Abstract

Coherent crosstalk mechanisms induced by polarization mode dispersion in polarization multiplexed fiber transmission are examined by systems experiments, analysis and supporting modeling. Primary mechanisms include destructive interference, edge effects, and beat effects, leading to pulse distortion and to bit-error-rate penalties. Rules of thumb for tolerable crosstalk levels are developed.

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References

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  1. A. R. Chraplyvy, A. H. Gnauck, R. W. Tkach, et al., "1-Tb/s Transmission Experiment," IEEE Photon. Technol. Lett. 8, 1264-1266 (1996).
    [CrossRef]
  2. T. Ito, K. Fukuchi, K. Sekiya, D. Ogasahara, R. Ohhira, and T. Ono, "6.4 Tb/s (160 x 40 Gb/s) WDM transmission experiment with 0.8 bit/s/Hz spectral efficiency," in Proceedings of European Conference on Optical Communications, Munich, Germany, 2000, Paper PD1.1.
  3. S. G. Evangelides, Jr., L. F. Mollenauer, J. P. Gordon, and N. S. Bergano, "Polarization multiplexing with solitons," J. Lightwave Technol. 10, 28-35 (1992).
    [CrossRef]
  4. X. Zhang, M. Karlsson, P. A. Andrekson, and E. Kolltveit, "Polarization-division multiplexed solitons in optical fibers with polarization-mode dispersion," IEEE Photon. Technol. Lett. 10, 1742-1744, (1998).
    [CrossRef]
  5. H. Heidrich, D. Hoffman, and R. I. MacDonald, "Polarization and wavelength multiplexed bidirectional single fiber subscriber loop," J. Opt. Commun. 7, 136-138 (1986).
  6. E. Dietrich, B. Enning, R. Gross, and H. Knupke, "Heterodyne transmission of a 560 Mb/s optical signal by means of polarization shift keying," Electron. Lett. 23, 421-422 (1987).
    [CrossRef]
  7. L. E. Nelson, T. N. Nielsen, and H. Kogelnik, "Observation of coherent crosstalk in polarization multiplexed transmission due to PMD," submitted to IEEE Photon. Technol. Lett.
  8. F. Forghieri, R. W. Tkach and A. R. Chraplyvy, "Fiber Nonlinearities and their Impact on Transmission Systems", in Optical Fiber Telecommunications, vol. III A,I.P.Kaminow and T.L.Koch, eds.,(Academic Press, San Diego, 1997), pp. 196-264.
  9. L. F. Mollenauer, J. P. Gordon, and F. Heismann, "Polarization scattering by soliton-soliton collisions," Opt. Lett. 20, 2060-2062 (1995).
    [CrossRef] [PubMed]
  10. B. C. Collings and L. Boivin, "Nonlinear polarization evolution induced by cross-phase modulation and its impact on transmission systems," IEEE Photon. Technol. Lett., Nov. 2000.
    [CrossRef]

Other

A. R. Chraplyvy, A. H. Gnauck, R. W. Tkach, et al., "1-Tb/s Transmission Experiment," IEEE Photon. Technol. Lett. 8, 1264-1266 (1996).
[CrossRef]

T. Ito, K. Fukuchi, K. Sekiya, D. Ogasahara, R. Ohhira, and T. Ono, "6.4 Tb/s (160 x 40 Gb/s) WDM transmission experiment with 0.8 bit/s/Hz spectral efficiency," in Proceedings of European Conference on Optical Communications, Munich, Germany, 2000, Paper PD1.1.

S. G. Evangelides, Jr., L. F. Mollenauer, J. P. Gordon, and N. S. Bergano, "Polarization multiplexing with solitons," J. Lightwave Technol. 10, 28-35 (1992).
[CrossRef]

X. Zhang, M. Karlsson, P. A. Andrekson, and E. Kolltveit, "Polarization-division multiplexed solitons in optical fibers with polarization-mode dispersion," IEEE Photon. Technol. Lett. 10, 1742-1744, (1998).
[CrossRef]

H. Heidrich, D. Hoffman, and R. I. MacDonald, "Polarization and wavelength multiplexed bidirectional single fiber subscriber loop," J. Opt. Commun. 7, 136-138 (1986).

E. Dietrich, B. Enning, R. Gross, and H. Knupke, "Heterodyne transmission of a 560 Mb/s optical signal by means of polarization shift keying," Electron. Lett. 23, 421-422 (1987).
[CrossRef]

L. E. Nelson, T. N. Nielsen, and H. Kogelnik, "Observation of coherent crosstalk in polarization multiplexed transmission due to PMD," submitted to IEEE Photon. Technol. Lett.

F. Forghieri, R. W. Tkach and A. R. Chraplyvy, "Fiber Nonlinearities and their Impact on Transmission Systems", in Optical Fiber Telecommunications, vol. III A,I.P.Kaminow and T.L.Koch, eds.,(Academic Press, San Diego, 1997), pp. 196-264.

L. F. Mollenauer, J. P. Gordon, and F. Heismann, "Polarization scattering by soliton-soliton collisions," Opt. Lett. 20, 2060-2062 (1995).
[CrossRef] [PubMed]

B. C. Collings and L. Boivin, "Nonlinear polarization evolution induced by cross-phase modulation and its impact on transmission systems," IEEE Photon. Technol. Lett., Nov. 2000.
[CrossRef]

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Figures (7)

Fig. 1.
Fig. 1.

Schematic of a polarization multiplexed system. The polarization beam splitters (PBS) combine and separate the multiplexed channels A and B. The (optional) polarization controller PC1 controls the launch into the fiber. PC2 controls proper alignment with the output PBS.

Fig. 2.
Fig. 2.

Complex plane diagram of the interference between complex amplitude A and coupled amplitude jκB at output port A. The corresponding effect on the upper rail of the detected signal intensity is shown on the right.

Fig. 3.
Fig. 3.

Modeled output intensity of channel A for a 40 Gb/s NRZ bit stream after an optical filter of 50 GHz FWHM with a 21 GHz flank (20% to 80%). A PDM case is shown with the interfering B channel at the same wavelength as the A channel. The B channel is independently modulated. The relative timing delay between the A and B bit streams is 12.5 ps and the phase difference is 0. The effect of crosstalk is shown for DGD values of 1.1 and 5.1 ps.

Fig. 4.
Fig. 4.

Modeled output intensity of channel A as in Fig. 3 but with two B carriers spaced ±50 GHz from the A carrier.

Fig. 5.
Fig. 5.

Measured coupled spectral power density from B to A (i.e. Aout in Fig. 1) in the PDM case (with A=0) for six DGD values after transmission through a PM fiber and an optical filter of 50 GHz FWHM and 21 GHz flank. The B channel was modulated at 40 Gb/s with a 12 ps pulse risetime. The measurement resolution was 0.1 nm.

Fig. 6.
Fig. 6.

Modeled coupled spectral power density from B to A (i.e. Aout in Fig. 1) in the polarization interleaving case (with A=0) for five DGD values after transmission through an optical filter of 50 GHz FWHM and 21 GHz flank. The B-channel is represented by a single Gaussian pulse of 25 ps FWHM and a 12 ps rise time.

Fig. 7.
Fig. 7.

Modeled eye diagram for polarization interleaving with a DGD of 5.1 ps. The A channel and two B channels were independent data streams of 27-1 bits each. The B channels were spaced ±50 GHz from A. The relative timing delays and relative phase shifts between the A and B channels were 0, resulting in one of the worst-case eye closings for the range of parameters examined. The pin-receiver 20 percent of T eye opening was 28 percent, as listed in Table 2.

Tables (2)

Tables Icon

Table 1. PMD Crosstalk for PDM Systems

Tables Icon

Table 2. PMD Crosstalk for Polarization Interleaving

Equations (20)

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A out = A + j κ B ,
B = A . e j Δ φ .
I A = A A ; I B = B B .
I B A = κ 2 B B * ,
I d A = A out A out * = A A * ( 1 + 2 κ sin Δ φ ) ,
= I A + 2 I A I B A sin Δ φ ,
B = B 0 . e j ( Δ φ + ω B t )
I d A = I A + 2 I A . I B A . sin ( Δ φ + ω B t ) .
κ = sin ( Δ τ . ω / 2 ) ,
A ˜ out = A ˜ + j ( Δ τ ω / 2 ) B , ˜
d dt A ( t ) = A ˙ = F T ( j ω A ) .
A out ( t ) = A + ( Δ τ / 2 ) B ˙ .
B ˙ = j ω B B + B ˙ 0 e j ( Δ φ + ω B t ) ,
B ( t ) = A 0 · sin ( t / Δ T )
I ˙ B max = A 0 2 / Δ T ,
B ˙ max = A 0 / Δ T .
I d A = A out A out * = A 2 ± Δ τ · A · B ˙
I d A = A 0 2 ( 1 ± Δ τ / Δ T ) .
A out = A + j κ 0 B + ( Δ τ / 2 ) B ˙ ,
A ˜ out ( ω ) = A ˜ · cos ( ω Δ τ / 2 ) + j B ˜ · sin ( ω Δ τ / 2 ) ,

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