Abstract

An analytical model considering modulation-dependent nonlinear effects and second-order interactions between signal and optical amplifier noise is presented for Nyquist-spaced wavelength-division-multiplexing optical communication systems. System performance of dual-polarization modulation formats, such as DP-QPSK, DP-16QAM, and DP-64QAM, is investigated using both the analytical model and numerical simulations. A good agreement between analytical and numerical results shows that, in the case of full-field nonlinearity compensation, accounting for second-order interactions becomes essential to predict system performance of both single- and multi-channel systems at optimum launched powers and beyond. This effect is validated via numerical simulations for signal bandwidths up to 1  THz.

Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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References

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T. Xu, N. A. Shevchenko, D. Lavery, D. Semrau, G. Liga, A. Alvarado, R. I. Killey, and P. Bayvel, Opt. Express 25, 3311 (2017).
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Eggleton, B. J.

E. Agrell, M. Karlsson, A. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, J. Opt. 18, 063002 (2016).
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E. Agrell, M. Karlsson, A. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, J. Opt. 18, 063002 (2016).
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Killey, R. I.

T. Xu, N. A. Shevchenko, D. Lavery, D. Semrau, G. Liga, A. Alvarado, R. I. Killey, and P. Bayvel, Opt. Express 25, 3311 (2017).
[Crossref]

P. Bayvel, R. Maher, T. Xu, G. Liga, N. A. Shevchenko, D. Lavery, A. Alvarado, and R. I. Killey, Phil. Trans. R. Soc. A 374, 20140440 (2016).
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R. Maher, T. Xu, L. Galdino, M. Sato, A. Alvarado, K. Shi, S. J. Savory, B. C. Thomsen, R. I. Killey, and P. Bayvel, Sci. Rep. 5, 08214 (2015).
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E. Agrell, M. Karlsson, A. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, J. Opt. 18, 063002 (2016).
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T. Xu, N. A. Shevchenko, D. Lavery, D. Semrau, G. Liga, A. Alvarado, R. I. Killey, and P. Bayvel, Opt. Express 25, 3311 (2017).
[Crossref]

P. Bayvel, R. Maher, T. Xu, G. Liga, N. A. Shevchenko, D. Lavery, A. Alvarado, and R. I. Killey, Phil. Trans. R. Soc. A 374, 20140440 (2016).
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Li, H.

S. Abbott, A. Pilipetskii, D. Foursa, and H. Li, SubOptic (2016).

Li, J.

Liga, G.

T. Xu, N. A. Shevchenko, D. Lavery, D. Semrau, G. Liga, A. Alvarado, R. I. Killey, and P. Bayvel, Opt. Express 25, 3311 (2017).
[Crossref]

P. Bayvel, R. Maher, T. Xu, G. Liga, N. A. Shevchenko, D. Lavery, A. Alvarado, and R. I. Killey, Phil. Trans. R. Soc. A 374, 20140440 (2016).
[Crossref]

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E. Agrell, M. Karlsson, A. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, J. Opt. 18, 063002 (2016).
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P. Bayvel, R. Maher, T. Xu, G. Liga, N. A. Shevchenko, D. Lavery, A. Alvarado, and R. I. Killey, Phil. Trans. R. Soc. A 374, 20140440 (2016).
[Crossref]

R. Maher, T. Xu, L. Galdino, M. Sato, A. Alvarado, K. Shi, S. J. Savory, B. C. Thomsen, R. I. Killey, and P. Bayvel, Sci. Rep. 5, 08214 (2015).
[Crossref]

McCarthy, M.

Mecozzi, A.

Nölle, M.

Pilipetskii, A.

S. Abbott, A. Pilipetskii, D. Foursa, and H. Li, SubOptic (2016).

Poggiolini, P.

Popov, S.

Prat, J.

E. Agrell, M. Karlsson, A. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, J. Opt. 18, 063002 (2016).
[Crossref]

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Rafique, D.

Richardson, D. J.

E. Agrell, M. Karlsson, A. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, J. Opt. 18, 063002 (2016).
[Crossref]

Roberts, K.

E. Agrell, M. Karlsson, A. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, J. Opt. 18, 063002 (2016).
[Crossref]

Sánchez, C.

Sato, M.

R. Maher, T. Xu, L. Galdino, M. Sato, A. Alvarado, K. Shi, S. J. Savory, B. C. Thomsen, R. I. Killey, and P. Bayvel, Sci. Rep. 5, 08214 (2015).
[Crossref]

Savory, S. J.

E. Agrell, M. Karlsson, A. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, J. Opt. 18, 063002 (2016).
[Crossref]

R. Maher, T. Xu, L. Galdino, M. Sato, A. Alvarado, K. Shi, S. J. Savory, B. C. Thomsen, R. I. Killey, and P. Bayvel, Sci. Rep. 5, 08214 (2015).
[Crossref]

Schubert, C.

Secondini, M.

E. Agrell, M. Karlsson, A. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, J. Opt. 18, 063002 (2016).
[Crossref]

M. Secondini, E. Forestieri, and G. Prati, J. Lightwave Technol. 31, 3839 (2013).
[Crossref]

Semrau, D.

Serena, P.

Shevchenko, N. A.

T. Xu, N. A. Shevchenko, D. Lavery, D. Semrau, G. Liga, A. Alvarado, R. I. Killey, and P. Bayvel, Opt. Express 25, 3311 (2017).
[Crossref]

P. Bayvel, R. Maher, T. Xu, G. Liga, N. A. Shevchenko, D. Lavery, A. Alvarado, and R. I. Killey, Phil. Trans. R. Soc. A 374, 20140440 (2016).
[Crossref]

Shi, K.

R. Maher, T. Xu, L. Galdino, M. Sato, A. Alvarado, K. Shi, S. J. Savory, B. C. Thomsen, R. I. Killey, and P. Bayvel, Sci. Rep. 5, 08214 (2015).
[Crossref]

Shtaif, M.

Srinivasan, S.

E. Agrell, M. Karlsson, A. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, J. Opt. 18, 063002 (2016).
[Crossref]

Tanimura, T.

Thomsen, B. C.

R. Maher, T. Xu, L. Galdino, M. Sato, A. Alvarado, K. Shi, S. J. Savory, B. C. Thomsen, R. I. Killey, and P. Bayvel, Sci. Rep. 5, 08214 (2015).
[Crossref]

Tomkos, I.

E. Agrell, M. Karlsson, A. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, J. Opt. 18, 063002 (2016).
[Crossref]

Vanin, E.

Vannucci, A.

Wang, K.

Winzer, P.

E. Agrell, M. Karlsson, A. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, J. Opt. 18, 063002 (2016).
[Crossref]

Winzer, P. J.

Xu, T.

T. Xu, N. A. Shevchenko, D. Lavery, D. Semrau, G. Liga, A. Alvarado, R. I. Killey, and P. Bayvel, Opt. Express 25, 3311 (2017).
[Crossref]

P. Bayvel, R. Maher, T. Xu, G. Liga, N. A. Shevchenko, D. Lavery, A. Alvarado, and R. I. Killey, Phil. Trans. R. Soc. A 374, 20140440 (2016).
[Crossref]

R. Maher, T. Xu, L. Galdino, M. Sato, A. Alvarado, K. Shi, S. J. Savory, B. C. Thomsen, R. I. Killey, and P. Bayvel, Sci. Rep. 5, 08214 (2015).
[Crossref]

T. Xu, G. Jacobsen, S. Popov, J. Li, E. Vanin, K. Wang, A. T. Friberg, and Y. Zhang, Opt. Express 18, 16243 (2010).
[Crossref]

Zhang, Y.

IEEE Photon. Technol. Lett. (1)

G. Bosco, A. Carena, V. Curri, R. Gaudino, P. Poggiolini, and S. Benedetto, IEEE Photon. Technol. Lett. 12, 489 (2000).
[Crossref]

J. Lightwave Technol. (7)

J. Opt. (1)

E. Agrell, M. Karlsson, A. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, J. Opt. 18, 063002 (2016).
[Crossref]

Opt. Express (7)

Opt. Lett. (1)

Phil. Trans. R. Soc. A (1)

P. Bayvel, R. Maher, T. Xu, G. Liga, N. A. Shevchenko, D. Lavery, A. Alvarado, and R. I. Killey, Phil. Trans. R. Soc. A 374, 20140440 (2016).
[Crossref]

Sci. Rep. (1)

R. Maher, T. Xu, L. Galdino, M. Sato, A. Alvarado, K. Shi, S. J. Savory, B. C. Thomsen, R. I. Killey, and P. Bayvel, Sci. Rep. 5, 08214 (2015).
[Crossref]

Other (2)

S. Abbott, A. Pilipetskii, D. Foursa, and H. Li, SubOptic (2016).

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2007).

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Figures (6)

Fig. 1.
Fig. 1.

Schematic of S–N noise interactions accumulation process in an optical communication system using FF DBP.

Fig. 2.
Fig. 2.

Theoretical predictions (lines) and numerical simulation results (marks) of SNR as a function of launched power per channel for a single-channel system using EDC and FF DBP. Colors refer to modulation formats.

Fig. 3.
Fig. 3.

SNR performance for five-channel Nyquist-spaced WDM transmission using (a) DP-QPSK and (b) DP-16QAM, DP-64QAM modulation formats. Colors refer to modulation formats.

Fig. 4.
Fig. 4.

Left side: SNR versus total transmission distance at 8 dBm and 10 dBm per channel optical launched power in five-channel WDM system using FF DBP. Numerical simulation results are indicated by marks. Right side: Distance evolution of optimum launched power per channel for FF DBP considering first- and second-order models.

Fig. 5.
Fig. 5.

SNR against the number of Nyquist-spaced WDM channels at optimum launched power after 2000 km transmission distance using FF DBP.

Fig. 6.
Fig. 6.

Ratio between the power of second- and first-order S-N FWM products against launched power per channels for different transmission distances calculated for C-band system.

Tables (2)

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Table 1. Overview of pre-factors κ4 and κ6 in Eq. (5) for different input modulation formats and distributions

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Table 2. System Parameter Values

Equations (6)

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SNRPNsσASE2+Pss+Psn,
Psn3ξ1ησASE2·P2+9ξ2η2σASE2·P4,
ξ2n=2Nsm=1n1mε+1ζ(ε1)ζ(ε1,Ns)2+ζ(ε2)ζ(ε2,Ns)ε+2,
η=η0η0,
η0κ4η1+κ42η2+κ6η3,
Popt(2)=132ξ1ξ2η(1+12Nsξ2ξ121)1/2.

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