Abstract

We show the extension of the Gaussian Noise model, which describes non-linear propagation in uncompensated links of multilevel modulation formats, to systems using Raman amplification. We successfully validate the analytical results by comparison with numerical simulations of Nyquist-WDM PM-16QAM channels transmission over multi-span uncompensated links made of a single fiber type and using hybrid EDFA/Raman amplification with counter-propagating pumps. We analyze two typical high- and low-dispersion fiber types. We show that Raman amplification always induces a limited non-linear interference enhancement compared to the dominant ASE noise reduction.

© 2013 OSA

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  1. M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photon. Technol. Lett.16(2), 674–676 (2004).
    [CrossRef]
  2. K. Roberts, M. O'Sullivan, W. Kuang-Tsan, H. Sun, A. Awadalla, D. J. Krause, and C. Laperle, “Performance of dual-Polarization QPSK for dptical dransport dystems,” J. Lightwave Technol.27, 3546–3559 (2009).
  3. J.-X. Cai, H. G. Batshon, H. Zhang, C. R. Davidson, Y. Sun, M. Mazurczyk, D. G. Foursa, A. Pilipetskii, G. Mohs, and Neal S. Bergano, “25 TB/s dransmission over 5,530 km dsing 16QAM at 5.2 Bits/s/Hz dpectral dfficiency,” ECOC 2012, paper Mo.1.C.1 (2012).
  4. V. Curri, P. Poggiolini, A. Carena, and F. Forghieri, “Dispersion compensation and mitigation of nonlinear effects in 111-Gb/s WDM coherent PM-QPSK systems,” IEEE Photon. Technol. Lett.20(17), 1473–1475 (2008).
    [CrossRef]
  5. M. S. Alfiad, D. van den Borne, S. L. Jansen, T. Wuth, M. Kuschnerov, G. Grosso, A. Napoli, and H. de Waardt, “A domparison of dlectrical and dptical dispersion dompensation for 111-Gb/s POLMUX–RZ–DQPSK,” J. Lightwave Technol.27(16), 3590–3598 (2009).
    [CrossRef]
  6. G. Bosco, A. Carena, V. Curri, P. Poggiolini, and F. Forghieri, “Performance limits of Nyquist-WDM and CO-OFDM in high-speed PM-QPSK systems,” IEEE Photon. Technol. Lett.22(15), 1129–1131 (2010).
    [CrossRef]
  7. P. Poggiolini, “The GN dodel of non-linear propagation in uncompensated coherent optical systems,” J. Lightwave Technol.30(24), 3857–3879 (2012).
    [CrossRef]
  8. A. Carena, V. Curri, G. Bosco, P. Poggiolini, and F. Forghieri, “Modeling of the impact of nonlinear propagation effects in uncompensated optical coherent transmission links,” J. Lightwave Technol.30(10), 1524–1539 (2012).
    [CrossRef]
  9. E. Torrengo, R. Cigliutti, G. Bosco, A. Carena, V. Curri, P. Poggiolini, A. Nespola, D. Zeolla, and F. Forghieri, “Experimental validation of an analytical model for nonlinear propagation in uncompensated optical links,” Opt. Express19(26), B790–B798 (2011).
    [CrossRef] [PubMed]
  10. S. Yamanaka, T. Kobayashi, A. Sano, H. Masuda, E. Yoshida, Y. Miyamoto, T. Nakagawa, M. Nagatani, and H. Nosaka, “11 × 171 Gb/s PDM 16-QAM transmission over 1440 km with a spectral efficiency of 6.4 b/s/Hz using high-speed DAC, ” ECOC 2010, paper We.8.C.1 (2010)
  11. V. Curri, A. Carena, P. Poggiolini, G. Bosco, and F. Forghieri, “Evaluation of Non-Linear interference in uncompensated links using Raman amplification,” ECOC 2012, paper We.2.C.5, (2012).
  12. A. Carena, G. Bosco, V. Curri, M. Tapia Taiba, P. Poggiolini, and F. Forghieri, “Statistical characterization of PM-QPSK signals after propagation in uncompensated fiber links,” ECOC 2010, paper P4.07 (2010)
  13. E. Grellier and A. Bononi, “Quality parameter for coherent transmissions with Gaussian-distributed nonlinear noise,” Opt. Express19(13), 12781–12788 (2011).
    [CrossRef] [PubMed]
  14. N. Shibata, R. Braun, and R. Waarts, “Phase-mismatch dependence of efficiency of wave generation through four-wave mixing in a single-mode optical fiber,” IEEE J. Quantum Electron.23(7), 1205–1210 (1987).
    [CrossRef]
  15. W. Zeiler, F. Di Pasquale, P. Bayvel, and J. E. Midwinter, “Modeling of four-wave mixing and gain peaking in amplified WDM optical communication systems and networks,” J. Lightwave Technol.14(9), 1933–1942 (1996).
    [CrossRef]
  16. P. B. Hansen, L. Eskildsen, A. J. Stentz, T. A. Strasser, J. Judkins, J. J. DeMarco, R. Pedrazzani, and D. J. DiGiovanni, “Rayleigh scattering limitations in distributed Raman pre-amplifiers,” IEEE Photon. Technol. Lett.10(1), 159–161 (1998).
    [CrossRef]
  17. G. Bosco, A. Carena, R. Cigliutti, V. Curri, G. Bosco, P. Poggiolini, and F. Forghieri, “Performance prediction for WDM PM-QPSK transmission over uncompensated links,” OFC 2011, paper OThO7, (2011).
  18. P. Poggiolini, G. Bosco, A. Carena, V. Curri, and F. Forghieri, “A detailed analytical derivation of the GN model of non-linear interference in coherent optical transmission systems,” posted on arXiv, www.arxiv.org , paper identifier: 1209.0394, (2012)
  19. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover Publications, 1965).

2012 (2)

2011 (2)

2010 (1)

G. Bosco, A. Carena, V. Curri, P. Poggiolini, and F. Forghieri, “Performance limits of Nyquist-WDM and CO-OFDM in high-speed PM-QPSK systems,” IEEE Photon. Technol. Lett.22(15), 1129–1131 (2010).
[CrossRef]

2009 (2)

2008 (1)

V. Curri, P. Poggiolini, A. Carena, and F. Forghieri, “Dispersion compensation and mitigation of nonlinear effects in 111-Gb/s WDM coherent PM-QPSK systems,” IEEE Photon. Technol. Lett.20(17), 1473–1475 (2008).
[CrossRef]

2004 (1)

M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photon. Technol. Lett.16(2), 674–676 (2004).
[CrossRef]

1998 (1)

P. B. Hansen, L. Eskildsen, A. J. Stentz, T. A. Strasser, J. Judkins, J. J. DeMarco, R. Pedrazzani, and D. J. DiGiovanni, “Rayleigh scattering limitations in distributed Raman pre-amplifiers,” IEEE Photon. Technol. Lett.10(1), 159–161 (1998).
[CrossRef]

1996 (1)

W. Zeiler, F. Di Pasquale, P. Bayvel, and J. E. Midwinter, “Modeling of four-wave mixing and gain peaking in amplified WDM optical communication systems and networks,” J. Lightwave Technol.14(9), 1933–1942 (1996).
[CrossRef]

1987 (1)

N. Shibata, R. Braun, and R. Waarts, “Phase-mismatch dependence of efficiency of wave generation through four-wave mixing in a single-mode optical fiber,” IEEE J. Quantum Electron.23(7), 1205–1210 (1987).
[CrossRef]

Al?ad, M. S.

Awadalla, A.

Bayvel, P.

W. Zeiler, F. Di Pasquale, P. Bayvel, and J. E. Midwinter, “Modeling of four-wave mixing and gain peaking in amplified WDM optical communication systems and networks,” J. Lightwave Technol.14(9), 1933–1942 (1996).
[CrossRef]

Bononi, A.

Bosco, G.

Braun, R.

N. Shibata, R. Braun, and R. Waarts, “Phase-mismatch dependence of efficiency of wave generation through four-wave mixing in a single-mode optical fiber,” IEEE J. Quantum Electron.23(7), 1205–1210 (1987).
[CrossRef]

Carena, A.

A. Carena, V. Curri, G. Bosco, P. Poggiolini, and F. Forghieri, “Modeling of the impact of nonlinear propagation effects in uncompensated optical coherent transmission links,” J. Lightwave Technol.30(10), 1524–1539 (2012).
[CrossRef]

E. Torrengo, R. Cigliutti, G. Bosco, A. Carena, V. Curri, P. Poggiolini, A. Nespola, D. Zeolla, and F. Forghieri, “Experimental validation of an analytical model for nonlinear propagation in uncompensated optical links,” Opt. Express19(26), B790–B798 (2011).
[CrossRef] [PubMed]

G. Bosco, A. Carena, V. Curri, P. Poggiolini, and F. Forghieri, “Performance limits of Nyquist-WDM and CO-OFDM in high-speed PM-QPSK systems,” IEEE Photon. Technol. Lett.22(15), 1129–1131 (2010).
[CrossRef]

V. Curri, P. Poggiolini, A. Carena, and F. Forghieri, “Dispersion compensation and mitigation of nonlinear effects in 111-Gb/s WDM coherent PM-QPSK systems,” IEEE Photon. Technol. Lett.20(17), 1473–1475 (2008).
[CrossRef]

Cigliutti, R.

Curri, V.

A. Carena, V. Curri, G. Bosco, P. Poggiolini, and F. Forghieri, “Modeling of the impact of nonlinear propagation effects in uncompensated optical coherent transmission links,” J. Lightwave Technol.30(10), 1524–1539 (2012).
[CrossRef]

E. Torrengo, R. Cigliutti, G. Bosco, A. Carena, V. Curri, P. Poggiolini, A. Nespola, D. Zeolla, and F. Forghieri, “Experimental validation of an analytical model for nonlinear propagation in uncompensated optical links,” Opt. Express19(26), B790–B798 (2011).
[CrossRef] [PubMed]

G. Bosco, A. Carena, V. Curri, P. Poggiolini, and F. Forghieri, “Performance limits of Nyquist-WDM and CO-OFDM in high-speed PM-QPSK systems,” IEEE Photon. Technol. Lett.22(15), 1129–1131 (2010).
[CrossRef]

V. Curri, P. Poggiolini, A. Carena, and F. Forghieri, “Dispersion compensation and mitigation of nonlinear effects in 111-Gb/s WDM coherent PM-QPSK systems,” IEEE Photon. Technol. Lett.20(17), 1473–1475 (2008).
[CrossRef]

de Waardt, H.

DeMarco, J. J.

P. B. Hansen, L. Eskildsen, A. J. Stentz, T. A. Strasser, J. Judkins, J. J. DeMarco, R. Pedrazzani, and D. J. DiGiovanni, “Rayleigh scattering limitations in distributed Raman pre-amplifiers,” IEEE Photon. Technol. Lett.10(1), 159–161 (1998).
[CrossRef]

Di Pasquale, F.

W. Zeiler, F. Di Pasquale, P. Bayvel, and J. E. Midwinter, “Modeling of four-wave mixing and gain peaking in amplified WDM optical communication systems and networks,” J. Lightwave Technol.14(9), 1933–1942 (1996).
[CrossRef]

DiGiovanni, D. J.

P. B. Hansen, L. Eskildsen, A. J. Stentz, T. A. Strasser, J. Judkins, J. J. DeMarco, R. Pedrazzani, and D. J. DiGiovanni, “Rayleigh scattering limitations in distributed Raman pre-amplifiers,” IEEE Photon. Technol. Lett.10(1), 159–161 (1998).
[CrossRef]

Eskildsen, L.

P. B. Hansen, L. Eskildsen, A. J. Stentz, T. A. Strasser, J. Judkins, J. J. DeMarco, R. Pedrazzani, and D. J. DiGiovanni, “Rayleigh scattering limitations in distributed Raman pre-amplifiers,” IEEE Photon. Technol. Lett.10(1), 159–161 (1998).
[CrossRef]

Forghieri, F.

A. Carena, V. Curri, G. Bosco, P. Poggiolini, and F. Forghieri, “Modeling of the impact of nonlinear propagation effects in uncompensated optical coherent transmission links,” J. Lightwave Technol.30(10), 1524–1539 (2012).
[CrossRef]

E. Torrengo, R. Cigliutti, G. Bosco, A. Carena, V. Curri, P. Poggiolini, A. Nespola, D. Zeolla, and F. Forghieri, “Experimental validation of an analytical model for nonlinear propagation in uncompensated optical links,” Opt. Express19(26), B790–B798 (2011).
[CrossRef] [PubMed]

G. Bosco, A. Carena, V. Curri, P. Poggiolini, and F. Forghieri, “Performance limits of Nyquist-WDM and CO-OFDM in high-speed PM-QPSK systems,” IEEE Photon. Technol. Lett.22(15), 1129–1131 (2010).
[CrossRef]

V. Curri, P. Poggiolini, A. Carena, and F. Forghieri, “Dispersion compensation and mitigation of nonlinear effects in 111-Gb/s WDM coherent PM-QPSK systems,” IEEE Photon. Technol. Lett.20(17), 1473–1475 (2008).
[CrossRef]

Grellier, E.

Grosso, G.

Hansen, P. B.

P. B. Hansen, L. Eskildsen, A. J. Stentz, T. A. Strasser, J. Judkins, J. J. DeMarco, R. Pedrazzani, and D. J. DiGiovanni, “Rayleigh scattering limitations in distributed Raman pre-amplifiers,” IEEE Photon. Technol. Lett.10(1), 159–161 (1998).
[CrossRef]

Jansen, S. L.

Judkins, J.

P. B. Hansen, L. Eskildsen, A. J. Stentz, T. A. Strasser, J. Judkins, J. J. DeMarco, R. Pedrazzani, and D. J. DiGiovanni, “Rayleigh scattering limitations in distributed Raman pre-amplifiers,” IEEE Photon. Technol. Lett.10(1), 159–161 (1998).
[CrossRef]

Krause, D. J.

Kuang-Tsan, W.

Kuschnerov, M.

Laperle, C.

Midwinter, J. E.

W. Zeiler, F. Di Pasquale, P. Bayvel, and J. E. Midwinter, “Modeling of four-wave mixing and gain peaking in amplified WDM optical communication systems and networks,” J. Lightwave Technol.14(9), 1933–1942 (1996).
[CrossRef]

Napoli, A.

Nespola, A.

O'Sullivan, M.

Pedrazzani, R.

P. B. Hansen, L. Eskildsen, A. J. Stentz, T. A. Strasser, J. Judkins, J. J. DeMarco, R. Pedrazzani, and D. J. DiGiovanni, “Rayleigh scattering limitations in distributed Raman pre-amplifiers,” IEEE Photon. Technol. Lett.10(1), 159–161 (1998).
[CrossRef]

Poggiolini, P.

Roberts, K.

Shibata, N.

N. Shibata, R. Braun, and R. Waarts, “Phase-mismatch dependence of efficiency of wave generation through four-wave mixing in a single-mode optical fiber,” IEEE J. Quantum Electron.23(7), 1205–1210 (1987).
[CrossRef]

Stentz, A. J.

P. B. Hansen, L. Eskildsen, A. J. Stentz, T. A. Strasser, J. Judkins, J. J. DeMarco, R. Pedrazzani, and D. J. DiGiovanni, “Rayleigh scattering limitations in distributed Raman pre-amplifiers,” IEEE Photon. Technol. Lett.10(1), 159–161 (1998).
[CrossRef]

Strasser, T. A.

P. B. Hansen, L. Eskildsen, A. J. Stentz, T. A. Strasser, J. Judkins, J. J. DeMarco, R. Pedrazzani, and D. J. DiGiovanni, “Rayleigh scattering limitations in distributed Raman pre-amplifiers,” IEEE Photon. Technol. Lett.10(1), 159–161 (1998).
[CrossRef]

Sun, H.

Taylor, M. G.

M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photon. Technol. Lett.16(2), 674–676 (2004).
[CrossRef]

Torrengo, E.

van den Borne, D.

Waarts, R.

N. Shibata, R. Braun, and R. Waarts, “Phase-mismatch dependence of efficiency of wave generation through four-wave mixing in a single-mode optical fiber,” IEEE J. Quantum Electron.23(7), 1205–1210 (1987).
[CrossRef]

Wuth, T.

Zeiler, W.

W. Zeiler, F. Di Pasquale, P. Bayvel, and J. E. Midwinter, “Modeling of four-wave mixing and gain peaking in amplified WDM optical communication systems and networks,” J. Lightwave Technol.14(9), 1933–1942 (1996).
[CrossRef]

Zeolla, D.

IEEE J. Quantum Electron. (1)

N. Shibata, R. Braun, and R. Waarts, “Phase-mismatch dependence of efficiency of wave generation through four-wave mixing in a single-mode optical fiber,” IEEE J. Quantum Electron.23(7), 1205–1210 (1987).
[CrossRef]

IEEE Photon. Technol. Lett. (4)

M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photon. Technol. Lett.16(2), 674–676 (2004).
[CrossRef]

V. Curri, P. Poggiolini, A. Carena, and F. Forghieri, “Dispersion compensation and mitigation of nonlinear effects in 111-Gb/s WDM coherent PM-QPSK systems,” IEEE Photon. Technol. Lett.20(17), 1473–1475 (2008).
[CrossRef]

G. Bosco, A. Carena, V. Curri, P. Poggiolini, and F. Forghieri, “Performance limits of Nyquist-WDM and CO-OFDM in high-speed PM-QPSK systems,” IEEE Photon. Technol. Lett.22(15), 1129–1131 (2010).
[CrossRef]

P. B. Hansen, L. Eskildsen, A. J. Stentz, T. A. Strasser, J. Judkins, J. J. DeMarco, R. Pedrazzani, and D. J. DiGiovanni, “Rayleigh scattering limitations in distributed Raman pre-amplifiers,” IEEE Photon. Technol. Lett.10(1), 159–161 (1998).
[CrossRef]

J. Lightwave Technol. (5)

Opt. Express (2)

Other (7)

G. Bosco, A. Carena, R. Cigliutti, V. Curri, G. Bosco, P. Poggiolini, and F. Forghieri, “Performance prediction for WDM PM-QPSK transmission over uncompensated links,” OFC 2011, paper OThO7, (2011).

P. Poggiolini, G. Bosco, A. Carena, V. Curri, and F. Forghieri, “A detailed analytical derivation of the GN model of non-linear interference in coherent optical transmission systems,” posted on arXiv, www.arxiv.org , paper identifier: 1209.0394, (2012)

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover Publications, 1965).

J.-X. Cai, H. G. Batshon, H. Zhang, C. R. Davidson, Y. Sun, M. Mazurczyk, D. G. Foursa, A. Pilipetskii, G. Mohs, and Neal S. Bergano, “25 TB/s dransmission over 5,530 km dsing 16QAM at 5.2 Bits/s/Hz dpectral dfficiency,” ECOC 2012, paper Mo.1.C.1 (2012).

S. Yamanaka, T. Kobayashi, A. Sano, H. Masuda, E. Yoshida, Y. Miyamoto, T. Nakagawa, M. Nagatani, and H. Nosaka, “11 × 171 Gb/s PDM 16-QAM transmission over 1440 km with a spectral efficiency of 6.4 b/s/Hz using high-speed DAC, ” ECOC 2010, paper We.8.C.1 (2010)

V. Curri, A. Carena, P. Poggiolini, G. Bosco, and F. Forghieri, “Evaluation of Non-Linear interference in uncompensated links using Raman amplification,” ECOC 2012, paper We.2.C.5, (2012).

A. Carena, G. Bosco, V. Curri, M. Tapia Taiba, P. Poggiolini, and F. Forghieri, “Statistical characterization of PM-QPSK signals after propagation in uncompensated fiber links,” ECOC 2010, paper P4.07 (2010)

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Figures (6)

Fig. 1
Fig. 1

Layout of the reference optical link used for the definition of the GN-model for NLI.

Fig. 2
Fig. 2

Structure of the link span used in the validation analysis for both PSCF and NZDSF setups.

Fig. 3
Fig. 3

On-off gain and HFA equivalent noise figure vs. Ppump for PSCF, (a) and (c), and NZDSF, (b) and (d).

Fig. 4
Fig. 4

(a) Contour plot of the NLI enhancement [dB] for PSCF links in the (GRA,LTOT) plane. (b) NLI enhancement vs. GRA at increasing distances for PSCF links.

Fig. 5
Fig. 5

PSCF setups. (a) GN-model analytical prediction of maximum reach vs. transmitted power for EDFA only setups (blue lines) and for HFA setups (red lines) and simulative results (markers). (b) Maxima vs. Pump power for HFA and equivalent “unrealistic” EDFA-only links: lines are GN-model analytical prediction while markers are simulative results.

Fig. 6
Fig. 6

NZDSF setups. GN-model analytical prediction of maximum reach vs. transmitted power for “unrealistic” EDFA-only setups (blue lines) and for HFA setups (red lines) and simulative results (markers). No predistortion (a) and transmission after predistortion equivalent to 10 fiber spans (b).

Tables (1)

Tables Icon

Table 1 Parameters of transmission fibers used for the validation analysis

Equations (14)

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G NLI ( f )= 16 27 γ 2 L eff 2 + + G WDM ( f 1 ) G WDM ( f 2 ) G WDM ( f 1 + f 2 f )ρ( f 1 , f 2 ,f )χ( f 1 , f 2 ,f )d f 2 d f 1
L eff = 0 L s p ch (z)dz ,
ρ( f )= 1 L eff 2 | 0 L s p ch (z)exp{ j4 π 2 β 2 f 2 z }dz | 2 ,
p ch (z)=exp{ 2[ 0 z α+g(ξ)dξ ] },
χ( f 1 , f 2 ,f )= sin 2 [ 2 N s π 2 ( f 1 f )( f 2 f ) β 2 L s ] sin 2 [ 2 π 2 ( f 1 f )( f 2 f ) β 2 L s ] .
G NLI 256 27 γ 2 L eff 2 P ch 3 R s 3 0 B opt 2 ρ( ν )ν sin 2 ( 2 N s π 2 ν 2 β 2 L s ) sin 2 ( 2 π 2 ν 2 β 2 L s ) log( B opt 2ν )dν,
OSN R NL = P ch ( G ASE + G NLI ) B n = P ch P ASE + P NLI ,
G ASE = N s F eq h f 0 ( A s 1 ) N s F eq h f 0 A s ,
N s max P ASE =2 P NLI .
10 log 10 ( N s max,HFA N s max,EDFA )= 2 3 Δ P ASE,dB 1 3 Δ P NLI,dB ,
g(z)= 1 2 C R P pump e 2 α p ( L s z ) ,
G RA =10 log 10 { exp[ 2 0 L s g(ξ)dξ ] }=10 log 10 ( e ) C R P pump 1 e 2 α p L s 2 α p [dB].
L eff = exp( g( 0 ) α p ) 2 α p [ g( 0 ) α p ] k α { Γ[ k α , g( 0 ) α p ]Γ[ k α , g( L s ) α p ] }
ρ( ν )= 1 L eff 2 | exp( g( 0 ) α p ) 2 α p [ g( 0 ) α p ] ( k α jB ν 2 ) { Γ[ ( k α jB ν 2 ), g( 0 ) α p ]Γ[ ( k α jB ν 2 ), g( L s ) α p ] } | 2

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