Abstract

With the extension of the spectral exploitation of optical fibers beyond the C-band, accurate modeling and simulation of nonlinear interference (NLI) generation is of the utmost performance. Models and numerical simulation tools rely on the widely used Manakov equation (ME): however, this approach when also considering the effect of polarization mode dispersion (PMD) is formally valid only over a narrow optical bandwidth. In order to analyze the range of validity of the ME and its applicability to future wide-band systems, we present numerical simulations, showing the interplay between NLI generation and PMD over long dispersion-uncompensated optical links, using coherent polarization division multiplexing (PDM) quadrature amplitude modulation (QAM) formats. Using a Monte-Carlo analysis of different PMD realizations based on the coupled nonlinear Schrödinger equations, we show that PMD has a negligible effect on NLI generation, independently from the total system bandwidth. Based on this, we give strong numerical evidence that the ME can be safely used to estimate NLI generation well beyond its bandwidth of validity that is limited to the PMD coherence bandwidth.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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References

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2019 (1)

2018 (3)

2017 (5)

2014 (4)

2013 (1)

2011 (1)

2006 (1)

W. A. Gardner, A. Napolitano, and L. Paura, “Cyclostationarity: Half a century of research,” Signal Processing 86(4), 639–697 (2006).
[Crossref]

2004 (1)

2000 (1)

M. Shtaif, A. Mecozzi, and J. A. Nagel, “Mean-square magnitude of all orders of polarization mode dispersion and the relation with the bandwidth of the principal states,” IEEE Photonics Technol. Lett. 12(1), 53–55 (2000).
[Crossref]

1998 (1)

1997 (1)

D. Marcuse, C. R. Manyuk, and P. K. A. Wai, “Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 15(9), 1735–1746 (1997).
[Crossref]

1996 (1)

P. K. A. Wai and C. R. Menyak, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 14(2), 148–157 (1996).
[Crossref]

Agrawal, G.

G. Agrawal, Nonlinear Fiber Optics (Elsevier Science Publishing Co Inc, 2012).

Augé, J. L.

Augé, J.-L.

J.-L. Augé, G. Grammel, E. le Rouzic, V. Curri, G. Galimberti, and J. Powell, “Open optical network planning demonstration,” in Optical Fiber Communication Conference (OFC) 2019, (Optical Society of America, 2019), p. M3Z.9.

Barnes, S.

M. Ionescu, D. Lavery, A. Edwards, E. Sillekens, L. Galdino, D. Semrau, R. Killey, W. Pelouch, S. Barnes, and P. Bayvel, “74.38 tb/s transmission over 6300 km single mode fiber with hybrid edfa/raman amplifiers,” in Optical Fiber Communication Conference (OFC) 2019, (Optical Society of America, 2019), p. Tu3F.3.

Bayvel, P.

Benedetto, S.

Bertran-Pardo, O.

Bononi, A.

Bosco, G.

P. Poggiolini, G. Bosco, A. Carena, V. Curri, Y. Jiang, and F. Forghieri, “The GN-model of fiber non-linear propagation and its applications,” J. Lightwave Technol. 32(4), 694–721 (2014).
[Crossref]

A. Carena, G. Bosco, V. Curri, Y. Jiang, P. Poggiolini, and F. Forghieri, “EGN model of non-linear fiber propagation,” Opt. Express 22(13), 16335–16362 (2014).
[Crossref]

R. Pastorelli, G. Bosco, A. Carena, P. Poggiolini, V. Curri, S. Piciaccia, and F. Forghieri, “Investigation of the dependence of non-linear interference on the number of WDM channels in coherent optical networks,” in Proc. 38th European Conf. and Exhibition Optical Communications, (2012), pp. 1–3.

Braimiotis, C.

M. Eberhard and C. Braimiotis, “Numerical implementation of the coarse-step method with a varying differential-group delay,” in Optical Networks and Technologies, (Kluwer Academic Publishers, 2005), pp. 530–534

Cantono, M.

M. Cantono, A. Ferrari, D. Pilori, E. Virgillito, J. L. Augé, and V. Curri, “Physical layer performance of multi-band optical line systems using Raman amplification,” J. Opt. Commun. Netw. 11(1), A103 (2019).
[Crossref]

M. Filer, M. Cantono, A. Ferrari, G. Grammel, G. Galimberti, and V. Curri, “Multi-vendor experimental validation of an open source qot estimator for optical networks,” J. Lightwave Technol. 36(15), 3073–3082 (2018).
[Crossref]

V. Curri, M. Cantono, and R. Gaudino, “Elastic all-optical networks: A new paradigm enabled by the physical layer. how to optimize network performances?” J. Lightwave Technol. 35(6), 1211–1221 (2017).
[Crossref]

M. Cantono, “Physical layer aware optical networks,” Ph.D. thesis, Politecnico di Torino (2018).

M. Cantono, D. Pilori, A. Ferrari, A. Carena, and V. Curri, “Observing the interaction of PMD with generation of NLI in uncompensated amplified optical links,” in Optical Fiber Communications Conference (OFC), (OSA, 2018).

D. Pilori, M. Cantono, A. Carena, and V. Curri, “FFSS: The fast fiber simulator software,” in Transparent Optical Networks (ICTON), 2017 19th International Conference on, (IEEE, 2017), pp. 1–4.

Carena, A.

P. Poggiolini, G. Bosco, A. Carena, V. Curri, Y. Jiang, and F. Forghieri, “The GN-model of fiber non-linear propagation and its applications,” J. Lightwave Technol. 32(4), 694–721 (2014).
[Crossref]

A. Carena, G. Bosco, V. Curri, Y. Jiang, P. Poggiolini, and F. Forghieri, “EGN model of non-linear fiber propagation,” Opt. Express 22(13), 16335–16362 (2014).
[Crossref]

A. Carena, V. Curri, R. Gaudino, P. Poggiolini, and S. Benedetto, “On the joint effects of fiber parametric gain and birefringence and their influence on ASE noise,” J. Lightwave Technol. 16(7), 1149–1157 (1998).
[Crossref]

M. Cantono, D. Pilori, A. Ferrari, A. Carena, and V. Curri, “Observing the interaction of PMD with generation of NLI in uncompensated amplified optical links,” in Optical Fiber Communications Conference (OFC), (OSA, 2018).

D. Pilori, M. Cantono, A. Carena, and V. Curri, “FFSS: The fast fiber simulator software,” in Transparent Optical Networks (ICTON), 2017 19th International Conference on, (IEEE, 2017), pp. 1–4.

R. Pastorelli, G. Bosco, A. Carena, P. Poggiolini, V. Curri, S. Piciaccia, and F. Forghieri, “Investigation of the dependence of non-linear interference on the number of WDM channels in coherent optical networks,” in Proc. 38th European Conf. and Exhibition Optical Communications, (2012), pp. 1–3.

Chraplyvy, A. R.

Curri, V.

M. Cantono, A. Ferrari, D. Pilori, E. Virgillito, J. L. Augé, and V. Curri, “Physical layer performance of multi-band optical line systems using Raman amplification,” J. Opt. Commun. Netw. 11(1), A103 (2019).
[Crossref]

M. Filer, M. Cantono, A. Ferrari, G. Grammel, G. Galimberti, and V. Curri, “Multi-vendor experimental validation of an open source qot estimator for optical networks,” J. Lightwave Technol. 36(15), 3073–3082 (2018).
[Crossref]

V. Curri, M. Cantono, and R. Gaudino, “Elastic all-optical networks: A new paradigm enabled by the physical layer. how to optimize network performances?” J. Lightwave Technol. 35(6), 1211–1221 (2017).
[Crossref]

A. Carena, G. Bosco, V. Curri, Y. Jiang, P. Poggiolini, and F. Forghieri, “EGN model of non-linear fiber propagation,” Opt. Express 22(13), 16335–16362 (2014).
[Crossref]

P. Poggiolini, G. Bosco, A. Carena, V. Curri, Y. Jiang, and F. Forghieri, “The GN-model of fiber non-linear propagation and its applications,” J. Lightwave Technol. 32(4), 694–721 (2014).
[Crossref]

A. Carena, V. Curri, R. Gaudino, P. Poggiolini, and S. Benedetto, “On the joint effects of fiber parametric gain and birefringence and their influence on ASE noise,” J. Lightwave Technol. 16(7), 1149–1157 (1998).
[Crossref]

M. Cantono, D. Pilori, A. Ferrari, A. Carena, and V. Curri, “Observing the interaction of PMD with generation of NLI in uncompensated amplified optical links,” in Optical Fiber Communications Conference (OFC), (OSA, 2018).

R. Pastorelli, G. Bosco, A. Carena, P. Poggiolini, V. Curri, S. Piciaccia, and F. Forghieri, “Investigation of the dependence of non-linear interference on the number of WDM channels in coherent optical networks,” in Proc. 38th European Conf. and Exhibition Optical Communications, (2012), pp. 1–3.

D. Pilori, M. Cantono, A. Carena, and V. Curri, “FFSS: The fast fiber simulator software,” in Transparent Optical Networks (ICTON), 2017 19th International Conference on, (IEEE, 2017), pp. 1–4.

J.-L. Augé, G. Grammel, E. le Rouzic, V. Curri, G. Galimberti, and J. Powell, “Open optical network planning demonstration,” in Optical Fiber Communication Conference (OFC) 2019, (Optical Society of America, 2019), p. M3Z.9.

Dar, R.

Eberhard, M.

M. Eberhard and C. Braimiotis, “Numerical implementation of the coarse-step method with a varying differential-group delay,” in Optical Networks and Technologies, (Kluwer Academic Publishers, 2005), pp. 530–534

Edwards, A.

M. Ionescu, D. Lavery, A. Edwards, E. Sillekens, L. Galdino, D. Semrau, R. Killey, W. Pelouch, S. Barnes, and P. Bayvel, “74.38 tb/s transmission over 6300 km single mode fiber with hybrid edfa/raman amplifiers,” in Optical Fiber Communication Conference (OFC) 2019, (Optical Society of America, 2019), p. Tu3F.3.

Ellis, A.

Elson, D. J.

Feder, M.

Ferrari, A.

Filer, M.

Forestieri, E.

Forghieri, F.

A. Carena, G. Bosco, V. Curri, Y. Jiang, P. Poggiolini, and F. Forghieri, “EGN model of non-linear fiber propagation,” Opt. Express 22(13), 16335–16362 (2014).
[Crossref]

P. Poggiolini, G. Bosco, A. Carena, V. Curri, Y. Jiang, and F. Forghieri, “The GN-model of fiber non-linear propagation and its applications,” J. Lightwave Technol. 32(4), 694–721 (2014).
[Crossref]

R. Pastorelli, G. Bosco, A. Carena, P. Poggiolini, V. Curri, S. Piciaccia, and F. Forghieri, “Investigation of the dependence of non-linear interference on the number of WDM channels in coherent optical networks,” in Proc. 38th European Conf. and Exhibition Optical Communications, (2012), pp. 1–3.

Galdino, L.

Galimberti, G.

M. Filer, M. Cantono, A. Ferrari, G. Grammel, G. Galimberti, and V. Curri, “Multi-vendor experimental validation of an open source qot estimator for optical networks,” J. Lightwave Technol. 36(15), 3073–3082 (2018).
[Crossref]

J.-L. Augé, G. Grammel, E. le Rouzic, V. Curri, G. Galimberti, and J. Powell, “Open optical network planning demonstration,” in Optical Fiber Communication Conference (OFC) 2019, (Optical Society of America, 2019), p. M3Z.9.

Galtarossa, A.

A. Galtarossa and C. R. Menyuk, Polarization mode dispersion (Springer Science & Business Media, 2006).

Gardner, W. A.

W. A. Gardner, A. Napolitano, and L. Paura, “Cyclostationarity: Half a century of research,” Signal Processing 86(4), 639–697 (2006).
[Crossref]

Gaudino, R.

Grammel, G.

M. Filer, M. Cantono, A. Ferrari, G. Grammel, G. Galimberti, and V. Curri, “Multi-vendor experimental validation of an open source qot estimator for optical networks,” J. Lightwave Technol. 36(15), 3073–3082 (2018).
[Crossref]

J.-L. Augé, G. Grammel, E. le Rouzic, V. Curri, G. Galimberti, and J. Powell, “Open optical network planning demonstration,” in Optical Fiber Communication Conference (OFC) 2019, (Optical Society of America, 2019), p. M3Z.9.

Harper, P.

Ionescu, M.

M. Ionescu, D. Lavery, A. Edwards, E. Sillekens, L. Galdino, D. Semrau, R. Killey, W. Pelouch, S. Barnes, and P. Bayvel, “74.38 tb/s transmission over 6300 km single mode fiber with hybrid edfa/raman amplifiers,” in Optical Fiber Communication Conference (OFC) 2019, (Optical Society of America, 2019), p. Tu3F.3.

Iqbal, M. A.

Jiang, Y.

Jopson, R. M.

Kanaev, A. V.

Killey, R.

D. J. Elson, G. Saavedra, K. Shi, D. Semrau, L. Galdino, R. Killey, B. C. Thomsen, and P. Bayvel, “Investigation of bandwidth loading in optical fibre transmission using amplified spontaneous emission noise,” Opt. Express 25(16), 19529–19537 (2017).
[Crossref]

M. Ionescu, D. Lavery, A. Edwards, E. Sillekens, L. Galdino, D. Semrau, R. Killey, W. Pelouch, S. Barnes, and P. Bayvel, “74.38 tb/s transmission over 6300 km single mode fiber with hybrid edfa/raman amplifiers,” in Optical Fiber Communication Conference (OFC) 2019, (Optical Society of America, 2019), p. Tu3F.3.

Killey, R. I.

Kogelnik, H.

Lavery, D.

G. Saavedra, M. Tan, D. J. Elson, L. Galdino, D. Semrau, M. A. Iqbal, I. D. Phillips, P. Harper, A. Ellis, B. C. Thomsen, D. Lavery, R. I. Killey, and P. Bayvel, “Experimental analysis of nonlinear impairments in fibre optic transmission systems up to 7.3 THz,” J. Lightwave Technol. 35(21), 4809–4816 (2017).
[Crossref]

M. Ionescu, D. Lavery, A. Edwards, E. Sillekens, L. Galdino, D. Semrau, R. Killey, W. Pelouch, S. Barnes, and P. Bayvel, “74.38 tb/s transmission over 6300 km single mode fiber with hybrid edfa/raman amplifiers,” in Optical Fiber Communication Conference (OFC) 2019, (Optical Society of America, 2019), p. Tu3F.3.

le Rouzic, E.

J.-L. Augé, G. Grammel, E. le Rouzic, V. Curri, G. Galimberti, and J. Powell, “Open optical network planning demonstration,” in Optical Fiber Communication Conference (OFC) 2019, (Optical Society of America, 2019), p. M3Z.9.

Maier, G.

Manyuk, C. R.

D. Marcuse, C. R. Manyuk, and P. K. A. Wai, “Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 15(9), 1735–1746 (1997).
[Crossref]

Marcuse, D.

D. Marcuse, C. R. Manyuk, and P. K. A. Wai, “Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 15(9), 1735–1746 (1997).
[Crossref]

McKinstrie, C. J.

Mecozzi, A.

Menyak, C. R.

P. K. A. Wai and C. R. Menyak, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 14(2), 148–157 (1996).
[Crossref]

Menyuk, C. R.

A. Galtarossa and C. R. Menyuk, Polarization mode dispersion (Springer Science & Business Media, 2006).

Musetti, S.

Nagel, J. A.

M. Shtaif, A. Mecozzi, and J. A. Nagel, “Mean-square magnitude of all orders of polarization mode dispersion and the relation with the bandwidth of the principal states,” IEEE Photonics Technol. Lett. 12(1), 53–55 (2000).
[Crossref]

Napolitano, A.

W. A. Gardner, A. Napolitano, and L. Paura, “Cyclostationarity: Half a century of research,” Signal Processing 86(4), 639–697 (2006).
[Crossref]

Neilson, D. T.

Pastorelli, R.

R. Pastorelli, G. Bosco, A. Carena, P. Poggiolini, V. Curri, S. Piciaccia, and F. Forghieri, “Investigation of the dependence of non-linear interference on the number of WDM channels in coherent optical networks,” in Proc. 38th European Conf. and Exhibition Optical Communications, (2012), pp. 1–3.

Pattavina, A.

Paura, L.

W. A. Gardner, A. Napolitano, and L. Paura, “Cyclostationarity: Half a century of research,” Signal Processing 86(4), 639–697 (2006).
[Crossref]

Pelouch, W.

M. Ionescu, D. Lavery, A. Edwards, E. Sillekens, L. Galdino, D. Semrau, R. Killey, W. Pelouch, S. Barnes, and P. Bayvel, “74.38 tb/s transmission over 6300 km single mode fiber with hybrid edfa/raman amplifiers,” in Optical Fiber Communication Conference (OFC) 2019, (Optical Society of America, 2019), p. Tu3F.3.

Phillips, I. D.

Piciaccia, S.

R. Pastorelli, G. Bosco, A. Carena, P. Poggiolini, V. Curri, S. Piciaccia, and F. Forghieri, “Investigation of the dependence of non-linear interference on the number of WDM channels in coherent optical networks,” in Proc. 38th European Conf. and Exhibition Optical Communications, (2012), pp. 1–3.

Pilori, D.

M. Cantono, A. Ferrari, D. Pilori, E. Virgillito, J. L. Augé, and V. Curri, “Physical layer performance of multi-band optical line systems using Raman amplification,” J. Opt. Commun. Netw. 11(1), A103 (2019).
[Crossref]

M. Cantono, D. Pilori, A. Ferrari, A. Carena, and V. Curri, “Observing the interaction of PMD with generation of NLI in uncompensated amplified optical links,” in Optical Fiber Communications Conference (OFC), (OSA, 2018).

D. Pilori, M. Cantono, A. Carena, and V. Curri, “FFSS: The fast fiber simulator software,” in Transparent Optical Networks (ICTON), 2017 19th International Conference on, (IEEE, 2017), pp. 1–4.

Poggiolini, P.

Powell, J.

J.-L. Augé, G. Grammel, E. le Rouzic, V. Curri, G. Galimberti, and J. Powell, “Open optical network planning demonstration,” in Optical Fiber Communication Conference (OFC) 2019, (Optical Society of America, 2019), p. M3Z.9.

Quagliotti, M.

Radic, S.

Renaudier, J.

Rizzelli, G.

Rossi, N.

Saavedra, G.

Schiano, M.

Secondini, M.

Semrau, D.

Serena, P.

Shi, K.

Shtaif, M.

Sillekens, E.

M. Ionescu, D. Lavery, A. Edwards, E. Sillekens, L. Galdino, D. Semrau, R. Killey, W. Pelouch, S. Barnes, and P. Bayvel, “74.38 tb/s transmission over 6300 km single mode fiber with hybrid edfa/raman amplifiers,” in Optical Fiber Communication Conference (OFC) 2019, (Optical Society of America, 2019), p. Tu3F.3.

Tan, M.

Thomsen, B. C.

Vannucci, A.

Virgillito, E.

Wai, P. K. A.

D. Marcuse, C. R. Manyuk, and P. K. A. Wai, “Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 15(9), 1735–1746 (1997).
[Crossref]

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Figures (7)

Fig. 1.
Fig. 1. General schematic of the simulation scenario.
Fig. 2.
Fig. 2. SNR as a function of the per-channel launch power $P_{\textrm {ch}}$ with $N_{\textrm {ch}}=21$ WDM channels ($B_{\textrm {WDM}}\approx 1$ THz).
Fig. 3.
Fig. 3. SNR as a function of the per-channel launch power $P_{\textrm {ch}}$ with $N_{\textrm {ch}}=41$ WDM channels ($B_{\textrm {WDM}}\approx 2$ THz).
Fig. 4.
Fig. 4. Cumulative average of the SNR over $20$ different PMD realizations ($N_{mc}$) at $P_{\textrm {ch}}=0$ dBm with $N_{\textrm {ch}}=41$ WDM channels ($B_{\textrm {WDM}}\approx 2$ THz) and $\delta _{\textrm {PMD}}=1~\mathrm {ps}/\sqrt {\mathrm {km}}$.
Fig. 5.
Fig. 5. Eye diagram of a $32$-GBaud PDM-QPSK signal at the transmitter (a) and after $23$ km of PMD-only fiber ($\alpha =0$, $\beta _2=0$, $\gamma =0$, $\delta _{\textrm {PMD}}=5~\mathrm {ps}/\sqrt {\mathrm {km}}$) (b) and CD-only fiber (c). $T$ is the symbol duration.
Fig. 6.
Fig. 6. SNR as a function of the per-channel launch power $P_{\textrm {ch}}$ with $N_{\textrm {ch}}=21$ WDM channels over $12\times 90$ km of NZDSF.
Fig. 7.
Fig. 7. SNR as a function of the total optical bandwidth $B_{\textrm {WDM}}$ with fixed per-channel launch power $P_{\textrm {ch}}=0$ dBm. Dashed line is a best-fit of an SNR decrease proportional to the logarithm of the optical bandwidth.

Equations (1)

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3 4 π 2 δ PMD 2 L eff 65   GHz .