Abstract

Enhanced coupled-nonlinear equations are introduced for full compensation of cross-phase modulation and partial compensation of four-wave mixing (FWM) via split-step digital backward propagation. Compared to full FWM compensation, the new backward propagation equations provide a significant reduction in the number of steps required in the split-step method. This increased step size together with more relaxed sampling requirements reduced the computational load by more than a factor of 20.

© 2009 Optical Society of America

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References

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  1. E. Yamazaki, F. Inuzuka, K. Yonenaga, A. Takada, and M. Koga, “Compensation of interchannel crosstalk induced by optical fiber nonlinearity in carrier phase-locked WDM system,” IEEE Photon. Technol. Lett. 19, 9-11 (2007).
    [CrossRef]
  2. X. Li, X. Chen, G. Goldfarb, E. Mateo, I. Kim, F. Yaman, and G. Li, “Electronic postcompensation of WDM transmission impairments using coherent detection and digital signal processing,” Opt. Express 16, 880-888 (2008).
    [CrossRef] [PubMed]
  3. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2005).
  4. E. Mateo, L. Zhu, and G. Li, “Impact of XPM and FWM on the digital implementation of impairment compensation for WDM transmission using backward propagation,” Opt. Express 16, 16124-16137 (2008).
    [CrossRef] [PubMed]
  5. T. Schneider, Nonlinear Optics in Telecommunications (Springer, 2004).

2008

2007

E. Yamazaki, F. Inuzuka, K. Yonenaga, A. Takada, and M. Koga, “Compensation of interchannel crosstalk induced by optical fiber nonlinearity in carrier phase-locked WDM system,” IEEE Photon. Technol. Lett. 19, 9-11 (2007).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2005).

Chen, X.

Goldfarb, G.

Inuzuka, F.

E. Yamazaki, F. Inuzuka, K. Yonenaga, A. Takada, and M. Koga, “Compensation of interchannel crosstalk induced by optical fiber nonlinearity in carrier phase-locked WDM system,” IEEE Photon. Technol. Lett. 19, 9-11 (2007).
[CrossRef]

Kim, I.

Koga, M.

E. Yamazaki, F. Inuzuka, K. Yonenaga, A. Takada, and M. Koga, “Compensation of interchannel crosstalk induced by optical fiber nonlinearity in carrier phase-locked WDM system,” IEEE Photon. Technol. Lett. 19, 9-11 (2007).
[CrossRef]

Li, G.

Li, X.

Mateo, E.

Schneider, T.

T. Schneider, Nonlinear Optics in Telecommunications (Springer, 2004).

Takada, A.

E. Yamazaki, F. Inuzuka, K. Yonenaga, A. Takada, and M. Koga, “Compensation of interchannel crosstalk induced by optical fiber nonlinearity in carrier phase-locked WDM system,” IEEE Photon. Technol. Lett. 19, 9-11 (2007).
[CrossRef]

Yaman, F.

Yamazaki, E.

E. Yamazaki, F. Inuzuka, K. Yonenaga, A. Takada, and M. Koga, “Compensation of interchannel crosstalk induced by optical fiber nonlinearity in carrier phase-locked WDM system,” IEEE Photon. Technol. Lett. 19, 9-11 (2007).
[CrossRef]

Yonenaga, K.

E. Yamazaki, F. Inuzuka, K. Yonenaga, A. Takada, and M. Koga, “Compensation of interchannel crosstalk induced by optical fiber nonlinearity in carrier phase-locked WDM system,” IEEE Photon. Technol. Lett. 19, 9-11 (2007).
[CrossRef]

Zhu, L.

IEEE Photon. Technol. Lett.

E. Yamazaki, F. Inuzuka, K. Yonenaga, A. Takada, and M. Koga, “Compensation of interchannel crosstalk induced by optical fiber nonlinearity in carrier phase-locked WDM system,” IEEE Photon. Technol. Lett. 19, 9-11 (2007).
[CrossRef]

Opt. Express

Other

T. Schneider, Nonlinear Optics in Telecommunications (Springer, 2004).

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2005).

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Figures (6)

Fig. 1
Fig. 1

Block diagram of the SSFM step implementing the EC-NLSEs.

Fig. 2
Fig. 2

Scheme of the WDM transmission and digital postprocessing stages for backward propagation implementation using T-NLSE and (C, EC)-NLSEs. MUX, multiplexer; DEMUX, demultiplexer.

Fig. 3
Fig. 3

Performance versus power for the different postcompensation cases, where EC-NLSEs(2, 4) represents the EC-NLSEs with (2, 4) neighboring channels (the Q value is averaged over all the WDM channels). Additionally, results for dispersion compensation (DC) only are shown.

Fig. 4
Fig. 4

Distribution of Q values with WDM channels ( power / channel = 0.2 dBm ).

Fig. 5
Fig. 5

Averaged Q value as a function of the SSFM step size for the respective optimum powers.

Fig. 6
Fig. 6

Q value per channel for different upsampling factors ( power / channel = 0.2 dBm ).

Equations (10)

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E = m = 1 N E ^ m exp ( i m Δ ω t ) ,
E z + α 2 E + i β 2 2 2 E t 2 β 3 6 3 E t 3 + i γ | E | 2 E = 0 ,
E ^ m z + α 2 E ^ m + p = 1 3 K p m p E ^ m t p + i γ ( 2 q = 1 N | E ^ q | 2 | E ^ m | 2 ) E ^ m = 0 ,
K 1 m = m β 2 Δ ω 1 2 m 2 β 3 Δ ω 2 , K 2 m = 1 2 i β 2 1 2 m β 3 Δ ω , K 3 m = 1 6 β 3 .
S T - NLSE = 2 N Δ f B , samples / symbol ,
E ^ m z + α 2 E ^ m + p = 1 3 K p m p E ^ m t p + i γ ( 2 q = 1 N | E ^ q | 2 | E ^ m | 2 ) E ^ m + F 2 m + F 4 m = 0 ,
F 2 m = 2 E ^ m + 1 E ^ m 1 E ^ m * ,
F 4 m = E ^ m + 1 2 E ^ m + 2 * + E ^ m 1 2 E ^ m 2 * + 2 E ^ m 1 E ^ m + 1 E ^ m + 1 * + 2 E ^ m + 1 E ^ m 2 E ^ m 1 * + 2 E ^ m + 2 E ^ m 2 E ^ m * .
E ^ m j + 1 = E ^ m j exp ( i γ | E ^ m j | 2 h ) + h ( F 2 m j + F 4 m j ) .
H m ( ω ) = exp [ ( i β 2 ( ω m Δ ω ) 2 2 + i β 3 ( ω m Δ ω ) 3 6 ) h ] .

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