Abstract

We compare techniques using two fibers connected either in series or in parallel for cancelling cross talk that is due to stimulated Raman scattering in wavelength-division-multiplexed systems. Theory shows that such cross talk can be completely eliminated by a series arrangement in lossy dispersionless fibers by means of midway amplification and spectral inversion. In dispersive fibers, cross-talk reduction of the order of the Raman gain G can be obtained by adding dispersion compensation and alternating dispersion. Alternatively, a similar cross-talk reduction can be obtained by use of parallel transmission of signals on different sets of wavelengths and differential detection; in the presence of dispersion, the dispersion for the different sets of wavelengths must be opposite. The parallel approach appears to be more practical.

© 1998 Optical Society of America

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References

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  1. A. R. Chraplyvy and R. W. Tkach, IEEE Photonics Technol. Lett. 5, 666 (1993).
    [CrossRef]
  2. K. Kikushima, H. Yoshinaga, and M. Yamada, in Optical Fiber Communication Conference, Vol. 8 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), post-deadline paper PD24.
  3. A. Li, C. J. Mahon, Z. Wang, G. Jacobsen, and E. Bodtker, Electron. Lett. 31, 1538 (1995).
    [CrossRef]
  4. Z. Wang, A. Li, C. J. Mahon, G. Jacobsen, and E. Bodtker, IEEE Photonics Technol. Lett. 7, 1492 (1995).
    [CrossRef]
  5. D. Cotter and A. M. Hill, Electron. Lett. 20, 185 (1984).
    [CrossRef]
  6. F. Forghieri, R. W. Tkach, and A. R. Chraplyvy, in Optical Amplifiers and Their Applications, Vol. 18 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), p. 212.
  7. M. E. Marhic, N. Kagi, T. K. Chiang, and L. G. Kazovsky, Opt. Lett. 20, 863 (1995).
    [CrossRef] [PubMed]
  8. G. P. Agrawal, Nonlinear Fiber Optics (Academic, Boston, 1989).
  9. Z. Wang, E. Bodtker, and G. Jacobsen, Electron. Lett. 31, 1591 (1995).
    [CrossRef]
  10. C.-Y. Kuo, D. Piehler, C. Gall, J. Kleefeld, A. Nilsson, and L. Middleton, in Optical Fiber Communications Conference, Vol. 2 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), paper WN2.

1995 (4)

A. Li, C. J. Mahon, Z. Wang, G. Jacobsen, and E. Bodtker, Electron. Lett. 31, 1538 (1995).
[CrossRef]

Z. Wang, A. Li, C. J. Mahon, G. Jacobsen, and E. Bodtker, IEEE Photonics Technol. Lett. 7, 1492 (1995).
[CrossRef]

Z. Wang, E. Bodtker, and G. Jacobsen, Electron. Lett. 31, 1591 (1995).
[CrossRef]

M. E. Marhic, N. Kagi, T. K. Chiang, and L. G. Kazovsky, Opt. Lett. 20, 863 (1995).
[CrossRef] [PubMed]

1993 (1)

A. R. Chraplyvy and R. W. Tkach, IEEE Photonics Technol. Lett. 5, 666 (1993).
[CrossRef]

1984 (1)

D. Cotter and A. M. Hill, Electron. Lett. 20, 185 (1984).
[CrossRef]

Bodtker, E.

Z. Wang, A. Li, C. J. Mahon, G. Jacobsen, and E. Bodtker, IEEE Photonics Technol. Lett. 7, 1492 (1995).
[CrossRef]

A. Li, C. J. Mahon, Z. Wang, G. Jacobsen, and E. Bodtker, Electron. Lett. 31, 1538 (1995).
[CrossRef]

Z. Wang, E. Bodtker, and G. Jacobsen, Electron. Lett. 31, 1591 (1995).
[CrossRef]

Chiang, T. K.

Chraplyvy, A. R.

A. R. Chraplyvy and R. W. Tkach, IEEE Photonics Technol. Lett. 5, 666 (1993).
[CrossRef]

Cotter, D.

D. Cotter and A. M. Hill, Electron. Lett. 20, 185 (1984).
[CrossRef]

Hill, A. M.

D. Cotter and A. M. Hill, Electron. Lett. 20, 185 (1984).
[CrossRef]

Jacobsen, G.

Z. Wang, A. Li, C. J. Mahon, G. Jacobsen, and E. Bodtker, IEEE Photonics Technol. Lett. 7, 1492 (1995).
[CrossRef]

Z. Wang, E. Bodtker, and G. Jacobsen, Electron. Lett. 31, 1591 (1995).
[CrossRef]

A. Li, C. J. Mahon, Z. Wang, G. Jacobsen, and E. Bodtker, Electron. Lett. 31, 1538 (1995).
[CrossRef]

Kagi, N.

Kazovsky, L. G.

Li, A.

A. Li, C. J. Mahon, Z. Wang, G. Jacobsen, and E. Bodtker, Electron. Lett. 31, 1538 (1995).
[CrossRef]

Z. Wang, A. Li, C. J. Mahon, G. Jacobsen, and E. Bodtker, IEEE Photonics Technol. Lett. 7, 1492 (1995).
[CrossRef]

Mahon, C. J.

Z. Wang, A. Li, C. J. Mahon, G. Jacobsen, and E. Bodtker, IEEE Photonics Technol. Lett. 7, 1492 (1995).
[CrossRef]

A. Li, C. J. Mahon, Z. Wang, G. Jacobsen, and E. Bodtker, Electron. Lett. 31, 1538 (1995).
[CrossRef]

Marhic, M. E.

Tkach, R. W.

A. R. Chraplyvy and R. W. Tkach, IEEE Photonics Technol. Lett. 5, 666 (1993).
[CrossRef]

Wang, Z.

Z. Wang, A. Li, C. J. Mahon, G. Jacobsen, and E. Bodtker, IEEE Photonics Technol. Lett. 7, 1492 (1995).
[CrossRef]

Z. Wang, E. Bodtker, and G. Jacobsen, Electron. Lett. 31, 1591 (1995).
[CrossRef]

A. Li, C. J. Mahon, Z. Wang, G. Jacobsen, and E. Bodtker, Electron. Lett. 31, 1538 (1995).
[CrossRef]

Electron. Lett. (3)

A. Li, C. J. Mahon, Z. Wang, G. Jacobsen, and E. Bodtker, Electron. Lett. 31, 1538 (1995).
[CrossRef]

D. Cotter and A. M. Hill, Electron. Lett. 20, 185 (1984).
[CrossRef]

Z. Wang, E. Bodtker, and G. Jacobsen, Electron. Lett. 31, 1591 (1995).
[CrossRef]

IEEE Photonics Technol. Lett. (2)

Z. Wang, A. Li, C. J. Mahon, G. Jacobsen, and E. Bodtker, IEEE Photonics Technol. Lett. 7, 1492 (1995).
[CrossRef]

A. R. Chraplyvy and R. W. Tkach, IEEE Photonics Technol. Lett. 5, 666 (1993).
[CrossRef]

Opt. Lett. (1)

Other (4)

K. Kikushima, H. Yoshinaga, and M. Yamada, in Optical Fiber Communication Conference, Vol. 8 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), post-deadline paper PD24.

C.-Y. Kuo, D. Piehler, C. Gall, J. Kleefeld, A. Nilsson, and L. Middleton, in Optical Fiber Communications Conference, Vol. 2 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), paper WN2.

F. Forghieri, R. W. Tkach, and A. R. Chraplyvy, in Optical Amplifiers and Their Applications, Vol. 18 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), p. 212.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, Boston, 1989).

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Figures (3)

Fig. 1
Fig. 1

Two-fiber series arrangement for SRS cancellation in the absence of dispersion. SI, spectral inverter; A, optical amplifier.

Fig. 2
Fig. 2

Two-fiber series arrangement for SRS cancellation in the presence of dispersion. DC, dispersion compensator; SI, spectral inverter; A, optical amplifier; ±D, fiber chromatic dispersion coefficient.

Fig. 3
Fig. 3

Schematic of the parallel-transmission system with four wavelengths.

Equations (51)

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dN1dz=-αN1-gN1N2,
dN2dz=-αN2+gN1N2,
N1(z)=N0 exp(-αz)1+N20N10 exp(Z),
N2(z)=N0 exp(-αz)1+N10N20 exp(-Z),
N10=N1(0)=N2(L)exp(αL),
N20=N2(0)=N1(L)exp(αL).
N1(z)=N0 exp(-αz)1+N20N10 exp(Z),
N2(z)=N0 exp(-αz)1+N10N20 exp(-Z),
N1(L)=N0 exp(-αL)1+N20N10 exp(ZL)=N0 exp(-αL)1+exp(ZL) 1+N10N20 exp(-ZL)1+N20N10 exp(ZL)=N20 exp(-αL).
N1z+1v1 N1t=-αN1-gN1N2,
N2z+1v2 N2t=-αN2+gN1N2,
N1(z, t)=exp(-αz)N10, t-zv1×exp-g0zN20, t+d12ξ-zv1×exp(-αξ)dξ,
N2(z, t)=exp(-αz)N20, t-zv2×expg0zN10, t-d12ξ-zv2×exp(-αξ)dξ,
N1DC(t)=N1L, t+Lv1-T,
N2DC(t)=N2L, t+Lv2-T,
N1(0, t)=exp(αL)N2DC(t)=N2(0, t-T)×expg0LN1(0, t-T-d12ξ)×exp(-αξ)dξ,
N2(0, t)=exp(αL)N1DC(t)=N1(0, t-T)×exp-g0LN2(0, t-T+d12ξ)×exp(-αξ)dξ.
N1(L, t)=exp(-αL)N2(0, t)×expg0LN1(0, t-d12ξ)×exp(-αξ)dξ×exp-g0LN1(0, t+d12η)×exp-g0LN2(0, t+d12η+d12μ)×exp(-αμ)dμexp(-αη)dη,
N1(L, t)=exp(-αL)N2(0, t)expg20L0LN1(0, t-d12η)N2[0, t+d12(μ-η)]×exp[-α(η+μ)]dηdμ.
N1(L, t)=exp(-αL)N20 expg2N20Leff×0LN1(0, t-d12η)exp(-αη)dη,
N2(L, t)=exp(-αL)N20 expg0LN1(0, t-d12ξ)×exp(-αξ)dξ.
N10=N20,N20=N10.
S12=N1(L)+N2(L)=N0 exp(-αL)1+N20N10 exp(ZL)+N0 exp(-αL)1+N10N20 exp(-ZL),
S12=N0 exp(-αL)1+N20N10 exp(ZL)+N0 exp(-αL)1+N20N10 exp(-ZL).
S12=2N10 exp(-αL)1+2R1+R S2×1+4R(1+R)2 S2-1.
S122N10 exp(-αL)1+R(R-1)2(1+R)2 ZL2.
CNR12=2mG2,
N1(L)N10 exp(-αL)1-1+m2G.
CNR1=2mG.
ρd=CNR1CNR12=G.
N1(L, t)=exp(-αL)N1(0, τ)exp-g0LN2(0, τ+d12ξ)×exp(-αξ)dξ,
N2(L, t)=exp(-αL)N2(0, τ)expg0LN1(0, τ-d12ξ)×exp(-αξ)dξ.
N1(L, t)=exp(-αL)N1(0, τ)exp-g0LN2(0, τ-d12ξ)×exp(-αξ)dξ,
N2(L, t)=exp(-αL)N2(0, τ)×expg0LN1(0, τ+d12ξ)exp(-αξ)dξ.
N2(0, τ)=N1(0, τ),N1(0, τ)=N2(0, τ).
N1(L, t)=exp(-αL)N2(0, τ)exp-g0LN1(0, τ-d12ξ)×exp(-αξ)dξ,
N2(L, t)=exp(-αL)N1(0, τ)expg0LN2(0, τ+d12ξ)×exp(-αξ)dξ.
S12(L, t)=N1(L, t)+N2(L, t)=2 exp(-αL)N1(0, τ)cosh(gI),
I=0LN2(0, τ+d12ξ)exp(-αξ)dξ.
gI=G(1+J),
J=1Leff 0Lm(τ+d12ξ)exp(-αξ)dξ,
cosh(gI)1+12 G2(1+2J),
CNR121G2J.
CNR11GJ.
N1(0, τ)=N2(0, τ)=N10,
N2(0, τ)=N10[1+m(τ)],
N1(0, τ)=N10[1-m(τ)].
N2(L, t)-N1(L, t)=2 exp(-αL)N10[sinh G+m(τ)cosh G].
S12(L, t)=N1(L, t)-N2(L, t)=2 exp(-αL)N10 exp(-GJ)sinh G;
SNR1=m(τ)GJ,
SNR2=m(τ)G2J.

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