Abstract

The intensity and the phase of ultrashort pulses from a self-mode-locked Ti:sapphire laser operating in the vicinity of zero group-delay dispersion (GDD) have been completely characterized by the technique of frequency-resolved optical gating (FROG). For small values of negative GDD, the appearance of a dispersive wave in the pulse spectrum is manifested in the measured FROG trace, and pulse retrieval directly shows its association with a broad leading-edge pedestal. For positive GDD, we confirm previous experimental observations of picosecond pulses with large positive chirp and report a new operating regime in which the output pulses are of picosecond duration but are intensity modulated at 20 THz. The physical origin of this modulation is discussed by analogy with similar effects observed during pulse propagation in optical fibers, and the experimental results are compared with a model of intracavity four-wave mixing about the cavity zero GDD wavelength.

© 1999 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  24. B. Chassagne, G. Jonusauskas, J. Oberlé, C. Rullière, “Multipulse operation regime in a self-modelocked Cr4+:forsterite femtosecond laser,” Opt. Commun. 150, 355–362 (1998).
    [CrossRef]
  25. Note that the frequency-resolved optical gating measurements reported in Ref. 21 were not used for pulse reconstruction in the presence of dispersive waves.
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    [CrossRef]
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    [CrossRef] [PubMed]
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  31. X. Zhu, J.-F. Cormier, M. Piché, “Study of dispersion compensation in femtosecond lasers,” J. Mod. Opt. 43, 1701–1721 (1996).
    [CrossRef]
  32. For example, at a wavelength of 810 nm, 1 mm of additional intracavity SF13 prism material introduces additional GDD of +163 fs2 and TOD of +105 fs3 per round trip.
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    [CrossRef] [PubMed]
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    [CrossRef]
  39. J. Schütz, W. Hodel, H. P. Weber, “Nonlinear pulse distortion at the zero dispersion wavelength of an optical fibre,” Opt. Commun. 95, 357–365 (1993).
    [CrossRef]
  40. V. P. Yanovsky, F. W. Wise, “Nonlinear propagation of high-power, sub-100-fs pulses near the zero dispersion wavelength of an optical fiber,” Opt. Lett. 19, 1547–1549 (1994).
    [CrossRef] [PubMed]
  41. R. H. Stolen, J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron. 18, 1062–1072 (1982).
    [CrossRef]
  42. G. P. Agrawal, M. J. Potasek, “Nonlinear pulse distortion in single-mode optical fibers at the zero dispersion wavelength,” Phys. Rev. A 33, 1765–1776 (1986).
    [CrossRef] [PubMed]
  43. G. R. Boyer, X. F. Carlotti, “Nonlinear propagation in a single-mode optical fiber in case of small group velocity dispersion,” Opt. Commun. 60, 18–22 (1986).
    [CrossRef]
  44. E. A. Golovchenko, A. N. Pilipetskii, “Unified analysis of four-photon mixing, modulational instability, and stimulated Raman scattering under various polarization conditions in fibers,” J. Opt. Soc. Am. B 11, 92–101 (1994).
    [CrossRef]
  45. Numerical simulations indicate that the opposite sign of TOD in the fiber is responsible for the fact that the intensity modulation in the fiber experiments appears on the pulse’s leading edge rather than on the trailing edge as in the Ti:sapphire experiments.
  46. Here we use an effective beam radius in the Ti:sapphire crystal of r ≈ 15 µm, and we estimate an effective peak power associated with FWM of P0 ≈ 10 kW.
  47. V. P. Kalosha, M. Müller, J. Hermann, S. Gatz, “Spatiotemporal model of femtosecond pulse generation in Kerr-lens mode-locked solid state lasers,” J. Opt. Soc. Am. B 15, 535–550 (1998).
    [CrossRef]
  48. I. P. Christov, V. D. Stoev, “Kerr-lens mode-locked laser model: role of space–time effects,” J. Opt. Soc. Am. B 15, 1960–1966 (1998).
    [CrossRef]

1998

1997

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

J. M. Dudley, L. P. Barry, P. G. Bollond, J. D. Harvey, R. Leonhardt, P. D. Drummond, “Direct measurement of pulse distortion near the zero-dispersion wavelength in optical fibers using frequency-resolved optical gating,” Opt. Lett. 22, 457–459 (1997).
[CrossRef] [PubMed]

D. T. Reid, C. McGowan, W. E. Sleat, W. Sibbett, “A real-time FROG trace acquisition system for non-amplified femtosecond oscillators,” Eng. Lab. Notes in Opt. Photon. News 8(5) (1997).

S. Uemura, K. Miyazaki, “Operation of a femtosecond Cr:LiSAF solitary laser near zero group-delay dispersion,” Opt. Commun. 133, 201–204 (1997).
[CrossRef]

G. Boyer, “Dispersive wave generation in a Cr4+:forsterite femtosecond soliton-like laser,” Opt. Commun. 141, 279–282 (1997).
[CrossRef]

Ch. Spielmann, T. Brabec, F. Krausz, “Reply to comment on ’Sub-10-fs mirror-dispersion-controlled Ti:sapphire laser” and ’Ultrabroadband ring oscillator for sub-10-fs pulse generation,’” Opt. Lett. 22, 1884–1886 (1997).

I. D. Jung, F. X. Kärtner, J. Henkmann, G. Zhang, U. Keller, “High-dynamic range characterisation of ultrashort pulses,” Appl. Phys. B 65, 307–310 (1997).
[CrossRef]

J. Hermann, V. P. Kalosha, M. Müller, “Higher-order phase dispersion in femtosecond Kerr-lens mode-locked solid-state lasers: sideband generation and pulse splitting,” Opt. Lett. 22, 236–238 (1997).
[CrossRef]

M. Santagiustina, “Third-order dispersion radiation in solid-state solitary lasers,” J. Opt. Soc. Am. B 14, 1484–1495 (1997).
[CrossRef]

1996

M. Piché, J.-F. Cormier, X. Zhu, “Bright optical soliton in the presence of fourth-order dispersion,” Opt. Lett. 21, 845–847 (1996).
[CrossRef] [PubMed]

X. Zhu, J.-F. Cormier, M. Piché, “Study of dispersion compensation in femtosecond lasers,” J. Mod. Opt. 43, 1701–1721 (1996).
[CrossRef]

1995

1994

1993

1992

F. Krausz, M. E. Fermann, T. Brabec, P. F. Curley, M. Hofer, M. H. Ober, C. Spielmann, E. Wintner, A. J. Schmidt, “Femtosecond solid-state lasers,” IEEE J. Quantum Electron. 28, 2097–2121 (1992).
[CrossRef]

M. Stern, J. P. Heritage, W. T. Anderson, J. Kilmer, “Soliton technique to characterize single-mode fiber dispersion,” J. Lightwave. Technol. 10, 1777–1780 (1992).
[CrossRef]

W. H. Knox, “In situ measurement of complete intracavity dispersion in an operating Ti:sapphire femtosecond laser,” Opt. Lett. 17, 514–516 (1992).
[CrossRef] [PubMed]

1991

1989

1986

K. Tai, A. Hasegawa, A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56, 135–137 (1986).
[CrossRef] [PubMed]

G. P. Agrawal, M. J. Potasek, “Nonlinear pulse distortion in single-mode optical fibers at the zero dispersion wavelength,” Phys. Rev. A 33, 1765–1776 (1986).
[CrossRef] [PubMed]

G. R. Boyer, X. F. Carlotti, “Nonlinear propagation in a single-mode optical fiber in case of small group velocity dispersion,” Opt. Commun. 60, 18–22 (1986).
[CrossRef]

1982

R. H. Stolen, J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron. 18, 1062–1072 (1982).
[CrossRef]

1981

Agrawal, G. P.

G. P. Agrawal, M. J. Potasek, “Nonlinear pulse distortion in single-mode optical fibers at the zero dispersion wavelength,” Phys. Rev. A 33, 1765–1776 (1986).
[CrossRef] [PubMed]

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Francisco, Calif., 1995).

Alfano, R. R.

Anderson, W. T.

M. Stern, J. P. Heritage, W. T. Anderson, J. Kilmer, “Soliton technique to characterize single-mode fiber dispersion,” J. Lightwave. Technol. 10, 1777–1780 (1992).
[CrossRef]

Baldeck, P. L.

Barry, L. P.

Bjorkholm, J. E.

R. H. Stolen, J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron. 18, 1062–1072 (1982).
[CrossRef]

Bollond, P. G.

Boyer, G.

G. Boyer, “Dispersive wave generation in a Cr4+:forsterite femtosecond soliton-like laser,” Opt. Commun. 141, 279–282 (1997).
[CrossRef]

Boyer, G. R.

G. R. Boyer, X. F. Carlotti, “Nonlinear propagation in a single-mode optical fiber in case of small group velocity dispersion,” Opt. Commun. 60, 18–22 (1986).
[CrossRef]

Brabec, T.

Budansky, Y.

Carlotti, X. F.

G. R. Boyer, X. F. Carlotti, “Nonlinear propagation in a single-mode optical fiber in case of small group velocity dispersion,” Opt. Commun. 60, 18–22 (1986).
[CrossRef]

Chassagne, B.

B. Chassagne, G. Jonusauskas, J. Oberlé, C. Rullière, “Multipulse operation regime in a self-modelocked Cr4+:forsterite femtosecond laser,” Opt. Commun. 150, 355–362 (1998).
[CrossRef]

Christov, I. P.

Cormier, J.-F.

M. Piché, J.-F. Cormier, X. Zhu, “Bright optical soliton in the presence of fourth-order dispersion,” Opt. Lett. 21, 845–847 (1996).
[CrossRef] [PubMed]

X. Zhu, J.-F. Cormier, M. Piché, “Study of dispersion compensation in femtosecond lasers,” J. Mod. Opt. 43, 1701–1721 (1996).
[CrossRef]

Curley, P. F.

Ch. Spielmann, P. F. Curley, T. Brabec, F. Krausz, “Ultrabroadband femtosecond lasers,” IEEE J. Quantum Electron. 30, 1100–1114 (1994).
[CrossRef]

P. F. Curley, Ch. Spielmann, T. Brabec, F. Krausz, E. Wintner, A. J. Schmidt, “Operation of a femtosecond Ti:sapphire solitary laser in the vicinity of zero group-delay dispersion,” Opt. Lett. 18, 54–56 (1993).
[CrossRef] [PubMed]

F. Krausz, M. E. Fermann, T. Brabec, P. F. Curley, M. Hofer, M. H. Ober, C. Spielmann, E. Wintner, A. J. Schmidt, “Femtosecond solid-state lasers,” IEEE J. Quantum Electron. 28, 2097–2121 (1992).
[CrossRef]

DeLong, K. W.

Drummond, P. D.

Dudley, J. M.

Elgin, J. N.

J. N. Elgin, T. Brabec, S. M. J. Kelly, “A perturbative theory of soliton propagation in the presence of third order dispersion,” Opt. Commun. 114, 321–328 (1995).
[CrossRef]

Fermann, M. E.

F. Krausz, M. E. Fermann, T. Brabec, P. F. Curley, M. Hofer, M. H. Ober, C. Spielmann, E. Wintner, A. J. Schmidt, “Femtosecond solid-state lasers,” IEEE J. Quantum Electron. 28, 2097–2121 (1992).
[CrossRef]

Fittinghoff, D. N.

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

Fujimoto, J. G.

Gatz, S.

Golovchenko, E. A.

Grant, R. S.

W. Sibbett, R. S. Grant, D. E. Spence, “Broadly tunable femtosecond solid-state laser sources,” Appl. Phys. B 58, 171–181 (1994).
[CrossRef]

Harvey, J. D.

Hasegawa, A.

K. Tai, A. Hasegawa, A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56, 135–137 (1986).
[CrossRef] [PubMed]

Haus, H. A.

Henkmann, J.

I. D. Jung, F. X. Kärtner, J. Henkmann, G. Zhang, U. Keller, “High-dynamic range characterisation of ultrashort pulses,” Appl. Phys. B 65, 307–310 (1997).
[CrossRef]

Heritage, J. P.

M. Stern, J. P. Heritage, W. T. Anderson, J. Kilmer, “Soliton technique to characterize single-mode fiber dispersion,” J. Lightwave. Technol. 10, 1777–1780 (1992).
[CrossRef]

Hermann, J.

Hodel, W.

J. Schütz, W. Hodel, H. P. Weber, “Nonlinear pulse distortion at the zero dispersion wavelength of an optical fibre,” Opt. Commun. 95, 357–365 (1993).
[CrossRef]

Hofer, M.

F. Krausz, M. E. Fermann, T. Brabec, P. F. Curley, M. Hofer, M. H. Ober, C. Spielmann, E. Wintner, A. J. Schmidt, “Femtosecond solid-state lasers,” IEEE J. Quantum Electron. 28, 2097–2121 (1992).
[CrossRef]

Huang, C.-P.

Hunter, J.

Ippen, E. P.

Jonusauskas, G.

B. Chassagne, G. Jonusauskas, J. Oberlé, C. Rullière, “Multipulse operation regime in a self-modelocked Cr4+:forsterite femtosecond laser,” Opt. Commun. 150, 355–362 (1998).
[CrossRef]

Jung, I. D.

I. D. Jung, F. X. Kärtner, J. Henkmann, G. Zhang, U. Keller, “High-dynamic range characterisation of ultrashort pulses,” Appl. Phys. B 65, 307–310 (1997).
[CrossRef]

Kalosha, V. P.

Kane, D. J.

Kapteyn, H. C.

Kärtner, F. X.

I. D. Jung, F. X. Kärtner, J. Henkmann, G. Zhang, U. Keller, “High-dynamic range characterisation of ultrashort pulses,” Appl. Phys. B 65, 307–310 (1997).
[CrossRef]

Kasper, A.

Keller, U.

I. D. Jung, F. X. Kärtner, J. Henkmann, G. Zhang, U. Keller, “High-dynamic range characterisation of ultrashort pulses,” Appl. Phys. B 65, 307–310 (1997).
[CrossRef]

Kelly, S. M. J.

J. N. Elgin, T. Brabec, S. M. J. Kelly, “A perturbative theory of soliton propagation in the presence of third order dispersion,” Opt. Commun. 114, 321–328 (1995).
[CrossRef]

T. Brabec, S. M. J. Kelly, “Third-order dispersion as a limiting factor to mode locking in femtosecond solitary lasers,” Opt. Lett. 18, 2002–2004 (1993).
[CrossRef] [PubMed]

Kilmer, J.

M. Stern, J. P. Heritage, W. T. Anderson, J. Kilmer, “Soliton technique to characterize single-mode fiber dispersion,” J. Lightwave. Technol. 10, 1777–1780 (1992).
[CrossRef]

Knox, W. H.

Krausz, F.

Krumbügel, M. A.

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

Lenzner, M.

Leonhardt, R.

Lin, C.

Lin, Q.

Q. Lin, I. Sorokina, “High-order dispersion effects in solitary mode-locked lasers: sideband generation,” Opt. Commun. 153, 285–288 (1998).
[CrossRef]

McGowan, C.

D. T. Reid, C. McGowan, W. E. Sleat, W. Sibbett, “A real-time FROG trace acquisition system for non-amplified femtosecond oscillators,” Eng. Lab. Notes in Opt. Photon. News 8(5) (1997).

Miyazaki, K.

S. Uemura, K. Miyazaki, “Operation of a femtosecond Cr:LiSAF solitary laser near zero group-delay dispersion,” Opt. Commun. 133, 201–204 (1997).
[CrossRef]

Moores, J. D.

Müller, M.

Murnane, M. M.

Nelson, L. E.

Ober, M. H.

F. Krausz, M. E. Fermann, T. Brabec, P. F. Curley, M. Hofer, M. H. Ober, C. Spielmann, E. Wintner, A. J. Schmidt, “Femtosecond solid-state lasers,” IEEE J. Quantum Electron. 28, 2097–2121 (1992).
[CrossRef]

Oberlé, J.

B. Chassagne, G. Jonusauskas, J. Oberlé, C. Rullière, “Multipulse operation regime in a self-modelocked Cr4+:forsterite femtosecond laser,” Opt. Commun. 150, 355–362 (1998).
[CrossRef]

Pearson, A. D.

Piché, M.

X. Zhu, J.-F. Cormier, M. Piché, “Study of dispersion compensation in femtosecond lasers,” J. Mod. Opt. 43, 1701–1721 (1996).
[CrossRef]

M. Piché, J.-F. Cormier, X. Zhu, “Bright optical soliton in the presence of fourth-order dispersion,” Opt. Lett. 21, 845–847 (1996).
[CrossRef] [PubMed]

Pilipetskii, A. N.

Potasek, M. J.

G. P. Agrawal, M. J. Potasek, “Nonlinear pulse distortion in single-mode optical fibers at the zero dispersion wavelength,” Phys. Rev. A 33, 1765–1776 (1986).
[CrossRef] [PubMed]

Proctor, B.

Reed, W. A.

Reid, D. T.

D. T. Reid, C. McGowan, W. E. Sleat, W. Sibbett, “A real-time FROG trace acquisition system for non-amplified femtosecond oscillators,” Eng. Lab. Notes in Opt. Photon. News 8(5) (1997).

Richman, B. A.

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

Rullière, C.

B. Chassagne, G. Jonusauskas, J. Oberlé, C. Rullière, “Multipulse operation regime in a self-modelocked Cr4+:forsterite femtosecond laser,” Opt. Commun. 150, 355–362 (1998).
[CrossRef]

Santagiustina, M.

Schmidt, A. J.

P. F. Curley, Ch. Spielmann, T. Brabec, F. Krausz, E. Wintner, A. J. Schmidt, “Operation of a femtosecond Ti:sapphire solitary laser in the vicinity of zero group-delay dispersion,” Opt. Lett. 18, 54–56 (1993).
[CrossRef] [PubMed]

F. Krausz, M. E. Fermann, T. Brabec, P. F. Curley, M. Hofer, M. H. Ober, C. Spielmann, E. Wintner, A. J. Schmidt, “Femtosecond solid-state lasers,” IEEE J. Quantum Electron. 28, 2097–2121 (1992).
[CrossRef]

Schütz, J.

J. Schütz, W. Hodel, H. P. Weber, “Nonlinear pulse distortion at the zero dispersion wavelength of an optical fibre,” Opt. Commun. 95, 357–365 (1993).
[CrossRef]

Shang, H.-T.

Sibbett, W.

D. T. Reid, C. McGowan, W. E. Sleat, W. Sibbett, “A real-time FROG trace acquisition system for non-amplified femtosecond oscillators,” Eng. Lab. Notes in Opt. Photon. News 8(5) (1997).

W. Sibbett, R. S. Grant, D. E. Spence, “Broadly tunable femtosecond solid-state laser sources,” Appl. Phys. B 58, 171–181 (1994).
[CrossRef]

Sleat, W. E.

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Eng. Lab. Notes in Opt. Photon. News

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[CrossRef]

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[CrossRef]

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X. Zhu, J.-F. Cormier, M. Piché, “Study of dispersion compensation in femtosecond lasers,” J. Mod. Opt. 43, 1701–1721 (1996).
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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

M. Piché, J.-F. Cormier, X. Zhu, “Bright optical soliton in the presence of fourth-order dispersion,” Opt. Lett. 21, 845–847 (1996).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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

Other

For example, at a wavelength of 810 nm, 1 mm of additional intracavity SF13 prism material introduces additional GDD of +163 fs2 and TOD of +105 fs3 per round trip.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Francisco, Calif., 1995).

Note that the frequency-resolved optical gating measurements reported in Ref. 21 were not used for pulse reconstruction in the presence of dispersive waves.

H. A. Haus, “Short pulse generation,” in Compact Sources of Ultrashort Light Pulses, I. N. Duling, ed. (Cambridge U. Press, New York, 1995), pp. 1–56.
[CrossRef]

Numerical simulations indicate that the opposite sign of TOD in the fiber is responsible for the fact that the intensity modulation in the fiber experiments appears on the pulse’s leading edge rather than on the trailing edge as in the Ti:sapphire experiments.

Here we use an effective beam radius in the Ti:sapphire crystal of r ≈ 15 µm, and we estimate an effective peak power associated with FWM of P0 ≈ 10 kW.

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram for real-time characterization by use of a SHG FROG.

Fig. 2
Fig. 2

Pulse spectra for increasing amounts of intracavity prism material (top to bottom). Dashed lines, calculated zero GDD wavelengths, with negative GDD on the short-wavelength side of each line. The GDD and the TOD at the peak of the spectrum are (a) -780 and -12 470 fs3, (b) -470 and -12 570 fs3, (c) -380 and -13 190 fs3, (d) +750 and -11500 fs3, and (e) +1100 and -11 285 fs3. Note that the GDD value for (c) corresponds to the negative GDD peak and not to the dispersive wave.

Fig. 3
Fig. 3

Results for values of negative GDD of (a) -780 fs2, (b) -470 fs2, and (c) -380 fs2. Top, measured SHG FROG traces; middle, retrieved intensities (solid curves, left axes) and phases (dashed curves, right axes); bottom, spectra derived from the retrieved pulses [curves (i)] compared with those experimentally measured [curves (ii)].

Fig. 4
Fig. 4

(a) Measured SHG FROG trace for operation with a positive GDD of +1100 fs2. (b) Retrieved intensity (solid curve, left axis) and phase (dotted curve, right axis). (c) Comparison of the spectrum derived from the retrieved pulse [curve (i)] with that experimentally measured [curve (ii)].

Fig. 5
Fig. 5

(a) Measured and (b) reconstructed SHG FROG traces for operation with a positive GDD of +750 fs2. (c) Retrieved intensity (solid curve, left axis) and phase (dotted curve, right axis).

Fig. 6
Fig. 6

Spectral and autocorrelation results corresponding to Fig. 5. (a) Calculated cavity GDD and comparison of the spectrum derived from the retrieved pulse [curve (i)] with that experimentally measured [curve (ii)]. (b) Comparison of the autocorrelation derived from the retrieved pulse [curve (i)] with that experimentally measured [curve (ii)]. (c) Detailed comparison near zero delay of the derived autocorrelation (open circles) with the measured autocorrelation (solid curve).

Fig. 7
Fig. 7

Results showing the severe pulse distortion that is due to FWM about the ZDW in optical fiber experiments. (a) Measured SHG FROG trace. (b) Measured spectrum, showing how it is split about the ZDW. (c) Measured autocorrelation function. (d) Retrieved pulse intensity (solid curve, left axis) and phase (dashed curve, right axis).

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