Abstract

Higher-order four-wave mixing effects are evaluated in WDM systems. Calculated and measured results show that higher-order FWM crosstalk, though small compared to the first-order FWM crosstalk, could be significant in unequal channel-spacing WDM systems where the first-order FWM is not a problem.

© 2000 Optical Society of America

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References

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  1. F. Forghieri, R. W. Tkach, and A. R. Chraplyvy, “WDM system with unequally spaced channels,” J. Lightwave Technology,  13, 889–897, (1995).
    [Crossref]
  2. N. Shibata, R. P. Braun, and R. G. Warrts, “Phase-mismatch dependence of efficiency of wave generation through four-wave mixing in a single-mode fiber,” IEEE J. of Quantum Electronics,  QE-23, 1205–1211, (1987).
    [Crossref]
  3. S. Song, C. Allen, K. Demarest, and R. Hui, “Intensity-dependent effects on FWM in optic fibers,” J. of Lightwave Technology,  17, 2285–2290, (1999).
    [Crossref]
  4. K. Inoue, “Polarization effect on four-wave mixing efficiency in a single-mode fiber,” IEEE J. of Quantum Electronics,  28, 883–895, (1992).
    [Crossref]
  5. S. Song, C. Allen, K. Demarest, and R. Hui, “A novel nonlinear method for measuring polarization mode dispersion,” J. of Lightwave Technology,  17, 12, 2530–2533, (1999).

1999 (2)

S. Song, C. Allen, K. Demarest, and R. Hui, “Intensity-dependent effects on FWM in optic fibers,” J. of Lightwave Technology,  17, 2285–2290, (1999).
[Crossref]

S. Song, C. Allen, K. Demarest, and R. Hui, “A novel nonlinear method for measuring polarization mode dispersion,” J. of Lightwave Technology,  17, 12, 2530–2533, (1999).

1995 (1)

F. Forghieri, R. W. Tkach, and A. R. Chraplyvy, “WDM system with unequally spaced channels,” J. Lightwave Technology,  13, 889–897, (1995).
[Crossref]

1992 (1)

K. Inoue, “Polarization effect on four-wave mixing efficiency in a single-mode fiber,” IEEE J. of Quantum Electronics,  28, 883–895, (1992).
[Crossref]

1987 (1)

N. Shibata, R. P. Braun, and R. G. Warrts, “Phase-mismatch dependence of efficiency of wave generation through four-wave mixing in a single-mode fiber,” IEEE J. of Quantum Electronics,  QE-23, 1205–1211, (1987).
[Crossref]

Allen, C.

S. Song, C. Allen, K. Demarest, and R. Hui, “Intensity-dependent effects on FWM in optic fibers,” J. of Lightwave Technology,  17, 2285–2290, (1999).
[Crossref]

S. Song, C. Allen, K. Demarest, and R. Hui, “A novel nonlinear method for measuring polarization mode dispersion,” J. of Lightwave Technology,  17, 12, 2530–2533, (1999).

Braun, R. P.

N. Shibata, R. P. Braun, and R. G. Warrts, “Phase-mismatch dependence of efficiency of wave generation through four-wave mixing in a single-mode fiber,” IEEE J. of Quantum Electronics,  QE-23, 1205–1211, (1987).
[Crossref]

Chraplyvy, A. R.

F. Forghieri, R. W. Tkach, and A. R. Chraplyvy, “WDM system with unequally spaced channels,” J. Lightwave Technology,  13, 889–897, (1995).
[Crossref]

Demarest, K.

S. Song, C. Allen, K. Demarest, and R. Hui, “Intensity-dependent effects on FWM in optic fibers,” J. of Lightwave Technology,  17, 2285–2290, (1999).
[Crossref]

S. Song, C. Allen, K. Demarest, and R. Hui, “A novel nonlinear method for measuring polarization mode dispersion,” J. of Lightwave Technology,  17, 12, 2530–2533, (1999).

Forghieri, F.

F. Forghieri, R. W. Tkach, and A. R. Chraplyvy, “WDM system with unequally spaced channels,” J. Lightwave Technology,  13, 889–897, (1995).
[Crossref]

Hui, R.

S. Song, C. Allen, K. Demarest, and R. Hui, “Intensity-dependent effects on FWM in optic fibers,” J. of Lightwave Technology,  17, 2285–2290, (1999).
[Crossref]

S. Song, C. Allen, K. Demarest, and R. Hui, “A novel nonlinear method for measuring polarization mode dispersion,” J. of Lightwave Technology,  17, 12, 2530–2533, (1999).

Inoue, K.

K. Inoue, “Polarization effect on four-wave mixing efficiency in a single-mode fiber,” IEEE J. of Quantum Electronics,  28, 883–895, (1992).
[Crossref]

Shibata, N.

N. Shibata, R. P. Braun, and R. G. Warrts, “Phase-mismatch dependence of efficiency of wave generation through four-wave mixing in a single-mode fiber,” IEEE J. of Quantum Electronics,  QE-23, 1205–1211, (1987).
[Crossref]

Song, S.

S. Song, C. Allen, K. Demarest, and R. Hui, “A novel nonlinear method for measuring polarization mode dispersion,” J. of Lightwave Technology,  17, 12, 2530–2533, (1999).

S. Song, C. Allen, K. Demarest, and R. Hui, “Intensity-dependent effects on FWM in optic fibers,” J. of Lightwave Technology,  17, 2285–2290, (1999).
[Crossref]

Tkach, R. W.

F. Forghieri, R. W. Tkach, and A. R. Chraplyvy, “WDM system with unequally spaced channels,” J. Lightwave Technology,  13, 889–897, (1995).
[Crossref]

Warrts, R. G.

N. Shibata, R. P. Braun, and R. G. Warrts, “Phase-mismatch dependence of efficiency of wave generation through four-wave mixing in a single-mode fiber,” IEEE J. of Quantum Electronics,  QE-23, 1205–1211, (1987).
[Crossref]

IEEE J. of Quantum Electronics (2)

N. Shibata, R. P. Braun, and R. G. Warrts, “Phase-mismatch dependence of efficiency of wave generation through four-wave mixing in a single-mode fiber,” IEEE J. of Quantum Electronics,  QE-23, 1205–1211, (1987).
[Crossref]

K. Inoue, “Polarization effect on four-wave mixing efficiency in a single-mode fiber,” IEEE J. of Quantum Electronics,  28, 883–895, (1992).
[Crossref]

J. Lightwave Technology (1)

F. Forghieri, R. W. Tkach, and A. R. Chraplyvy, “WDM system with unequally spaced channels,” J. Lightwave Technology,  13, 889–897, (1995).
[Crossref]

J. of Lightwave Technology (2)

S. Song, C. Allen, K. Demarest, and R. Hui, “A novel nonlinear method for measuring polarization mode dispersion,” J. of Lightwave Technology,  17, 12, 2530–2533, (1999).

S. Song, C. Allen, K. Demarest, and R. Hui, “Intensity-dependent effects on FWM in optic fibers,” J. of Lightwave Technology,  17, 2285–2290, (1999).
[Crossref]

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Figures (7)

Fig. 1.
Fig. 1.

Higher-order FWM products produced from two channels

Fig. 2.
Fig. 2.

Experiment setup for measuring FWM power DFB—DFB laser, MZM—Mach-Zehnder Modulator, MUX—Multiplexer, EDFA—Erbium-doped fiber-amplifier, DSF—Dispersion-shifted fiber, Att-1, 2---Tunable attenuators, DEMUX—Demultiplexer, OSA—Optical spectrum analyzer,

Fig. 2.
Fig. 2.

Measured and calculated the first-order and second-order FWM power

Fig. 3.
Fig. 3.

Calculated FWM power for the second-order FWM products overlapped with the two channels

Fig. 4.
Fig. 4.

Measured Q as a function of input power to fiber

Fig. 5.
Fig. 5.

Measured OSNR as a function of input power to fiber

Fig. 6.
Fig. 6.

Measured Q as a function of system OSNR

Equations (17)

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P F 11 = η 11 P 1 2 P 2
P F 12 = η 12 P 2 2 P 1
P F 21 c = η 21 c 1 P 2 2 P F 12 + η 21 c 2 P 1 P 2 P F 11
= η 21 c 1 η 12 P 1 P 2 4 + η 21 c 2 η 11 P 1 3 P 2 2
P F 22 c = η 22 c 1 P 1 2 P F 11 + η 22 c 2 P 1 P 2 P F 12
= η 22 c 1 η 11 P 1 4 P 2 + η 22 c 2 η 12 P 1 2 P 2 3
P F 21 = η 21 1 P 1 2 P F 12 + η 21 2 P 1 P 2 P F 11
= η 21 1 η 12 P 1 3 P 2 2 + η 21 2 η 11 P 1 3 P 2 2
P F 22 = η 22 1 P 2 2 P F 11 + η 22 2 P 1 P 2 P F 12
= η 22 1 η 11 P 1 2 P 2 3 + η 22 2 η 12 P 1 2 P 2 3
P F 31 = η 31 1 P 1 2 P F 22 + η 31 2 P F 11 2 P 2 + η 31 3 P 1 P F 11 P F 12 + η 31 4 P 1 P 2 P F 21
= η 31 1 ( η 22 1 η 11 + η 22 2 η 12 ) P 1 4 P 2 3 + η 31 2 η 11 P 1 4 P 2 3
+ η 31 3 η 11 η 12 P 1 4 P 2 3 + η 31 4 ( η 21 1 η 12 + η 21 2 η 11 ) P 1 4 P 2 3
P F 32 = η 32 1 P 2 2 P F 21 + η 32 2 P F 12 2 P 1 + η 32 3 P 2 P F 11 P F 12 + η 32 4 P 1 P 2 P F 22
= η 32 1 ( η 21 1 η 12 + η 21 2 η 11 ) P 1 3 P 2 4 + η 32 2 η 12 P 1 3 P 2 4
+ η 32 3 η 11 η 12 P 1 3 P 2 4 + η 32 4 ( η 22 1 η 11 + η 22 2 η 12 ) P 1 3 P 2 4
P Fmn = η ¯ mn P 0 2 m + 1 ,

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