Abstract

An investigation is made of ultrafast pump–probe pulse collisions near the zero-dispersion wavelength in an optical single-mode fiber. A steplike probe frequency shift is observed when the pump power is gradually increased. The magnitude of this frequency jump is shown to depend on the phase difference between the pulses. This new effect is investigated numerically and experimentally and is attributed to four-wave mixing.

© 2001 Optical Society of America

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References

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  1. G. R. Boyer, M. A. Franco, M. Lachgar, B. Grèzes-Besset, and A. Alexandrou, “Femtosecond pulse-shaping scheme for cross-phase modulation in single-mode optical fibers,” J. Opt. Soc. Am. B 11, 1451–1455 (1994).
    [CrossRef]
  2. G. R. Boyer, B. Hall, D. Anderson, M. Lisak, M. Karlsson, and A. Berntson, “Four-wave mixing of femtosecond pump-probe pulses in optical fibers,” in Nonlinear Guided Waves and Their Applications, 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), paper WB2–1.
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  4. C. Froely, B. Colombeau, and M. Vampouile, “Shaping and analysis of picosecond light pulses,” Prog. Opt. 20, 65–153 (1983).
  5. J. L. A. Chilla and O. E. Martinez, “Analysis of a method of phase measurement of ultrashort pulses in the frequency domain,” IEEE J. Quantum Electron. 27, 1228–1235 (1991).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  9. S. B. Cavalcanti, J. C. Cressoni, H. R. da Cruz, and A. S. Gouveia-Neto, “Modulational instability in the region of minimum group-velocity dispersion of single-mode optical fibers via an extended nonlinear Schrödinger equation,” Phys. Rev. A 43, 6162–6165 (1991).
    [CrossRef] [PubMed]
  10. A. S. Gouveia-Neto, A. S. L. Gomes, and J. R. Taylor, “Suppression and manipulation of the soliton self-frequency shift,” Opt. Lett. 14, 514–516 (1989).
    [CrossRef] [PubMed]
  11. J. M. Dudley, L. P. Barry, P. G. Bollond, J. D. Harvey, R. Leonhardt, and P. D. Drummond, “Direct measurement of pulse distortion near the zero-dispersion wavelength in an optical fiber by frequency-resolved optical gating,” Opt. Lett. 22, 457–459 (1997).
    [CrossRef] [PubMed]
  12. G. Boyer, “High-power femtosecond-pulse reshaping near the zero-dispersion wavelength of an optical fiber,” Opt. Lett. 24, 945–947 (1999).
    [CrossRef]
  13. See, e.g., R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron. 18, 1062–1071 (1982).
    [CrossRef]
  14. G. Cappellini and S. Trillo, “Third-order three-wave mixing in single-mode fibers: exact solutions and spatial instability effects,” J. Opt. Soc. Am. B 8, 824–838 (1991).
    [CrossRef]

1999

1997

1994

1993

1991

S. B. Cavalcanti, J. C. Cressoni, H. R. da Cruz, and A. S. Gouveia-Neto, “Modulational instability in the region of minimum group-velocity dispersion of single-mode optical fibers via an extended nonlinear Schrödinger equation,” Phys. Rev. A 43, 6162–6165 (1991).
[CrossRef] [PubMed]

J. L. A. Chilla and O. E. Martinez, “Analysis of a method of phase measurement of ultrashort pulses in the frequency domain,” IEEE J. Quantum Electron. 27, 1228–1235 (1991).
[CrossRef]

G. Cappellini and S. Trillo, “Third-order three-wave mixing in single-mode fibers: exact solutions and spatial instability effects,” J. Opt. Soc. Am. B 8, 824–838 (1991).
[CrossRef]

1989

1987

1983

C. Froely, B. Colombeau, and M. Vampouile, “Shaping and analysis of picosecond light pulses,” Prog. Opt. 20, 65–153 (1983).

1982

See, e.g., R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron. 18, 1062–1071 (1982).
[CrossRef]

Alexandrou, A.

Barry, L. P.

Bjorkholm, J. E.

See, e.g., R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron. 18, 1062–1071 (1982).
[CrossRef]

Bollond, P. G.

Boyer, G.

Boyer, G. R.

Cappellini, G.

Cavalcanti, S. B.

S. B. Cavalcanti, J. C. Cressoni, H. R. da Cruz, and A. S. Gouveia-Neto, “Modulational instability in the region of minimum group-velocity dispersion of single-mode optical fibers via an extended nonlinear Schrödinger equation,” Phys. Rev. A 43, 6162–6165 (1991).
[CrossRef] [PubMed]

Chen, H. H.

Chilla, J. L. A.

J. L. A. Chilla and O. E. Martinez, “Analysis of a method of phase measurement of ultrashort pulses in the frequency domain,” IEEE J. Quantum Electron. 27, 1228–1235 (1991).
[CrossRef]

Colombeau, B.

C. Froely, B. Colombeau, and M. Vampouile, “Shaping and analysis of picosecond light pulses,” Prog. Opt. 20, 65–153 (1983).

Cressoni, J. C.

S. B. Cavalcanti, J. C. Cressoni, H. R. da Cruz, and A. S. Gouveia-Neto, “Modulational instability in the region of minimum group-velocity dispersion of single-mode optical fibers via an extended nonlinear Schrödinger equation,” Phys. Rev. A 43, 6162–6165 (1991).
[CrossRef] [PubMed]

da Cruz, H. R.

S. B. Cavalcanti, J. C. Cressoni, H. R. da Cruz, and A. S. Gouveia-Neto, “Modulational instability in the region of minimum group-velocity dispersion of single-mode optical fibers via an extended nonlinear Schrödinger equation,” Phys. Rev. A 43, 6162–6165 (1991).
[CrossRef] [PubMed]

Drummond, P. D.

Dudley, J. M.

Franco, M. A.

Froely, C.

C. Froely, B. Colombeau, and M. Vampouile, “Shaping and analysis of picosecond light pulses,” Prog. Opt. 20, 65–153 (1983).

Gomes, A. S. L.

Gouveia-Neto, A. S.

S. B. Cavalcanti, J. C. Cressoni, H. R. da Cruz, and A. S. Gouveia-Neto, “Modulational instability in the region of minimum group-velocity dispersion of single-mode optical fibers via an extended nonlinear Schrödinger equation,” Phys. Rev. A 43, 6162–6165 (1991).
[CrossRef] [PubMed]

A. S. Gouveia-Neto, A. S. L. Gomes, and J. R. Taylor, “Suppression and manipulation of the soliton self-frequency shift,” Opt. Lett. 14, 514–516 (1989).
[CrossRef] [PubMed]

Grèzes-Besset, B.

Harvey, J. D.

Höök, A.

Karlsson, M.

Lachgar, M.

Lee, Y. C.

Leonhardt, R.

Martinez, O. E.

J. L. A. Chilla and O. E. Martinez, “Analysis of a method of phase measurement of ultrashort pulses in the frequency domain,” IEEE J. Quantum Electron. 27, 1228–1235 (1991).
[CrossRef]

Menyuk, C. R.

Minkov, Bl.

Pang, Y.

Stolen, R. H.

See, e.g., R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron. 18, 1062–1071 (1982).
[CrossRef]

Taylor, J. R.

Trillo, S.

Vampouile, M.

C. Froely, B. Colombeau, and M. Vampouile, “Shaping and analysis of picosecond light pulses,” Prog. Opt. 20, 65–153 (1983).

Wai, P. K. A.

Wise, F.

Yanovsky, V.

IEEE J. Quantum Electron.

J. L. A. Chilla and O. E. Martinez, “Analysis of a method of phase measurement of ultrashort pulses in the frequency domain,” IEEE J. Quantum Electron. 27, 1228–1235 (1991).
[CrossRef]

See, e.g., R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron. 18, 1062–1071 (1982).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Lett.

Phys. Rev. A

S. B. Cavalcanti, J. C. Cressoni, H. R. da Cruz, and A. S. Gouveia-Neto, “Modulational instability in the region of minimum group-velocity dispersion of single-mode optical fibers via an extended nonlinear Schrödinger equation,” Phys. Rev. A 43, 6162–6165 (1991).
[CrossRef] [PubMed]

Prog. Opt.

C. Froely, B. Colombeau, and M. Vampouile, “Shaping and analysis of picosecond light pulses,” Prog. Opt. 20, 65–153 (1983).

Other

G. R. Boyer, B. Hall, D. Anderson, M. Lisak, M. Karlsson, and A. Berntson, “Four-wave mixing of femtosecond pump-probe pulses in optical fibers,” in Nonlinear Guided Waves and Their Applications, 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), paper WB2–1.

G. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, 1995).

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Figures (9)

Fig. 1
Fig. 1

Experimental setup (schematic).

Fig. 2
Fig. 2

Experimentally observed spectral plots of the fiber output for increasing pump power. Shown is a XPM-induced probe frequency shift for moderate pump power, followed by a frequency jump at higher power. The maximum attained input power for this figure is 530 W.

Fig. 3
Fig. 3

Experimental output spectra. Just the pump (red), just the probe (green), and a copropagated pulse pair (thinner purple curve). Comparison with simulations suggest that the relative pump–probe time delay is close to zero.

Fig. 4
Fig. 4

Experimentally obtained cross-correlation trace of the jump signal with the full propagated signal. The width of the trace is 2.3 ps FWHM, suggesting a pulse width of approximately 600 fs.

Fig. 5
Fig. 5

Numerical simulation of the frequency jump: fiber input (dash-dotted), output (solid). The dashed curve shows the output with the probe blocked, for comparison with the red trace in Fig. 3.

Fig. 6
Fig. 6

Numerical simulation of the full propagation along the fiber. Red color means high intensity, and blue is low intensity. The color map cuts off at -80 dB, i.e., everything below that is dark blue. The white patches are due to errors in rendering the picture, corresponding to rapid numerical oscillations at intensities of -100 to -400 dB.

Fig. 7
Fig. 7

Dependence on the relative phase difference between the pump and the probe. The output from a 15-m length of fiber is shown for varying relative phase. Note that an interval of 3π is plotted for clarity. The color map is tuned to allocate most colors to the probe dynamics; most of the pump dynamics is blocked out.

Fig. 8
Fig. 8

Output from a 15-m fiber as the λzd is varied. The jump signal is always group-velocity matched with the pump.

Fig. 9
Fig. 9

Output from a 15-m fiber as the probe wavelength is varied. The jump-signal wavelength is only slightly affected, but its detailed structure is modified.

Equations (1)

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i Az=β22 2At2+iβ36 3At3-κ|A|2A,

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