Abstract

In this Letter, we theoretically and numerically analyze the performance of coherent optical transmission systems that deploy inline or transceiver based nonlinearity compensation techniques. For systems where signal-signal nonlinear interactions are fully compensated, we find that beyond the performance peak the signal-to-noise ratio degradation has a slope of 3  dBSNR/dBPower suggesting a quartic rather than quadratic dependence on signal power. This is directly related to the fact that signals in a given span will interact not only with linear amplified spontaneous emission noise, but also with the nonlinear four-wave mixing products generated from signal-noise interaction in previous (hitherto) uncompensated spans. The performance of optical systems employing different nonlinearity compensation schemes were numerically simulated and compared against analytical predictions, showing a good agreement within a 0.4 dB margin of error.

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References

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2015 (1)

2014 (1)

2012 (2)

G. Gao, X. Chen, and W. Shieh, Opt. Express 20, 14406 (2012).
[Crossref]

A. D. Ellis, Nonlinear Opt. Appl. VI 8434, 84340H (2012).

2011 (2)

D. Rafique and A. D. Ellis, Opt. Express 19, 3449 (2011).
[Crossref]

W. Shieh and X. Chen, IEEE Photon. J. 3, 158 (2011).
[Crossref]

2010 (2)

F. Yaman and G. Li, IEEE Photon. J. 2, 816 (2010).
[Crossref]

X. Chen and W. Shieh, Opt. Express 18, 19039 (2010).
[Crossref]

2008 (1)

2001 (1)

P. P. Mitra and J. B. Stark, Nature 411, 1027 (2001).
[Crossref]

1992 (1)

D. A. Cleland, J. D. Cox, and A. D. Ellis, Electron. Lett. 28, 307 (1992).
[Crossref]

1990 (1)

1979 (1)

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Elsevier, 2006).

Al-Khateeb, M. A. Z.

A. D. Ellis, M. E. McCarthy, M. A. Z. Al-Khateeb, and S. Sygletos, Opt. Express 23, 20381 (2015).
[Crossref]

A. D. Ellis, S. T. Le, M. A. Z. Al-Khateeb, S. K. Turitsyn, G. Liga, D. Lavery, T. Xu, and P. Bayvel, IEEE Photonics Society Summer Topical Meeting Series (SUM), Nassau (2015).

Bayvel, P.

A. D. Ellis, S. T. Le, M. A. Z. Al-Khateeb, S. K. Turitsyn, G. Liga, D. Lavery, T. Xu, and P. Bayvel, IEEE Photonics Society Summer Topical Meeting Series (SUM), Nassau (2015).

Chen, X.

Cleland, D. A.

D. A. Cleland, J. D. Cox, and A. D. Ellis, Electron. Lett. 28, 307 (1992).
[Crossref]

Cox, J. D.

D. A. Cleland, J. D. Cox, and A. D. Ellis, Electron. Lett. 28, 307 (1992).
[Crossref]

Ellis, A. D.

A. D. Ellis, M. E. McCarthy, M. A. Z. Al-Khateeb, and S. Sygletos, Opt. Express 23, 20381 (2015).
[Crossref]

A. D. Ellis, Nonlinear Opt. Appl. VI 8434, 84340H (2012).

D. Rafique and A. D. Ellis, Opt. Express 19, 3449 (2011).
[Crossref]

D. A. Cleland, J. D. Cox, and A. D. Ellis, Electron. Lett. 28, 307 (1992).
[Crossref]

A. D. Ellis, S. T. Le, M. A. Z. Al-Khateeb, S. K. Turitsyn, G. Liga, D. Lavery, T. Xu, and P. Bayvel, IEEE Photonics Society Summer Topical Meeting Series (SUM), Nassau (2015).

A. D. Ellis, S. T. Le, M. E. McCarthy, and S. K. Turitsyn, 17th International Conference on Transparent Optical Networks (ICTON), Budapest (2015), pp. 1–4.

Fehenberger, T.

T. Fehenberger and N. Hanik, Eur. Conf. Opt. Commun. (ECOC) (2014), pp. 1–3.

Fekete, D.

Gao, G.

Goldfarb, G.

Gordon, J. P.

Hanik, N.

T. Fehenberger and N. Hanik, Eur. Conf. Opt. Commun. (ECOC) (2014), pp. 1–3.

Kim, I.

Lavery, D.

A. D. Ellis, S. T. Le, M. A. Z. Al-Khateeb, S. K. Turitsyn, G. Liga, D. Lavery, T. Xu, and P. Bayvel, IEEE Photonics Society Summer Topical Meeting Series (SUM), Nassau (2015).

Le, S. T.

A. D. Ellis, S. T. Le, M. A. Z. Al-Khateeb, S. K. Turitsyn, G. Liga, D. Lavery, T. Xu, and P. Bayvel, IEEE Photonics Society Summer Topical Meeting Series (SUM), Nassau (2015).

A. D. Ellis, S. T. Le, M. E. McCarthy, and S. K. Turitsyn, 17th International Conference on Transparent Optical Networks (ICTON), Budapest (2015), pp. 1–4.

Li, G.

Li, X.

Liga, G.

A. D. Ellis, S. T. Le, M. A. Z. Al-Khateeb, S. K. Turitsyn, G. Liga, D. Lavery, T. Xu, and P. Bayvel, IEEE Photonics Society Summer Topical Meeting Series (SUM), Nassau (2015).

Mateo, E.

McCarthy, M. E.

A. D. Ellis, M. E. McCarthy, M. A. Z. Al-Khateeb, and S. Sygletos, Opt. Express 23, 20381 (2015).
[Crossref]

A. D. Ellis, S. T. Le, M. E. McCarthy, and S. K. Turitsyn, 17th International Conference on Transparent Optical Networks (ICTON), Budapest (2015), pp. 1–4.

Mitra, P. P.

P. P. Mitra and J. B. Stark, Nature 411, 1027 (2001).
[Crossref]

Mollenauer, L. F.

Pepper, D. M.

Rafique, D.

Shieh, W.

Shoreh, M. H.

Stark, J. B.

P. P. Mitra and J. B. Stark, Nature 411, 1027 (2001).
[Crossref]

Sygletos, S.

Turitsyn, S. K.

A. D. Ellis, S. T. Le, M. E. McCarthy, and S. K. Turitsyn, 17th International Conference on Transparent Optical Networks (ICTON), Budapest (2015), pp. 1–4.

A. D. Ellis, S. T. Le, M. A. Z. Al-Khateeb, S. K. Turitsyn, G. Liga, D. Lavery, T. Xu, and P. Bayvel, IEEE Photonics Society Summer Topical Meeting Series (SUM), Nassau (2015).

Xu, T.

A. D. Ellis, S. T. Le, M. A. Z. Al-Khateeb, S. K. Turitsyn, G. Liga, D. Lavery, T. Xu, and P. Bayvel, IEEE Photonics Society Summer Topical Meeting Series (SUM), Nassau (2015).

Yaman, F.

Yariv, A.

Electron. Lett. (1)

D. A. Cleland, J. D. Cox, and A. D. Ellis, Electron. Lett. 28, 307 (1992).
[Crossref]

IEEE Photon. J. (2)

W. Shieh and X. Chen, IEEE Photon. J. 3, 158 (2011).
[Crossref]

F. Yaman and G. Li, IEEE Photon. J. 2, 816 (2010).
[Crossref]

J. Opt. Commun. Netw. (1)

Nature (1)

P. P. Mitra and J. B. Stark, Nature 411, 1027 (2001).
[Crossref]

Nonlinear Opt. Appl. VI (1)

A. D. Ellis, Nonlinear Opt. Appl. VI 8434, 84340H (2012).

Opt. Express (5)

Opt. Lett. (2)

Other (4)

G. P. Agrawal, Nonlinear Fiber Optics (Elsevier, 2006).

A. D. Ellis, S. T. Le, M. A. Z. Al-Khateeb, S. K. Turitsyn, G. Liga, D. Lavery, T. Xu, and P. Bayvel, IEEE Photonics Society Summer Topical Meeting Series (SUM), Nassau (2015).

A. D. Ellis, S. T. Le, M. E. McCarthy, and S. K. Turitsyn, 17th International Conference on Transparent Optical Networks (ICTON), Budapest (2015), pp. 1–4.

T. Fehenberger and N. Hanik, Eur. Conf. Opt. Commun. (ECOC) (2014), pp. 1–3.

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Figures (3)

Fig. 1.
Fig. 1. Nonlinear signal–noise interactions accumulation along the nonlinearity DBP compensated optical transmission link. The red triangles represent inline amplifiers that inject linear ASE noise while the blue triangles are ideal DBP amplifiers that do not introduce any noise. The blue colored fibers in the receiver side represent fibers with the negative values γ and β 2 of the red fiber. The green solid lines represent the power evolution of the signal interaction with noise, the filled green triangles represent the first-order signal–noise products, and the black arrows represent second-order signal–noise products.
Fig. 2.
Fig. 2. Q 2 factor, as a function of optical signal launched power, for system (A) and system (B). Theory considering the first- and second-order signal–noise products (solid line), theory considering only the first-order signal–noise products (dashed line), and simulation results (dots). EDC system without nonlinearity compensation (blue), DBP (red), 1-OPC (green), 3-OPCs (purple), and 11-OPCs (black).
Fig. 3.
Fig. 3. Q 2 as a function of the optical link distance for mid-link OPC (System B). Theory considering the first-order and second-order signal–noise products (solid line), theory considering only the first-order signal–noise products (dashed line), and simulation results (dots).

Equations (7)

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P FWM = ( | E A | 2 + | E a | 2 ) ( | E B | 2 + | E b | 2 ) ( | E C * | 2 + | E c * | 2 ) η = [ ( P A P B P C ) + ( P A P B P c ) + ( P A P b P C ) + ( P a P B P C ) + ( P A P b P c ) + ( P a P B P c ) + ( P a P b P C ) + ( P a P b P c ) ] η ,
SNR = I S N I n + I S 3 f A ( N ) + 3 I S 2 I n ξ PAN ( N ) ,
f Lumped ( N ) = γ 2 N π    α | β 2 | log ( 2 π 2 | β 2 | B W 2 α ) ,
f Raman ( N ) = 2 γ 2 NL π | β 2 | log ( 2 π 2    NL | β 2 | B W 2 ) .
ξ PAN = N even { x = 1 N S ( f ( x ) + [ 3 I S 2 f ( 1 ) y = 1 x 1 f ( y ) ] ) } + N odd { x = 1 N S ( f ( N S x ) + [ 3 I S 2 f ( 1 ) y = 1 x 1 f ( N S y ) ] ) } ,
SNR = I S N I n + 3 N ( N + 1 ) 2 I S 2 I n f lumped ( 1 ) [ 1 + ( N 1 ) I S 2 f lumped ( 1 ) ] .
I PAN 2 nd - Order = I S 4 I n 6 ( 2 γ 2 L π | β 2 | ) 2 log ( 2 π 2 L | β 2 | B w 2 ) .

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