Abstract

We investigate the energy optimization (minimization) for amplified links. We show that using the using a well-established analytic nonlinear signal-to-noise ratio noise model that for a simple amplifier model there are very clear, fiber independent, amplifier gains which minimize the total energy requirement. With a generalized amplifier model we establish the spacing for the optimum power per bit as well as the nonlinear limited optimum power. An amplifier spacing corresponding to 13 dB gain is shown to be a suitable compromise for practical amplifiers operating at the optimum nonlinear power.

© 2014 Optical Society of America

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References

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  • Year
  • Author
  • Publication
  1. X. Chen and W. Shieh, “Closed-form expressions for nonlinear transmission performance of densely spaced coherent optical OFDM systems,” Opt. Express 18(18), 19039–19054 (2010).
    [Crossref] [PubMed]
  2. P. Poggiolini, “Modeling of Non-Linear Propagation in Uncompensated Coherent Systems,” in Proceedings of OFC/NFOEC (2013), OTh3G.1.
    [Crossref]
  3. S. Gringeri, E. Basch, and T. J. Xia, “Technical Considerations for Supporting Data Rates Beyond 100 Gb/s,” IEEE Commun. Mag. 50(2), s21–s30 (2012).
    [Crossref]
  4. M. Huang, S. Zhang, E. Mateo, D. Qian, F. Yaman, T. Inoue, Y. Inada, and T. Wang, “EDFA-Only WDM 4200-km Transmission of OFDM-16QAM and 32QAM,” IEEE Photon. Technol. Lett. 24(17), 1466–1468 (2012).
    [Crossref]
  5. X. Zhou, L. E. Nelson, P. Magill, R. Isaac, B. Zhu, D. W. Peckham, P. I. Borel, and K. Carlson, “PDM-Nyquist-32QAM for 450-Gb/s Per-Channel WDM Transmission on the 50 GHz ITU-T Grid,” J. Lightwave Technol. 30(4), 553–559 (2012).
    [Crossref]
  6. S. Kilmurray, T. Fehenberger, P. Bayvel, and R. I. Killey, “Comparison of the nonlinear transmission performance of quasi-Nyquist WDM and reduced guard interval OFDM,” Opt. Express 20(4), 4198–4205 (2012).
    [Crossref] [PubMed]
  7. O. V. Sinkin, J. Cai, D. Foursa, H. Zhang, A. Pilipetskii, G. Mohs, and N. Bergano, “Scaling of Nonlinear Impairments in Dispersion Uncompensated Long-Haul Transmission,” in Proceedings of OFC/NFOEC (2012), OTu1A.2.
    [Crossref]
  8. A. D. Ellis and N. J. Doran, “Optical Link Design for Minimum Power Consumption and Maximum Capacity,” in Proceedings of ECOC (2013) Paper P4.9.
    [Crossref]
  9. R. S. Tucker, “Green Optical Communications-Part I:Energy Limitations in Transport,” IEEE J. Sel. Top. Quantum Electron. 17(2), 245–260 (2011).
    [Crossref]
  10. M. Hirano, T. Haruna, Y. Tamura, T. Kawano, S. Ohnuki, Y. Yamamoto, Y. Koyano, and T. Sasaki, “Record Low Loss, Record High FOM Optical Fiber with Manufacturable Process,” in Proceedings of OFC/NFOEC (2013), PDP5A.7.
    [Crossref]
  11. P. K. Runge and E. K. Stafford, “AT&T optical amplifier systems,” in Tech. Dig., 2nd Int. Conf. Opt. Fiber Submarine Telecommun. Syst., Suboptic’93, Versailles, France, 1993, paper 3.5.

2012 (4)

S. Gringeri, E. Basch, and T. J. Xia, “Technical Considerations for Supporting Data Rates Beyond 100 Gb/s,” IEEE Commun. Mag. 50(2), s21–s30 (2012).
[Crossref]

M. Huang, S. Zhang, E. Mateo, D. Qian, F. Yaman, T. Inoue, Y. Inada, and T. Wang, “EDFA-Only WDM 4200-km Transmission of OFDM-16QAM and 32QAM,” IEEE Photon. Technol. Lett. 24(17), 1466–1468 (2012).
[Crossref]

X. Zhou, L. E. Nelson, P. Magill, R. Isaac, B. Zhu, D. W. Peckham, P. I. Borel, and K. Carlson, “PDM-Nyquist-32QAM for 450-Gb/s Per-Channel WDM Transmission on the 50 GHz ITU-T Grid,” J. Lightwave Technol. 30(4), 553–559 (2012).
[Crossref]

S. Kilmurray, T. Fehenberger, P. Bayvel, and R. I. Killey, “Comparison of the nonlinear transmission performance of quasi-Nyquist WDM and reduced guard interval OFDM,” Opt. Express 20(4), 4198–4205 (2012).
[Crossref] [PubMed]

2011 (1)

R. S. Tucker, “Green Optical Communications-Part I:Energy Limitations in Transport,” IEEE J. Sel. Top. Quantum Electron. 17(2), 245–260 (2011).
[Crossref]

2010 (1)

Basch, E.

S. Gringeri, E. Basch, and T. J. Xia, “Technical Considerations for Supporting Data Rates Beyond 100 Gb/s,” IEEE Commun. Mag. 50(2), s21–s30 (2012).
[Crossref]

Bayvel, P.

Borel, P. I.

Carlson, K.

Chen, X.

Fehenberger, T.

Gringeri, S.

S. Gringeri, E. Basch, and T. J. Xia, “Technical Considerations for Supporting Data Rates Beyond 100 Gb/s,” IEEE Commun. Mag. 50(2), s21–s30 (2012).
[Crossref]

Haruna, T.

M. Hirano, T. Haruna, Y. Tamura, T. Kawano, S. Ohnuki, Y. Yamamoto, Y. Koyano, and T. Sasaki, “Record Low Loss, Record High FOM Optical Fiber with Manufacturable Process,” in Proceedings of OFC/NFOEC (2013), PDP5A.7.
[Crossref]

Hirano, M.

M. Hirano, T. Haruna, Y. Tamura, T. Kawano, S. Ohnuki, Y. Yamamoto, Y. Koyano, and T. Sasaki, “Record Low Loss, Record High FOM Optical Fiber with Manufacturable Process,” in Proceedings of OFC/NFOEC (2013), PDP5A.7.
[Crossref]

Huang, M.

M. Huang, S. Zhang, E. Mateo, D. Qian, F. Yaman, T. Inoue, Y. Inada, and T. Wang, “EDFA-Only WDM 4200-km Transmission of OFDM-16QAM and 32QAM,” IEEE Photon. Technol. Lett. 24(17), 1466–1468 (2012).
[Crossref]

Inada, Y.

M. Huang, S. Zhang, E. Mateo, D. Qian, F. Yaman, T. Inoue, Y. Inada, and T. Wang, “EDFA-Only WDM 4200-km Transmission of OFDM-16QAM and 32QAM,” IEEE Photon. Technol. Lett. 24(17), 1466–1468 (2012).
[Crossref]

Inoue, T.

M. Huang, S. Zhang, E. Mateo, D. Qian, F. Yaman, T. Inoue, Y. Inada, and T. Wang, “EDFA-Only WDM 4200-km Transmission of OFDM-16QAM and 32QAM,” IEEE Photon. Technol. Lett. 24(17), 1466–1468 (2012).
[Crossref]

Isaac, R.

Kawano, T.

M. Hirano, T. Haruna, Y. Tamura, T. Kawano, S. Ohnuki, Y. Yamamoto, Y. Koyano, and T. Sasaki, “Record Low Loss, Record High FOM Optical Fiber with Manufacturable Process,” in Proceedings of OFC/NFOEC (2013), PDP5A.7.
[Crossref]

Killey, R. I.

Kilmurray, S.

Koyano, Y.

M. Hirano, T. Haruna, Y. Tamura, T. Kawano, S. Ohnuki, Y. Yamamoto, Y. Koyano, and T. Sasaki, “Record Low Loss, Record High FOM Optical Fiber with Manufacturable Process,” in Proceedings of OFC/NFOEC (2013), PDP5A.7.
[Crossref]

Magill, P.

Mateo, E.

M. Huang, S. Zhang, E. Mateo, D. Qian, F. Yaman, T. Inoue, Y. Inada, and T. Wang, “EDFA-Only WDM 4200-km Transmission of OFDM-16QAM and 32QAM,” IEEE Photon. Technol. Lett. 24(17), 1466–1468 (2012).
[Crossref]

Nelson, L. E.

Ohnuki, S.

M. Hirano, T. Haruna, Y. Tamura, T. Kawano, S. Ohnuki, Y. Yamamoto, Y. Koyano, and T. Sasaki, “Record Low Loss, Record High FOM Optical Fiber with Manufacturable Process,” in Proceedings of OFC/NFOEC (2013), PDP5A.7.
[Crossref]

Peckham, D. W.

Qian, D.

M. Huang, S. Zhang, E. Mateo, D. Qian, F. Yaman, T. Inoue, Y. Inada, and T. Wang, “EDFA-Only WDM 4200-km Transmission of OFDM-16QAM and 32QAM,” IEEE Photon. Technol. Lett. 24(17), 1466–1468 (2012).
[Crossref]

Sasaki, T.

M. Hirano, T. Haruna, Y. Tamura, T. Kawano, S. Ohnuki, Y. Yamamoto, Y. Koyano, and T. Sasaki, “Record Low Loss, Record High FOM Optical Fiber with Manufacturable Process,” in Proceedings of OFC/NFOEC (2013), PDP5A.7.
[Crossref]

Shieh, W.

Tamura, Y.

M. Hirano, T. Haruna, Y. Tamura, T. Kawano, S. Ohnuki, Y. Yamamoto, Y. Koyano, and T. Sasaki, “Record Low Loss, Record High FOM Optical Fiber with Manufacturable Process,” in Proceedings of OFC/NFOEC (2013), PDP5A.7.
[Crossref]

Tucker, R. S.

R. S. Tucker, “Green Optical Communications-Part I:Energy Limitations in Transport,” IEEE J. Sel. Top. Quantum Electron. 17(2), 245–260 (2011).
[Crossref]

Wang, T.

M. Huang, S. Zhang, E. Mateo, D. Qian, F. Yaman, T. Inoue, Y. Inada, and T. Wang, “EDFA-Only WDM 4200-km Transmission of OFDM-16QAM and 32QAM,” IEEE Photon. Technol. Lett. 24(17), 1466–1468 (2012).
[Crossref]

Xia, T. J.

S. Gringeri, E. Basch, and T. J. Xia, “Technical Considerations for Supporting Data Rates Beyond 100 Gb/s,” IEEE Commun. Mag. 50(2), s21–s30 (2012).
[Crossref]

Yamamoto, Y.

M. Hirano, T. Haruna, Y. Tamura, T. Kawano, S. Ohnuki, Y. Yamamoto, Y. Koyano, and T. Sasaki, “Record Low Loss, Record High FOM Optical Fiber with Manufacturable Process,” in Proceedings of OFC/NFOEC (2013), PDP5A.7.
[Crossref]

Yaman, F.

M. Huang, S. Zhang, E. Mateo, D. Qian, F. Yaman, T. Inoue, Y. Inada, and T. Wang, “EDFA-Only WDM 4200-km Transmission of OFDM-16QAM and 32QAM,” IEEE Photon. Technol. Lett. 24(17), 1466–1468 (2012).
[Crossref]

Zhang, S.

M. Huang, S. Zhang, E. Mateo, D. Qian, F. Yaman, T. Inoue, Y. Inada, and T. Wang, “EDFA-Only WDM 4200-km Transmission of OFDM-16QAM and 32QAM,” IEEE Photon. Technol. Lett. 24(17), 1466–1468 (2012).
[Crossref]

Zhou, X.

Zhu, B.

IEEE Commun. Mag. (1)

S. Gringeri, E. Basch, and T. J. Xia, “Technical Considerations for Supporting Data Rates Beyond 100 Gb/s,” IEEE Commun. Mag. 50(2), s21–s30 (2012).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

R. S. Tucker, “Green Optical Communications-Part I:Energy Limitations in Transport,” IEEE J. Sel. Top. Quantum Electron. 17(2), 245–260 (2011).
[Crossref]

IEEE Photon. Technol. Lett. (1)

M. Huang, S. Zhang, E. Mateo, D. Qian, F. Yaman, T. Inoue, Y. Inada, and T. Wang, “EDFA-Only WDM 4200-km Transmission of OFDM-16QAM and 32QAM,” IEEE Photon. Technol. Lett. 24(17), 1466–1468 (2012).
[Crossref]

J. Lightwave Technol. (1)

Opt. Express (2)

Other (5)

P. Poggiolini, “Modeling of Non-Linear Propagation in Uncompensated Coherent Systems,” in Proceedings of OFC/NFOEC (2013), OTh3G.1.
[Crossref]

M. Hirano, T. Haruna, Y. Tamura, T. Kawano, S. Ohnuki, Y. Yamamoto, Y. Koyano, and T. Sasaki, “Record Low Loss, Record High FOM Optical Fiber with Manufacturable Process,” in Proceedings of OFC/NFOEC (2013), PDP5A.7.
[Crossref]

P. K. Runge and E. K. Stafford, “AT&T optical amplifier systems,” in Tech. Dig., 2nd Int. Conf. Opt. Fiber Submarine Telecommun. Syst., Suboptic’93, Versailles, France, 1993, paper 3.5.

O. V. Sinkin, J. Cai, D. Foursa, H. Zhang, A. Pilipetskii, G. Mohs, and N. Bergano, “Scaling of Nonlinear Impairments in Dispersion Uncompensated Long-Haul Transmission,” in Proceedings of OFC/NFOEC (2012), OTu1A.2.
[Crossref]

A. D. Ellis and N. J. Doran, “Optical Link Design for Minimum Power Consumption and Maximum Capacity,” in Proceedings of ECOC (2013) Paper P4.9.
[Crossref]

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Figures (4)
Fig. 1
Fig. 1 Spectral density against total optical launch power for a fixed 3000 km system with a 5.THz bandwidth, channels spaced at 50 GHz, a fiber loss of 0.2 dB/km, nonlinear coefficient of 1.4 /W/km, dispersion coefficient of 20 ps/nm/km and an amplifier noise figure of 4.7 dB. For a range of amplifier spans; 180 (dark blue dotted line), 150, 120, 90, 60 (blue dashed line), 30, 20, 15, 10, 5, and 1 (solid red line) km, and showing the locus of ISD for operation at the nonlinear threshold as the amplifier spacing is varied (thick black line).

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Fig. 2
Fig. 2 Achievable ISD (contours) as a function of total amplifier output optical power vs amplifier spacing with dispersion 20 ps/nm/km, loss 0.046 /km (0.2 dB/km), nonlinearity 1.4/W/km and a system length of 3000 km. Blue dotted line is the optimum nonlinear capacity for a given amplifier span. The red line is the minimum total power for a specific capacity.

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Fig. 3
Fig. 3 Achievable ISD (contours) as a function of total added optical power and amplifier spacing with a dispersion 20 ps/nm/km, loss 0.046 /km (0.2 dB/km), nonlinearity 1.1/W/km and a system length of 6,000 km. The insertion loss of each amplifier is 0 dB (a) and 3 dB (b) equally distributed between the amplifier input and output.

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Fig. 4
Fig. 4 Optimum amplifier spacing versus insertion loss of all components at the amplifier input for a fiber with 0.2 dB/km loss, assuming operation at the nonlinear threshold (blue curves) and the minimum possible added signal power (red curves). Lines represent; thin solid – 0 dB output loss, short dashed – 1 dB, medium dash – 2 dB and long dashed - 3 dB output losses. Thick solid lines represent analytical approximations based on total output power (Eqs. (7) and (9) respectively). Note that the amplifier population inversion (nsp) rather than effective black-box noise figure is held constant in this plot.

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Equations (11)

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SNR= P S / B amp N(G−1) σ ASE +N L eff σ NL P S 3 / B amp 3
σ ase = n sp hυ, σ NL = γ 2 c λ 2 D log( π B amp 2 λ 2 D αc )
P opt B amp = ( G−1 ) σ ASE 2 L eff σ NL 3 ≅ αG σ ASE 2 σ NL 3
SN R T = N P T / B amp N 3 ( G−1 ) σ ASE + L eff σ NL P T 3 / B amp 3
P T =N P S
P add−T =N P s ( 1 Λ out − Λ in G )
L a = 3 α
2+ e αL ( αL−2 )+ e −αL σ NL σ ASE 1 N 3 ( αL+ e +α⋅L −1 α ) P T 3 =0
L b = 2+W( −2/ e 2 ) α
SN R add−T = N P T / B amp N 3 ( G−1 ) σ ASE Λ in + L eff σ NL ( G⋅ Λ out P T / B amp G− Λ out Λ in ) 3
P elect =N( P s η ( 1 Λ out − Λ in G )+ P overhead )

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