring broadband pulses. We show that use of a noncollinear beam geometry that matches the group velocities of the pump, signal, and idler pulses permits use of relatively thick crystals for high gain without significant distortion in the measured trace, yielding bandwidths of 100nm.

© 2006 Optical Society of America

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References

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  1. 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]
  2. R. Trebino and D. J. Kane, "Using phase retrieval to measure the intensity and phase of ultrashort pulses: frequency-resolved optical gating," J. Opt. Soc. Am. B 10, 1101-1111 (1993).
    [CrossRef]
  3. R. Trebino, Frequency-Resolved Optical Gating: the Measurement of Ultrashort Laser Pulses (Kluwer Academic, 2002).
    [CrossRef]
  4. S. Linden, H. Giessen, and J. Kuhl, "XFROG--a new method for amplitude and phase characterization of weak ultrashort pulses," Phys. Status Solidi B 206, 119-124 (1998).
    [CrossRef]
  5. P.Miller, ed., Ultrafast Phenomena XIII, (Springer-Verlag, 2003).
  6. D. N. Fittinghoff, J. L. Bowie, J. N. Sweetser, R. T. Jennings, M. A. Krumbügel, K. W. DeLong, R. Trebino, and I. A. Walmsley, "Measurement of the intensity and phase of ultraweak, ultrashort laser pulse," Opt. Lett. 21, 884-886 (1996).
    [CrossRef] [PubMed]
  7. J. Y. Zhang, A. P. Shreenath, M. Kimmel, E. Zeek, R. Trebino, and S. Link, "Measurement of the intensity and phase of attojoule femtosecond light pulses using optical-parametric-amplification cross-correlation frequency-resolved optical gating," Opt. Express 11, 601-609 (2003).
    [CrossRef] [PubMed]
  8. G. Cerullo and S. De Silvestri, "Ultrafast optical parametric amplifiers," Rev. Sci. Instrum. 74, 1-18 (2003).
    [CrossRef]
  9. E. Riedle, M. Beutter, S. Lochbrunner, J. Piel, S. Schenkl, S. Sporlein, and W. Zinth, "Generation of 10to50 fs pulses tunable through all of the visible and the NIR," Appl. Phys. B 71, 457-465 (2000).
    [CrossRef]
  10. V. Krylov, J. Gallus, U. P. Wild, A. Kalintsev, and A. Rebane, "Femtosecond noncollinear and collinear parametric generation and amplification in BBO crystal," Appl. Phys. B 70, 163-168 (2000).
    [CrossRef]
  11. R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic, 2003).
  12. J. Y. Zhang, C. K. Lee, J. Y. Huang, and C. L. Pan, "Sub femto-joule sensitive single-shot OPA-XFROG and its application in study of white-light supercontinuum generation," Opt. Express 12, 574-581 (2004).
    [CrossRef] [PubMed]
  13. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, 1984).
  14. A. Smith, "Group-velocity-matched three-wave mixing in birefringent crystals," Opt. Lett. 26, 719-721 (2001).
    [CrossRef]
  15. M. A. Dreger and J. K. McIver, "Second-harmonic generation in a nonlinear, anisotropic medium with diffraction and depletion," J. Opt. Soc. Am. B 7, 776-784 (1990).
    [CrossRef]
  16. N. Bloembergen, Nonlinear Optics, 4th ed. (World Scientific, 1996).
    [CrossRef]
  17. J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic, 1996).
  18. A. V. Smith, SNLO Nonlinear Optics Code (Sandia National Laboratories, Albuquerque, N.M. 87185-1423).
  19. R. Trebino, "Geometrical issues: single-shot FROG," in Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses, R.Trebino, ed. (Kluwer Academic, 2002), pp. 141-156.
  20. X. Gu, L. Xu, M. Kimmel, E. Zeek, P. O'Shea, A. P. Shreenath, R. Trebino, and R. S. Windeler, "Frequency-resolved optical gating and single-shot spectral measurements reveal fine structure in microstructure-fiber continuum," Opt. Lett. 27, 1174-1176 (2002).
    [CrossRef]
  21. A. L. Gaeta, "Nonlinear propagation and continuum generation in microstructured optical fibers," Opt. Lett. 27, 924-926 (2002).
    [CrossRef]
  22. J. M. Dudley, X. Gu, L. Xu, M. Kimmel, E. Zeek, P. O'Shea, R. Trebino, S. Coen, and R. S. Windeler, "Cross-correlation frequency resolved optical gating analysis of broadband continuum generation in photonic crystal fiber: simulations and experiments," Opt. Express 10, 1215-1221 (2002).
    [PubMed]

2004 (1)

2003 (2)

2002 (3)

2001 (1)

2000 (2)

E. Riedle, M. Beutter, S. Lochbrunner, J. Piel, S. Schenkl, S. Sporlein, and W. Zinth, "Generation of 10to50 fs pulses tunable through all of the visible and the NIR," Appl. Phys. B 71, 457-465 (2000).
[CrossRef]

V. Krylov, J. Gallus, U. P. Wild, A. Kalintsev, and A. Rebane, "Femtosecond noncollinear and collinear parametric generation and amplification in BBO crystal," Appl. Phys. B 70, 163-168 (2000).
[CrossRef]

1998 (1)

S. Linden, H. Giessen, and J. Kuhl, "XFROG--a new method for amplitude and phase characterization of weak ultrashort pulses," Phys. Status Solidi B 206, 119-124 (1998).
[CrossRef]

1996 (1)

1993 (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]

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

1990 (1)

Beutter, M.

E. Riedle, M. Beutter, S. Lochbrunner, J. Piel, S. Schenkl, S. Sporlein, and W. Zinth, "Generation of 10to50 fs pulses tunable through all of the visible and the NIR," Appl. Phys. B 71, 457-465 (2000).
[CrossRef]

Bloembergen, N.

N. Bloembergen, Nonlinear Optics, 4th ed. (World Scientific, 1996).
[CrossRef]

Bowie, J. L.

Boyd, R. W.

R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic, 2003).

Cerullo, G.

G. Cerullo and S. De Silvestri, "Ultrafast optical parametric amplifiers," Rev. Sci. Instrum. 74, 1-18 (2003).
[CrossRef]

Coen, S.

De Silvestri, S.

G. Cerullo and S. De Silvestri, "Ultrafast optical parametric amplifiers," Rev. Sci. Instrum. 74, 1-18 (2003).
[CrossRef]

DeLong, K. W.

Diels, J.-C.

J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic, 1996).

Dreger, M. A.

Dudley, J. M.

Fittinghoff, D. N.

Gaeta, A. L.

Gallus, J.

V. Krylov, J. Gallus, U. P. Wild, A. Kalintsev, and A. Rebane, "Femtosecond noncollinear and collinear parametric generation and amplification in BBO crystal," Appl. Phys. B 70, 163-168 (2000).
[CrossRef]

Giessen, H.

S. Linden, H. Giessen, and J. Kuhl, "XFROG--a new method for amplitude and phase characterization of weak ultrashort pulses," Phys. Status Solidi B 206, 119-124 (1998).
[CrossRef]

Gu, X.

Huang, J. Y.

Jennings, R. T.

Kalintsev, A.

V. Krylov, J. Gallus, U. P. Wild, A. Kalintsev, and A. Rebane, "Femtosecond noncollinear and collinear parametric generation and amplification in BBO crystal," Appl. Phys. B 70, 163-168 (2000).
[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]

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

Kimmel, M.

Krumbügel, M. A.

Krylov, V.

V. Krylov, J. Gallus, U. P. Wild, A. Kalintsev, and A. Rebane, "Femtosecond noncollinear and collinear parametric generation and amplification in BBO crystal," Appl. Phys. B 70, 163-168 (2000).
[CrossRef]

Kuhl, J.

S. Linden, H. Giessen, and J. Kuhl, "XFROG--a new method for amplitude and phase characterization of weak ultrashort pulses," Phys. Status Solidi B 206, 119-124 (1998).
[CrossRef]

Lee, C. K.

Linden, S.

S. Linden, H. Giessen, and J. Kuhl, "XFROG--a new method for amplitude and phase characterization of weak ultrashort pulses," Phys. Status Solidi B 206, 119-124 (1998).
[CrossRef]

Link, S.

Lochbrunner, S.

E. Riedle, M. Beutter, S. Lochbrunner, J. Piel, S. Schenkl, S. Sporlein, and W. Zinth, "Generation of 10to50 fs pulses tunable through all of the visible and the NIR," Appl. Phys. B 71, 457-465 (2000).
[CrossRef]

McIver, J. K.

O'Shea, P.

Pan, C. L.

Piel, J.

E. Riedle, M. Beutter, S. Lochbrunner, J. Piel, S. Schenkl, S. Sporlein, and W. Zinth, "Generation of 10to50 fs pulses tunable through all of the visible and the NIR," Appl. Phys. B 71, 457-465 (2000).
[CrossRef]

Rebane, A.

V. Krylov, J. Gallus, U. P. Wild, A. Kalintsev, and A. Rebane, "Femtosecond noncollinear and collinear parametric generation and amplification in BBO crystal," Appl. Phys. B 70, 163-168 (2000).
[CrossRef]

Riedle, E.

E. Riedle, M. Beutter, S. Lochbrunner, J. Piel, S. Schenkl, S. Sporlein, and W. Zinth, "Generation of 10to50 fs pulses tunable through all of the visible and the NIR," Appl. Phys. B 71, 457-465 (2000).
[CrossRef]

Rudolph, W.

J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic, 1996).

Schenkl, S.

E. Riedle, M. Beutter, S. Lochbrunner, J. Piel, S. Schenkl, S. Sporlein, and W. Zinth, "Generation of 10to50 fs pulses tunable through all of the visible and the NIR," Appl. Phys. B 71, 457-465 (2000).
[CrossRef]

Shen, Y. R.

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, 1984).

Shreenath, A. P.

Smith, A.

Smith, A. V.

A. V. Smith, SNLO Nonlinear Optics Code (Sandia National Laboratories, Albuquerque, N.M. 87185-1423).

Sporlein, S.

E. Riedle, M. Beutter, S. Lochbrunner, J. Piel, S. Schenkl, S. Sporlein, and W. Zinth, "Generation of 10to50 fs pulses tunable through all of the visible and the NIR," Appl. Phys. B 71, 457-465 (2000).
[CrossRef]

Sweetser, J. N.

Trebino, R.

J. Y. Zhang, A. P. Shreenath, M. Kimmel, E. Zeek, R. Trebino, and S. Link, "Measurement of the intensity and phase of attojoule femtosecond light pulses using optical-parametric-amplification cross-correlation frequency-resolved optical gating," Opt. Express 11, 601-609 (2003).
[CrossRef] [PubMed]

X. Gu, L. Xu, M. Kimmel, E. Zeek, P. O'Shea, A. P. Shreenath, R. Trebino, and R. S. Windeler, "Frequency-resolved optical gating and single-shot spectral measurements reveal fine structure in microstructure-fiber continuum," Opt. Lett. 27, 1174-1176 (2002).
[CrossRef]

J. M. Dudley, X. Gu, L. Xu, M. Kimmel, E. Zeek, P. O'Shea, R. Trebino, S. Coen, and R. S. Windeler, "Cross-correlation frequency resolved optical gating analysis of broadband continuum generation in photonic crystal fiber: simulations and experiments," Opt. Express 10, 1215-1221 (2002).
[PubMed]

D. N. Fittinghoff, J. L. Bowie, J. N. Sweetser, R. T. Jennings, M. A. Krumbügel, K. W. DeLong, R. Trebino, and I. A. Walmsley, "Measurement of the intensity and phase of ultraweak, ultrashort laser pulse," Opt. Lett. 21, 884-886 (1996).
[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]

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

R. Trebino, Frequency-Resolved Optical Gating: the Measurement of Ultrashort Laser Pulses (Kluwer Academic, 2002).
[CrossRef]

R. Trebino, "Geometrical issues: single-shot FROG," in Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses, R.Trebino, ed. (Kluwer Academic, 2002), pp. 141-156.

Walmsley, I. A.

Wild, U. P.

V. Krylov, J. Gallus, U. P. Wild, A. Kalintsev, and A. Rebane, "Femtosecond noncollinear and collinear parametric generation and amplification in BBO crystal," Appl. Phys. B 70, 163-168 (2000).
[CrossRef]

Windeler, R. S.

Xu, L.

Zeek, E.

Zhang, J. Y.

Zinth, W.

E. Riedle, M. Beutter, S. Lochbrunner, J. Piel, S. Schenkl, S. Sporlein, and W. Zinth, "Generation of 10to50 fs pulses tunable through all of the visible and the NIR," Appl. Phys. B 71, 457-465 (2000).
[CrossRef]

Appl. Phys. B (2)

E. Riedle, M. Beutter, S. Lochbrunner, J. Piel, S. Schenkl, S. Sporlein, and W. Zinth, "Generation of 10to50 fs pulses tunable through all of the visible and the NIR," Appl. Phys. B 71, 457-465 (2000).
[CrossRef]

V. Krylov, J. Gallus, U. P. Wild, A. Kalintsev, and A. Rebane, "Femtosecond noncollinear and collinear parametric generation and amplification in BBO crystal," Appl. Phys. B 70, 163-168 (2000).
[CrossRef]

IEEE J. Quantum Electron. (1)

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. Opt. Soc. Am. B (2)

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

M. A. Dreger and J. K. McIver, "Second-harmonic generation in a nonlinear, anisotropic medium with diffraction and depletion," J. Opt. Soc. Am. B 7, 776-784 (1990).
[CrossRef]

Opt. Express (3)

Opt. Lett. (4)

Phys. Status Solidi B (1)

S. Linden, H. Giessen, and J. Kuhl, "XFROG--a new method for amplitude and phase characterization of weak ultrashort pulses," Phys. Status Solidi B 206, 119-124 (1998).
[CrossRef]

Rev. Sci. Instrum. (1)

G. Cerullo and S. De Silvestri, "Ultrafast optical parametric amplifiers," Rev. Sci. Instrum. 74, 1-18 (2003).
[CrossRef]

Other (8)

R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic, 2003).

P.Miller, ed., Ultrafast Phenomena XIII, (Springer-Verlag, 2003).

R. Trebino, Frequency-Resolved Optical Gating: the Measurement of Ultrashort Laser Pulses (Kluwer Academic, 2002).
[CrossRef]

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, 1984).

N. Bloembergen, Nonlinear Optics, 4th ed. (World Scientific, 1996).
[CrossRef]

J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic, 1996).

A. V. Smith, SNLO Nonlinear Optics Code (Sandia National Laboratories, Albuquerque, N.M. 87185-1423).

R. Trebino, "Geometrical issues: single-shot FROG," in Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses, R.Trebino, ed. (Kluwer Academic, 2002), pp. 141-156.

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Figures (14)

Fig. 1
Fig. 1

Apparent group velocity ( V ̂ g ) of a slanted pulse. The propagation vector is tilted by α relative to the z axis, and V g is the group velocity of an unslanted pulse. The birefringent walk-off angle is ρ, and ϕ is the slant angle of the pulse front relative to the normal to the z axis.

Fig. 2
Fig. 2

Requirements for the highest accuracy. The signal crosses the pump at an angle. The gray lines inside the signal represent the temporal structure.

Fig. 3
Fig. 3

(a) Ideal OPA XFROG trace of a pulse and (b) its retrieval with a 2 mm thick BBO crystal. The FROG error was 4.339 × 10 5 . The solid curves with circular markers in (c) and (d) show the retrieved temporal and spectral intensities of the pulse. The dotted curves with circular markers refer to the retrieved signal temporal and spectral phases. The solid curves without any markers refer to the intensities of the actual pulse. The dashed curves without any markers are the corresponding phases of the actual pulse.

Fig. 4
Fig. 4

Typical configuration of our experiments. The gray lines inside the signal represent the temporal structure.

Fig. 5
Fig. 5

OPA XFROG trace and its retrieval with a 2 mm thick BBO crystal (conventions are the same as in Fig. 3). The crossing angle between the pump and the input pulse is 7.15°. The FROG error was 4.102 × 10 4 .

Fig. 6
Fig. 6

OPA XFROG trace of the signal and its retrieval with a 3 mm BBO crystal (conventions are the same as in Fig. 3). The input energy of the pump is 2 μ J . The FROG error was 4.254 × 10 4 .

Fig. 7
Fig. 7

OPA XFROG trace and its retrieval with a 1 mm thick BBO crystal (conventions are the same as in Fig. 3). The input energy of the pump was 30 μ J . The FROG error was 2.547 × 10 4 .

Fig. 8
Fig. 8

OPA XFROG trace and its retrieved pulse with collinear beams ( α s = 0 ° ; conventions are the same as in Fig. 3). The FROG error was 5.250 × 10 3 . The retrieved spectral FWHM was 14 nm .

Fig. 9
Fig. 9

OPA XFROG trace and its retrieved pulse with crossing angle α s = 3 ° (conventions are the same as in Fig. 3). The FROG error was 5.844 × 10 3 . The retrieved spectral FWHM was 16 nm .

Fig. 10
Fig. 10

OPA XFROG trace and its retrieved pulse with a crossing angle α s = 6.52 ° (conventions are the same as in Fig. 3). The FROG error was 1.500 × 10 3 . The retrieved spectral FWHM was 50 nm .

Fig. 11
Fig. 11

OPA XFROG trace and its retrieved pulse with a crossing angle α s = 10 ° (conventions are the same as in Fig. 3). The FROG error was 5.863 × 10 3 . The retrieved spectral FWHM was only 14 nm .

Fig. 12
Fig. 12

(a) DFG XFROG trace of a pulse and (b) its retrieval with a 2 nm thick BBO crystal. The FROG error was 5.922 × 10 4 . The solid curves with circular markers in (c) and (d) show the retrieved temporal and spectral intensities of the signal pulse. The dotted curves with circular markers refer to the retrieved signal temporal and spectral phases. The solid curves without any markers refer to the intensities of the actual signal pulse. The dashed curves without any markers are the corresponding phases of the actual signal pulse.

Fig. 13
Fig. 13

Schematic of the experimental apparatus for OPA–DFG XFROG. The gate pulse is characterized using a GRENOUILLE (not shown) before it enters the XFROG setup.

Fig. 14
Fig. 14

Measured and retrieved OPA XFROG measurements of a broadband white-light continuum for a pulse of 5 fJ , showing a gain of 1490 .

Equations (19)

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E sig OPA ( t , τ ) = E ( t ) E gate OPA ( t τ ) ,
E gate OPA ( t ) = cosh ( g E ref ( t ) z ) ,
I XFROG ( ω , τ ) = E ( t ) E gate ( t τ ) exp ( i ω t ) d t 2 .
E OPA z = i κ E ref E DFG * ,
E DFG z = i κ E ref E OPA * ,
E sig DFG ( t , τ ) = E ( t ) E gate DFG * ( t τ ) ,
E gate DFG ( t ) = exp [ i ϕ ref ( t ) ] sinh [ g E ref ( t ) z ] ,
E j ( t , z ) = 1 2 { E j ( t , z ) exp [ i ( ω j t k j z ) ] + E * j ( t , z ) exp [ i ( ω j t k j z ) ] } .
( z + 1 V s t + i 1 2 2 k s ω 2 2 t 2 ) E ( t , z ) = i ω s n s c d eff E p E i * exp ( i Δ k z ) ,
( z + 1 V i t + i 1 2 2 k i ω 2 2 t 2 ) E ( t , z ) = i ω i n i c d eff E p E s * exp ( i Δ k z ) ,
( z + 1 V p t + i 1 2 2 k p ω 2 2 t 2 ) E ( t , z ) = i ω p n p c d eff E s E i exp ( i Δ k z ) ,
V ̂ g = V g cos ( α + ϕ + ρ ) cos ϕ cos ρ ,
D ̂ = 1 2 d 2 k z d ω 2 = 1 2 V g 2 cos ϕ cos ρ cos ( α + ϕ + ρ ) GVD + 1 V g 2 cos ϕ cos 3 ρ sin 2 ( α + ϕ ) cos 3 ( α + ϕ + ρ ) A .
A = 1 2 k 1 2 k 2 2 k α 2 .
E j z + 1 V ̂ g j E j t i D ̂ 2 E j t 2 = P ̃ j ,
P ̃ s = i ω s n ̃ s c d eff E p E i * exp ( i Δ k z ) ,
P ̃ i = i ω i n ̃ i c d eff E p E s * exp ( i Δ k z ) ,
P ̃ p = i ω p n ̃ p c d eff E s E i exp ( i Δ k z ) .
n ̃ j = { n j cos ρ j cos ( α j + ρ j ) x polarized n j cos α j y polarized } .

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