Abstract

In this work, we will derive, validate, and analyze the theoretical description of nonlinear Kerr effects resulting from various transmission systems that deploy single or multiple optical phase conjugators (OPCs). We will show that the nonlinear Kerr compensation can be achieved, with various efficiencies, in both lumped and distributed Raman transmission systems. The results show that first order distributed Raman systems are superior to the discretely amplified systems in terms of the nonlinear Kerr compensation efficiency that a mid-link OPC can achieve. Also, we will show that the multi-OPC approach will diminish the nonlinearity compensation efficiency in any system as it will act as periodic dispersion compensators.

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References

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  1. A. D. Ellis, M. E. McCarthy, M. A. Z. Al Khateeb, M. Sorokina, and N. J. Doran, “Performance limits in optical communications due to fiber nonlinearity,” Adv. Opt. Photonics 9(3), 429–503 (2017).
  2. P. Poggiolini, “The GN model of non-linear propagation in uncompensated coherent optical systems,” J. Lightwave Technol. 30(24), 3857–3879 (2012).
  3. K. O. Hill, D. C. Johnson, B. S. Kawasaki, and R. I. MacDonald, “CW three-wave mixing in single-mode optical fibers,” J. Appl. Phys. 49(10), 5098–5106 (1978).
  4. A. D. Ellis and W. A. Stallard, “Four wave mixing in ultra long transmission systems incorporating linear amplifiers,” in Proceedings of IEE Colloquium on Non-Linear Effects in Fibre Communications (IEEE, 1990), 6/1–6/4.
  5. D. G. Schadt, “Effect of amplifier spacing on four-wave mixing in multichannel coherent communications,” Electron. Lett. 27(20), 1805–1807 (1991).
  6. K. Inoue, “Phase-mismatching characteristic of four-wave mixing in fiber lines with multistage optical amplifiers,” Opt. Lett. 17(11), 801–803 (1992).
    [PubMed]
  7. D. A. Cleland, A. D. Ellis, and C. H. F. Sturrock, “Precise modelling of four wave mixing products over 400 km of step-index fibre,” Electron. Lett. 28(12), 1171–1173 (1992).
  8. 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).
  9. C. Kurtzke, “Suppression of fiber nonlinearities by appropriate dispersion management,” IEEE Photonics Technol. Lett. 5(10), 1250–1253 (1993).
  10. M. E. Marhic, N. Kagi, T. K. Chiang, and L. G. Kazovsky, “Optimizing the location of dispersion compensators in periodically amplified fiber links in the presence of third-order nonlinear effects,” IEEE Photonics Technol. Lett. 8(1), 145–147 (1996).
  11. K. Nakajima, M. Ohashi, K. Shiraki, T. Horiguchi, K. Kurokawa, and Y. Miyajima, “Four-wave mixing suppression effect of dispersion distributed fibers,” J. Lightwave Technol. 17(10), 1814–1822 (1999).
  12. K. Inoue and H. Toba, “Fiber four-wave mixing in multi-amplifier systems with nonuniform chromatic dispersion,” J. Lightwave Technol. 13(1), 88–93 (1995).
  13. 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).
  14. S. Radic, G. Pendock, A. Srivastava, P. Wysocki, and A. Chraplyvy, “Four-wave mixing in optical links using quasi-distributed optical amplifiers,” J. Lightwave Technol. 19(5), 636–645 (2001).
  15. S. Watanabe and M. Shirasaki, “Exact compensation for both chromatic dispersion and Kerr effect in a transmission fiber using optical phase conjugation,” J. Lightwave Technol. 14(3), 243–248 (1996).
  16. V. Pechenkin and I. J. Fair, “On four-wave mixing suppression in dispersion-managed fiber-optic OFDM systems with an optical phase conjugation module,” J. Lightwave Technol. 29(11), 1678–1691 (2011).
  17. M. Al-Khateeb, M. E. McCarthy, and A. D. Ellis, “Experimental verification of four wave mixing in lumped optical transmission systems that employ mid-link optical phase conjugation,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2017), paper JTh2A.64.
  18. A. D. Ellis, M. E. McCarthy, M. A. Z. Al-Khateeb, and S. Sygletos, “Capacity limits of systems employing multiple optical phase conjugators,” Opt. Express 23(16), 20381–20393 (2015).
    [PubMed]
  19. M. A. Z. Al-Khateeb, M. McCarthy, C. Sánchez, and A. Ellis, “Effect of second order signal-noise interactions in nonlinearity compensated optical transmission systems,” Opt. Lett. 41(8), 1849–1852 (2016).
    [PubMed]
  20. M. E. McCarthy, M. A. Z. Al Kahteeb, F. M. Ferreira, and A. D. Ellis, “PMD tolerant nonlinear compensation using in-line phase conjugation,” Opt. Express 24(4), 3385–3392 (2016).
    [PubMed]
  21. M. A. Z. Al-Khateeb, M. Tan, M. A. Iqbal, M. McCarthy, P. Harper, and A. D. Ellis, “Four wave mixing in distributed Raman amplified optical transmission systems,” in Proceedings of IEEE Photonics Conference (IEEE, 2016), pp. 795–796.
  22. W. Shieh, “Information spectral efficiency and launch power density limits due to fiber nonlinearity for coherent optical OFDM systems,” J. Photonics 3(2), 158–173 (2011).
  23. 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).
    [PubMed]
  24. C. Headley and G. P. Agrawal, Raman Amplification in Fiber Optical Communication Systems (Elsevier, 2005).
  25. M. Tan, P. Rosa, M. A. Iqbal, I. Phillips, J. Nuño, J. D. Ania-Castanon, and P. Harper, “RIN mitigation in second-order pumped Raman fibre laser based amplification,” in Asia Communications and Photonics Conference, OSA Technical Digest (online) (Optical Society of America, 2015), paper AM2E.6.
  26. M. H. Shoreh, “Compensation of nonlinearity impairments in coherent optical OFDM systems using multiple optical phase conjugate modules,” J. Opt. Commun. Netw. 6(6), 549–558 (2014).
  27. P. Minzioni and A. Schiffini, “Unifying theory of compensation techniques for intrachannel nonlinear effects,” Opt. Express 13(21), 8460–8468 (2005).
    [PubMed]
  28. S. L. Jansen, D. Van Den Borne, B. Spinnler, S. Calabrò, H. Suche, P. M. Krummrich, W. Sohler, G. Khoe, and H. De Waardt, “Optical phase conjugation for ultra long-haul a phase-shift-keyed transmission,” J. Lightwave Technol. 24(1), 54–64 (2006).
  29. P. Minzioni, “Nonlinearity compensation in a fiber optic link by optical phase conjugation,” Fiber Integr. Opt. 28, 179–209 (2009).

2017 (1)

A. D. Ellis, M. E. McCarthy, M. A. Z. Al Khateeb, M. Sorokina, and N. J. Doran, “Performance limits in optical communications due to fiber nonlinearity,” Adv. Opt. Photonics 9(3), 429–503 (2017).

2016 (2)

2015 (1)

2014 (1)

2012 (1)

2011 (2)

W. Shieh, “Information spectral efficiency and launch power density limits due to fiber nonlinearity for coherent optical OFDM systems,” J. Photonics 3(2), 158–173 (2011).

V. Pechenkin and I. J. Fair, “On four-wave mixing suppression in dispersion-managed fiber-optic OFDM systems with an optical phase conjugation module,” J. Lightwave Technol. 29(11), 1678–1691 (2011).

2010 (1)

2009 (1)

P. Minzioni, “Nonlinearity compensation in a fiber optic link by optical phase conjugation,” Fiber Integr. Opt. 28, 179–209 (2009).

2006 (1)

2005 (1)

2001 (1)

1999 (1)

1996 (3)

S. Watanabe and M. Shirasaki, “Exact compensation for both chromatic dispersion and Kerr effect in a transmission fiber using optical phase conjugation,” J. Lightwave Technol. 14(3), 243–248 (1996).

M. E. Marhic, N. Kagi, T. K. Chiang, and L. G. Kazovsky, “Optimizing the location of dispersion compensators in periodically amplified fiber links in the presence of third-order nonlinear effects,” IEEE Photonics Technol. Lett. 8(1), 145–147 (1996).

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).

1995 (1)

K. Inoue and H. Toba, “Fiber four-wave mixing in multi-amplifier systems with nonuniform chromatic dispersion,” J. Lightwave Technol. 13(1), 88–93 (1995).

1993 (1)

C. Kurtzke, “Suppression of fiber nonlinearities by appropriate dispersion management,” IEEE Photonics Technol. Lett. 5(10), 1250–1253 (1993).

1992 (2)

K. Inoue, “Phase-mismatching characteristic of four-wave mixing in fiber lines with multistage optical amplifiers,” Opt. Lett. 17(11), 801–803 (1992).
[PubMed]

D. A. Cleland, A. D. Ellis, and C. H. F. Sturrock, “Precise modelling of four wave mixing products over 400 km of step-index fibre,” Electron. Lett. 28(12), 1171–1173 (1992).

1991 (1)

D. G. Schadt, “Effect of amplifier spacing on four-wave mixing in multichannel coherent communications,” Electron. Lett. 27(20), 1805–1807 (1991).

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).

1978 (1)

K. O. Hill, D. C. Johnson, B. S. Kawasaki, and R. I. MacDonald, “CW three-wave mixing in single-mode optical fibers,” J. Appl. Phys. 49(10), 5098–5106 (1978).

Al Kahteeb, M. A. Z.

Al Khateeb, M. A. Z.

A. D. Ellis, M. E. McCarthy, M. A. Z. Al Khateeb, M. Sorokina, and N. J. Doran, “Performance limits in optical communications due to fiber nonlinearity,” Adv. Opt. Photonics 9(3), 429–503 (2017).

Al-Khateeb, M. A. Z.

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).

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).

Calabrò, S.

Chen, X.

Chiang, T. K.

M. E. Marhic, N. Kagi, T. K. Chiang, and L. G. Kazovsky, “Optimizing the location of dispersion compensators in periodically amplified fiber links in the presence of third-order nonlinear effects,” IEEE Photonics Technol. Lett. 8(1), 145–147 (1996).

Chraplyvy, A.

Cleland, D. A.

D. A. Cleland, A. D. Ellis, and C. H. F. Sturrock, “Precise modelling of four wave mixing products over 400 km of step-index fibre,” Electron. Lett. 28(12), 1171–1173 (1992).

De Waardt, H.

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).

Doran, N. J.

A. D. Ellis, M. E. McCarthy, M. A. Z. Al Khateeb, M. Sorokina, and N. J. Doran, “Performance limits in optical communications due to fiber nonlinearity,” Adv. Opt. Photonics 9(3), 429–503 (2017).

Ellis, A.

Ellis, A. D.

A. D. Ellis, M. E. McCarthy, M. A. Z. Al Khateeb, M. Sorokina, and N. J. Doran, “Performance limits in optical communications due to fiber nonlinearity,” Adv. Opt. Photonics 9(3), 429–503 (2017).

M. E. McCarthy, M. A. Z. Al Kahteeb, F. M. Ferreira, and A. D. Ellis, “PMD tolerant nonlinear compensation using in-line phase conjugation,” Opt. Express 24(4), 3385–3392 (2016).
[PubMed]

A. D. Ellis, M. E. McCarthy, M. A. Z. Al-Khateeb, and S. Sygletos, “Capacity limits of systems employing multiple optical phase conjugators,” Opt. Express 23(16), 20381–20393 (2015).
[PubMed]

D. A. Cleland, A. D. Ellis, and C. H. F. Sturrock, “Precise modelling of four wave mixing products over 400 km of step-index fibre,” Electron. Lett. 28(12), 1171–1173 (1992).

M. A. Z. Al-Khateeb, M. Tan, M. A. Iqbal, M. McCarthy, P. Harper, and A. D. Ellis, “Four wave mixing in distributed Raman amplified optical transmission systems,” in Proceedings of IEEE Photonics Conference (IEEE, 2016), pp. 795–796.

Fair, I. J.

V. Pechenkin and I. J. Fair, “On four-wave mixing suppression in dispersion-managed fiber-optic OFDM systems with an optical phase conjugation module,” J. Lightwave Technol. 29(11), 1678–1691 (2011).

Ferreira, F. M.

Harper, P.

M. A. Z. Al-Khateeb, M. Tan, M. A. Iqbal, M. McCarthy, P. Harper, and A. D. Ellis, “Four wave mixing in distributed Raman amplified optical transmission systems,” in Proceedings of IEEE Photonics Conference (IEEE, 2016), pp. 795–796.

Hill, K. O.

K. O. Hill, D. C. Johnson, B. S. Kawasaki, and R. I. MacDonald, “CW three-wave mixing in single-mode optical fibers,” J. Appl. Phys. 49(10), 5098–5106 (1978).

Horiguchi, T.

Inoue, K.

K. Inoue and H. Toba, “Fiber four-wave mixing in multi-amplifier systems with nonuniform chromatic dispersion,” J. Lightwave Technol. 13(1), 88–93 (1995).

K. Inoue, “Phase-mismatching characteristic of four-wave mixing in fiber lines with multistage optical amplifiers,” Opt. Lett. 17(11), 801–803 (1992).
[PubMed]

Iqbal, M. A.

M. A. Z. Al-Khateeb, M. Tan, M. A. Iqbal, M. McCarthy, P. Harper, and A. D. Ellis, “Four wave mixing in distributed Raman amplified optical transmission systems,” in Proceedings of IEEE Photonics Conference (IEEE, 2016), pp. 795–796.

Jansen, S. L.

Johnson, D. C.

K. O. Hill, D. C. Johnson, B. S. Kawasaki, and R. I. MacDonald, “CW three-wave mixing in single-mode optical fibers,” J. Appl. Phys. 49(10), 5098–5106 (1978).

Kagi, N.

M. E. Marhic, N. Kagi, T. K. Chiang, and L. G. Kazovsky, “Optimizing the location of dispersion compensators in periodically amplified fiber links in the presence of third-order nonlinear effects,” IEEE Photonics Technol. Lett. 8(1), 145–147 (1996).

Kawasaki, B. S.

K. O. Hill, D. C. Johnson, B. S. Kawasaki, and R. I. MacDonald, “CW three-wave mixing in single-mode optical fibers,” J. Appl. Phys. 49(10), 5098–5106 (1978).

Kazovsky, L. G.

M. E. Marhic, N. Kagi, T. K. Chiang, and L. G. Kazovsky, “Optimizing the location of dispersion compensators in periodically amplified fiber links in the presence of third-order nonlinear effects,” IEEE Photonics Technol. Lett. 8(1), 145–147 (1996).

Khoe, G.

Krummrich, P. M.

Kurokawa, K.

Kurtzke, C.

C. Kurtzke, “Suppression of fiber nonlinearities by appropriate dispersion management,” IEEE Photonics Technol. Lett. 5(10), 1250–1253 (1993).

MacDonald, R. I.

K. O. Hill, D. C. Johnson, B. S. Kawasaki, and R. I. MacDonald, “CW three-wave mixing in single-mode optical fibers,” J. Appl. Phys. 49(10), 5098–5106 (1978).

Marhic, M. E.

M. E. Marhic, N. Kagi, T. K. Chiang, and L. G. Kazovsky, “Optimizing the location of dispersion compensators in periodically amplified fiber links in the presence of third-order nonlinear effects,” IEEE Photonics Technol. Lett. 8(1), 145–147 (1996).

McCarthy, M.

M. A. Z. Al-Khateeb, M. McCarthy, C. Sánchez, and A. Ellis, “Effect of second order signal-noise interactions in nonlinearity compensated optical transmission systems,” Opt. Lett. 41(8), 1849–1852 (2016).
[PubMed]

M. A. Z. Al-Khateeb, M. Tan, M. A. Iqbal, M. McCarthy, P. Harper, and A. D. Ellis, “Four wave mixing in distributed Raman amplified optical transmission systems,” in Proceedings of IEEE Photonics Conference (IEEE, 2016), pp. 795–796.

McCarthy, M. E.

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).

Minzioni, P.

P. Minzioni, “Nonlinearity compensation in a fiber optic link by optical phase conjugation,” Fiber Integr. Opt. 28, 179–209 (2009).

P. Minzioni and A. Schiffini, “Unifying theory of compensation techniques for intrachannel nonlinear effects,” Opt. Express 13(21), 8460–8468 (2005).
[PubMed]

Miyajima, Y.

Nakajima, K.

Ohashi, M.

Pechenkin, V.

V. Pechenkin and I. J. Fair, “On four-wave mixing suppression in dispersion-managed fiber-optic OFDM systems with an optical phase conjugation module,” J. Lightwave Technol. 29(11), 1678–1691 (2011).

Pendock, G.

Poggiolini, P.

Radic, S.

Sánchez, C.

Schadt, D. G.

D. G. Schadt, “Effect of amplifier spacing on four-wave mixing in multichannel coherent communications,” Electron. Lett. 27(20), 1805–1807 (1991).

Schiffini, A.

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).

Shieh, W.

W. Shieh, “Information spectral efficiency and launch power density limits due to fiber nonlinearity for coherent optical OFDM systems,” J. Photonics 3(2), 158–173 (2011).

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).
[PubMed]

Shiraki, K.

Shirasaki, M.

S. Watanabe and M. Shirasaki, “Exact compensation for both chromatic dispersion and Kerr effect in a transmission fiber using optical phase conjugation,” J. Lightwave Technol. 14(3), 243–248 (1996).

Shoreh, M. H.

Sohler, W.

Sorokina, M.

A. D. Ellis, M. E. McCarthy, M. A. Z. Al Khateeb, M. Sorokina, and N. J. Doran, “Performance limits in optical communications due to fiber nonlinearity,” Adv. Opt. Photonics 9(3), 429–503 (2017).

Spinnler, B.

Srivastava, A.

Sturrock, C. H. F.

D. A. Cleland, A. D. Ellis, and C. H. F. Sturrock, “Precise modelling of four wave mixing products over 400 km of step-index fibre,” Electron. Lett. 28(12), 1171–1173 (1992).

Suche, H.

Sygletos, S.

Tan, M.

M. A. Z. Al-Khateeb, M. Tan, M. A. Iqbal, M. McCarthy, P. Harper, and A. D. Ellis, “Four wave mixing in distributed Raman amplified optical transmission systems,” in Proceedings of IEEE Photonics Conference (IEEE, 2016), pp. 795–796.

Toba, H.

K. Inoue and H. Toba, “Fiber four-wave mixing in multi-amplifier systems with nonuniform chromatic dispersion,” J. Lightwave Technol. 13(1), 88–93 (1995).

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).

Watanabe, S.

S. Watanabe and M. Shirasaki, “Exact compensation for both chromatic dispersion and Kerr effect in a transmission fiber using optical phase conjugation,” J. Lightwave Technol. 14(3), 243–248 (1996).

Wysocki, P.

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).

Adv. Opt. Photonics (1)

A. D. Ellis, M. E. McCarthy, M. A. Z. Al Khateeb, M. Sorokina, and N. J. Doran, “Performance limits in optical communications due to fiber nonlinearity,” Adv. Opt. Photonics 9(3), 429–503 (2017).

Electron. Lett. (2)

D. G. Schadt, “Effect of amplifier spacing on four-wave mixing in multichannel coherent communications,” Electron. Lett. 27(20), 1805–1807 (1991).

D. A. Cleland, A. D. Ellis, and C. H. F. Sturrock, “Precise modelling of four wave mixing products over 400 km of step-index fibre,” Electron. Lett. 28(12), 1171–1173 (1992).

Fiber Integr. Opt. (1)

P. Minzioni, “Nonlinearity compensation in a fiber optic link by optical phase conjugation,” Fiber Integr. Opt. 28, 179–209 (2009).

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).

IEEE Photonics Technol. Lett. (2)

C. Kurtzke, “Suppression of fiber nonlinearities by appropriate dispersion management,” IEEE Photonics Technol. Lett. 5(10), 1250–1253 (1993).

M. E. Marhic, N. Kagi, T. K. Chiang, and L. G. Kazovsky, “Optimizing the location of dispersion compensators in periodically amplified fiber links in the presence of third-order nonlinear effects,” IEEE Photonics Technol. Lett. 8(1), 145–147 (1996).

J. Appl. Phys. (1)

K. O. Hill, D. C. Johnson, B. S. Kawasaki, and R. I. MacDonald, “CW three-wave mixing in single-mode optical fibers,” J. Appl. Phys. 49(10), 5098–5106 (1978).

J. Lightwave Technol. (8)

S. Radic, G. Pendock, A. Srivastava, P. Wysocki, and A. Chraplyvy, “Four-wave mixing in optical links using quasi-distributed optical amplifiers,” J. Lightwave Technol. 19(5), 636–645 (2001).

K. Nakajima, M. Ohashi, K. Shiraki, T. Horiguchi, K. Kurokawa, and Y. Miyajima, “Four-wave mixing suppression effect of dispersion distributed fibers,” J. Lightwave Technol. 17(10), 1814–1822 (1999).

K. Inoue and H. Toba, “Fiber four-wave mixing in multi-amplifier systems with nonuniform chromatic dispersion,” J. Lightwave Technol. 13(1), 88–93 (1995).

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).

S. Watanabe and M. Shirasaki, “Exact compensation for both chromatic dispersion and Kerr effect in a transmission fiber using optical phase conjugation,” J. Lightwave Technol. 14(3), 243–248 (1996).

V. Pechenkin and I. J. Fair, “On four-wave mixing suppression in dispersion-managed fiber-optic OFDM systems with an optical phase conjugation module,” J. Lightwave Technol. 29(11), 1678–1691 (2011).

P. Poggiolini, “The GN model of non-linear propagation in uncompensated coherent optical systems,” J. Lightwave Technol. 30(24), 3857–3879 (2012).

S. L. Jansen, D. Van Den Borne, B. Spinnler, S. Calabrò, H. Suche, P. M. Krummrich, W. Sohler, G. Khoe, and H. De Waardt, “Optical phase conjugation for ultra long-haul a phase-shift-keyed transmission,” J. Lightwave Technol. 24(1), 54–64 (2006).

J. Opt. Commun. Netw. (1)

J. Photonics (1)

W. Shieh, “Information spectral efficiency and launch power density limits due to fiber nonlinearity for coherent optical OFDM systems,” J. Photonics 3(2), 158–173 (2011).

Opt. Express (4)

Opt. Lett. (2)

Other (5)

C. Headley and G. P. Agrawal, Raman Amplification in Fiber Optical Communication Systems (Elsevier, 2005).

M. Tan, P. Rosa, M. A. Iqbal, I. Phillips, J. Nuño, J. D. Ania-Castanon, and P. Harper, “RIN mitigation in second-order pumped Raman fibre laser based amplification,” in Asia Communications and Photonics Conference, OSA Technical Digest (online) (Optical Society of America, 2015), paper AM2E.6.

A. D. Ellis and W. A. Stallard, “Four wave mixing in ultra long transmission systems incorporating linear amplifiers,” in Proceedings of IEE Colloquium on Non-Linear Effects in Fibre Communications (IEEE, 1990), 6/1–6/4.

M. Al-Khateeb, M. E. McCarthy, and A. D. Ellis, “Experimental verification of four wave mixing in lumped optical transmission systems that employ mid-link optical phase conjugation,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2017), paper JTh2A.64.

M. A. Z. Al-Khateeb, M. Tan, M. A. Iqbal, M. McCarthy, P. Harper, and A. D. Ellis, “Four wave mixing in distributed Raman amplified optical transmission systems,” in Proceedings of IEEE Photonics Conference (IEEE, 2016), pp. 795–796.

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Figures (11)

Fig. 1
Fig. 1 (a) Simulation and experimental setup, (b) and (c) show the nonlinear Kerr product power as a function of the frequency separation between two CW lasers (0dBm each) for single span, two spans, respectively. Fiber type: G.652, L = 100km, α = 0.2dB/km, Dc = 16.4ps/nm/km, γ = 1.33/km/W.
Fig. 2
Fig. 2 (a) Nonlinear Kerr product power as a function of frequency separation between two CW lasers (0dBm each) propagating through 1st order Raman pumped 62km span, (b) corresponding power profiles for each rf. Fiber type: G.652.
Fig. 3
Fig. 3 (a) Nonlinear Kerr product power as a function of frequency separation between two CW lasers (0.5dBm, 0.1dBm, −0.3dBm, and −0.6dBm each for rf = 0%, 20%, 79%, and 100%, respectively) propagating through 2nd order Raman pumped 62km span and (b) shows the corresponding power profiles [21]. Fiber type: G.652.
Fig. 4
Fig. 4 OPC deployment techniques. (top) single segment spaced OPCs, (bottom) double segment spaced OPCs.
Fig. 5
Fig. 5 Nonlinear Kerr product power as a function of frequency separation between two CW lasers (0dBm each) propagating through 200km lumped transmission system (with different span length). (left column) fully dispersion compensated system with 0% residual dispersion, (right column) dispersion uncompensated system. Fiber type: G.652.
Fig. 6
Fig. 6 Nonlinear Kerr product power as a function of frequency separation between two CW lasers (0dBm each) propagating through 24x100km lumped transmission system with different number of equally spaced and symmetrically located OPCs (1OPC, 3OPCs, 5OPCs, and 7OPCs). (red) without OPC, (blue) with OPCs, (solid lines) theory, (open circles) simulation results. Fiber type: G.652.
Fig. 7
Fig. 7 Nonlinear Kerr power as a function between two CW lasers passing through 2x100km transmission system with a mid-link OPC [17]. Fiber type: G.652.
Fig. 8
Fig. 8 (left column) the power profiles of distributed Raman ranging from rf = 0% to 100% with a step of 20%. (right column) Nonlinear Kerr product power as a function of frequency separation between two CW lasers (0dBm each) propagating through 200km first order distributed Raman transmission system (with different span length). (solid lines) without mid-link OPC, (dashed lines) with mid-link OPC, the color code represents the different power profiles displayed on the left side. Fiber type: G.652.
Fig. 9
Fig. 9 Nonlinear Kerr product power as a function of frequency separation between two CW lasers (0dBm each) propagating through 24x50km distributed Raman transmission system with different number of equally spaced and symmetrically located OPCs (1OPC, 3OPCs, 5OPCs, and 7OPCs). (solid lines) theory, (open circles) simulation results, colors represent different rf values, same color code as Fig. 8. Fiber type: G.652.
Fig. 10
Fig. 10 2x50km backward pumped 1st order distributed Raman transmission system (with and without mid-link OPC) passing through two CW lasers (with varying frequency separation). Each CW propagating through the system enter the Raman span with 6dBm power, Raman pump (1455nm) power was calibrated to achieve 0dB net gain. The inset figure on the bottom right shows the OTDR measurements of the power profile along the 1st order distributed Raman amplified 50km spans compared with the theory [as reported in Fig. 8].
Fig. 11
Fig. 11 The nonlinear Kerr power as a function between two CW lasers passing through 2x50km backward pumped 1st order distributed Raman transmission system without OPC (a) with mid-link OPC (b).

Equations (13)

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E F ( NL )=i γD 3 E q ( 0 ) E r ( 0 ) E s * ( 0 ) e ( iδ β F NL ) [ e ( [ α+iΔβ ]L ) 1 α+iΔβ ] n=1 N e ( i( n1 )δΔβL )
Δβ=4 π 2 β''( f q f s )( f r f s )
P F ( NL )= D 2 γ 2 9 P q P r P s [ α 2 L eff 2 α 2 +Δ β 2 ][ 1+ 4 e ( αL ) sin 2 ( ΔβL/2 ) ( 1 e ( αL ) ) 2 ] sin 2 ( NδΔβL/2 ) sin 2 ( δΔβL/2 )
P F ( NL )= D 2 γ 2 9 P q P r P s | k=1 M [ e ( g k +iΔβ ) L k 1 g k +iΔβ ][ l=1 k1 e ( g l +iΔβ ) L l ] | 2 sin 2 ( NΔβL/2 ) sin 2 ( ΔβL/2 )
P F ( NL )= D 2 γ 2 9 P q P r P s 4 sin 2 ( NΔβL/2 ) Δ β 2
E F ( NL )= N seg 2 [ E F ( evensegment )+ [ E F ( oddsegment ) ] * e ( iδ β F NL/ N seg ) ]
E F ( oddsegment )=i γD 3 E q ( 0 ) E r ( 0 ) E s * ( 0 ) e ( iδ β F NL/ N seg ) [ e ( [ α+iΔβ ]L ) 1 α+iΔβ ] n=1 N/ N seg e ( i( n1 )δΔβL )
E F ( evensegment )=i γD 3 E q * ( 0 ) E r * ( 0 ) E s ( 0 ) e ( iδΔβL ) [ e ( [ α+iΔβ ]L ) 1 α+iΔβ ] n=1 N/ N seg e ( i( n1 )δΔβL )
E F ( NL )=i γD N seg 6 E q * ( 0 ) E r * ( 0 ) E s ( 0 ) [ e ( iδΔβL ) e ( [ α+iΔβ ]L ) 1 α+iΔβ e ( [ αiΔβ ]L ) 1 αiΔβ ] n=1 N/ N seg e ( i( n1 )δΔβL )
P F ( NL )= D 2 γ 2 N seg 2 36 P q P r P s | e ( iδΔβL ) e ( [ α+iΔβ ]L ) 1 α+iΔβ e ( [ αiΔβ ]L ) 1 αiΔβ | 2 sin 2 ( NδΔβL/[ 2 N seg ] ) sin 2 ( δΔβL/2 )
P F ( NL )= D 2 γ 2 9 P q P r P s N 2 ( α 2 +Δ β 2 ) 2 [ α e αL sin( ΔβL )+Δβ( e αL cos( ΔβL )1 ) ] 2
P F ( NL )= D 2 γ 2 N seg 2 9 P q P r P s ( α 2 +Δ β 2 ) 2 [ α( e αL +1 )sin( ΔβL 2 )+Δβ( e αL 1 )cos( ΔβL 2 ) ] 2 sin 2 ( NδΔβL/[ 2 N seg ] ) sin 2 ( δΔβL/2 )
P F ( NL )= D 2 γ 2 N seg 2 9 P q P r P s sin 2 ( NΔβL/[ 2 N seg ] ) sin 2 ( ΔβL/2 ) | e ( iΔβL ) k=1 M [ e ( g k +iΔβ ) L k 1 g k +iΔβ ][ l=1 k1 e ( g l +iΔβ ) L l ] k=1 M [ e ( g k iΔβ ) L k 1 g k iΔβ ][ l=1 k1 e ( g l iΔβ ) L l ] | 2

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