Abstract

We investigate the transmission performance of advanced modulation formats in nonlinear regenerative channels based on cascaded phase sensitive amplifiers. We identify the impact of amplitude and phase noise dynamics along the transmission line and show that after a cascade of regenerators, densely packed single ring PSK constellations outperform multi-ring constellations. The results of this study will greatly simplify the design of future nonlinear regenerative channels for ultra-high capacity transmission.

© 2013 Optical Society of America

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2013 (3)

2012 (4)

X. Chen and W. Shieh, “Closed-form expressions for nonlinear transmission performance of densely spaced coherent optical OFDM systems,” Opt. Express18(18), 19039–19054 (2012).
[CrossRef]

K. S. Turitsyn and S. K. Turitsyn, “Nonlinear communication channels with capacity above the linear Shannon limit,” Opt. Lett.37(17), 3600–3602 (2012).
[CrossRef] [PubMed]

A. Mecozzi and R.J. Essiambre, “Nonlinear Shannon limit in pseudo-linear coherent systems,” IEEE J. Lightwave Technol.30(12), 2011–2024 (2012).
[CrossRef]

M. Matsumoto, “Fiber-based all-optical signal regeneration,” IEEE J. Sel. Top. Quantum Electron.18(2), 738–752 (2012).
[CrossRef]

2011 (4)

J. Kakande, R. Slavik, F. Parmigiani, A. Bogris, D. Syvridis, L. Gruner-Nielsen, R. Phelan, P. Petropoulos, and D. J. Richardson, “Multilevel quantization of optical phase in a novel coherent parametric mixer architecture,” Nat. Photonics4(12), 748–752 (2011).
[CrossRef]

S. Sygletos, P. Frascella, S. K. Ibrahim, L. Gruner-Nielsen, R. Phelan, J. O’Gorman, and A. D. Ellis, “A practical phase sensitive amplification scheme for two channel phase regeneration,” Opt. Express19(26), 938–945 (2011).
[CrossRef]

P. Poggiolini, A. Carena, V. Curri, G. Bosco, and F. Forghieri, “Analytical modeling of non-linear propagation in uncompensated optical transmission links,” IEEE Photonics Technol. Lett.23(11), 742–744 (2011).
[CrossRef]

D. Rafique and A. D. Ellis, “Impact of signal-ASE four wave mixing on the effectiveness of digital back-propagation in 112 Gbit/s PM-QPSK systems,” Opt. Express19(4), 3449–3454 (2011).
[CrossRef] [PubMed]

2010 (4)

R. J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightwave Technol.28(4), 662–701 (2010).
[CrossRef]

R. Tkach, “Scaling optical communications for the next decade and beyond,” Bell Labs Tech. J.14(4), 3–9 (2010).
[CrossRef]

A. D. Ellis, J. Zhao, and D. Cotter, “Approaching the non-linear Shannon limit,” IEEE J. Lightwave Technol.28(4), 423–433 (2010).
[CrossRef]

R. Slavik, F. Parmigiani, J. Kakande, C. Lundstrom, M. Sjodin, P. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gruner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. Richardson, “All-optical phase and amplitude regenerator for next generation telecommunications systems,” Nat. Photonics4(10), 690–695 (2010).
[CrossRef]

2006 (1)

2004 (1)

2003 (2)

S. Boscolo, K. J. Blow, and S. K. Turitsyn, “All-optical passive 2R regeneration for Nx40 Gbit/s WDM transmission using NOLM and novel filtering technique,” Opt. Commun.217, 227–232 (2003).
[CrossRef]

H. Louchet, A. Hodzic, and K. Petermann, “Analytical model for the performance evaluation of DWDM transmission systems,” IEEE Photonics Technol. Lett.15(9), 1219–1221 (2003).
[CrossRef]

2001 (1)

P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature411(6841), 1027–1030 (2001).
[CrossRef] [PubMed]

1997 (2)

1991 (1)

M. Nakazawa, E. Yamada, H. Kubota, and K. Suzuki, “10 Gbit/s soliton data transmission over one million kilometres,” Electron. Lett.27(14), 1270–1272 (1991).
[CrossRef]

1990 (1)

H. J. Thiele, A. D. Ellis, and I. D. Phillips, “Recirculating loop demonstration of 40 Gbit/s all-optical 3R data regeneration using a semiconductor nonlinear interferometer,” Electron. Lett.35(3), 230–231 (1990).
[CrossRef]

1984 (1)

M. C. Jeruchim, “Techniques of estimating the bit error rate in the simulation of digital communication systems,” IEEE J. Sel. Top. Quantum Electron.2(1), 153–170 (1984).

1948 (1)

C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J.27, 379–423 (1948).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Springer, 2000).

Agrell, E.

E. Agrell and M. Karlsson, “Satellite constellations: towards the nonlinear channel capacity,” in Proceedings of IEEE Photonics Conference, 2012, paper TuM1.

L. Beygi, E. Agrell, and M. Karlsson, “On the optimization of 16-point ring constellations in the presence of nonlinear phase noise,” in Proceedings of Optical Communication Conference, 2011 OSA Technical Digest Series (Optical Society of America), paper OThO4 (2011).

Andrekson, P.

R. Slavik, F. Parmigiani, J. Kakande, C. Lundstrom, M. Sjodin, P. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gruner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. Richardson, “All-optical phase and amplitude regenerator for next generation telecommunications systems,” Nat. Photonics4(10), 690–695 (2010).
[CrossRef]

Asobe, M.

Audouin, O.

O. Leclerc, U. E. Desurvire, and O. Audouin, “Synchronous WDM soliton regeneration: toward 80–160 Gbit/s transoceanic systems,” Opt. Fiber Technol.3(2), 97–116 (1997).
[CrossRef]

Bayart, D.

E. Desurvire, D. Bayart, B. Desthieux, and S. Bigo, Erbium-Doped Fiber Amplifiers: Device and System Developments (John Wiley, 2002).

Bennion, I.

Beygi, L.

L. Beygi, E. Agrell, and M. Karlsson, “On the optimization of 16-point ring constellations in the presence of nonlinear phase noise,” in Proceedings of Optical Communication Conference, 2011 OSA Technical Digest Series (Optical Society of America), paper OThO4 (2011).

Bhardwaj, A.

I. Kang, C. Dorrer, L. Zhang, M. Rasras, L. Buhl, A. Bhardwaj, S. Cabot, M. Dinu, X. Liu, M. Cappuzzo, L. Gomez, A. Wong-Foy, Y. F. Chen, S. Patel, D. T. Neilson, J. Jacques, and C. R. Giles, “Regenerative all optical wavelength conversion of 40 Gbit/s DPSK signals using a SOA MZI,” in Proceedings of European Conference on Optical Communication (ECOC 2005), Amsterdam, paper Thu 4.3.3 (2005).
[CrossRef]

Bigo, S.

E. Desurvire, D. Bayart, B. Desthieux, and S. Bigo, Erbium-Doped Fiber Amplifiers: Device and System Developments (John Wiley, 2002).

Blow, K. J.

S. Boscolo, K. J. Blow, and S. K. Turitsyn, “All-optical passive 2R regeneration for Nx40 Gbit/s WDM transmission using NOLM and novel filtering technique,” Opt. Commun.217, 227–232 (2003).
[CrossRef]

Bogris, A.

J. Kakande, R. Slavik, F. Parmigiani, A. Bogris, D. Syvridis, L. Gruner-Nielsen, R. Phelan, P. Petropoulos, and D. J. Richardson, “Multilevel quantization of optical phase in a novel coherent parametric mixer architecture,” Nat. Photonics4(12), 748–752 (2011).
[CrossRef]

R. Slavik, F. Parmigiani, J. Kakande, C. Lundstrom, M. Sjodin, P. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gruner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. Richardson, “All-optical phase and amplitude regenerator for next generation telecommunications systems,” Nat. Photonics4(10), 690–695 (2010).
[CrossRef]

A. Bogris and D. Syvridis, “All-optical signal processing for 16-QAM using four-level optical phase quantizers based on phase sensitive amplifiers,” in Proceedings of European Conference in Optical Communications (ECOC 2013), London, paper We.3A.6 (2013).

Bosco, G.

P. Poggiolini, A. Carena, V. Curri, G. Bosco, and F. Forghieri, “Analytical modeling of non-linear propagation in uncompensated optical transmission links,” IEEE Photonics Technol. Lett.23(11), 742–744 (2011).
[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,” in Proceedings of European Conference on Optical Communication (ECOC 2011), Amsterdam, paper We.7.B.2 (2011).

Boscolo, S.

S. Boscolo, K. J. Blow, and S. K. Turitsyn, “All-optical passive 2R regeneration for Nx40 Gbit/s WDM transmission using NOLM and novel filtering technique,” Opt. Commun.217, 227–232 (2003).
[CrossRef]

Buhl, L.

I. Kang, C. Dorrer, L. Zhang, M. Rasras, L. Buhl, A. Bhardwaj, S. Cabot, M. Dinu, X. Liu, M. Cappuzzo, L. Gomez, A. Wong-Foy, Y. F. Chen, S. Patel, D. T. Neilson, J. Jacques, and C. R. Giles, “Regenerative all optical wavelength conversion of 40 Gbit/s DPSK signals using a SOA MZI,” in Proceedings of European Conference on Optical Communication (ECOC 2005), Amsterdam, paper Thu 4.3.3 (2005).
[CrossRef]

Cabot, S.

I. Kang, C. Dorrer, L. Zhang, M. Rasras, L. Buhl, A. Bhardwaj, S. Cabot, M. Dinu, X. Liu, M. Cappuzzo, L. Gomez, A. Wong-Foy, Y. F. Chen, S. Patel, D. T. Neilson, J. Jacques, and C. R. Giles, “Regenerative all optical wavelength conversion of 40 Gbit/s DPSK signals using a SOA MZI,” in Proceedings of European Conference on Optical Communication (ECOC 2005), Amsterdam, paper Thu 4.3.3 (2005).
[CrossRef]

Cappuzzo, M.

I. Kang, C. Dorrer, L. Zhang, M. Rasras, L. Buhl, A. Bhardwaj, S. Cabot, M. Dinu, X. Liu, M. Cappuzzo, L. Gomez, A. Wong-Foy, Y. F. Chen, S. Patel, D. T. Neilson, J. Jacques, and C. R. Giles, “Regenerative all optical wavelength conversion of 40 Gbit/s DPSK signals using a SOA MZI,” in Proceedings of European Conference on Optical Communication (ECOC 2005), Amsterdam, paper Thu 4.3.3 (2005).
[CrossRef]

Carena, A.

P. Poggiolini, A. Carena, V. Curri, G. Bosco, and F. Forghieri, “Analytical modeling of non-linear propagation in uncompensated optical transmission links,” IEEE Photonics Technol. Lett.23(11), 742–744 (2011).
[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,” in Proceedings of European Conference on Optical Communication (ECOC 2011), Amsterdam, paper We.7.B.2 (2011).

Chen, X.

Chen, Y. F.

I. Kang, C. Dorrer, L. Zhang, M. Rasras, L. Buhl, A. Bhardwaj, S. Cabot, M. Dinu, X. Liu, M. Cappuzzo, L. Gomez, A. Wong-Foy, Y. F. Chen, S. Patel, D. T. Neilson, J. Jacques, and C. R. Giles, “Regenerative all optical wavelength conversion of 40 Gbit/s DPSK signals using a SOA MZI,” in Proceedings of European Conference on Optical Communication (ECOC 2005), Amsterdam, paper Thu 4.3.3 (2005).
[CrossRef]

Cigliutti, R.

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,” in Proceedings of European Conference on Optical Communication (ECOC 2011), Amsterdam, paper We.7.B.2 (2011).

Coquelin, A.

D. Wolfson, P. B. Hansen, A. Kloch, T. Fjelde, C. Janz, A. Coquelin, I. Guillemont, F. Gaborit, and M. Renaud, “All-optical 2R regeneration at 40 Gbit/s in an SOA-based Mach-Zehnder interferometer,” in Proceedings of Optical Communication Conference, Beijing, pp. 456–457 (1999).

Cotter, D.

A. D. Ellis, J. Zhao, and D. Cotter, “Approaching the non-linear Shannon limit,” IEEE J. Lightwave Technol.28(4), 423–433 (2010).
[CrossRef]

Croussore, K.

Curri, V.

P. Poggiolini, A. Carena, V. Curri, G. Bosco, and F. Forghieri, “Analytical modeling of non-linear propagation in uncompensated optical transmission links,” IEEE Photonics Technol. Lett.23(11), 742–744 (2011).
[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,” in Proceedings of European Conference on Optical Communication (ECOC 2011), Amsterdam, paper We.7.B.2 (2011).

Dasgupta, S.

R. Slavik, F. Parmigiani, J. Kakande, C. Lundstrom, M. Sjodin, P. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gruner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. Richardson, “All-optical phase and amplitude regenerator for next generation telecommunications systems,” Nat. Photonics4(10), 690–695 (2010).
[CrossRef]

Desthieux, B.

E. Desurvire, D. Bayart, B. Desthieux, and S. Bigo, Erbium-Doped Fiber Amplifiers: Device and System Developments (John Wiley, 2002).

Desurvire, E.

E. Desurvire, D. Bayart, B. Desthieux, and S. Bigo, Erbium-Doped Fiber Amplifiers: Device and System Developments (John Wiley, 2002).

Desurvire, U. E.

O. Leclerc, U. E. Desurvire, and O. Audouin, “Synchronous WDM soliton regeneration: toward 80–160 Gbit/s transoceanic systems,” Opt. Fiber Technol.3(2), 97–116 (1997).
[CrossRef]

Dinu, M.

I. Kang, C. Dorrer, L. Zhang, M. Rasras, L. Buhl, A. Bhardwaj, S. Cabot, M. Dinu, X. Liu, M. Cappuzzo, L. Gomez, A. Wong-Foy, Y. F. Chen, S. Patel, D. T. Neilson, J. Jacques, and C. R. Giles, “Regenerative all optical wavelength conversion of 40 Gbit/s DPSK signals using a SOA MZI,” in Proceedings of European Conference on Optical Communication (ECOC 2005), Amsterdam, paper Thu 4.3.3 (2005).
[CrossRef]

Doran, N. J.

Dorrer, C.

I. Kang, C. Dorrer, L. Zhang, M. Rasras, L. Buhl, A. Bhardwaj, S. Cabot, M. Dinu, X. Liu, M. Cappuzzo, L. Gomez, A. Wong-Foy, Y. F. Chen, S. Patel, D. T. Neilson, J. Jacques, and C. R. Giles, “Regenerative all optical wavelength conversion of 40 Gbit/s DPSK signals using a SOA MZI,” in Proceedings of European Conference on Optical Communication (ECOC 2005), Amsterdam, paper Thu 4.3.3 (2005).
[CrossRef]

Ellis, A. D.

D. Rafique and A. D. Ellis, “Impact of signal-ASE four wave mixing on the effectiveness of digital back-propagation in 112 Gbit/s PM-QPSK systems,” Opt. Express19(4), 3449–3454 (2011).
[CrossRef] [PubMed]

S. Sygletos, P. Frascella, S. K. Ibrahim, L. Gruner-Nielsen, R. Phelan, J. O’Gorman, and A. D. Ellis, “A practical phase sensitive amplification scheme for two channel phase regeneration,” Opt. Express19(26), 938–945 (2011).
[CrossRef]

R. Slavik, F. Parmigiani, J. Kakande, C. Lundstrom, M. Sjodin, P. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gruner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. Richardson, “All-optical phase and amplitude regenerator for next generation telecommunications systems,” Nat. Photonics4(10), 690–695 (2010).
[CrossRef]

A. D. Ellis, J. Zhao, and D. Cotter, “Approaching the non-linear Shannon limit,” IEEE J. Lightwave Technol.28(4), 423–433 (2010).
[CrossRef]

I. D. Phillips, A. Gloag, P. N. Kean, N. J. Doran, I. Bennion, and A. D. Ellis, “Simultaneous de-multiplexing, data regeneration and clock recovery using a single semiconductor optical amplifier based nonlinear optical loop mirror,” Opt. Lett.22(17), 1326–1328 (1997).
[CrossRef]

H. J. Thiele, A. D. Ellis, and I. D. Phillips, “Recirculating loop demonstration of 40 Gbit/s all-optical 3R data regeneration using a semiconductor nonlinear interferometer,” Electron. Lett.35(3), 230–231 (1990).
[CrossRef]

Essiambre, R. J.

Essiambre, R.J.

A. Mecozzi and R.J. Essiambre, “Nonlinear Shannon limit in pseudo-linear coherent systems,” IEEE J. Lightwave Technol.30(12), 2011–2024 (2012).
[CrossRef]

Fini, J. M.

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics7(5), 354–362 (2013).
[CrossRef]

Fjelde, T.

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Figures (7)

Fig. 1
Fig. 1

(a) Schematic diagram of a future high capacity digital link formed by cascading R PSA based 2R- regenerators, R+1 links, each comprising a number of optically amplified spans adding noise with variance N, (b) Representation of simplified simulation model.

Fig. 2
Fig. 2

(a) Normalized phase response and (b) normalized amplitude response of an 8-level phase sensitive amplifier as a function of the phase of the input signal.

Fig. 3
Fig. 3

Phase symmetric constellations for 8-symbols before (leftmost) and after transmission in linear channels and nonlinear regenerative channels with cascaded 1, 10, 20 phase regenerators for the fixed value of SNR =15 dB.

Fig. 4
Fig. 4

SERs as a function of SNR for the examined 8-symbol constellation types; 1 amplitude level: 8-PSK (index a, blue lines), 2 amplitude levels: 2-ASK/4-PSK (index b, red lines), and 4 amplitude levels: 8-star QAM (index c, green line) for linear channel (sub-index 0) and nonlinear regenerative channels with cascaded 1, 10, 20 phase regenerators (sub-indexes 1, 10, and 20 respectively). Formats are also identified by line color, whilst the number of regenerators in the link is identified by the dashing of the line (dash length increases with number of regenerators).

Fig. 5
Fig. 5

(a) Definition of amplitude and phase error for the received signal. Phase, amplitude and total distortion of the output constellation (b) as a function of the number of in-line regenerators for the fixed value SNR=15 dB and (c) as a function of the SNR for 10 cascaded regenerators.

Fig. 6
Fig. 6

Phase symmetric constellations formats for 16 symbols before (leftmost) and after transmission in linear channels (index 0) and nonlinear regenerative channel with cascaded 1, 10, 20 phase regenerators (indexes 1,10, and 20 respectively) for the fixed value SNR=18 dB.

Fig. 7
Fig. 7

The SERs as a function of SNR for the various types of modulation formats shown in Fig. 6, 1 amplitude level: 16-PSK (index a), 2 amplitude levels: 2-ASK/8-PSK (index b), and 4 amplitude levels: 16-star QAM (index c) for linear channel (index 0) and nonlinear regenerative channels with cascaded 1, 10, 20 phase regenerators (indexes 1, 10 and 20 respectively). Formats are also identified by line color, whilst the number of regenerators in the link is identified by the dashing of the line (dash length increases with number of regenerators). The SER of unregenerated 16-QAM format is shown for reference (index d).

Equations (2)

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SNR = < | y 0 | 2 > k = 1 R + 1 < | n k | 2 >
r out e i φ out = T ( r i n e i φ i n ) = r i n e i φ i n ( 1 + m e i M φ i n )

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